OptiSystem Component Library Optical Communication System Design Software Version 14 OptiSystem Component Library Optical Communication System Design Software Copyright © 2015 Optiwave All rights reserved. All OptiSystem documents, including this one, and the information contained therein, is copyright material. No part of this document may be reproduced, stored in a retrieval system, or transmitted in any form or by any means whatsoever, including recording, photocopying, or faxing, without prior written approval of Optiwave. Disclaimer Optiwave makes no representation or warranty with respect to the adequacy of this documentation or the programs which it describes for any particular purpose or with respect to its adequacy to produce any particular result. In no event shall Optiwave, its employees, its contractors or the authors of this documentation, be liable for special, direct, indirect, or consequential damages, losses, costs, charges, claims, demands, or claim for lost profits, fees, or expenses of any nature or kind. Technical Support If you purchased Optiwave software from a distributor that is not listed here, please send technical questions to your distributor. Optiwave Canada/US Tel (613) 224-4700 E-mail [email protected] Fax (613) 224-4706 URL www.optiwave.com Optiwave Japan Japan Tel +81.43.375.2644 E-mail [email protected] Fax +81.43.375.2644 URL www.optiwave.jp Optiwave Europe Europe Tel +33 (0) 494 08 27 97 E-mail [email protected] Fax +33 (0) 494 33 65 76 URL www.optiwave.eu Table of contents Visualizer Library ........................................................................................... 17 Optical ...................................................................................................................... 17 Optical Spectrum Analyzer (OSA)............................................................................19 Optical Time Domain Visualizer (OTDV)..................................................................27 Optical Power Meter.................................................................................................35 Polarization Meter ....................................................................................................39 Polarization Analyzer ...............................................................................................45 WDM Analyzer (WDMA) ..........................................................................................53 Dual Port WDM Analyzer (DPWDMA) .....................................................................61 Spatial Visualizer......................................................................................................71 Encircled Flux Analyzer............................................................................................81 Electrical .................................................................................................................. 87 Oscilloscope Visualizer ............................................................................................89 RF Spectrum Analyzer (RFSA) ...............................................................................93 Eye Diagram Analyzer .............................................................................................97 BER Analyzer.........................................................................................................115 Electrical Power Meter ...........................................................................................133 Electrical Carrier Analyzer (ECAN) ........................................................................137 Dual Port Electrical Carrier Analyzer......................................................................143 Electrical Constellation Visualizer ..........................................................................149 Directly Detected Eye Analyzer Visualizer .............................................................157 Binary ..................................................................................................................... 167 Binary Sequence Visualizer ...................................................................................169 M-ary Sequence Visualizer ....................................................................................173 Compare................................................................................................................. 177 Dual Port Binary Sequence Visualizer ...................................................................179 Dual Port M-ary Sequence Visualizer ....................................................................181 Dual Port Optical Spectrum Analyzer.....................................................................183 Dual Port Optical Time Domain Visualizer .............................................................187 Dual Port Oscilloscope Visualizer ..........................................................................193 Dual Port RF Spectrum Analyzer ...........................................................................197 View Signal ............................................................................................................ 201 View Signal Visualizer............................................................................................203 Cpp CoSimulation Visualizer..................................................................................205 Transmitters Library - Electrical................................................................. 207 Bit Sequence Generators ..................................................................................... 207 Pseudo-Random Bit Sequence Generator.............................................................209 User-Defined Bit Sequence Generator ..................................................................213 Pulse & Symbol Generators................................................................................. 215 Duobinary Pulse Generator....................................................................................217 Electrical Jitter........................................................................................................219 Noise Source..........................................................................................................221 RZ Pulse Generator ...............................................................................................223 NRZ Pulse Generator.............................................................................................227 Gaussian Pulse Generator.....................................................................................231 Hyperbolic-Secant Pulse Generator.......................................................................235 Sine Generator.......................................................................................................239 Triangle Pulse Generator .......................................................................................241 Saw-Up Pulse Generator .......................................................................................245 Saw-Down Pulse Generator...................................................................................249 Impulse Generator .................................................................................................253 Raised Cosine Pulse Generator.............................................................................257 Sine Pulse Generator.............................................................................................261 Measured Pulse .....................................................................................................265 Measured Pulse Sequence ....................................................................................269 Bias Generator .......................................................................................................271 M-ary Pulse Generator...........................................................................................273 M-ary Raised Cosine Pulse Generator ..................................................................277 Predistortion ...........................................................................................................279 PAM Pulse Generator ............................................................................................281 QAM Pulse Generator............................................................................................285 PSK Pulse Generator.............................................................................................289 DPSK Pulse Generator ..........................................................................................291 OQPSK Pulse Generator .......................................................................................295 MSK Pulse Generator ............................................................................................297 Electrical Modulators............................................................................................ 301 Electrical Amplitude Modulator (AM)......................................................................303 Electrical Frequency Modulator (FM) .....................................................................305 Electrical Phase Modulator (PM)............................................................................307 Quadrature Modulator ............................................................................................309 PAM Modulator ......................................................................................................311 QAM Modulator ......................................................................................................313 PSK Modulator .......................................................................................................315 DPSK Modulator ....................................................................................................317 OQPSK Modulator .................................................................................................319 MSK Modulator ......................................................................................................321 FSK Modulator .......................................................................................................323 CPFSK Modulator ..................................................................................................325 OFDM Modulation (OS12) .....................................................................................329 OFDM Modulator Measured...................................................................................337 OFDM Modulation ..................................................................................................345 Burst Modulator......................................................................................................355 Carrier Generators ................................................................................................ 357 Carrier Generator ...................................................................................................359 Carrier Generator Measured ..................................................................................363 PAM Sequence Generator .....................................................................................367 QAM Sequence Generator.....................................................................................371 PSK Sequence Generator......................................................................................377 DPSK Sequence Generator ...................................................................................381 PPM Sequence Generator .....................................................................................385 DPIM Sequence Generator....................................................................................387 4B5B Sequence Generator ....................................................................................389 NRZI Sequence Generator ....................................................................................391 AMI Sequence Generator ......................................................................................393 Manchester Sequence Generator ..........................................................................397 4B3T Sequence Generator ....................................................................................399 8B10B Sequence Generator ..................................................................................401 Duobinary Precoder ...............................................................................................403 4-DPSK Precoder...................................................................................................405 Transmitters Library - Optical..................................................................... 407 Optical Sources..................................................................................................... 407 CW Laser ...............................................................................................................409 Ideal Single Mode Laser ........................................................................................413 Laser Measured .....................................................................................................419 Fabry Perot Laser ..................................................................................................427 LED ........................................................................................................................435 White Light Source.................................................................................................439 Pump Laser............................................................................................................441 Pump Laser Array ..................................................................................................443 Controlled Pump Laser ..........................................................................................447 CW Laser Array......................................................................................................449 CW Laser Array ES................................................................................................453 CW Laser Measured ..............................................................................................457 Directly Modulated Laser Measured ......................................................................463 VCSEL Laser .........................................................................................................471 VCSEL Laser Measured ........................................................................................483 DFB Laser ..............................................................................................................499 Empirical Laser Measured .....................................................................................509 Spectral Light Source.............................................................................................519 Set OSNR ..............................................................................................................523 Optical Pulse Generators ..................................................................................... 525 Optical Gaussian Pulse Generator.........................................................................527 Optical Sech Pulse Generator................................................................................531 Optical Impulse Generator .....................................................................................535 Measured Optical Pulse .........................................................................................539 Measured Optical Pulse Sequence........................................................................543 Time Resolve Chirp (TRC) Measurement Data .....................................................547 Optical Modulators................................................................................................ 551 MZ Modulator Analytical.........................................................................................553 EA Modulator Analytical .........................................................................................555 Amplitude Modulator ..............................................................................................557 Phase Modulator ....................................................................................................559 Frequency Modulator .............................................................................................561 Dual Drive MZ Absorption-Phase...........................................................................563 EA Modulator Measured ........................................................................................567 Single Drive MZ Modulator Absorption-Phase .......................................................571 Dual Port Dual Drive MZ Modulator Absorption-Phase..........................................575 Dual Port MZ Modulator Measured ........................................................................579 Optical Transmitters ............................................................................................. 585 WDM Transmitter ...................................................................................................587 Optical Transmitter.................................................................................................595 Optical Duobinary Transmitter ...............................................................................601 Optical DPSK Transmitter ......................................................................................607 Optical CSRZ Transmitter ......................................................................................613 Optical QPSK Transmitter......................................................................................617 Optical DP-QPSK Transmitter................................................................................621 16-QAM Transmitter...............................................................................................625 Optical DP-16-QAM Transmitter ............................................................................629 Optical Fibers Library.................................................................................. 633 Optical fiber ............................................................................................................635 Optical fiber CWDM ...............................................................................................673 Bidirectional Optical Fiber ......................................................................................697 Nonlinear Dispersive Fiber (Obsolete) ...................................................................719 Receivers Library......................................................................................... 737 Regenerators ......................................................................................................... 737 Clock Recovery ......................................................................................................739 Data Recovery .......................................................................................................741 3R Regenerator......................................................................................................745 Electronic Equalizer ...............................................................................................749 MLSE Equalizer .....................................................................................................755 Integrate And Dump ...............................................................................................759 Voltage-Controlled Oscillator .................................................................................761 Photodetectors and detectors ............................................................................. 763 Photodiode PIN ......................................................................................................765 APD........................................................................................................................775 Optical Chirp Detector............................................................................................783 Optical Phase Detector ..........................................................................................787 Optical Power Detector ..........................................................................................791 Digital Signal Processing ..................................................................................... 795 Viterbi & Viterbi Feed Forward Phase Recovery....................................................797 Dual Port Viterbi & Viterbi Feed Forward Phase Recovery ...................................799 DSP for QPSK........................................................................................................801 DSP for 16-QAM ....................................................................................................821 Universal DSP........................................................................................................843 Demodulators ........................................................................................................ 853 Electrical Amplitude Demodulator ..........................................................................855 Electrical Phase Demodulator................................................................................857 Electrical Frequency Demodulator .........................................................................861 Quadrature Demodulator .......................................................................................865 OFDM Demodulation (OS12).................................................................................867 OFDM Demodulator Measured ..............................................................................871 OFDM Demodulation .............................................................................................875 OFDM Demodulation Dual Polarization .................................................................885 Burst Demodulator .................................................................................................895 M-ary Threshold Detector ......................................................................................897 Decision .................................................................................................................899 PAM Decision.........................................................................................................909 Decoders................................................................................................................ 913 PAM Sequence Decoder........................................................................................915 QAM Sequence Decoder .......................................................................................919 PSK Sequence Decoder ........................................................................................925 DPSK Sequence Decoder......................................................................................929 PPM Sequence Decoder........................................................................................933 DPIM Sequence Decoder ......................................................................................935 4B5B Sequence Decoder.......................................................................................937 NRZI Sequence Decoder .......................................................................................939 AMI Sequence Decoder .........................................................................................941 Manchester Sequence Decoder.............................................................................945 4B3T Sequence Decoder.......................................................................................947 8B10B Sequence Decoder.....................................................................................949 Optical receivers ................................................................................................... 951 Optical Receiver.....................................................................................................953 Optical DPSK Receiver ..........................................................................................959 Optical Coherent PSK/QAM Receiver....................................................................965 Optical Coherent QAM Receiver............................................................................969 Optical Coherent DP PSK/QAM Receiver..............................................................973 Optical Coherent DP-16-QAM Receiver ................................................................977 90 Degree Optical Hybrid.......................................................................................983 Amplifiers Library ........................................................................................ 987 Optical .................................................................................................................... 987 EDFA Black Box.....................................................................................................989 EDFA....................................................................................................................1001 Optical Amplifier ..................................................................................................1009 Optical Amplifier Measured ..................................................................................1015 Optical Fiber Amplifier..........................................................................................1021 Raman Amplifier Component (Obsolete) .............................................................1037 Raman Amplifier-Average Power Model ..............................................................1055 Raman Amplifier-Dynamic Model.........................................................................1067 Er Doped Fiber Dynamic......................................................................................1079 Er Doped Fiber Dynamic Analytical .....................................................................1087 Er Doped Fiber.....................................................................................................1095 Er-Yb Codoped Fiber ...........................................................................................1137 Er-Yb Codoped Fiber Dynamic ............................................................................1153 Er-Yb Codoped Waveguide ................................................................................1165 Pr Doped Fiber.....................................................................................................1185 Yb-Doped Fiber....................................................................................................1197 Yb-Doped Fiber Dynamic.....................................................................................1211 Tm Doped Fiber ...................................................................................................1223 Traveling Wave SOA ...........................................................................................1237 Wideband Traveling Wave SOA ..........................................................................1243 Reflective SOA.....................................................................................................1251 Electrical .............................................................................................................. 1257 Limiting Amplifier..................................................................................................1259 Electrical Amplifier................................................................................................1263 Transimpedance Amplifier ...................................................................................1265 AGC Amplifier ......................................................................................................1271 Filters Library ............................................................................................. 1273 Optical .................................................................................................................. 1273 Optical IIR Filter (Obsolete)..................................................................................1275 Optical Digital Filter ..............................................................................................1279 Measured Optical Filter ........................................................................................1283 Measured Group Delay Optical Filter...................................................................1287 Rectangle Optical Filter........................................................................................1293 Trapezoidal Optical Filter .....................................................................................1295 Gaussian Optical Filter.........................................................................................1297 Butterworth Optical Filter......................................................................................1299 Bessel Optical Filter .............................................................................................1301 Fabry Perot Optical Filter .....................................................................................1305 Acousto Optical Filter ...........................................................................................1307 Mach-Zehnder Interferometer ..............................................................................1311 Inverted Optical IIR Filter (Obsolete)....................................................................1313 Inverted Optical Digital Filter ................................................................................1317 Inverted Rectangle Optical Filter..........................................................................1321 Inverted Trapezoidal Optical Filter .......................................................................1323 Inverted Gaussian Optical Filter...........................................................................1325 Inverted Butterworth Optical Filter........................................................................1327 Inverted Bessel Optical Filter ...............................................................................1329 Raised Cosine Optical Filter.................................................................................1331 Inverse Gaussian Optical Filter ............................................................................1333 Inverse Sinc Optical Filter ....................................................................................1335 Gain Flattening Filter............................................................................................1337 Delay Interferometer ............................................................................................1341 Transmission Filter Bidirectional ..........................................................................1343 Reflective Filter Bidirectional................................................................................1347 3-Port Filter Bidirectional......................................................................................1351 Periodic Optical Filter ...........................................................................................1355 FBG ................................................................................................................................1359 Fiber Bragg Grating (FBG)...................................................................................1361 Uniform Fiber Bragg Grating ................................................................................1367 Ideal Dispersion Compensation FBG...................................................................1369 Electrical .............................................................................................................. 1375 IIR Filter (Obsolete)..............................................................................................1377 Digital Filter ..........................................................................................................1381 Low Pass Rectangle Filter ...................................................................................1385 Low Pass Gaussian Filter ....................................................................................1387 Low Pass Butterworth Filter .................................................................................1389 Low Pass Bessel Filter.........................................................................................1391 Low Pass Chebyshev Filter..................................................................................1395 Low Pass RC Filter ..............................................................................................1397 Low Pass Raised Cosine Filter ............................................................................1399 Low Pass Cosine Roll Off Filter ...........................................................................1401 Low Pass Squared Cosine Roll Off Filter.............................................................1403 Low Pass Inverse Gaussian Filter........................................................................1405 Low Pass Inverse Sinc Filter................................................................................1407 Band Pass IIR Filter (Obsolete) ...........................................................................1409 Measured Filter ....................................................................................................1413 Band Pass Rectangle Filter..................................................................................1417 Band Pass Gaussian Filter...................................................................................1419 Band Pass Butterworth Filter ...............................................................................1421 Band Pass Bessel Filter .......................................................................................1423 Band Pass Chebyshev Filter................................................................................1427 Band Pass RC Filter.............................................................................................1429 Band Pass Raised Cosine Filter ..........................................................................1431 Band Pass Cosine Roll Off Filter..........................................................................1433 Band Pass Squared Cosine Roll Off Filter ...........................................................1435 Band Pass Inverse Gaussian Filter......................................................................1437 Band Pass Inverse Sinc Filter ..............................................................................1439 S Parameters Measured Filter .............................................................................1441 Optical Filter Analyzer ..........................................................................................1447 Photonic All-parameter Analyzer..........................................................................1451 Convergence Monitor...........................................................................................1455 Differential Mode Delay Analyzer.........................................................................1459 Electrical Filter Analyzer.......................................................................................1465 S Parameter Extractor..........................................................................................1467 BER Test Set .......................................................................................................1473 Lightwave Analyzer............................................................................................. 1485 Lightwave Analyzer ..............................................................................................1487 WDM Multiplexers Library......................................................................... 1491 Add and Drop ...................................................................................................... 1491 WDM Add.............................................................................................................1493 WDM Drop ...........................................................................................................1497 WDM Add and Drop .............................................................................................1501 Demultiplexers .................................................................................................... 1505 WDM Demux 1x2 .................................................................................................1507 WDM Demux 1x4 .................................................................................................1511 WDM Demux 1x8 .................................................................................................1515 WDM Demux........................................................................................................1519 WDM Demux ES ..................................................................................................1523 WDM Interleaver Demux......................................................................................1525 Ideal Demux .........................................................................................................1527 Multiplexers ......................................................................................................... 1529 WDM Mux 2x1......................................................................................................1531 WDM Mux 4x1......................................................................................................1535 WDM Mux 8x1......................................................................................................1539 WDM Mux ............................................................................................................1543 WDM Mux ES.......................................................................................................1547 Ideal Mux..............................................................................................................1549 Nx1 Mux Bidirectional ..........................................................................................1551 AWG ..................................................................................................................... 1555 AWG NxN.............................................................................................................1557 AWG NxN Bidirectional ........................................................................................1559 Optical switches......................................................................................... 1565 Optical Switches ................................................................................................. 1565 Dynamic Y Select Nx1 Measured ........................................................................1567 Dynamic Y Switch 1xN Measured........................................................................1571 Dynamic Y Switch 1xN.........................................................................................1575 Dynamic Y Select Nx1 .........................................................................................1579 Dynamic Space Switch Matrix NxM Measured ....................................................1583 Dynamic Space Switch Matrix NxM .....................................................................1587 Optical Switch ......................................................................................................1591 Digital Optical Switch ...........................................................................................1595 Optical Y Switch ...................................................................................................1597 Optical Y Select....................................................................................................1599 Ideal Switch 2x2 ...................................................................................................1601 Ideal Y Switch ......................................................................................................1603 Ideal Y Select .......................................................................................................1605 Ideal Y Switch 1x4................................................................................................1607 Ideal Y Select 4x1 ................................................................................................1609 Ideal Y Switch 1x8................................................................................................1611 Ideal Y Select 8x1 ................................................................................................1613 Ideal Y Select Nx1................................................................................................1615 Ideal Y Switch 1xN ...............................................................................................1617 2x2 Switch Bidirectional .......................................................................................1619 Signal Processing Library......................................................................... 1621 Arithmetic - Electrical ......................................................................................... 1621 Electrical Gain ......................................................................................................1623 Electrical Adder ....................................................................................................1625 Electrical Subtractor .............................................................................................1627 Electrical Multiplier ...............................................................................................1629 Electrical Bias.......................................................................................................1631 Electrical Norm.....................................................................................................1633 Electrical Differentiator .........................................................................................1635 Electrical Integrator ..............................................................................................1637 Electrical Rescale.................................................................................................1639 Electrical Reciprocal.............................................................................................1641 Electrical Abs .......................................................................................................1643 Electrical Sgn .......................................................................................................1645 Arithmetic - Optical ............................................................................................. 1647 Optical Gain .........................................................................................................1649 Optical Adder .......................................................................................................1651 Optical Subtractor ................................................................................................1653 Optical Bias ..........................................................................................................1655 Optical Multiplier...................................................................................................1657 Optical Hard Limiter .............................................................................................1659 Tools - Electrical ................................................................................................. 1661 Convert To Electrical Individual Samples.............................................................1663 Convert From Electrical Individual Samples ........................................................1665 Electrical Downsampler........................................................................................1667 Digital to Analog ...................................................................................................1669 Analog to Digital ...................................................................................................1673 Tools - Optical ..................................................................................................... 1677 Merge Optical Signal Bands.................................................................................1679 Convert to Parameterized ....................................................................................1681 Convert to Noise Bins ..........................................................................................1683 Convert To Optical Individual Samples ................................................................1685 Convert From Optical Individual Samples............................................................1687 Optical Downsampler ...........................................................................................1689 Signal Type Selector ............................................................................................1691 Convert To Sampled Signals ...............................................................................1693 Channel Attacher .................................................................................................1695 Ideal Frequency Converter...................................................................................1697 Tools - Binary ...................................................................................................... 1699 Convert To Individual Bits ....................................................................................1701 Convert From Individual Bits ................................................................................1703 Serial To Parallel Converter .................................................................................1705 Serial To Parallel Converter 1xN..........................................................................1707 Parallel To Serial Converter .................................................................................1709 Parallel To Serial Converter Nx1..........................................................................1711 Logic - Binary ...................................................................................................... 1713 Binary NOT ..........................................................................................................1715 Binary AND ..........................................................................................................1717 Binary OR.............................................................................................................1719 Binary XOR ..........................................................................................................1721 Binary NAND........................................................................................................1723 Binary NOR ..........................................................................................................1725 Binary XNOR........................................................................................................1727 Delay ....................................................................................................................1729 Logic - Electrical ................................................................................................. 1731 Electrical NOT ......................................................................................................1733 Electrical AND ......................................................................................................1735 Electrical OR ........................................................................................................1737 Electrical XOR......................................................................................................1739 Electrical NAND ...................................................................................................1741 Electrical NOR......................................................................................................1743 Electrical XNOR ...................................................................................................1745 T Flip-Flop ............................................................................................................1747 D Flip-Flop............................................................................................................1749 JK Flip-Flop ..........................................................................................................1751 RS Flip-Flop .........................................................................................................1753 RS NOR Latch .....................................................................................................1755 RS NAND Latch ...................................................................................................1757 Clocked RS NAND Latch .....................................................................................1759 Passives Library ........................................................................................ 1761 Electrical .............................................................................................................. 1761 Electrical Phase Shift ...........................................................................................1763 Electrical Signal Time Delay ................................................................................1765 Electrical Attenuator .............................................................................................1767 90 Degree Hybrid Coupler ...................................................................................1769 180 Degree Hybrid Coupler .................................................................................1771 DC Block ..............................................................................................................1773 Splitter 1x2 ...........................................................................................................1774 Splitter 1xN...........................................................................................................1776 Combiner 2x1.......................................................................................................1779 Combiner Nx1 ......................................................................................................1781 1 Port S Parameters.............................................................................................1783 2 Port S Parameters.............................................................................................1785 3 Port S Parameters.............................................................................................1789 4 Port S Parameters.............................................................................................1791 Coaxial Cable.......................................................................................................1793 Transmission Line ................................................................................................1799 Two Wire Cable....................................................................................................1803 RLCG Transmission Line .....................................................................................1809 Parallel Plate Transmission Line..........................................................................1813 Optical .................................................................................................................. 1819 Phase Shift...........................................................................................................1823 Time Delay ...........................................................................................................1825 Optical Attenuator ................................................................................................1827 Attenuator Bidirectional ........................................................................................1829 Connector.............................................................................................................1833 Connector Bidirectional ........................................................................................1835 Reflector Bidirectional ..........................................................................................1839 Saturable Absorber ..............................................................................................1843 Tap Bidirectional ..................................................................................................1845 Luna Technologies OVA Measurement ...............................................................1849 Measured Component..........................................................................................1853 X Coupler .............................................................................................................1857 Pump Coupler Co-Propagating ............................................................................1859 Pump Coupler Counter-Propagating....................................................................1861 Coupler Bidirectional ............................................................................................1863 Pump Coupler Bidirectional..................................................................................1869 Power Splitter 1x2 ................................................................................................1875 Power Splitter 1x4 ................................................................................................1877 Power Splitter 1x8 ................................................................................................1881 Power Splitter.......................................................................................................1883 1xN Splitter Bidirectional ......................................................................................1885 Power Combiner 2x1............................................................................................1889 Power Combiner 4x1............................................................................................1891 Power Combiner 8x1............................................................................................1893 Power Combiner ..................................................................................................1895 Linear Polarizer ....................................................................................................1897 Circular Polarizer..................................................................................................1899 Polarization Attenuator.........................................................................................1901 Polarization Delay ................................................................................................1903 Polarization Phase Shift .......................................................................................1905 Polarization Combiner..........................................................................................1907 Polarization Controller..........................................................................................1909 Polarization Rotator..............................................................................................1911 Polarization Splitter ..............................................................................................1913 PMD Emulator......................................................................................................1915 Polarization Combiner Bidirectional .....................................................................1919 Polarization Waveplate ........................................................................................1923 Polarization Filter .................................................................................................1925 Isolator .................................................................................................................1927 Ideal Isolator.........................................................................................................1929 Isolator Bidirectional.............................................................................................1931 Circulator..............................................................................................................1935 Ideal Circulator .....................................................................................................1937 Circulator Bidirectional .........................................................................................1939 Tools Library .............................................................................................. 1943 Switch...................................................................................................................1945 Select ...................................................................................................................1947 Fork 1x2 ...............................................................................................................1949 Loop Control.........................................................................................................1950 Ground .................................................................................................................1951 Buffer Selector .....................................................................................................1952 Fork 1xN...............................................................................................................1955 Binary Null............................................................................................................1956 Optical Null...........................................................................................................1957 Electrical Null .......................................................................................................1958 Binary Delay.........................................................................................................1959 Optical Delay........................................................................................................1960 Electrical Delay ....................................................................................................1961 Optical Ring Controller .........................................................................................1963 Electrical Ring Controller......................................................................................1965 Duplicator .............................................................................................................1967 Limiter ..................................................................................................................1969 Initializer ...............................................................................................................1971 Save to file ...........................................................................................................1973 Load from file .......................................................................................................1975 Command Line Application ..................................................................................1977 Swap Horiz...........................................................................................................1981 Termination ..........................................................................................................1983 Optiwave Software Tools .......................................................................... 1985 OptiAmplifier.........................................................................................................1987 OptiGrating...........................................................................................................1995 WDM_Phasar Demux 1xN ...................................................................................1999 WDM_Phasar Mux Nx1........................................................................................2001 OptiBPM Component NxM...................................................................................2005 OptiSPICE Output ................................................................................................2009 OptiSPICE NetList................................................................................................2011 External Software Tools ............................................................................ 2013 MATLAB Filter Component ..................................................................................2015 MATLAB Optical Filter Component ......................................................................2019 MATLAB Component ...........................................................................................2023 Scilab Component................................................................................................2039 Cpp Component ...................................................................................................2045 Save ADS File......................................................................................................2051 Load ADS File ......................................................................................................2055 Save Spice Stimulus File .....................................................................................2059 Load Spice CSDF File..........................................................................................2065 Triggered Save Spice Stimulus File .....................................................................2069 Triggered Load Spice CSDF File .........................................................................2075 Multimode Library...................................................................................... 2079 Optical Fibers ...................................................................................................... 2079 Linear Multimode Fiber ........................................................................................2081 Parabolic-Index Multimode Fiber .........................................................................2087 Measured-Index Multimode Fiber ........................................................................2099 Amplifiers............................................................................................................. 2121 Er Doped Multimode Fiber ...................................................................................2123 Yb Doped Multimode Fiber ..................................................................................2141 Receivers ............................................................................................................. 2157 Spatial PIN Photodiode ........................................................................................2159 Spatial APD..........................................................................................................2163 Spatial Optical Receiver.......................................................................................2167 Spatial Demultiplexer ...........................................................................................2173 Transmitters ........................................................................................................ 2179 Spatial CW Laser .................................................................................................2181 Spatiotemporal VCSEL ........................................................................................2187 Spatial VCSEL .....................................................................................................2195 Spatial single mode laser ....................................................................................2205 Spatial LED ..........................................................................................................2211 Spatial Optical Transmitter...................................................................................2215 Pulse Generators ................................................................................................ 2223 Spatial Optical Gaussian Pulse Generator...........................................................2225 Spatial Optical Sech Pulse Generator..................................................................2231 Spatial Optical Impulse Generator .......................................................................2237 Mode Generators................................................................................................. 2243 Donut Transverse Mode Generator .....................................................................2245 Hermite Transverse Mode Generator ..................................................................2249 Laguerre Transverse Mode Generator.................................................................2253 Multimode Generator ...........................................................................................2257 Measured Transverse Mode ................................................................................2263 Passives & Tools................................................................................................. 2267 Spatial Aperture ...................................................................................................2269 Thin Lens .............................................................................................................2271 Vortex Lens ..........................................................................................................2273 Spatial Connector.................................................................................................2275 Mode Combiner....................................................................................................2279 Save Transverse Mode ........................................................................................2281 Mode Selector ......................................................................................................2285 Mode ID Modifier..................................................................................................2287 Free Space Optics Library ........................................................................ 2289 FSO Channel .......................................................................................................2291 OWC Channel ......................................................................................................2297 Diffuse Channel....................................................................................................2303 Visualizer Library Optical • Optical Spectrum Analyzer (OSA) • Optical Time Domain Visualizer (OTDV) • Optical Power Meter • Polarization Meter • Polarization Analyzer • WDM Analyzer (WDMA) • Dual Port WDM Analyzer (DPWDMA) • Spatial Visualizer • Encircled Flux Analyzer 17 Notes: 18 OPTICAL SPECTRUM ANALYZER (OSA) Optical Spectrum Analyzer (OSA) This visualizer allows the user to calculate and display optical signals in the frequency domain. It can display the signal intensity, power spectral density, phase, group delay and dispersion for X and Y polarizations. Ports Name and description Port type Signal type Optical Input Optical Parameters Resolution bandwidth Name and description Default value Default unit Value range Resolution bandwidth Off — On, Off Rectangle — Rectangle, Gaussian, Butterworth 0.01 nm [0, 1e+100] Name and description Default value Default unit Value range Power unit dBm — dBm, W –100 dBm [-1e+100, 1e+100] Determines whether or not the resolution filter is enabled Filter type Determines the type of resolution filter Bandwidth Resolution filter bandwidth Graphs Power unit for the vertical axis Minimum value Minimum value for power when using units in dBm 19 OPTICAL SPECTRUM ANALYZER (OSA) Name and description Default value Default unit Value range Scale factor 0 dB [-1e+100, 1e+100] False — True, False m — m, Hz False — True, False True — True, False False — True, False False — True, False True — True, False 128000 — [100, 1e+008] False — True, False Name and description Default value Default unit Value range Enabled True — True, False Vertical axis scale factor Power spectral density Determines whether or not to calculate the power spectral density for the vertical axis Frequency unit Frequency unit for the horizontal axis Calculate phase Determines whether or not to calculate the phase graphs Unwrap phase Determines whether or not to remove the phase discontinuity Calculate group delay Determines whether or not to calculate group delay graphs Calculate dispersion Determines whether or not to calculate dispersion graphs Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Simulation Determines whether or not the component is enabled 20 OPTICAL SPECTRUM ANALYZER (OSA) Graphs Sampled signals Name and description X Title Y Title Sampled signal spectrum Wavelength (m) Power (dBm) Sampled signal spectrum X Wavelength (m) Power (dBm) Sampled signal spectrum Y Wavelength (m) Power (dBm) Sampled signal phase X Wavelength (m) Phase (rad) Sampled signal phase Y Wavelength (m) Phase (rad) Sampled signal group delay X Wavelength (m) Delay (s) Sampled signal group delay Y Wavelength (m) Delay (s) Sampled signal dispersion X Wavelength (m) Dispersion (ps/nm) Sampled signal dispersion Y Wavelength (m) Dispersion (ps/nm) Parameterized signals Name and description X Title Y Title Parameterized signal spectrum Wavelength (m) Power (dBm) Parameterized signal spectrum X Wavelength (m) Power (dBm) Parameterized signal spectrum Y Wavelength (m) Power (dBm) Name and description X Title Y Title Noise bins signal spectrum Wavelength (m) Power (dBm) Noise bins signal spectrum X Wavelength (m) Power (dBm) Noise bins signal spectrum Y Wavelength (m) Power (dBm) Noise bins 21 OPTICAL SPECTRUM ANALYZER (OSA) Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser Access the Optical Spectrum Analyzer (OSA) parameters, graphs, and results from the simulation (see Figure 2). 22 OPTICAL SPECTRUM ANALYZER (OSA) Figure 2 OSA display Use the signal index to select the signal to display from the signal buffer. Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3). • Signal • Noise • Signal + Noise • All Figure 3 Multiple signal types display 23 OPTICAL SPECTRUM ANALYZER (OSA) Use the tabs at the bottom of the graph to access the optical signal polarization (see Figure 4). • Power: Total power • Power X: Power from polarization X • Power Y: Power from polarization Y Figure 4 Signal polarization display Resolution bandwidth parameter When selected, The Resolution bandwidth parameter applies an optical filter aperture function (square, Gaussian or Butterworth) to the OSA data. It can be used to reduce the noisiness of the spectral data (see Fig 5 and Fig 6) but also affects the ability to resolve closely spaced frequency signals. It is a common performance feature of commercial OSAs [1]. 24 OPTICAL SPECTRUM ANALYZER (OSA) Figure 5 CW laser OSA output with Resolution bandwidth = 0.1 nm Figure 6 CW laser OSA output with Resolution bandwidth = 0.01 nm 25 OPTICAL SPECTRUM ANALYZER (OSA) References [1] Optical Spectrum Analysis, Application Note 1550-4, Optical Spectrum Analysis Basics, Agilent Technologies, 2000 (Accessed 24 May 2015 - http://mnp.ucsd.edu/ece183_2015/notes/59637145E.pdf) 26 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Optical Time Domain Visualizer (OTDV) This visualizer allows the user to calculate and display optical signals in the time domain. It can display the signal intensity, frequency, phase and alpha parameter for polarizations X and Y. It also provides enhanced features to characterize ultra short pulses such as autocorrelation and Frequency Resolved Optical Gating (FROG). Note: The phase or chirp (alpha) parameter is only accessible if the Power X or Power Y tab (bottom of graph) is selected. Ports Name and description Port type Signal type Optical Input Optical Parameters Graphs Name and description Default value Default unit Units Value range Plot individual mode False - - True, False 0 - - [0, 1e+008] s - - s, bits Bit rate Bits/s Bits/s [0, 1e+012] Determines whether or not to plot a individual mode Individual mode number The individual mode number Time unit Time unit for the horizontal axis Reference bit rate Reference bit rate to use when the time unit is Bit period MBits/s GBits/s Retracing False - - True, False Time window 1/(Bit rate) s - ]0, +INF[ Defines the retracing time window 27 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Name and description Default value Default unit Units Value range Autocorrelation Off - - Off, Field, Intensity False - - True, False deg - - deg, rad True - - True, False False - - True, False W - - W, dBm –100 dBm - [-1e+100, 1e+100] True - - True, False 128,000 - - [100, 1e+008] False - - True, False False - - True, False 500 - - [10, 5000] Determines the type of calculation for the autocorrelation graphs Calculate phase and chirp Determines whether or not to calculate phase and chirp graphs NOTE: This feature is only active if the Power X or Power Y tab has been selected. Phase unit Phase unit for the vertical axis Unwrap phase Determines whether or not to remove the phase discontinuity Calculate alpha parameter Determines whether or not to calculate alpha parameter graphs Power unit Power unit for the vertical axis Minimum value Minimum value for power when using units in dBm Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs Number of color bins Number of vertical and horizontal bins of the display 28 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Name and description Default value Default unit Units Value range Color grade palette Default - - Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow Name and description Default value Default unit Default unit Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30,3e5] 5*(Sample rate) THz Hz, GHz, THz, nm [1, 1e+100] Determines the color grade palette Downsampling Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined Center frequency User-defined center frequency of the internal filter Sample rate Bandwidth of the internal filter Enhanced Name and description Default value Default unit Value range Calculate FROG False - True, False X - X, Y True - True, False Sample rate Hz [0, 1e100] Time window / 2 s [0, 1e100] 128 - True, False Determines whether or not to calculate the Frequency Resolved Optical Gating (FROG) graph FROG polarization Determines the signal polarization for the FROG analysis Add noise to FROG signal Determines whether or not to convert and add noise bins to the signal FROG frequency range Frequency range for the vertical axis FROG delay range Delay range for the horizontal axis Number of FROG delay points Number of points for the horizontal axis 29 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Simulation Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Name and description Default value Default unit Value range Generate random seed True - True, False 0 - [0,4999] Determines whether or not the component is enabled Signal access option Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Graphs Signal Name and description X Title Y Title Signal power Time (s) Power (W) Signal power X Time (s) Power (W) Signal power Y Time (s) Power (W) Signal phase X Time (s) Phase (deg) Signal phase Y Time (s) Phase (deg) Signal chirp X Time (s) Frequency (Hz) Signal chirp Y Time (s) Frequency (Hz) Signal autocorrelation X Delay (s) Intensity (a.u.) Signal autocorrelation Y Delay (s) Intensity (a.u.) Signal alpha parameter X Time (s) Alpha (ratio) Signal alpha parameter Y Time (s) Alpha (ratio) 30 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Noise Name and description X Title Y Title Noise power Time (s) Power (W) Noise power X Time (s) Power (W) Noise power Y Time (s) Power (W) Noise phase X Time (s) Phase (deg) Noise phase Y Time (s) Phase (deg) Noise chirp X Time (s) Frequency (Hz) Noise chirp Y Time (s) Frequency (Hz) Noise autocorrelation X Delay (s) Intensity (a.u.) Noise autocorrelation Y Delay (s) Intensity (a.u.) Noise alpha parameter X Time (s) Alpha (ratio) Noise alpha parameter Y Time (s) Alpha (ratio) Name and description X Title Y Title Signal + Noise power Time (s) Power (W) Signal + Noise power X Time (s) Power (W) Signal + Noise power Y Time (s) Power (W) Signal + Noise phase X Time (s) Phase (deg) Signal + Noise phase Y Time (s) Phase (deg) Signal + Noise chirp X Time (s) Frequency (Hz) Signal + Noise chirp Y Time (s) Frequency (Hz) Signal + Noise autocorrelation X Delay (s) Intensity (a.u.) Signal + Noise autocorrelation Y Delay (s) Intensity (a.u.) Signal + Noise alpha parameter X Time (s) Alpha (ratio) Signal + Noise alpha parameter Y Time (s) Alpha (ratio) Signal + Noise 3D Graphs Name and description X Title Y Title Z Title FROG 3D Graph Delay (ns) Frequency (THz) Intensity (a.u.) 31 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser The Optical Time Domain Visualizer (OTDV) is an Oscilloscope for optical signals. Access the OTDV parameters, graphs, and results from the simulation (see Figure 2). 32 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Figure 2 OTDV display. Use the signal index to select the signal to display from the signal buffer. Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3). • Signal • Noise • Signal + Noise • All Figure 3 Multiple signal types display 33 OPTICAL TIME DOMAIN VISUALIZER (OTDV) Use the tabs at the bottom of the graph to access the optical signal polarization (see Figure 4). • Power: Total power • Power X: Power from polarization X • Power Y: Power from polarization Y Figure 4 Signal polarization display When you select Power X or Power Y, you can access the signal phase and chirp by selecting the Analysis option. 34 OPTICAL POWER METER Optical Power Meter This visualizer allows the user to calculate and display the average power of optical signals. It can also calculate the power for polarizations X and Y. Ports Name and description Port type Signal type Optical Input Optical Parameters Main Name and description Default value Default unit Value range Minimum value –100 dBm [-1e+100, 1e+100] Name and description Default value Default unit Value range Enabled True — True, False Minimum value for power when using units in dBm Simulation Determines whether or not the component is enabled 35 OPTICAL POWER METER Results Name and description Unit Total power dBm Total power W Total power X dBm Total power X W Total power Y dBm Total power Y W Signal power dBm Signal power W Signal power X dBm Signal power X W Signal power Y dBm Signal power Y W Sampled signal power dBm Sampled signal power W Sampled signal power X dBm Sampled signal power X W Sampled signal power Y dBm Sampled signal power Y W Parameterized signal power dBm Parameterized signal power W Parameterized signal power X dBm Parameterized signal power X dBm Parameterized signal power Y W Parameterized signal power Y W Noise power dBm Noise power W Noise power X dBm Noise power X W Noise power Y dBm 36 OPTICAL POWER METER Name and description Unit Noise power Y W Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser Access the Optical Power Meter (OPM) parameters, graphs, and results from the simulation (see Figure 2). 37 OPTICAL POWER METER Figure 2 OPM display You can select the total signal power to display for each signal type. When you select the signal power, the result is the sum of the sampled and parameterized signals. Note: For sampled signals, all the data samples are added and then divided by the Number of samples to obtain the average optical power over the simulation time window. Thus the power level displayed will frequently be less than the peak signal power of the sampled data set. Also signals which are linked to Bit Sequence Generators may display different optical powers between simulations due to variations in the bit sequence pattern. The same applies to noise signals which are set to have different Random number seeds per iteration. 38 POLARIZATION METER Polarization Meter This visualizer allows the user to calculate the average polarization state of the optical signal, including the degree of polarization (DOP), differential group delay (DGD), Stokes parameters, azimuth and ellipticity. Ports Name and description Port type Signal type Optical Input Optical Parameters Main Name and description Default value Default unit Value range Frequency 193.1 Hz, THz, nm [30, 30000] 100 Hz, GHz, THz, nm [0, 1e100] –100 dBm [-1e+100, 1e100] Polarization X - Polarization X, Polarization Y User-defined center frequency of the internal filter Bandwidth Resolution filter bandwidth Minimum value Minimum value for power when using units in dBm DGD reference The reference used to calculate the delay between polarizations X and Y Downsampling Name and description Default value Default unit Default unit Value range Sample rate 5*(Sample rate) THz Hz, GHz, THz, nm [1, 1e+100] Bandwidth of the internal filter 39 POLARIZATION METER Simulation Name and description Default value Default unit Value range Enabled True — True, False Determines whether or not the component is enabled Noise Name and description Default value Convert noise bins True Default unit Units Value range [True, False] Determines if the generated noise bins are incorporated into the signal Random Numbers Name and description Default value Default unit Units Value range Generate random seed True [True, False] 0 [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Results Name and description Unit S0 dBm S0 W S1 dBm S1 W S2 dBm S2 W S3 dBm S3 W s1 ratio s2 ratio s3 ratio 40 POLARIZATION METER Name and description Unit DOP % DGD s Azimuth deg Ellipticity deg Sampled signal power X W Sampled Signal S0 dBm Sampled Signal S0 W Sampled Signal S1 dBm Sampled Signal S1 W Sampled Signal S2 dBm Sampled Signal S2 W Sampled Signal S3 dBm Sampled Signal S3 W Sampled Signal s1 ratio Sampled Signal s2 ratio Sampled Signal s3 ratio Sampled Signal DOP % Sampled Signal DGD s Sampled Signal Azimuth deg Sampled Signal Ellipticity deg Parameterized Signal S0 dBm Parameterized Signal S0 W Parameterized Signal S1 dBm Parameterized Signal S1 W Parameterized Signal S2 dBm Parameterized Signal S2 W Parameterized Signal S3 dBm Parameterized Signal S3 W Parameterized Signal s1 ratio Parameterized Signal s2 ratio Parameterized Signal s3 ratio 41 POLARIZATION METER Name and description Unit Parameterized Signal DOP % Parameterized Signal DGD s Parameterized Signal Azimuth deg Parameterized Signal Ellipticity deg Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser displaying the Polarization Meter 42 POLARIZATION METER Use the Polarization Meter display to access the key results from the simulation (see Figure 2). Figure 2 Polarization Meter display By default, the total signal power is displayed in the visualizer (the sum of the sampled and parameterized signals). The polarization properties are measured at the user defined frequency and bandwidth. The differential group delay is measured by the correlation between polarization states and its signal depends on the parameter DGD reference. 43 POLARIZATION METER Notes: 44 POLARIZATION ANALYZER Polarization Analyzer This visualizer allows the user to calculate and display different properties of the signal polarization, including the polarization ellipse and the Poincaré sphere. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals, Noise bins, Parameterized signals Parameters Main Name and description Default value Default unit Units Value range Lower frequency limit 185 THz Hz, THz, nm [30, 300000] 200 THz Hz, THz, nm [30, 300000] 193.1 THz Hz, THz, nm [30, 300000] Name and description Default value Default unit Units Value range Minimum value -100 dBm Defines the lower limit of the calculation range Upper frequency limit Defines the upper limit of the calculation range Reference frequency Defines the reference, or marker, frequency used to calculate the results Graphs Minimum value for power when displaying S0 [-1e+100, 1e+100] 45 POLARIZATION ANALYZER Name and description Default value Default unit Units Value range Frequency unit Hz [m, Hz] True True, False 128000 [100, 1e+008] False True, False Frequency unit for the graphs Limit number of points Determines if the user can enter the maximum number of points Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Export Name and description Default value Default unit Units Value range Save Stokes parameters False [True, False] False [True, False] Defines whether to export the Stokes parameters to a file MATLAB format Defines whether to use MATLAB format for the file Filename Sphere.dat Export data destination file name Simulation Name and description Default value Default unit Units Value range Enabled True [True, False] True [True, False] Determines whether the component is enabled Dynamic update Noise Name and description Default value Convert noise bins True Determines if the generated noise bins are incorporated into the signal 46 Default unit Units Value range [True, False] POLARIZATION ANALYZER Random Numbers Name and description Default value Default unit Units Value range Generate random seed True [True, False] 0 [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Graphs Name and description X Title Y Title Sampled signal S0 Wavelength (m) Power (dBm) Sampled signal s1 Wavelength (m) s1 (ratio) Sampled signal s2 Wavelength (m) s2 (ratio) Sampled signal s3 Wavelength (m) s3 (ratio) Sampled signal azimuth Wavelength (m) Phase (deg) Sampled signal ellipticity Wavelength (m) Phase (deg) Parameterized signal S0 Wavelength (m) Power (deg) Parameterized signal s1 Wavelength (m) s1 (ratio) Parameterized signal s2 Wavelength (m) s2 (ratio) Parameterized signal s3 Wavelength (m) s3 (ratio) Parameterized signal azimuth Wavelength (m) Phase (deg) Parameterized signal ellipticity Wavelength (m) Phase (deg) Sampled signal elliptical display Polarization X Polarization Y Parameterized signal elliptical display Polarization X Polarization Y Results Name and description Sampled signal frequency (Hz) Sampled signal wavelength (nm) Sampled signal S0 (dBm) Sampled signal s1 (ratio) 47 POLARIZATION ANALYZER Name and description Sampled signal s2 (ratio) Sampled signal s3 (ratio) Sampled signal azimuth (deg) Sampled signal ellipticity (deg) Parameterized signal frequency (Hz) Parameterized signal wavelength (nm) Parameterized signal S0 (dBm) Parameterized signal s1 (ratio) Parameterized signal s2 (ratio) Parameterized signal s3 (ratio) Parameterized signal azimuth (deg) Parameterized signal ellipticity (deg) Technical Background This visualizer is a Polarization Analyzer [1]. It calculates the Stokes and Jones parameters in a range defined by the parameters Lower limit calculation range and Upper limit calculation range. Additionally, the user can specify a Reference frequency that makes the analyzer display the polarization elliptical display and the Stokes parameters S0, s1, s2 and s3, and the signal azimuth and ellipticity. The user can access the graphs by double-clicking directly on the visualizer icon (Figure 1), from the Component Viewer, or from the project browser (Figure 2). 48 POLARIZATION ANALYZER Figure 1 Polarization analyzer 49 POLARIZATION ANALYZER Figure 2 Project browser The first two tabs are the Stokes parameters and polarization state versus frequency graphs (Figure 3 and Figure 4). 50 POLARIZATION ANALYZER Figure 3 Stokes graphs Figure 4 Polarization state graph The polarization ellipse displays the polarization state at the reference frequency (Figure 5). 51 POLARIZATION ANALYZER Figure 5 Elliptical display at the reference frequency The Poincaré sphere is calculated using the Stokes parameters. The color palette represents the power calculated from S0. The marker allows the user to identify the Stokes parameters at the reference frequency (Figure 1). References [1] “Polarization Measurements of Signals and Components”, Product Note 8509-1, Agilent Technologies. 52 WDM ANALYZER (WDMA) WDM Analyzer (WDMA) This visualizer automatically detects, calculates and displays the optical power, noise, SNR, OSNR, frequency and wavelength for each WDM channel at the visualizer input. Ports Name and description Port type Signal type Optical Input Optical Parameters Main Name and description Default value Default unit Value range Lower frequency limit 185 Hz, THz, and nm [30,+INF[ 200 Hz, THz, and nm [30,+INF[ 2 * Symbol rate / 125e9 nm [0,+INF[ –100 dBm ]-INF,+INF[ Defines the lower frequency limit for the calculation bandwidth Upper frequency limit Defines the upper frequency limit for the calculation bandwidth Resolution bandwidth Determines whether or not the resolution filter is enabled Minimum value Minimum value for power when using units in dBm Extended scan False True, False 10 [1,100] 5 [1,20] Determines whether or not to scan for additional WDM channels Max. number of additional channels Defines the maximum number of additional channels Precision Number of decimal places used to compare two channel frequencies 53 WDM ANALYZER (WDMA) Name and description Default value Default unit Value range Peak threshold 10 dB [0,100] 15 dB [0,100] 15 dB [0,100] Peaks with amplitudes below this value, relative to the max power peak, will not be included in the channel count Peak excursion This is the level the signal has to go up and down for a spectral feature to be considered a peak, or a WDM channel. Pit excursion Maximum excursion from the lowest point between adjacent channels (pit). Interpolation Name and description Default value Default unit Value range Noise interpolation Auto — On, Off, Auto Sample rate / 125e9 nm [0,+INF[ Name and description Default value Default unit Value range Frequency unit nm — nm, m, Hz, THz Name and description Default value Default unit Value range Enabled True — True, False Index — Index, Average, Last Index Determines if the noise will be estimated by using the signal Interpolation offset Spacing between the signal maximum and the signal value used as noise value Graphs Frequency unit for the horizontal axis Simulation Determines whether or not the component is enabled Signal access option Determines whether or not the component is enabled 54 WDM ANALYZER (WDMA) Graphs Name and description X Title Y Title Signal spectrum Wavelength (nm) Power (dBm) Noise spectrum Wavelength (nm) Power (dBm) Results Signal Name and description Unit Min. signal power dBm Min. signal power W Frequency at min. signal power Hz Wavelength at min. signal power nm Max. signal power dBm Max. signal power W Frequency at max. signal power Hz Wavelength at max. signal power nm Total signal power dBm Total signal power W Ratio max/min signal power dB Ratio max/min signal power — Noise Name and description Unit Min. noise power dBm Min. noise power W Frequency at min. noise power Hz Wavelength at min. noise power nm Max. noise power dBm Max. noise power W Frequency at max. noise power (0.1 nm) Hz Wavelength at max. noise power (0.1 nm) nm 55 WDM ANALYZER (WDMA) Name and description Unit Total noise power (0.1 nm) dBm Total noise power (0.1 nm) W Ratio max/min noise power (0.1 nm) dB Ratio max/min noise power (0.1 nm) — OSNR Name and description Unit Min. SNR dB Frequency at min. SNR Hz Wavelength at min. SNR nm Max. SNR dB Frequency at max. ONR Hz Wavelength at max. SNR nm Ratio max/min SNR dB Total SNR dB Min. OSNR Frequency at Min. OSNR Hz Wavelength at Min. OSNR nm Max. OSNR dB Frequency at Max. OSNR Hz Wavelength at Max. OSNR nm Ratio max/min OSNR dB Total OSNR dB 56 WDM ANALYZER (WDMA) Technical background Noise interpolation offset The Noise interpolation parameter sets the interpolation method to be used to calculate the signal to noise ratio. The settings are as follows: • Auto: When set to “Auto”, and when there is a noise bin power at the signal frequency data point (f0), then: Noise power (f0) = Noise bin power (f0). • If the noise bin power is zero at f0 (does not exist) then the noise is only interpolated from the signal data: Noise power (f0) = [Signal power (f0 - fi) + Signal power (f0 + fi)]/2 where fi is the Interpolation offset • On: When set to “On” then: Noise power (f0) = Noise bin power (f0) + [Signal power (f0 - fi) + Signal power (f0 + fi)]/2 • Off: When set to “Off” then Noise power (f0) = Noise bin power (f0). If the noise bins are converted (recommended for OSNR measurements), then the Noise interpolation setting of “Auto” or “On” will provide the same results. Single channel operation The WDMA estimates the signal and the noise power for the optical channel based on the resolution bandwidth (see Figure 1). The resulting signal to noise ratio (SNR) is calculated as follows: P s mW SNR dB = 10 log 10 --------------------- = P s dBm – P n dBm P n mW (1) where Ps and Pn are the signal power and noise power within the selected resolution bandwidth (RBW) for the analyzer. Normally, RBW = 2*Symbol rate. 57 WDM ANALYZER (WDMA) Figure 1 WDM Analyzer operation for single channel The resulting optical signal to noise ratio (OSNR) is calculated as follows:: P s mW OSNR dB = 10 log 10 -------------------------- = P s dBm – P n0.1 dBm P n0.1 mW (2) where Ps is the signal power within the selected resolution bandwidth (RBW) for the analyzer and Pn0.1 is the noise power within a 0.1 nm bandwidth The Interpolation offset should be larger than the Sample rate/2 to ensure that the measured Pn does not include the signal's power. The bandwidth of the added noise should however be greater than the Sample rate. WDM operation The WDMA estimates the signal and the noise power for all detected WDM channels based on the resolution bandwidth For multiple channel operation, there are two ways to set the Interpolation offset. One way is to set Interpolation offset = Channel spacing/2. However, this method is accurate only when the overlap between adjacent channels is insignificant. If the 58 WDM ANALYZER (WDMA) overlap is significant, the measured noise power will include the overlapped signals, and will lead to an inaccurate measurement of the OSNR. Figure 2 Interpolation offset Method 1 The second method is to set Interpolation offset to be: Total WDM channel's bandwidth - (1/2)*Sample rate where, Total WDM channel's bandwidth = Sample rate + (channel number - 1) * Channel spacing. This method measures the Out-of-band noise power which is equal to the In-band noise power width when the noise level is flat. If the noise is flat and the noise bandwidth is larger than signal bandwidth, this second method is recommended. Figure 3 Interpolation offset Method 2 59 WDM ANALYZER (WDMA) 60 DUAL PORT WDM ANALYZER (DPWDMA) Dual Port WDM Analyzer (DPWDMA) This visualizer automatically detects, calculates and displays the optical power, noise, OSNR, Gain, noise figure, frequency and wavelength for each WDM channel at the visualizer inputs. Ports Name and description Port type Signal type Input 1 Input Optical Input 2 Input Optical Parameters Main Name and description Default value Default unit Value range Lower frequency limit 185 Hz, THz, and nm [30,+INF[ 200 Hz, THz, and nm [30,+INF[ 2*Symbol rate/ 125e9 nm [0,+INF[ –100 dBm ]-INF,+INF[ Defines the lower frequency limit for the calculation bandwidth Upper frequency limit Defines the upper frequency limit for the calculation bandwidth Resolution bandwidth Determines whether or not the resolution filter is enabled Minimum value Minimum value for power when using units in dBm Extended scan False True, False 10 [1,100] 5 [1,20] Determines whether or not to scan for additional WDM channels Max. number of additional channels Defines the maximum number of additional channels Precision Number of decimal places used to compare two channel frequencies 61 DUAL PORT WDM ANALYZER (DPWDMA) Name and description Default value Default unit Value range Peak threshold 10 dB [0,100] 15 dB [0,100] 15 dB [0,100] Peaks with amplitudes below this value, relative to the max power peak, will not be included in the channel count Peak excursion This is the level the signal has to go up and down for a spectral feature to be considered a peak, or a WDM channel. Pit excursion Maximum excursion from the lowest point between adjacent channels (pit). Input noise for NF calculation Determines which method to use when calculating the Noise Figure metric EDFA with shot noise limited input EDFA with shot-noise limited noise, From external input noise Interpolation Name and description Default value Default unit Value range Noise interpolation Auto — On, Off, Auto Sample rate/ 125e9 nm [0,+INF[ Name and description Default value Default unit Value range Frequency unit nm — nm, m, Hz, THz Name and description Default value Default unit Value range Enabled True — True, False Determines if the noise will be estimated by using the signal Interpolation offset Spacing between the signal maximum and the signal value used as noise value Graphs Frequency unit for the horizontal axis Simulation Determines whether or not the component is enabled 62 DUAL PORT WDM ANALYZER (DPWDMA) Graphs Name and description X Title Y Title Input signal spectrum Wavelength (nm) Power (dBm) Input noise spectrum Wavelength (nm) Power (dBm) Output signal spectrum Wavelength (nm) Power (dBm) Output noise spectrum Wavelength (nm) Power (dBm) Gain Wavelength (nm) Gain (dB) Noise figure Wavelength (nm) NF (dB) Results Input signal Name and description Unit Input: Min. signal power (dBm) dBm Input: Min. signal power (W) W Input: Frequency at min. signal power (Hz) Hz Input: Wavelength at min. signal power (nm) nm Input: Max. signal power (dBm) dBm Input: Max. signal power (W) W Input: Frequency at max. signal power (Hz) Hz Input: Wavelength at max. signal power (nm) nm Input: Total signal power (dBm) dBm Input: Total signal power (W) W Input: Ratio max/min signal power (dB) dB Input: Ratio max/min signal power — Input noise Name and description Unit Input: Min. noise power (dBm) dBm Input: Min. noise power (W) W Input: Frequency at min. noise power (Hz) Hz Input: Wavelength at min. noise power (nm) nm 63 DUAL PORT WDM ANALYZER (DPWDMA) Name and description Unit Input: Max. noise power (dBm) dBm Input: Max. noise power (W) W Input: Frequency at max. noise power (Hz) Hz Input: Wavelength at max. noise power (nm) nm Input: Total noise power (dBm) dBm Input: Total noise power (W) W Input: Ratio max/min noise power (dB) dB Input: Ratio max/min noise power — Input: Min. noise power: 0.1nm (dBm) dBm Input: Min. noise power: 0.1nm (W) W Input: Frequency at min. noise power: 0.1nm (Hz) Hz Input: Wavelength at min. noise power: 0.1nm(nm) nm Input: Max. noise power: 0.1nm (dBm) dBm Input: Max. noise power: 0.1nm (W) W Input: Frequency at max. noise power: 0.1nm (Hz) Hz Input: Wavelength at max. noise power: 0.1nm (nm) nm Input: Total noise power: 0.1nm (dBm) dBm Input: Total noise power: 0.1nm (W) W Input: Ratio max/min noise power: 0.1nm (dB) dB Input: Ratio max/min noise power: 0.1nm — Input OSNR Name and description Unit Input: Min. SNR (dB) dB Input: Frequency at max. SNR (Hz) Hz Input: Wavelength at max. SNR (nm) nm Input: Max. SNR (dB) dB Input: Frequency at min. SNR (Hz) Hz Input: Wavelength at min. SNR (nm) nm Input: Ratio max/min SNR (dB) dB Input: Min. OSNR (dB) dB 64 DUAL PORT WDM ANALYZER (DPWDMA) Name and description Unit Input: Frequency at max. OSNR (Hz) Hz Input: Wavelength at max. OSNR (nm) nm Input: Max. OSNR (dB) dB Input: Frequency at min. OSNR (Hz) Hz Input: Wavelength at min. OSNR (nm) nm Input: Ratio max/min OSNR (dB) dB Output signal Name and description Unit Output: Min. signal power (dBm) dBm Output: Min. signal power (W) W Output: Frequency at min. signal power (Hz) Hz Output: Wavelength at min. signal power (nm) nm Output: Max. signal power (dBm) dBm Output: Max. signal power (W) W Output: Frequency at max. signal power (Hz) Hz Output: Wavelength at max. signal power (nm) nm Output: Total signal power (dBm) dBm Output: Total signal power (W) W Output: Ratio max/min signal power (dB) dB Output: Ratio max/min signal power — Output noise Name and description Unit Output: Min. noise power (dBm) dBm Output: Min. noise power (W) W Output: Frequency at min. noise power (Hz) Hz Output: Wavelength at min. noise power (nm) nm Output: Max. noise power (dBm) dBm Output: Max. noise power (W) W Output: Frequency at max. noise power (Hz) Hz 65 DUAL PORT WDM ANALYZER (DPWDMA) Name and description Unit Output: Wavelength at max. noise power (nm) nm Output: Total noise power (dBm) dBm Output: Total noise power (W) W Output: Ratio max/min noise power (dB) dB Output: Ratio max/min noise power — Output OSNR Name and description Unit Output: Min. SNR (dB) dB Output: Frequency at min. SNR (Hz) Hz Output: Wavelength at min. SNR (nm) nm Output: Max. SNR (dB) dB Output: Frequency at max. SNR (Hz) Hz Output: Wavelength at max. SNR (nm) nm Output: Ratio max/min SNR (dB) dB Output: Min. OSNR (dB) dB Output: Frequency at min. OSNR (Hz) Hz Output: Wavelength at min. OSNR (nm) nm Output: Max. OSNR (dB) dB Output: Frequency at max. OSNR (Hz) Hz Output: Wavelength at max. OSNR (nm) nm Output: Ratio max/min OSNR (dB) dB Details Gain Name and description Unit Min. gain (dB) dB Frequency at min. gain (Hz) Hz Wavelength at min. gain (nm) nm Max. gain (dB) dB 66 DUAL PORT WDM ANALYZER (DPWDMA) Name and description Unit Frequency at max. gain (Hz) Hz Wavelength at max. gain (nm) nm Total gain (dB) dB Ratio max/min gain (dB) dB Noise figure Name and description Unit Min. noise figure (dB) dB Frequency at min. noise figure (Hz) Hz Wavelength at min. noise figure (nm) nm Max. noise figure (dB) dB Frequency at max. noise figure (Hz) Hz Wavelength at max. noise figure (nm) nm Ratio max/min noise figure (dB) dB 67 DUAL PORT WDM ANALYZER (DPWDMA) Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser The Dual Port WDM Analyzer (DPWDMA) estimates the signal and the noise power for each optical signal channel based on the resolution bandwidth for each input port. Click the Analysis tab to view the results (such as gain and noise figure) comparing the signal from the two input ports (see Figure 2). 68 DUAL PORT WDM ANALYZER (DPWDMA) Figure 2 DPWDMA analysis tab Click the Details tab to view the detailed analysis for the results, such as the minimum and maximum values for the signals (see Figure 3). Figure 3 DPWDMA details tab Noise Figure calculation When the parameter Input noise for NF calculation is set to “EDFA with shot noise limited input”, the Noise Figure is calculated as follows [1]: N out – Gain N in 1 NF = ------------- + -----------------------------------------h v Gain BW Gain (1) where Nout and Nin are the output and input noise levels; respectively, h is Planck’s constant, v is the signal frequency and BW is the resolution bandwidth of the measurement. When the parameter Input noise for NF calculation is set to “From external input noise”, the Noise Figure is calculated as follows: OSNR in NF = ---------------------OSNR out (2) References [1] Douglas M. Baney, Philippe Gallion, Rodney S. Tucker; “Polarization Measurements of Signals and Components”, Theory and Measurement Techniques for the Noise Figure of Optical Amplifiers, Optical Fiber Technology, Volume 6, Issue 2, April 2000, Pages 122-154 69 DUAL PORT WDM ANALYZER (DPWDMA) 70 SPATIAL VISUALIZER Spatial Visualizer Spatial visualizer presents the transverse mode profiles of optical signals. It also calculates and lists the power, label and wavelength for each transverse mode profile. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals Units Value range Parameters Graphs Name and description Default value Default unit Polarization X and Y dBm X and Y, X, Y Defines the polarization type when calculating the mode profile graphs Format Power and Phase [Power and Phase, Real and Imag] True [True, False] False [True, False] True [True, False] 0 [0, 1e+008] Defines whether to calculate the graphs using rectangular or polar format Add modes coherently Defines whether the input modes are summed coherently (sum of complex fields - magnitude & relative phase) Sum of mode profiles Defines whether to calculate and plot the sum of mode profiles Individual mode profile Defines whether to calculate and plot the individual mode profile Individual mode number The individual mode number used to select and plot the mode profile 71 SPATIAL VISUALIZER Name and description Default value Centered at max power True Default unit Units Value range [True, False] Defines whether the analysis will be done at the wavelength of signal with maximum power or it will be user defined Center wavelength 820 nm Hz, THz, nm [100, 2000] Center wavelength for the analysis of the mode profiles under test Reduce field False [True, False] Defines whether the mode profile will be reduced or not Minimum outer value -50 dB [-10000, 10] Minimum outer value for the spatial mode profile Limit number of points True [True, False] 128000 [128, 1e+008] Determines if the user can enter the maximum number of points Max. number of points Maximum number of points displayed per graph Results Name and description Default value Generate report True Default unit Units Value range [True, False] Determines whether or not the component will generate a report with the power for each wavelength, mode number and polarization Report Report with the power for each wavelength, mode number and polarization Minimum value Minimum value for power when using units in dBm 72 -100 dBm [-1e100, +1e100] SPATIAL VISUALIZER Simulation Name and description Default value Enabled True Default unit Units Value range [True, False] Determines whether or not the component is enabled Graphs Name and description X Title Y Title Spatial Ex profile - individual a X (m) Y (m) Spatial Ex profile - individual b X (m) Y (m) Spatial Ey profile - individual a X (m) Y (m) Spatial Ey profile - individual b X (m) Y (m) Spatial Ex profile - sum a X (m) Y (m) Spatial Ex profile - sum b X (m) Y (m) Spatial Ey profile - sum a X (m) Y (m) Spatial Ey profile - sum b X (m) Y (m) Results Name and description Frequency (Hz) Wavelength (nm) Power (dBm) Power (W) Power X (dBm) Power X (W) Power Y (dBm) Power Y (W) Technical Background After running a simulation, this visualizer component will generate 3D graphs with the transverse mode profiles of an optical signal. You can access the graphs by doubleclicking directly on the visualizer icon (see Figs 1-3) or from the project browser (Fig 4). 73 SPATIAL VISUALIZER The Spatial visualizer can generate graphs of an individual mode or the sum of all modes (either incoherently or coherently) according to: N For incoherent summation of fields: Esum x y = E i i x y i=1 N For coherent summation of fields: E sum x y = E i i x y e (1) i i i=1 where Ei is the mode amplitude weighting factor, i(r) is the normalized transverse profile for each mode and i is the relative phase shift between each mode. Note: To perform the analysis of coherent fields (complex sum of magnitude and phase) the Add modes coherently parameter within Component properties must be checked (set to enabled). Otherwise the modal fields will be summed incoherently (sum of magnitudes). When using the project browser, the graphs are labeled with “a” and “b” according to the format selection. If the format is “Power and Phase”, “a” is power and “b” is phase. If the format is “Real and Imag” then “a” is the real and “b” is the imaginary part. The parameter Mode number affects the display of the individual spatial mode. The parameter Report (Fig 5) allows the user to visualize the power for each mode, including its polarization, wavelength, and label. Example graphs for an incoherent sum of modes, a coherent sum of modes and an individual mode are shown in Figs 1-3, respectively. The Mode number field can be used to query and display any of the modes listed in the Report (the Mode number index - first column - is used to identify the mode). 74 SPATIAL VISUALIZER Figure 1 Spatial Visualizer - Example of incoherent sum of fields 75 SPATIAL VISUALIZER Figure 2 Spatial Visualizer - Example of coherent sum of fields 76 SPATIAL VISUALIZER Figure 3 Spatial Visualizer - Example of individual mode field. 77 SPATIAL VISUALIZER Figure 4 Project browser displaying the Spatial Visualizer Figure 5 Report 78 SPATIAL VISUALIZER Notes: 79 SPATIAL VISUALIZER 80 ENCIRCLED FLUX ANALYZER Encircled Flux Analyzer This component measures the percentage of optical power that falls within a given radial distance from the center of a fiber. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals Default unit Units Value range Parameters Graphs Name and description Default value Centered at max power True [True, False] Defines whether the analysis will be done at the wavelength of signal with maximum power or it will be user defined Center wavelength 820 nm 25 um Hz, THz, nm [100, 2000] Center wavelength for the analysis of the mode profiles under test Analysis radius [0, 10000] Analysis radius for the mode profiles under test Number of points 20 [5, 100000] True [True, False] Number of points for the graphs Add modes coherently Determines whether or not to add the modes coherently (amplitude and phase) 81 ENCIRCLED FLUX ANALYZER Simulation Name and description Default value Default unit Units Value range Grid spacing X Grid spacing X um [1e-100, 1e+100] Grid spacing Y um [1e-100, 1e+100] Horizontal grid spacing Grid spacing Y Horizontal grid spacing Enabled True [True, False] Determines whether or not the component is enabled Graphs Name and description X Title Y Title Encircled flux Radius (m) Encircled flux (%) Average intensity Radius (m) Average intensity Average intensity*radius Radius (m) Average intensity*radius Technical Background After running a simulation, this visualizer will measure the percentage of optical power that falls within a given radial distance from the center of a fiber, know as an encircled flux graph [1]. You can access the graphs by double-clicking directly on the visualize icon or from the project browser. The encircled flux analyzer generates three graphs: the Encircled Flux, the Average radial intensity and the Average radial intensity x radius (see Figs 1-3). 82 ENCIRCLED FLUX ANALYZER Figure 1 Encircled Flux Visualizer - Encircled Flux tab Figure 2 Encircled Flux Visualizer - Average Intensity tab 83 ENCIRCLED FLUX ANALYZER Figure 3 Encircled Flux Visualizer - Average Intensity * Radius tab To determine the encircled flux, the transverse modal fields must first be summed as follows: N For incoherent summation of fields: Ei i r E sum r = i=1 N For coherent summation of fields: Esum r = Ei i r e (1) i i i=1 where Ei is the mode amplitude weighting factor, i(r) is the normalized transverse profile for each mode and i is the relative phase shift between each mode. Note: To perform the analysis of coherent fields (complex sum of magnitude and phase) the Add modes coherently parameter within Component properties must be checked (set to enabled). Otherwise the modal fields will be summed incoherently (sum of magnitudes). The average radial intensity is calculated as follows: 1 I r = ------ 2 2 I r d (2) 0 where I(r,) is the intensity (magnitude squared) of the complex spatial field at angular positions along the radial arm r. 84 ENCIRCLED FLUX ANALYZER The encircled flux is then calculated as follows: r 1 EF r = ------ rI r dr PT (3) 0 where PT is the total power for all the spatial modes. Note: The Average Intensity and Average Intensity * Radius graphs are normalized to a maximum value of 1. The Encircled Flux graph is set to a maximum value of 100% 85 ENCIRCLED FLUX ANALYZER 86 ENCIRCLED FLUX ANALYZER Visualizer Library Electrical • Oscilloscope Visualizer • RF Spectrum Analyzer (RFSA) • Eye Diagram Analyzer • BER Analyzer • Electrical Power Meter • Electrical Carrier Analyzer (ECAN) • Dual Port Electrical Carrier Analyzer • Electrical Constellation Visualizer • Directly Detected Eye Analyzer Visualizer 87 ENCIRCLED FLUX ANALYZER Notes: 88 OSCILLOSCOPE VISUALIZER Oscilloscope Visualizer This visualizer allows the user to calculate and display electrical signals in the time domain. It can display the signal amplitude and autocorrelation. Ports Name and description Port type Signal type Supported modes Input Input Electrical Sampled signals Parameters Graphs Name and description Default value Default unit Units Value range Time unit s - - s, bits Bit rate Bits/s Bits/s [0, 1e+012] Time unit for the horizontal axis Reference bit rate Reference bit rate to use when the time unit is Bit period MBits/s GBits/s Retracing False - - True, False Time window 1/(Bit rate) s - ]0, +INF[ False - - True, False True - - True, False 128,000 - - [100, 1e+008] Defines the retracing time window Calculate autocorrelation Determines whether or not to calculate autocorrelation graphs Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph 89 OSCILLOSCOPE VISUALIZER Name and description Default value Default unit Units Value range Invert colors False - - True, False False - - True, False 500 - - [10, 5000] Default - - Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Name and description Default value Default unit Value range Generate random seed True - True, False 0 - [0,4999] Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs Number of color bins Number of vertical and horizontal bins of the display Color grade palette Determines the color grade palette Simulation Determines whether or not the component is enabled Signal access option Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 90 OSCILLOSCOPE VISUALIZER Graphs Name and description X Title Y Title Signal amplitude Time (s) Amplitude (a.u.) Noise amplitude Time (s) Amplitude (a.u.) Signal + noise amplitude Time (s) Amplitude (a.u.) Signal autocorrelation Delay (s) Intensity (a.u.) Noise autocorrelation Delay (s) Intensity (a.u.) Signal + noise autocorrelation Delay (s) Intensity (a.u.) Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser Access the Oscilloscope parameters, graphs, and results from the simulation (see Figure 2). 91 OSCILLOSCOPE VISUALIZER Figure 2 Oscilloscope display Use the signal index to select the signal to display from the signal buffer. Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3). • Signal • Noise • Signal + Noise • All Figure 3 Multiple signal types display 92 RF SPECTRUM ANALYZER (RFSA) RF Spectrum Analyzer (RFSA) This visualizer allows the user to calculate and display electrical signals in the frequency domain. It can display the signal intensity, power spectral density and phase. Ports Name and description Port type Signal type Electrical Input Electrical Parameters Resolution bandwidth Name and description Default value Default unit Value range Resolution bandwidth Off — On, Off Rectangle — Rectangle, Gaussian, Butterworth 10 MHz [0,+INF[ Name and description Default value Default unit Value range Power unit dB — dBm, W –100 dBm [-1e+100, 1e+100] Determines whether or not the resolution filter is enabled Filter type Determines the type for the resolution filter Bandwidth Resolution filter bandwidth Graphs Power unit for the vertical axis Minimum value Minimum value for power when using units in dBm 93 RF SPECTRUM ANALYZER (RFSA) Name and description Default value Default unit Value range Scale factor 0 dB [-1e+100, 1e+100] False — True, False False — True, False True — True, False False — True, False True — True, False 128000 — [100, 1e+008] False — True, False Name and description Default value Default unit Value range Enabled True — True, False Name and description Default value Default unit Value range Generate random seed True — True, False 0 — [0,4999] Vertical axis scale factor (for an impedance of 50 ohms, use a scale of 16.9897, for voltage input, and a scale of -16.898 for current input) Power spectral density Determines whether or not to calculate the power spectral density for the vertical axis Calculate phase Determines whether or not to calculate the phase graphs Unwrap phase Determines whether or not to remove the phase discontinuity Negative frequencies Determines whether or not the negative frequencies are displayed Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Simulation Determines whether or not the component is enabled Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 94 RF SPECTRUM ANALYZER (RFSA) Graphs Name and description X Title Y Title Signal spectrum Frequency (GHz) Power (dBm) Noise spectrum Frequency (GHz) Power (dBm) Signal + noise spectrum Frequency (GHz) Power (dBm) Signal phase Frequency (GHz) Phase (rad) Noise phase Frequency (GHz) Phase (rad) Signal + noise phase Frequency (GHz) Phase (rad) Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser 95 RF SPECTRUM ANALYZER (RFSA) Access the RF Spectrum Analyzer (RFSA) parameters, graphs, and results from the simulation (see Figure 2). Figure 2 RFSA display Use the signal index to select the signal to display from the signal buffer. Use the tabs on the left side of the graph to select the representation that you want to view (see Figure 3). • Signal • Noise • Signal + Noise • All Figure 3 Multiple signal types display 96 EYE DIAGRAM ANALYZER Eye Diagram Analyzer This visualizer allows the user to calculate and display the electrical signal eye diagram automatically. It can calculate different metrics from the eye diagram, such as Q factor, eye opening, eye closure, extinction ratio, eye height, mask violation ratio, etc. It can also display histograms and standard eye masks. Ports Name and description Port type Signal type Bit sequence Input Binary Reference Input Electrical Input Input Electrical Parameters Main Name and description Default value Default unit Value range Time window 1.5 bit [1,3] 1 bits [0,+INF[ 1 bits [0,+INF[ Name and description Default value Default unit Value range Clock recovery On — On, Off Time window for the eye diagram display Ignore start bits Number of start bits to be ignored in the eye diagram Ignore end bits Number of end bits to be ignored in the eye diagram Clock Determines if the delay compensation between the reference and the received signal will be applied 97 EYE DIAGRAM ANALYZER Threshold Name and description Default value Default unit Value range Threshold mode Relative — Relative, Absolute 0 (a.u.) ]–INF,+INF[ 50 % [0,100] 0.5 Bit [0,1] Name and description Default value Default unit Value range Time unit Bit period — s, Bit period dB — none, dB, % True — True, False 128000 — [100, 1e+008] False — [100, 1e+008] False — True, False 500 — [100, 1e+008] Default — Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow Determines the value mode for the user-defined threshold Absolute threshold Amplitude value for the threshold Relative threshold Relative value for the threshold, relative to the average values of 1s and 0s Decision instant The user-defined decision instant for the eye analysis Graphs Time unit for the horizontal axis Ratio unit Ratio unit for the vertical axis Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs Number of color bins Number of vertical and horizontal bins of the display Color grade palette Determines the color grade palette 98 EYE DIAGRAM ANALYZER Name and description Default value Default unit Value range Smoothness 10 % [0, 1000] Name and description Default value Default unit Value range Calculate histograms False — True, False 500 — [10, 5000] 500 — [10, 5000] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] Determines how smooth is the transition between color grades Histograms Determines whether to calculate histograms or not Number of X bins Number of horizontal histogram bins Number of Y bins Number of vertical histogram bins Region 1 X0 Determines the first point along the horizontal axis for the region Region 1 X1 Determines the second point along the horizontal axis for the region Region 1 Y0 Determines the first point along the vertical axis for the region Region 1 Y1 Determines the second point along the vertical axis for the region Region 2 X0 Determines the first point along the horizontal axis for the region Region 2 X1 Determines the second point along the horizontal axis for the region Region 2 Y0 Determines the first point along the vertical axis for the region Region 2 Y1 Determines the second point along the vertical axis for the region Region 3 X0 Determines the first point along the horizontal axis for the region Region 3 X1 Determines the second point along the horizontal axis for the region Region 3 Y0 Determines the first point along the vertical axis for the region 99 EYE DIAGRAM ANALYZER Name and description Default value Default unit Value range Region 3 Y1 0 a.u. [-1e100,1e100] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 a.u. [-1e100,1e100] Name and description Default value Default unit Value range Calculate mask False — True, False Eye.msk — — 0 Bit period [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 % [-100,100] Name and description Default value Default unit Value range Enabled True — True, False Determines the second point along the vertical axis for the region Region 4 X0 Determines the first point along the horizontal axis for the region Region 4 X1 Determines the second point along the horizontal axis for the region Region 4 Y0 Determines the first point along the vertical axis for the region Region 4 Y1 Determines the second point along the vertical axis for the region Mask Determines whether or not to display the eye mask Mask filename The file which contains the mask data Mask horizontal shift User defined mask horizontal shift Mask vertical shift User defined mask vertical shift Mask margin Mask margins are used to determine the margin of compliance for a standard or scaled mask. You can use positive mask margins to determine how much larger you will be able to increase the size of the mask before violations will occur or negative margins to determine how much smaller you have to decrease the size of the mask before violations no longer occur Simulation Determines whether or not the component is enabled 100 EYE DIAGRAM ANALYZER Noise Name and description Default value Default unit Value range True — True, False Name and description Default value Default unit Value range Generate random seed True — True, False 0 — [0,49999] Add noise to signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 101 EYE DIAGRAM ANALYZER Graphs Name and description X Title Y Title Eye diagram Time (s) Amplitude (a.u.) Min. BER Time (s) log (BER) Q-factor Time (s) Q Threshold at min. BER Time (s) Amplitude (a.u.) Eye Height Time (s) Amplitude (a.u.) Eye Amplitude Time (s) Amplitude (a.u.) Eye Closure Time (s) Amplitude (a.u.) Eye Opening Factor Time (s) Ratio (dB) Eye Extinction Ratio Time (s) Ratio (dB) Histogram Region 1 Time (s) Amplitude (a.u.) Histogram Region 2 Time (s) Amplitude (a.u.) Histogram Region 3 Time (s) Amplitude (a.u.) Histogram Region 4 Time (s) Amplitude (a.u.) Vertical Histogram 1 Time (s) Amplitude (a.u.) Vertical Histogram 2 Time (s) Amplitude (a.u.) Vertical Histogram 3 Time (s) Amplitude (a.u.) Vertical Histogram 4 Time (s) Amplitude (a.u.) Horizontal Histogram 1 Time (s) Amplitude (a.u.) Horizontal Histogram 2 Time (s) Amplitude (a.u.) Horizontal Histogram 3 Time (s) Amplitude (a.u.) Horizontal Histogram 4 Time (s) Amplitude (a.u.) Eye Mask Time (s) Amplitude (a.u.) Results Name and description Unit Total Power dBm Total Power W Signal Power dBm Signal Power W 102 EYE DIAGRAM ANALYZER Name and description Unit Noise Power dBm Noise Power W Signal Delay s Signal Delay samples Bit Rate Bits/s Max. Q Factor — Min. BER — Min. log of BER — Max. Eye Height a.u. Threshold at Min. BER a.u. Decision Instant at Min. BER Bit period Max. Eye Amplitude a.u. Max. Eye Closure a.u. Max. Eye Opening Factor dB Max. Eye Opening Factor — Max. Eye Opening Factor % Extinction Ratio at Min. BER dB Extinction Ratio at Min. BER — Extinction Ratio at Min. BER % Q Factor at User Defined Decision Instant — Eye Height at User Defined Decision Instant a.u. Min. BER at User Defined Decision Instant — Min. log of BER at User Defined Decision Instant — BER at User Defined Threshold — BER at User Defined Decision Instant and Threshold — log of BER at User Defined Threshold — log of BER at User Defined Decision Instant and Threshold — Eye Amplitude at User Defined Decision Instant a.u. Eye Closure at User Defined Decision Instant a.u Eye Opening Factor at User Defined Decision Instant dB Eye Opening Factor at User Defined Decision Instant — 103 EYE DIAGRAM ANALYZER Name and description Unit Eye Opening Factor at User Defined Decision Instant % Extinction Ratio at User Defined Decision Instant dB Extinction Ratio at User Defined Decision Instant — Extinction Ratio at User Defined Decision Instant % Vertical Histogram 1 Mean — Vertical Histogram 1 Standard Deviation — Vertical Histogram 1 Range — Horizontal Histogram 1 Mean — Horizontal Histogram 1 Standard Deviation — Horizontal Histogram 1 Range — Vertical Histogram 2 Mean — Vertical Histogram 2 Standard Deviation — Vertical Histogram 2 Range — Horizontal Histogram 2 Mean — Horizontal Histogram 2 Standard Deviation — Horizontal Histogram 2 Range — Vertical Histogram 3 Mean — Vertical Histogram 3 Standard Deviation — Vertical Histogram 3 Range — Horizontal Histogram 3 Mean — Horizontal Histogram 3 Standard Deviation — Horizontal Histogram 3 Range — Vertical Histogram 4 Mean — Vertical Histogram 4 Standard Deviation — Vertical Histogram 4 Range — Horizontal Histogram 4 Mean — Horizontal Histogram 4 Standard Deviation — Horizontal Histogram 4 Range — Eye Mask Violation Ratio % 104 EYE DIAGRAM ANALYZER Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser 105 EYE DIAGRAM ANALYZER The Eye Diagram Analyzer generates eye diagrams and BER analysis. Double-click the Eye Diagram Analyzer to access the parameters, graphs, and results from the simulation (see Figure 2). Figure 2 Eye diagram display Use the signal index to select the signal to display from the signal buffer. The available results in the display are: • Max Q-factor: Maximum value for the Q-factor in the eye time window. • Min BER: Minimum value for the bit error rate in the eye time window. • Eye height: Maximum value for the eye height in the eye time window. • Threshold: Value of the threshold at the decision instant for the maximum Qfactor / minimum BER. • Decision inst: Value of the decision instant for the maximum Q-factor/minimum BER. Note: For additional results and graphs, you should use the Project Browser or the Component Viewer. 106 EYE DIAGRAM ANALYZER Figure 3 Eye diagram analysis 107 EYE DIAGRAM ANALYZER BER and Q-Factor estimation The BER estimation method in this visualizer compare the bits generated by a binary signal and the signal received. Assuming Gaussian noise with the standard deviations 0 and 1 the BER is [1]: M N P e = --------------- P e0 + --------------- P e1 N+M N+M (4) where P0 and P1 are the probabilities of the symbols, M is the number of samples for the logical 0, and N is the number of samples for the logical 1. Pe0 and Pe1 are: S – 0 1 P e0 = --- erfc -------------- , 2 2 (5) 1 – S 1 P e1 = --- erfc -------------- 2 2 (6) 0 1 where 0 , 1 , 0 , and 1 are average values and standard deviations of the sampled values respectively, and S is the threshold value. The Q-factor is calculated by: 1 – 0 Q = -------------------1 + 0 (7) The eye height is calculated by [2] E H = 1 – 3 1 – 0 + 3 0 108 (8) EYE DIAGRAM ANALYZER The eye amplitude is calculated by: EA = 1 – 0 (9) The eye closure is calculated by: E c = min V 1 – max V 0 (10) where min(V1) is the minimum value of the amplitude for the marks and max(V0) is the maximum value for the amplitude of the spaces. The eye-opening factor is calculated by: 1 – 1 – 0 – 0 E 0 = -------------------------------------------------- 1 – 0 (11) 1 E R = ----0 (12) The extinction ratio is: Histograms The Histogram tab enables the histogram calculation feature of the Eye Analyzer. The user can select up to four regions for analysis. Simply select the region of interest and click on Calculate Histogram button. The user can display the region of interest, vertical and horizontal histograms (Figure 4). 109 EYE DIAGRAM ANALYZER Figure 4 Histograms The statistical properties of the histograms are displayed in the Statistics grid.The available results in the grid are: • H. Mean: The mean value of the horizontal histogram. • H. Std. Dev.: The standard deviation of the horizontal histogram. • H. Range: The difference between the maximum and minimum values of the horizontal histogram. • V. Mean: The mean value of the vertical histogram. • V. Std. Dev.: The standard deviation of the vertical histogram. • V. Range: The difference between the maximum and minimum values of the vertical histogram. Note: If you are changing the dimensions of a given region, you must click Calculate Histograms in order to update the visualizer graphs and the results. Eye Masks Parameter Calculate mask allows the user to display a standard eye mask and calculate the mask margin for a given eye diagram. You can copy and modify the standard mask files located on the folder \Components\Data\Eye Mask, or create your own mask file from scratch. Figure 5 shows the eye diagram and the eye mask using the Component Viewer feature of OptiSystem. 110 EYE DIAGRAM ANALYZER The following mask files are available with OptiSystem: Standard Filename OTU-1, 2.66 Gb/s OTU-1.msk OTU-2, 10.71 Gb/s OTU-2.msk STM0/OC1, 51.8 Mb/s STM000_OC1.msk STM1/OC3, 155.5 Mb/s STM001_OC3.msk STM4/OC12, 621.8 Mb/s STM004_OC12.msk STM16/OC48, 2.488 Gb/s STM016_OC48.msk STM64/OC192, 9.953 Gb/s STM064_OC192.msk XFP MSA Point C' XFI_RX_OUT.msk XFP MSA Point B' XFI_TX_IN.msk OptiSystem eye mask file follows the convention from Agilent Infiniium DCAs.These files have several elements that contain necessary information for the visualizer to display the mask properly. Note: You will have to use the Project Browser or the Component Viewer in order to visualize the Eye Mask 111 EYE DIAGRAM ANALYZER Figure 5 Eye mask from Component Viewer Any mask files you edit or create should retain these elements as specified in the following descriptions: Mask File Identifier: The mask file identifier is the first line in a mask file. When you load a mask file, OptiSystem checks the first line of the file for the following: MASK_FILE_OPTISYSTEM6 Mask Title: The mask title is a quoted string. Change this title to reflect the name of the mask you are creating. An example mask title is: "OTU-1, 2.66 Gb/s" Region Number: The region number is an integer that defines a mask violation area (or polygon). The region number can be further identified with a commented line describing the region number location, for example: /* Top Region */. You can specify 1 to a maximum of 8 regions in a mask file. Region Type: You can define three types of regions for each region number you have specified: 112 • STD defines the actual mask region. • MARGIN_MAX defines the maximum margin area when test margins are set to 100%. EYE DIAGRAM ANALYZER • MARGIN_MIN defines the minimum margin area when test margins are set to 100%. Note: If no MARGIN_MAX or MARGIN_MIN regions are defined, the mask margin calculation will not work. Number of Vertices: The number of vertices is an integer that specifies the quantity of X and Y coordinates needed to define a mask region or polygon. You can define a mask region or polygon with a minimum of 3 vertices. X and Y Coordinates: These are the floating-point numbers that define the locations of the mask polygon vertices for each region and region type defined in the mask file. For Y values, the special value MIN automatically defines the bottom of the display, and MAX automatically defines the top of the display. The X-coordinate values are referenced to the eye crossing points; the first or left crossing point X-value is 0.0, and the second or right crossing point X-value is 1.0. The Y-coordinate values are referenced in the same manner with respect to the eye zero and one levels; the eye zero level Y-value is 0.0 while the eye one level Y-value is 1.0. References [1] G.P. Agrawal, "Fiber Optic Communication Systems," John Wiley & Sons, New York, 1997. [2] D. Derickson, "Fiber Optic Test and Measurement," Prentice Hall, New Jersey, 1998. 113 EYE DIAGRAM ANALYZER Notes: 114 BER ANALYZER BER Analyzer This visualizer allows the user to calculate and display the bit error rate (BER) of an electrical signal automatically. It can estimate the BER using different algorithms such as Gaussian and Chi-Squared and derive different metrics from the eye diagram, such as Q factor, eye opening, eye closure, extinction ratio, eye height, jitter, etc. It can also take in account Forward Error Correction (FEC), plot BER patterns and estimate system penalties and margins. Ports Name and description Port type Signal type Bit sequence Input Binary Reference Input Electrical Input Input Electrical Parameters Main Name and description Default value Default unit Value range Algorithm Gaussian — Gaussian, Average Gaussian, Gaussian Worse Case, Chi-Squared, Average ChiSquared, ChiSquared Worst Case, Measured 1.5 bit [1, 3] 1 bits [0,+INF[ Determines the algorithm used to estimate the BER Time window Time window for the eye diagram display Ignore start bits Number of start bits to be ignored in the eye diagram 115 BER ANALYZER Name and description Default value Default unit Value range Ignore end bits 1 bits [0,+INF[ 0 Bit period [0,1.5] 1 Bit period [0,1.5] True — True, False 2 % [0,100] Name and description Default value Default unit Value range Clock recovery On — On, Off Name and description Default value Default unit Value range Enabled FEC gain estimation False — True, False FEC estimation type Analytical — Analytical, Measured Measured FEC filename FEC.dat — — Name and description Default value Default unit Value range Threshold mode Relative — Relative, Absolute 0 (a.u.) ]–INF,+INF[ Number of end bits to be ignored in the eye diagram Lower calculation limit Defines the lower calculation limit for the time window Upper calculation limit Defines the upper calculation limit for the time window Eye must be open Define whether the eye is considered open only if marks are above spaces or not. Eye opening tolerance The tolerance used to estimate the eye opening. The eye is considered open if this percentage of spaces is above the marks. Clock Determines if the delay compensation between the reference and the received signal will be applied Enhanced Threshold Determines the value mode for the user-defined threshold Absolute threshold Amplitude value for the threshold 116 BER ANALYZER Name and description Default value Default unit Value range Relative threshold 50 % [0,100] False — True, false Threshold.dat — — False — True, false 0.5 Bit period [0,100] Name and description Default value Default unit Value range Time unit Bit period — s, Bit period dB — none, dB, % True — True, False 128000 — [100, 1e+008] False — [100, 1e+008] False — True, False 500 — [100, 1e+008] Relative value for the threshold, relative to the average values of 1s and 0s Load threshold from file Defines whether the threshold will be loaded from a file or not Measured threshold filename Threshold file name Reload before calculation Defines whether the file should be reloaded when the calculation starts Decision instant The user-defined decision instant for the eye analysis, jitter calculation, histogram and probability graphs Graphs Time unit for the horizontal axis Ratio unit Ratio unit for the vertical axis Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs Number of color bins Number of vertical and horizontal bins of the display 117 BER ANALYZER Name and description Default value Default unit Value range Color grade palette Default — Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow 10 % [0, 1000] Name and description Default value Default unit Value range Calculate patterns False — True, False 16 — [10, 1e+008] BER for pattern 1 1e-012 — [0,1] BER for pattern 2 1e-011 — [0,1] BER for pattern 3 1e-010 — [0,1] BER for pattern 4 1e-009 — [0,1] BER for pattern 5 1e-008 — [0,1] Calculate 3D graph False — True, False Determines the color grade palette Smoothness Determines how smooth is the transition between color grades BER patterns Determines whether or not the component will generate BER patterns Number of points Number of vertical points for the patterns Determines whether or not the component generates a 3D graph with the BER 118 BER ANALYZER Penalty calculations Name and description Default value Default unit Value range Reference values setup User-defined — User defined, First sweep iteration, Current sweep iteration Total power –1000 dBm [-1e+100, 1e+100] Signal power –1000 dBm [-1e+100, 1e+100] Noise power –1000 dBm [-1e+100, 1e+100] Min. BER 1 — [0, 1] Q factor from min. BER 0 — [0, 1000] Max. Q factor 0 — [0, 1000] Max. eye height 0 a.u. [-1e+100, 1e+100] Max. eye amplitude 0 a.u. [-1e+100, 1e+100] Max. eye closure 0 a.u. [-1e+100, 1e+100] Max. eye opening factor 0 dB [-1e+100, 1e+100] Extinction ratio at min. BER 0 dB [-1e+100, 1e+100] Min. BER at user defined decision instant 1 — [0, 1] Q factor from min. BER at user defined decision instant 0 — [0, 1000] Q factor at user defined decision instant 0 — [0, 1000] BER at user-defined threshold 1 — [0, 1] Q factor from BER at user defined threshold 0 — [0, 1000] BER at user defined decision instant and threshold 1 — [0, 1] Q factor from BER at user defined decision instant and threshold 0 — [0, 1000] Eye height at user defined decision instant 0 a.u. [-1e+100, 1e+100] Eye amplitude at user defined decision instant 0 a.u. [-1e+100, 1e+100] Eye closure at user defined decision instant 0 a.u. [-1e+100, 1e+100] Eye opening factor at user defined decision instant 0 dB [-1e+100, 1e+100] Extinction ratio at user defined decision instant 0 dB [-1e+100, 1e+100] 119 BER ANALYZER Simulation Name and description Default value Default unit Value range Enabled True — True, False Default value Default unit Value range True — True, False Name and description Default value Default unit Value range Generate random seed True — True, False 0 — [0,4999] Determines whether or not the component is enabled Noise Name and description Add noise to signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 120 BER ANALYZER Graphs Name and description X Title Y Title Amplitude Histogram Amplitude Amplitude (a.u.) Amplitude Probability Amplitude Amplitude (a.u.) Eye diagram Time (s) Amplitude (a.u.) Min. BER Time (s) log of BER Q-factor Time (s) Q Threshold at min. BER Time (s) Amplitude (a.u.) Eye height Time (s) Amplitude (a.u.) Eye Amplitude Time (s) Amplitude (a.u.) Eye Closure Time (s) Amplitude (a.u.) Eye Opening Factor Time (s) Ratio (dB) Eye Extinction Ratio Time (s) Ratio (dB) BER pattern 1 Time (s) Amplitude (a.u.) BER pattern 2 Time (s) Amplitude (a.u.) BER pattern 3 Time (s) Amplitude (a.u.) BER pattern 4 Time (s) Amplitude (a.u.) BER pattern 5 Time (s) Amplitude (a.u.) BER pattern 3D graph Amplitude (a.u.) Time (s) Measured Threshold Time (Bit period) Amplitude (a.u.) BER at Measured Threshold Time (s) log of BER Amplitude Histogram Amplitude Amplitude (a.u.) Amplitude Probability Amplitude Amplitude (a.u.) Results Name and description Unit Total Power dBm Total Power W Signal Power dBm Signal Power W Noise Power dBm 121 BER ANALYZER Name and description Unit Noise Power W Signal Delay s Signal Delay samples Bit Rate Bits/s Max. Q Factor — Q Factor from Min. BER — Min. BER — Min. log of BER — Max. Eye Height a.u. Threshold at Min. BER a.u. Decision Instant at Min. BER Bit period Max. Eye Amplitude a.u. Max. Eye Closure a.u. Max. Eye Opening Factor dB Max. Eye Opening Factor — Max. Eye Opening Factor % Extinction Ratio at Min. BER dB Extinction Ratio at Min. BER — Extinction Ratio at Min. BER % Q Factor at User Defined Decision Instant — Eye Height at User Defined Decision Instant a.u. Min. BER at User Defined Decision Instant — Q Factor from Min. BER at User Defined Decision Instant — Min. log of BER at User Defined Decision Instant — BER at User Defined Threshold — BER at User Defined Decision Instant and Threshold — Q Factor from BER at User Defined Threshold — Q Factor from BER at User Defined Decision Instant and Threshold — log of BER at User Defined Threshold — log of BER at User Defined Decision Instant and Threshold — Eye Amplitude at User Defined Decision Instant a.u. 122 BER ANALYZER Name and description Unit Eye Closure at User Defined Decision Instant a.u. Eye Opening Factor at User Defined Decision Instant dB Eye Opening Factor at User Defined Decision Instant — Eye Opening Factor at User Defined Decision Instant % Extinction Ratio at User Defined Decision Instant dB Extinction Ratio at User Defined Decision Instant — Extinction Ratio at User Defined Decision Instant % Penalty: Total Power dB Penalty: Signal Power dB Penalty: Noise Power dB Penalty: Max. Q Factor dB Penalty: Q Factor from Min. BER dB Penalty: Min. BER dB Penalty: Max. Eye Height dB Penalty: Max. Eye Amplitude dB Penalty: Max. Eye Closure dB Penalty: Max. Eye Opening Factor dB Penalty: Extinction Ratio at Min. BER dB Penalty: Q Factor at User Defined Decision Instant dB Penalty: Eye Height at User Defined Decision Instant dB Penalty: Min. BER at User Defined Decision Instant dB Penalty: Q Factor from Min. BER at User Defined Decision Instant dB Penalty: BER at User Defined Threshold dB Penalty: BER at User Defined Decision Instant and Threshold dB Penalty: Q Factor from BER at User Defined Threshold dB Penalty: Q Factor from BER at User Defined Decision Instant and Threshold dB Penalty: Eye Amplitude at User Defined Decision Instant dB Penalty: Eye Closure at User Defined Decision Instant dB Penalty: Eye Opening Factor at User Defined Decision Instant dB Penalty: Extinction Ratio at User Defined Decision Instant dB 123 BER ANALYZER Name and description Unit Min. BER after FEC — Min. log of BER after FEC — Min. BER after FEC at User Defined Decision Instant — Min. log of BER after FEC at User Defined Decision Instant — BER after FEC at User Defined Threshold — BER after FEC at User Defined Decision Instant and Threshold — log of BER after FEC at User Defined Threshold — log of BER after FEC at User Defined Decision Instant and Threshold — Peak to Peak Jitter at User Defined Threshold UI RMS Jitter at User Defined Threshold UI Number of Bits — Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser 124 BER ANALYZER The BER Analyzer estimates and analyzes the BER of the signal received. Doubleclick the BER Analyzer to access the parameters, graphs, and results from the simulation (see Figure 2). Figure 2 BER Analyzer display Use the signal index to select the signal to display from the signal buffer (see Figure 3). The available results are: • Max Q-factor: Maximum value for the Q-factor in the eye time window. • Min BER: Minimum value for the bit error rate in the eye time window. • Eye height: Maximum value for the eye height in the eye time window. • Threshold: Value of the threshold at the decision instant for the maximum Qfactor / minimum BER. • Decision inst: Value of the decision instant for the maximum Q-factor/minimum BER. Note: For additional results and graphs, you should use the Project Browser or the Component Viewer. 125 BER ANALYZER Figure 3 BER analysis When the parameter Calculate 3D graph is enabled, you can visualize a 3D graph that shows the values of BER versus the decision instant and threshold (see Figure 4). 126 BER ANALYZER Figure 4 3D BER graph 127 BER ANALYZER BER and Q-factor estimation The parameter Algorithm defines the numerical method to use for the BER estimation. Gaussian Assuming Gaussian noise with the standard deviations 0 and 1 , the BER is [1]: M N P e = --------------- P e0 + --------------- P e1 N+M N+M (1) where P0 and P1 are the probabilities of the symbols, M is the number of samples for the logical 0, and N is the number of samples for the logical 1. Also, Pe0 and Pe1 are: S – 0 1 P e0 = --- erfc -------------- , 2 2 (2) 1 – S 1 P e1 = --- erfc -------------- 2 2 (3) 0 1 where 0 , 1 , 0 , and 1 are average values and standard deviations of the sampled values respectively, and S is the threshold value. Average Gaussian An enhancement of the simple Gaussian approximation can be achieved by averaging the separately estimated BERs for different sampled symbols [2]. For M sampled values for the logical 0 and N sampled values for the logical 1, the corresponding error rates are: N P e1 1i – S 1 = ------- erfc ---------------- 2N 2 1i i=1 128 (1) BER ANALYZER M P e0 S – 0i 1 = -------- erfc ---------------- 2M 2 0i (2) i=1 If the signal is mixed with the noise, the Average Gaussian method is modified to calculate the average error patterns. The detailed description is [4]: 8 Pe = i – S NP ----erfc N ------------2 i=1 (3) i where NP is the number of one occurrence of any pattern, N is the total number of patterns, i and i are average values and standard deviations of the sampled values for each pattern respectively, and S is the threshold value. Worst-case Gaussian Since the Average Gaussian method can estimate the BER per bit or per pattern, the Worst-case Gaussian searches for the min BER for each bit or pattern instead of calculating the average values. Chi-Squared The Chi-Squared estimator is adequate for received signals with non-Gaussian statistics [5][6][7]. The analyzer will estimate the Chi-squared parameters after statistical analysis of the received signal. The probability of error is calculated according to: 129 BER ANALYZER M N P e = --------------- f 2 x 0 + -------------- N+M N+M S S f x 1 2 (4) – The model can also calculate the average error pattern and the worst case pattern. Measured The measured method will count the errors directly. E.g. the total number of marks bellow spaces divided by the total number of bits. Calculated results There are two modes to calculate the Q-Factor: The Q-Factor from BER is calculated numerically by: 1 Q P e = --- erfc ------- 2 2 (1) where the Q-factor is calculated 1 – 0 Q = -------------------1 + 0 (2) The eye height is calculated by [2]: E H = 1 – 3 1 – 0 + 3 0 (3) The eye amplitude is calculated by: EA = 1 – 0 130 (4) BER ANALYZER The eye closure is calculated by: E c = min V 1 – max V 0 (5) where min(V1) is the minimum value of the amplitude for the marks and max(V0) is the maximum value for the amplitude of the spaces. The eye-opening factor is calculated by: 1 – 1 – 0 – 0 E 0 = -------------------------------------------------- 1 – 0 (6) The extinction ratio is calculated by: 1 E R = ----0 (7) For the user defined threshold, the input file, given by the parameter Measured threshold filename, is formatted with two items per line, the time and threshold amplitude. Time is given in ratio of the bit period, and amplitude is given in arbitrary units (voltage or current) As an example of input file, we have: 0 0.5 0.1 0.5 0.2 0.5 ... 0.9 0.5 FEC estimation Parameter Enable FEC gain estimation allows the user to select between an analytical FEC estimation [8] or to use measurements. For the measured FEC, the 131 BER ANALYZER input file, given by the parameter Measured FEC filename, is formatted with two items per line, the current BER (before FEC), and the BER after FEC gain. As an example of input file, we have: 1.0e-2 2.0e-3 1.0e-3 2.0e-4 1.0e-4 2.0e-5 ... ... References [1] G.P. Agrawal, "Fiber Optic Communication Systems," John Wiley & Sons, New York, 1997. [2] J.C. Cartledge, G.S. Burley, "The Effect of Laser Chirping on Lightwave System Performance," Journal of Lightwave Technology, Vol. 7, No. 3, 1989, S. 568-573. [3] D. Derickson, "Fiber Optic Test and Measurement," Prentice Hall, New Jersey, 1998. [4] C.J. Anderson, J.A. Lyle, “Technique for evaluation of systems performance using Q in numerical simulation exhibiting intersymbol interference,” Electronic Letters, Vol. 30, No. 1, 1994, S. 71-72. [5] P. A. Humblet, "On the Bit Error Rate of Lightwave Systems with Optical Amplifiers", Journal of Lightwave Technology, Vol. 9, No. 11, pp. 1576–1582, November 1991. [6] D. Marcuse, "Calculation of Bit-Error Probability for a Lightwave System with Optical Amplifiers and Post-Detection Gaussian Noise", Journal of Lightwave Technology, Vol. 9, No. 4, pp. 505– 513, April 1991 [7] D. Marcuse, "Derivation of Analytical Expressions for the Bit-Error Probability in Lightwave Systems with Optical Amplifiers", Journal of Lightwave Technology, Vol. 8, No. 12, pp. 1816– 1823, December 1990. [8] Keang-Po Ho, Chinlon Lin, “Performance analysis of optical transmission system with polarization-mode dispersion and forward error correction”, Photonics Technology Letters, Vol. 9, No. 9, pp. 1288-1290, September 1997. 132 ELECTRICAL POWER METER Electrical Power Meter This visualizer allows the user to calculate and display the average power of electrical signals. It can also calculate the AC and DC power. Ports Name and description Port type Signal type Input Input Electrical Parameters Main Name and description Default value Default unit Value range Minimum value -100 dBm - 0 dB - Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Minimum value for power when using units in dBm. Scale factor Factor used for scaling. Simulation Determines whether or not the component is enabled Signal access option 133 ELECTRICAL POWER METER Results Name and description Unit Total Power dBm Total Power W Signal Power dBm Signal Power W Noise Power dBm Noise Power W Total Power AC dBm Total Power AC W Signal Power AC dBm Signal Power AC W Noise Power AC dBm Noise Power AC W Total Power DC dBm Total Power DC W Signal Power DC dBm Signal Power DC W Noise Power DC dBm Noise Power DC W Technical Background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser, from the Component Viewer, or by double-clicking a visualizer in the Main Layout. 134 ELECTRICAL POWER METER Figure 1 Project Browser Figure 2 EPMV Display 135 ELECTRICAL POWER METER Notes: 136 ELECTRICAL CARRIER ANALYZER (ECAN) Electrical Carrier Analyzer (ECAN) The Electrical Carrier Analyzer (ECAN) measures and compares different results in two different frequencies. It can also calculate carrier to noise ratio. Ports Name and description Port type Signal type Input Input Electrical Parameters Main Name and description Default value Default unit Value range Frequency 1 50 MHz, Hz, kHz, THz [0,+INF[ 10 MHz, Hz, kHz, GHz [0,+INF[ 50 MHz, Hz, kHz, THz [0,+INF[ 10 MHz, Hz, kHz, GHz [0,+INF[ Filter type Gaussian - Gaussian, Rectangle Filter order 1 - [1,+INF[ -100 dBm ]-INF,+INF[ 0 dB ]-INF,+INF[ Center frequency of the first filter. Bandwidth 1 Bandwidth of the first filter. Frequency 2 Center frequency of the second filter. Bandwidth 2 Bandwidth of the second filter. Order of the Gaussian filter. Minimum value Minimum value for power when using units in dBm. Scale factor Factor used for scaling. 137 ELECTRICAL CARRIER ANALYZER (ECAN) Simulation Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Determines whether or not the component is enabled Signal access option Results Frequency 1 Name and description Unit Total Power1 dBm Total Power1 W Signal Power1 dBm Signal Power1 W Noise Power1 dBm Noise Power1 W SNR1 dB Frequency 2 Name and description Unit Total Power2 dBm Total Power2 W Signal Power2 dBm Signal Power2 W Noise Power2 dBm Noise Power2 W SNR2 dB 138 ELECTRICAL CARRIER ANALYZER (ECAN) Details Total Power Name and description Unit Min. Total Power dBm Min. Total Power W Frequency at Max. Total Power Hz Max. Total Power dBm Max. Total Power W Frequency at Min. Signal Power Hz Ratio Max/Min Signal Power dB Ratio Max/Min Signal Power — Signal Name and description Unit Min. Total Power dBm Min. Total Power W Frequency at Max. Total Power Hz Max. Total Power dBm Max. Total Power W Frequency at Min. Signal Power Hz Ratio Max/Min Signal Power dB Ratio Max/Min Signal Power — Noise Name and description Unit Min. Total Power dBm Min. Total Power W Frequency at Max. Total Power Hz Max. Total Power dBm Max. Total Power W Frequency at Min. Signal Power Hz 139 ELECTRICAL CARRIER ANALYZER (ECAN) Name and description Unit Ratio Max/Min Signal Power dB Ratio Max/Min Signal Power — SNR Name and description Unit Min. SNR dB Frequency at Min. SNR Hz Max. SNR dB Frequency at Max. SNR Hz Ratio Max/Min SNR dB Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser, from the Component Viewer, or by double-clicking a visualizer in the Main Layout. 140 ELECTRICAL CARRIER ANALYZER (ECAN) Figure 1 Project Browser The ECAN will estimate the signal and the noise power for each electrical signal channel based on the central frequency of the internal filters. The analysis tab displays results such as frequency, power, noise, and SNR. 141 ELECTRICAL CARRIER ANALYZER (ECAN) Figure 2 Analysis tab The Details tab displays the detailed analysis for the results shown in the Analysis tab, including the minimum and maximum values for the signals. Figure 3 Details tab 142 DUAL PORT ELECTRICAL CARRIER ANALYZER Dual Port Electrical Carrier Analyzer The Dual Port Electrical Carrier Analyzer measures and compares different results in two different frequencies. Ports Name and description Port type Signal type Input 1 Input Electrical Input 2 Input Electrical Parameters Main Name and description Default value Default unit Value range Frequency 1 50 MHz, Hz, kHz, THz [0,+INF[ 10 MHz, Hz, kHz, GHz [0,+INF[ 50 MHz, Hz, kHz, THz [0,+INF[ 10 MHz, Hz, kHz, GHz [0,+INF[ Filter type Gaussian - Gaussian, Rectangle Filter order 1 - [1,+INF[ -100 dBm ]-INF,+INF[ 0 dB ]-INF,+INF[ Center frequency of the first filter. Bandwidth 1 Bandwidth of the first filter. Frequency 2 Center frequency of the second filter. Bandwidth 2 Bandwidth of the second filter. Order of the Gaussian filter. Minimum value Minimum value for power when using units in dBm. Scale factor Factor used for scaling. 143 DUAL PORT ELECTRICAL CARRIER ANALYZER Simulation Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Determines whether or not the component is enabled Signal access option Results Frequency 1 Input and Output Name and description Unit Total Power1 dBm Total Power1 W Signal Power1 dBm Signal Power1 W Noise Power1 dBm Noise Power1 W SNR1 dB Frequency 2 Input and Output Name and description Unit Total Power2 dBm Total Power2 W Signal Power2 dBm Signal Power2 W Noise Power2 dBm Noise Power2 W SNR2 dB 144 DUAL PORT ELECTRICAL CARRIER ANALYZER Details Gain Name and description Unit Min. Gain dBm Frequency at Min. Gain Hz Max. Gain dBm Frequency at Max. Gain Hz Ratio Max/Min Gain dB Noise Figure Name and description Unit Min. Noise Figure dBm Frequency at Min. Noise Figure Hz Max. Noise Figure dBm Frequency at Max. Noise Figure Hz Ratio Max/Min Noise Figure dB Total Power Input and Output Name and description Unit Min. Total Power dBm Min. Total Power W Frequency at Min. Signal Power Hz Max. Total Power dBm Max. Total Power W Frequency at Max. Total Power Hz Ratio Max/Min Signal Power dB Ratio Max/Min Signal Power — Signa 145 DUAL PORT ELECTRICAL CARRIER ANALYZER Input and Outputl Name and description Unit Min. Total Power dBm Min. Total Power W Frequency at Min. Total Power Hz Max. Total Power dBm Max. Total Power W Frequency at Max. Signal Power Hz Ratio Max/Min Signal Power dB Ratio Max/Min Signal Power — Noise Input and Output Name and description Unit Min. Noise Power dBm Min. Noise Power W Frequency at Min. Noise Power Hz Max. Noise Power dBm Max. Noise Power W Frequency at Max. Noise Power Hz Ratio Max/Min Noise Power dB Ratio Max/Min Noise Power — SNR Input and Output Name and description Unit Min. SNR dB Frequency at Min. SNR Hz Max. SNR dB Frequency at Max. SNR Hz Ratio Max/Min SNR dB 146 DUAL PORT ELECTRICAL CARRIER ANALYZER Technical background After you run a simulation, the visualizers in the project generate results based on the signal input and output. You can access the results from the Project Browser, from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project Browser The Dual Port Electrical Carrier Analyzer will estimate the signal and the noise power for each electrical signal channel based on the central frequency of the internal filters and on the resolution bandwidth. The analysis tab displays results such as gain and noise figure. 147 DUAL PORT ELECTRICAL CARRIER ANALYZER Figure 2 Analysis tab The Details tab displays the detailed analysis for the results shown in the Analysis tab, including the minimum and maximum values for the signals. Figure 3 Details tab 148 ELECTRICAL CONSTELLATION VISUALIZER Electrical Constellation Visualizer Displays the In-Phase and Quadrature-Phase electrical signals in a constellation diagram. It can also display the polar diagram and estimate the probability of symbol error for M-ary signals. Ports Name and description Port type Signal type Electrical - I Input Electrical Electrical - Q Input Electrical Parameters Main Name and description Default value Default unit Value range Polar diagram False - True, False Bit rate Bits/s, MBits/s GBits/s [0, 1e12] 0 s [-1e100, 1e100] 0 s [-1e100, 1e100] 0.5 Bit [0, 1] Ignore start symbols 0 symbols [0, +INF[ Ignore end symbols 0 symbols [0, +INF[ Estimate symbol error False - True, False Defines whether to display the detected symbols or the polar diagram Reference bit rate Reference bit rate to use when calculating bit period Delay compensation I Delay to apply to the In-Phase signal input Delay compensation Q Delay to apply to the Quadrature-Phase signal input Decision instant Value for the decision instant to use when recovering the symbols Defines whether to calculate symbol error or not 149 ELECTRICAL CONSTELLATION VISUALIZER Name and description Default value Default unit Value range Targets (a.u.) 64x3 - - QAM64.dat - - 1 a.u. [-1e100, 1e100] 0 a.u. [-1e100, 1e100] 0 a.u. [-1e100, 1e100] 1 a.u. [-1e100, 1e100] 1 a.u. [-1e100, 1e100] 0 deg [-1e100, 1e100] Name and description Default value Default unit Value range Limit number of points True - [0, +INF[ 128,000 - False - [100, 1e+008] False - True, False 500 - [100, 1e+008] Circular decision regions used to calculate symbol error probability Targets file name Filename with the targets data Distance scale Distance or radius scale factor to be applied to the decision region I target shift Horizontal shift to be applied to the decision region Q target shift Vertical shift to be applied to the decision region I target scale Horizontal scale factor to be applied to the decision regions Q target scale Vertical scale factor to be applied to the decision regions Phase offset Rotation offset to be applied to the decision regions Graphs Defines whether you can enter the maximum number of points to be displayed. Maximum number of points Maximum number of points that can be displayed in a graph. Invert colors Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs Number of color bins Number of vertical and horizontal bins of the display 150 ELECTRICAL CONSTELLATION VISUALIZER Name and description Default value Default unit Value range Color grade palette Default - Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow 10 % [0, 1000] Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Name and description Default value Default unit Value range Generate random seed True - True, False 0 - [0, 4999] Determines the color grade palette Smoothness Determines how smooth is the transition between color grades Simulation Determines whether or not the component is enabled Signal access option Random numbers Defines whether the seed is automatically defined and unique. Random seed index User defined seed index for noise generation. 151 ELECTRICAL CONSTELLATION VISUALIZER Graphs Name and description X Title Y Title Signal Amplitude Amplitude - I (a.u.) Amplitude - Q (a.u.) Noise Amplitude Amplitude - I (a.u.) Amplitude - Q (a.u.) Signal + Noise Amplitude Amplitude - I (a.u.) Amplitude - Q (a.u.) Targets Amplitude - I (a.u.) Amplitude - Q (a.u.) Results Name and description Unit log of Symbol Error at User Defined Decision Instant - Symbol Error at User Defined Decision Instant - Q Factor from Symbol Error at User Defined Decision Instant - Error Vector Magnitude at User Defined Decision Instant - 152 ELECTRICAL CONSTELLATION VISUALIZER Technical Background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project Browser displaying the Constellation Visualizer 153 ELECTRICAL CONSTELLATION VISUALIZER Figure 2 Constellation display You can select the signal to be displayed from the signal buffer by selecting the signal index. The vertical tab gives access to the signal types: • Signal • Noise • Signal and Noise Figure 3 Multiple signal types display 154 ELECTRICAL CONSTELLATION VISUALIZER Symbol error estimation If Estimate symbol error is enabled, the symbol error is calculated according to [1]: M Pe = M Pm k k=1 l = 1 l k Q kl 1--erfc -------- 2 2 (1) where M is the number of received symbols, P m k is the probability of occurrence of symbol k, calculated from the total number of symbols and the number of symbols contained in region k. Q kl is calculated according to: : d kl Q kl = -------------------- kl + lk where and (2) d kl is the distance between the centers of mass of regions k and l, kl lk are the standard deviations of regions k and l respectively. The Q-Factor from BER is calculated by numerically isolating Q from: 1 Q P e = --- erfc ------- 2 2 (3) The Error Vector Magnitude (EVM) [2][3] is calculated according to: M 1 2 d --2 -----kl- M l-------------------------= 1 l k EVM = M 2 dk - ---M l = 1 l k where (4) d k is the reference distance of region k. Parameter Targets defines the contour regions used to calculate the statistical properties of a given symbol in the constellation diagram. Figure 4 shows the constellation diagram and the target regions using the Component Viewer feature of OptiSystem. 155 ELECTRICAL CONSTELLATION VISUALIZER Note: You will have to use the Project Browser or the Component Viewer in order to visualize the target regions. Figure 4 Target regions from Component Viewer References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] IEEE Standard for Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: High-Speed Physical Layer in the 5 GHz Band, IEEE Standard 802.11aTM1999. [3] IEEE Standard for Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY)Specifications: Higher-Speed Physical Layer Extension in the 2.4 GHz Band, IEEE Standard 802.11b-1999. 156 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Directly Detected Eye Analyzer Visualizer The Directly Detected Eye Pattern Visualizer is similar to the Eye Diagram Visualizer with the exception that the signal input is optical.This visualizer includes a PIN photodiode and an Eye Diagram Visualizer. It can be used to inspect the eye diagram of an optical waveform based solely on magnitude information Ports Name and description Port type Signal type Bit sequence Input Binary Input Input Electrical Parameters Main Name and description Default value Default unit Value range Time window 1.5 bit [1,3] 1 bits [0,+INF[ 1 bits [0,+INF[ Time window for the eye diagram display Ignore start bits Number of start bits to be ignored in the eye diagram Ignore end bits Number of end bits to be ignored in the eye diagram Eye must be open True Eye opening tolerance 2 % Sample rate Sample rate Hz True, False [0,100 157 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Clock Name and description Default value Default unit Value range Clock recovery On — On, Off Name and description Default value Default unit Value range Threshold mode Relative — Relative, Absolute 0 (a.u.) ]–INF,+INF[ 50 % [0,100] 0.5 Bit [0,1] Name and description Default value Default unit Value range Time unit Bit period — s, Bit period dB — none, dB, % True — True, False 128000 — [100, 1e+008] False — [100, 1e+008] False — True, False Determines if the delay compensation between the reference and the received signal will be applied Threshold Determines the value mode for the user-defined threshold Absolute threshold Amplitude value for the threshold Relative threshold Relative value for the threshold, relative to the average values of 1s and 0s Decision instant The user-defined decision instant for the eye analysis Graphs Time unit for the horizontal axis Ratio unit Ratio unit for the vertical axis Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs 158 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Name and description Default value Default unit Value range Number of color bins 500 — [100, 1e+008] Default — Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow 10 % [0, 1000] Name and description Default value Default unit Value range Calculate histograms False — True, False 500 — [10, 5000] 500 — [10, 5000] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] Number of vertical and horizontal bins of the display Color grade palette Determines the color grade palette Smoothness Determines how smooth is the transition between color grades Histograms Determines whether to calculate histograms or not Number of X bins Number of horizontal histogram bins Number of Y bins Number of vertical histogram bins Region 1 X0 Determines the first point along the horizontal axis for the region Region 1 X1 Determines the second point along the horizontal axis for the region Region 1 Y0 Determines the first point along the vertical axis for the region Region 1 Y1 Determines the second point along the vertical axis for the region Region 2 X0 Determines the first point along the horizontal axis for the region Region 2 X1 Determines the second point along the horizontal axis for the region Region 2 Y0 Determines the first point along the vertical axis for the region 159 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Name and description Default value Default unit Value range Region 2 Y1 0 a.u. [-1e100,1e100] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 — [-1e100,1e100] 0 — [-1e100,1e100] 0 a.u. [-1e100,1e100] 0 a.u. [-1e100,1e100] Name and description Default value Default unit Value range Calculate mask False — True, False Eye.msk — — 0 Bit period [-1e100,1e100] 0 a.u. [-1e100,1e100] Determines the second point along the vertical axis for the region Region 3 X0 Determines the first point along the horizontal axis for the region Region 3 X1 Determines the second point along the horizontal axis for the region Region 3 Y0 Determines the first point along the vertical axis for the region Region 3 Y1 Determines the second point along the vertical axis for the region Region 4 X0 Determines the first point along the horizontal axis for the region Region 4 X1 Determines the second point along the horizontal axis for the region Region 4 Y0 Determines the first point along the vertical axis for the region Region 4 Y1 Determines the second point along the vertical axis for the region Mask Determines whether or not to display the eye mask Mask filename The file which contains the mask data Mask horizontal shift User defined mask horizontal shift Mask vertical shift User defined mask vertical shift 160 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Name and description Default value Default unit Value range Mask margin 0 % [-100,100] Name and description Default value Default unit Value range Enabled True — True, False Default value Default unit Value range True — True, False Name and description Default value Default unit Value range Generate random seed True — True, False 0 — [0,49999] Mask margins are used to determine the margin of compliance for a standard or scaled mask. You can use positive mask margins to determine how much larger you will be able to increase the size of the mask before violations will occur or negative margins to determine how much smaller you have to decrease the size of the mask before violations no longer occur Simulation Determines whether or not the component is enabled Noise Name and description Add noise to signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 161 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Graphs Name and description X Title Y Title Eye diagram Time (s) Amplitude (a.u.) Min. BER Time (s) log (BER) Q-factor Time (s) Q Threshold at min. BER Time (s) Amplitude (a.u.) Eye Height Time (s) Amplitude (a.u.) Eye Amplitude Time (s) Amplitude (a.u.) Eye Closure Time (s) Amplitude (a.u.) Eye Opening Factor Time (s) Ratio (dB) Eye Extinction Ratio Time (s) Ratio (dB) Histogram Region 1 Time (s) Amplitude (a.u.) Histogram Region 2 Time (s) Amplitude (a.u.) Histogram Region 3 Time (s) Amplitude (a.u.) Histogram Region 4 Time (s) Amplitude (a.u.) Vertical Histogram 1 Time (s) Amplitude (a.u.) Vertical Histogram 2 Time (s) Amplitude (a.u.) Vertical Histogram 3 Time (s) Amplitude (a.u.) Vertical Histogram 4 Time (s) Amplitude (a.u.) Horizontal Histogram 1 Time (s) Amplitude (a.u.) Horizontal Histogram 2 Time (s) Amplitude (a.u.) Horizontal Histogram 3 Time (s) Amplitude (a.u.) Horizontal Histogram 4 Time (s) Amplitude (a.u.) Eye Mask Time (s) Amplitude (a.u.) Results Name and description Unit Total Power dBm Total Power W Signal Power dBm Signal Power W 162 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Name and description Unit Noise Power dBm Noise Power W Signal Delay s Signal Delay samples Bit Rate Bits/s Max. Q Factor — Min. BER — Min. log of BER — Max. Eye Height a.u. Threshold at Min. BER a.u. Decision Instant at Min. BER Bit period Max. Eye Amplitude a.u. Max. Eye Closure a.u. Max. Eye Opening Factor dB Max. Eye Opening Factor — Max. Eye Opening Factor % Extinction Ratio at Min. BER dB Extinction Ratio at Min. BER — Extinction Ratio at Min. BER % Q Factor at User Defined Decision Instant — Eye Height at User Defined Decision Instant a.u. Min. BER at User Defined Decision Instant — Min. log of BER at User Defined Decision Instant — BER at User Defined Threshold — BER at User Defined Decision Instant and Threshold — log of BER at User Defined Threshold — log of BER at User Defined Decision Instant and Threshold — Eye Amplitude at User Defined Decision Instant a.u. Eye Closure at User Defined Decision Instant a.u Eye Opening Factor at User Defined Decision Instant dB Eye Opening Factor at User Defined Decision Instant — 163 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Name and description Unit Eye Opening Factor at User Defined Decision Instant % Extinction Ratio at User Defined Decision Instant dB Extinction Ratio at User Defined Decision Instant — Extinction Ratio at User Defined Decision Instant % Vertical Histogram 1 Mean — Vertical Histogram 1 Standard Deviation — Vertical Histogram 1 Range — Horizontal Histogram 1 Mean — Horizontal Histogram 1 Standard Deviation — Horizontal Histogram 1 Range — Vertical Histogram 2 Mean — Vertical Histogram 2 Standard Deviation — Vertical Histogram 2 Range — Horizontal Histogram 2 Mean — Horizontal Histogram 2 Standard Deviation — Horizontal Histogram 2 Range — Vertical Histogram 3 Mean — Vertical Histogram 3 Standard Deviation — Vertical Histogram 3 Range — Horizontal Histogram 3 Mean — Horizontal Histogram 3 Standard Deviation — Horizontal Histogram 3 Range — Vertical Histogram 4 Mean — Vertical Histogram 4 Standard Deviation — Vertical Histogram 4 Range — Horizontal Histogram 4 Mean — Horizontal Histogram 4 Standard Deviation — Horizontal Histogram 4 Range — Eye Mask Violation Ratio % 164 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Technical background For further details on the operation of the Directly Detected Eye Pattern Visualizer please refer to the technical background for the Eye Diagram Analyzer 165 DIRECTLY DETECTED EYE ANALYZER VISUALIZER 166 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Visualizer Library Binary • Binary Sequence Visualizer • M-ary Sequence Visualizer 167 DIRECTLY DETECTED EYE ANALYZER VISUALIZER Notes: 168 BINARY SEQUENCE VISUALIZER Binary Sequence Visualizer This visualizer allows the user to calculate and display binary signals in the time domain. Ports Name and description Port type Signal type Supported modes Input Input Binary Binary signals Parameters Graphs Name and description Default value Default unit Units Value range Time unit s - - s, bits False - - True, False Name and description Default value Default unit Value range Export False - True, False Sequence.dat - - Time unit for the horizontal axis Invert colors Determines whether or not to invert the colors of the display Export Determines whether or not to save the signal to a file Filename Destination file name 169 BINARY SEQUENCE VISUALIZER Simulation Name and description Default value Default unit Value range Enabled True - [True, False] Determines whether or not the component is enabled Graphs Name and description X Title Y Title Amplitude Time (s) Amplitude (a.u.) Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser Access the visualizer parameters, graphs, and results from the simulation (see Figure 2). 170 BINARY SEQUENCE VISUALIZER Figure 2 Binary Visualizer display Use the signal index to select the signal to display from the signal buffer. 171 BINARY SEQUENCE VISUALIZER Notes: 172 M-ARY SEQUENCE VISUALIZER M-ary Sequence Visualizer This visualizer allows the user to calculate and display m-ary signals in the time domain. Ports Name and description Port type Signal type Supported modes Input Input M-ary M-ary signals Parameters Graphs Name and description Default value Default unit Units Value range Time unit s - - s, bits False - - True, False Name and description Default value Default unit Value range Export False - True, False Sequence.dat - - Time unit for the horizontal axis Invert colors Determines whether or not to invert the colors of the display Export Determines whether or not to save the signal to a file Filename Destination file name 173 M-ARY SEQUENCE VISUALIZER Simulation Name and description Default value Default unit Value range Enabled True - True, False Determines whether or not the component is enabled Graphs Name and description X Title Y Title Amplitude Time (s) Amplitude (a.u.) Technical background After you run a simulation, the visualizers in the project generate graphs and results based on the signal input. You can access the graphs and results from the Project Browser (see Figure 1), from the Component Viewer, or by double-clicking a visualizer in the Main Layout. Figure 1 Project browser Access the visualizer parameters, graphs, and results from the simulation (see Figure 2). 174 M-ARY SEQUENCE VISUALIZER Figure 2 M-ary Visualizer display Use the signal index to select the signal to display from the signal buffer. 175 M-ARY SEQUENCE VISUALIZER Notes: 176 M-ARY SEQUENCE VISUALIZER Visualizer Library Compare • Dual Port Binary Sequence Visualizer • Dual Port M-ary Sequence Visualizer • Dual Port Optical Spectrum Analyzer • Dual Port Optical Time Domain Visualizer • Dual Port Oscilloscope Visualizer • Dual Port RF Spectrum Analyzer 177 M-ARY SEQUENCE VISUALIZER Notes: 178 DUAL PORT BINARY SEQUENCE VISUALIZER Dual Port Binary Sequence Visualizer This visualizer performs the exact same function as the Binary Sequence Visualizer and allows for the simultaneous viewing of any two binary signal inputs. Ports Name and description Port type Signal type Supported modes Input 1 Input Binary Binary signals Input 2 Input Binary Binary signals Parameters Graphs Name and description Default value Default unit Units Value range Time unit s - - s, bits False - - True, False Name and description Default value Default unit Value range Export False - True, False Sequence.dat - - Time unit for the horizontal axis Invert colors Determines whether or not to invert the colors of the display Export Determines whether or not to save the signal to a file Filename Destination file name 179 DUAL PORT BINARY SEQUENCE VISUALIZER Simulation Name and description Default value Default unit Value range Enabled True - [True, False] Determines whether or not the component is enabled Graphs Name and description X Title Y Title Amplitude Time (s) Amplitude (a.u.) Technical background Please refer to the Binary Sequence Visualizer for technical information on this component 180 DUAL PORT M-ARY SEQUENCE VISUALIZER Dual Port M-ary Sequence Visualizer This visualizer performs the exact same function as the M-ary Sequence Visualizer and allows for the simultaneous viewing of any two M-ary signal inputs. Ports Name and description Port type Signal type Supported modes Input 1 Input M-ary M-ary signals Input 2 Input M-ary M-ary signals Parameters Graphs Name and description Default value Default unit Units Value range Time unit s - - s, bits False - - True, False Name and description Default value Default unit Value range Export False - True, False Sequence.dat - - Time unit for the horizontal axis Invert colors Determines whether or not to invert the colors of the display Export Determines whether or not to save the signal to a file Filename Destination file name 181 DUAL PORT M-ARY SEQUENCE VISUALIZER Simulation Name and description Default value Default unit Value range Enabled True - True, False Determines whether or not the component is enabled Graphs Name and description X Title Y Title Amplitude Time (s) Amplitude (a.u.) Technical background Please refer to the M-ary Sequence Visualizer for technical information on this component. 182 DUAL PORT OPTICAL SPECTRUM ANALYZER Dual Port Optical Spectrum Analyzer This visualizer allows the user to calculate and display optical signals in the frequency domain. It can simultaneously view two optical signal inputs and operates identically to the Optical Spectrum Analyzer visualizer Ports Name and description Port type Signal type Input 1 Input Optical Input 2 Input Optical Parameters Resolution bandwidth Name and description Default value Default unit Value range Resolution bandwidth Off — On, Off Rectangle — Rectangle, Gaussian, Butterworth 0.01 nm [0, 1e+100] Name and description Default value Default unit Value range Power unit dBm — dBm, W –100 dBm [-1e+100, 1e+100] Determines whether or not the resolution filter is enabled Filter type Determines the type of resolution filter Bandwidth Resolution filter bandwidth Graphs Power unit for the vertical axis Minimum value Minimum value for power when using units in dBm 183 DUAL PORT OPTICAL SPECTRUM ANALYZER Name and description Default value Default unit Value range Scale factor 0 dB [-1e+100, 1e+100] False — True, False m — m, Hz False — True, False True — True, False False — True, False False — True, False True — True, False 128000 — [100, 1e+008] False — True, False Name and description Default value Default unit Value range Enabled True — True, False Vertical axis scale factor Power spectral density Determines whether or not to calculate the power spectral density for the vertical axis Frequency unit Frequency unit for the horizontal axis Calculate phase Determines whether or not to calculate the phase graphs Unwrap phase Determines whether or not to remove the phase discontinuity Calculate group delay Determines whether or not to calculate group delay graphs Calculate dispersion Determines whether or not to calculate dispersion graphs Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Simulation Determines whether or not the component is enabled 184 DUAL PORT OPTICAL SPECTRUM ANALYZER Graphs Sampled signals Name and description X Title Y Title Sampled signal spectrum Wavelength (m) Power (dBm) Sampled signal spectrum X Wavelength (m) Power (dBm) Sampled signal spectrum Y Wavelength (m) Power (dBm) Sampled signal phase X Wavelength (m) Phase (rad) Sampled signal phase Y Wavelength (m) Phase (rad) Sampled signal group delay X Wavelength (m) Delay (s) Sampled signal group delay Y Wavelength (m) Delay (s) Sampled signal dispersion X Wavelength (m) Dispersion (ps/nm) Sampled signal dispersion Y Wavelength (m) Dispersion (ps/nm) Parameterized signals Name and description X Title Y Title Parameterized signal spectrum Wavelength (m) Power (dBm) Parameterized signal spectrum X Wavelength (m) Power (dBm) Parameterized signal spectrum Y Wavelength (m) Power (dBm) Name and description X Title Y Title Noise bins signal spectrum Wavelength (m) Power (dBm) Noise bins signal spectrum X Wavelength (m) Power (dBm) Noise bins signal spectrum Y Wavelength (m) Power (dBm) Noise bins 185 DUAL PORT OPTICAL SPECTRUM ANALYZER Technical background Please refer to the Optical Spectrum Analyzer Visualizer for technical information on this component. 186 DUAL PORT OPTICAL TIME DOMAIN VISUALIZER Dual Port Optical Time Domain Visualizer This visualizer allows the user to calculate and display optical signals in the time domain. It can simultaneously view two optical signal inputs and operates identically to the Optical Time Domain Visualizer. Ports Name and description Port type Signal type Input 1 Input Optical Input 2 Input Optical Parameters Graphs Name and description Default value Default unit Units Value range Plot individual mode False - - True, False 0 - - [0, 1e+008] s - - s, bits Bit rate Bits/s Bits/s [0, 1e+012] Determines whether or not to plot a individual mode Individual mode number The individual mode number Time unit Time unit for the horizontal axis Reference bit rate Reference bit rate to use when the time unit is Bit period MBits/s GBits/s Retracing False - - True, False Time window 1/(Bit rate) s - ]0, +INF[ Defines the retracing time window 187 DUAL PORT OPTICAL TIME DOMAIN VISUALIZER Name and description Default value Default unit Units Value range Autocorrelation Off - - Off, Field, Intensity False - - True, False deg - - deg, rad True - - True, False False - - True, False W - - W, dBm –100 dBm - [-1e+100, 1e+100] True - - True, False 128,000 - - [100, 1e+008] False - - True, False False - - True, False 500 - - [10, 5000] Default - - Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow Determines the type of calculation for the autocorrelation graphs Calculate phase and chirp Determines whether or not to calculate phase and chirp graphs Phase unit Phase unit for the vertical axis Unwrap phase Determines whether or not to remove the phase discontinuity Calculate alpha parameter Determines whether or not to calculate alpha parameter graphs Power unit Power unit for the vertical axis Minimum value Minimum value for power when using units in dBm Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs Number of color bins Number of vertical and horizontal bins of the display Color grade palette Determines the color grade palette 188 DUAL PORT OPTICAL TIME DOMAIN VISUALIZER Downsampling Name and description Default value Default unit Default unit Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30,3e5] 5*(Sample rate) THz Hz, GHz, THz, nm [1, 1e+100] Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined Center frequency User-defined center frequency of the internal filter Sample rate Bandwidth of the internal filter Enhanced Name and description Default value Default unit Value range Calculate FROG False - True, False X - X, Y True - True, False Sample rate Hz [0, 1e100] Time window / 2 s [0, 1e100] 128 - True, False Determines whether or not to calculate the Frequency Resolved Optical Gating (FROG) graph FROG polarization Determines the signal polarization for the FROG analysis Add noise to FROG signal Determines whether or not to convert and add noise bins to the signal FROG frequency range Frequency range for the vertical axis FROG delay range Delay range for the horizontal axis Number of FROG delay points Number of points for the horizontal axis Simulation Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Determines whether or not the component is enabled Signal access option 189 DUAL PORT OPTICAL TIME DOMAIN VISUALIZER Random numbers Name and description Default value Default unit Value range Generate random seed True - True, False 0 - [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Graphs Signal Name and description X Title Y Title Signal power Time (s) Power (W) Signal power X Time (s) Power (W) Signal power Y Time (s) Power (W) Signal phase X Time (s) Phase (deg) Signal phase Y Time (s) Phase (deg) Signal chirp X Time (s) Frequency (Hz) Signal chirp Y Time (s) Frequency (Hz) Signal autocorrelation X Delay (s) Intensity (a.u.) Signal autocorrelation Y Delay (s) Intensity (a.u.) Signal alpha parameter X Time (s) Alpha (ratio) Signal alpha parameter Y Time (s) Alpha (ratio) Name and description X Title Y Title Noise power Time (s) Power (W) Noise power X Time (s) Power (W) Noise power Y Time (s) Power (W) Noise phase X Time (s) Phase (deg) Noise phase Y Time (s) Phase (deg) Noise chirp X Time (s) Frequency (Hz) Noise chirp Y Time (s) Frequency (Hz) Noise 190 DUAL PORT OPTICAL TIME DOMAIN VISUALIZER Name and description X Title Y Title Noise autocorrelation X Delay (s) Intensity (a.u.) Noise autocorrelation Y Delay (s) Intensity (a.u.) Noise alpha parameter X Time (s) Alpha (ratio) Noise alpha parameter Y Time (s) Alpha (ratio) Name and description X Title Y Title Signal + Noise power Time (s) Power (W) Signal + Noise power X Time (s) Power (W) Signal + Noise power Y Time (s) Power (W) Signal + Noise phase X Time (s) Phase (deg) Signal + Noise phase Y Time (s) Phase (deg) Signal + Noise chirp X Time (s) Frequency (Hz) Signal + Noise chirp Y Time (s) Frequency (Hz) Signal + Noise autocorrelation X Delay (s) Intensity (a.u.) Signal + Noise autocorrelation Y Delay (s) Intensity (a.u.) Signal + Noise alpha parameter X Time (s) Alpha (ratio) Signal + Noise alpha parameter Y Time (s) Alpha (ratio) Signal + Noise 3D Graphs Name and description X Title Y Title Z Title FROG 3D Graph Delay (ns) Frequency (THz) Intensity (a.u.) 191 DUAL PORT OPTICAL TIME DOMAIN VISUALIZER Technical background Please refer to the Optical Time Domain Visualizer for technical information on this component. 192 DUAL PORT OSCILLOSCOPE VISUALIZER Dual Port Oscilloscope Visualizer This visualizer allows the user to calculate and display electrical signals in the time domain. It can simultaneously view two electrical signal inputs and operates identically to the Oscilloscope Visualizer. Ports Name and description Port type Signal type Supported modes Input 1 Input Electrical Sampled signals Input 2 Input Electrical Sampled signals Parameters Graphs Name and description Default value Default unit Units Value range Time unit s - - s, bits Bit rate Bits/s Bits/s [0, 1e+012] Time unit for the horizontal axis Reference bit rate Reference bit rate to use when the time unit is Bit period MBits/s GBits/s Retracing False - - True, False Time window 1/(Bit rate) s - ]0, +INF[ False - - True, False Defines the retracing time window Calculate autocorrelation Determines whether or not to calculate autocorrelation graphs 193 DUAL PORT OSCILLOSCOPE VISUALIZER Name and description Default value Default unit Units Value range Limit number of points True - - True, False 128,000 - - [100, 1e+008] False - - True, False False - - True, False 500 - - [10, 5000] Default - - Default, Agilent, Gray, Black, Red, Green,Blue, Agilent red, Agilent blue, Agilent green, Agilent yellow Name and description Default value Default unit Value range Enabled True - True, False Index - Index, Average Name and description Default value Default unit Value range Generate random seed True - True, False 0 - [0,4999] Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Enable color grade Determines whether or not to color grade the displayed graphs Number of color bins Number of vertical and horizontal bins of the display Color grade palette Determines the color grade palette Simulation Determines whether or not the component is enabled Signal access option Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 194 DUAL PORT OSCILLOSCOPE VISUALIZER Graphs Name and description X Title Y Title Signal amplitude Time (s) Amplitude (a.u.) Noise amplitude Time (s) Amplitude (a.u.) Signal + noise amplitude Time (s) Amplitude (a.u.) Signal autocorrelation Delay (s) Intensity (a.u.) Noise autocorrelation Delay (s) Intensity (a.u.) Signal + noise autocorrelation Delay (s) Intensity (a.u.) Technical background Please refer to the Oscilloscope Visualizer for technical information on this component. 195 DUAL PORT OSCILLOSCOPE VISUALIZER 196 DUAL PORT RF SPECTRUM ANALYZER Dual Port RF Spectrum Analyzer This visualizer allows the user to calculate and display electrical signals in the frequency domain. It can simultaneously view two electrical signal inputs and operates identically to the RF Spectrum Analyzer. Ports Name and description Port type Signal type Input 1 Input Electrical Input 2 Input Electrical Parameters Resolution bandwidth Name and description Default value Default unit Value range Resolution bandwidth Off — On, Off Rectangle — Rectangle, Gaussian, Butterworth 10 MHz [0,+INF[ Name and description Default value Default unit Value range Power unit dB — dBm, W –100 dBm [-1e+100, 1e+100] Determines whether or not the resolution filter is enabled Filter type Determines the type for the resolution filter Bandwidth Resolution filter bandwidth Graphs Power unit for the vertical axis Minimum value Minimum value for power when using units in dBm 197 DUAL PORT RF SPECTRUM ANALYZER Name and description Default value Default unit Value range Scale factor 0 dB [-1e+100, 1e+100] False — True, False False — True, False True — True, False False — True, False True — True, False 128000 — [100, 1e+008] False — True, False Name and description Default value Default unit Value range Enabled True — True, False Name and description Default value Default unit Value range Generate random seed True — True, False 0 — [0,4999] Vertical axis scale factor (for an impedance of 50 ohms, use a scale of 16.9897, for voltage input, and a scale of -16.898 for current input) Power spectral density Determines whether or not to calculate the power spectral density for the vertical axis Calculate phase Determines whether or not to calculate the phase graphs Unwrap phase Determines whether or not to remove the phase discontinuity Negative frequencies Determines whether or not the negative frequencies are displayed Limit number of points Determines if you can enter the maximum number of points to display Max. number of points Maximum number of points displayed per graph Invert colors Determines whether or not to invert the colors of the display Simulation Determines whether or not the component is enabled Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 198 DUAL PORT RF SPECTRUM ANALYZER Graphs Name and description X Title Y Title Signal spectrum Frequency (GHz) Power (dBm) Noise spectrum Frequency (GHz) Power (dBm) Signal + noise spectrum Frequency (GHz) Power (dBm) Signal phase Frequency (GHz) Phase (rad) Noise phase Frequency (GHz) Phase (rad) Signal + noise phase Frequency (GHz) Phase (rad) Technical background Please refer to the RF Spectrum Analyzer for technical information on this component. 199 DUAL PORT RF SPECTRUM ANALYZER 200 DUAL PORT RF SPECTRUM ANALYZER Visualizer Library View Signal • View Signal Visualizer • Cpp CoSimulation Visualizer 201 DUAL PORT RF SPECTRUM ANALYZER 202 VIEW SIGNAL VISUALIZER View Signal Visualizer This visualizer allows the user to calculate and display the average power of optical signals. It can also calculate the power for polarizations X and Y. Ports Name and description Port type Signal type Input Input Any type Parameters Main Name and description Default value Default unit Sampled signal domain Time [Time, Frequency] Real & Imag Real & Imag, Mag & Phase Time [Space, Frequency] View either time-sampled or frequency domain signal data Sampled signal format View complex field sampled data in Real-Imag or Mag-Phase format Spatial mode domain View either spatial or frequency domain signal modes data Generate random seed Value range True — True, False False — True, False — True, False Random seed index Save Data to OptiSystem Data Signal Specifies whether to save the signal data into the “.ods” format ODS filename Signal_1.ods Specifies the “.ods” filename to which to save the signal data Save data as text file False Specifies whether to save the signal data into the “.txt” format Text Filename File.txt Specifies the “.txt” filename to which to save the signal data 203 VIEW SIGNAL VISUALIZER Technical background The View Signal Visualizer allows the user to directly access the signal data set associated with all signal types in OptiSystem. As shown in Figure 1, the real or complex field data associated with any signal type can be viewed directly from within a text screen. Either data associated with the Frequency domain or Time domain can be shown (this is selected with the Sampled signal domain parameter). Similarly spatial mode domain can be displayed, either spatially or in the frequency domain (this is selected with the Sampled mode domain parameter) Within the View signal panel, the following functions are provided: • Refresh. Use the Refresh button to refresh the screen. Also after a refresh it is possible to left click on your mouse and to hover over segments of the data set for copying and pasting • Export to.txt. Select this button to save all the data contained in the View signal panel to a text-formatted file (you will be requested to specify the file name and location) • Export to Excel. Select this button to save all the data contained in the View signal panel to an Microsoft Excel compatible file (you will be requested to specify the file name and location) • Signal Index. If several iterations are performed during a simulation, use the Signal Index scroll function to view the data sets for each available iteration. Figure 1 View Signal Visualizer 204 CPP COSIMULATION VISUALIZER Cpp CoSimulation Visualizer The Cpp CoSimulation Visualizer’s primary function is to duplicate all the signals that are designed to enter the Cpp component. These duplicated signals are saved as text files and loaded into the component design project when running in debug mode. Ports Name and description Port type Signal type Input Input Any type Output Input Any type Parameters Main Name and description Default value Default unit Value range Resize True — True, False Save Data as CPP XML Load File False — True, False Name and description Default value Default unit Value range Number of input ports 1 Signal type (input 1) Optical — Optical, Electrical, Binary, M-ary CPP XML Filename Inputs CPP Filename (input 1) 205 CPP COSIMULATION VISUALIZER Outputs Name and description Default value Default unit Value range Number of output ports 1 Signal type (output 1) Optical — Optical, Electrical, Binary, M-ary Name and description Default value Default unit Value range Enabled TRUE Simulation TRUE, FALSE Technical background When using the Cpp component, the user cannot directly enter the debugger of their project from OptiSystem because OptiSystem is built in release mode. The Cpp CoSimulation Visualizer can however be used to duplicate all the signals that are designed to enter the Cpp component. These duplicated signals are saved as text files and then loaded into the component design project when running in debug mode. The input and output ports must be configured exactly the same as the corresponding Cpp component. In addition, for each input, a file name must be specified where that port's signal information will be stored. The information about the port structures, as well as the location and names of all the signal data files, will be saved in the CPP XML Load File. In addition to saving the signals to files, this component also acts like the View Signal Visualizer as the raw signal data from each incoming port can be viewed To learn how to use the Cpp CoSimulation Visualizer please refer to Tutorial 1: Release and Debug modes, basic manipulation of Binary Signal at: http:/optiwave.com/?p=28551 206 Transmitters Library - Electrical Bit Sequence Generators • Pseudo-Random Bit Sequence Generator • User-Defined Bit Sequence Generator 207 Notes: 208 PSEUDO-RANDOM BIT SEQUENCE GENERATOR Pseudo-Random Bit Sequence Generator Generates a Pseudo Random Binary Sequence (PRBS) according to different operation modes. The bit sequence is designed to approximate the characteristics of random data. Ports Name and description Port type Signal type Bit sequence Output Binary Parameters Main Name and description Default value Default unit Value range Bit rate Bit rate Bits/s [0, 1e+012] MBits/s GBits/s Operation mode Order — Probability, Order, Alternate, Ones, Zeros Order log(Sequence length)/log(2) — [2,30] 0.5 — [0,1] Number of leading zeros (Time window * 3 / 100) * Bit rate — [0,+INF[ Number of trailing zeros (Time window * 3 / 100) * Bit rate — [0,+INF[ Order of the PRBS generator Mark probability Probability of ones in the sequence 209 PSEUDO-RANDOM BIT SEQUENCE GENERATOR Simulation Name and description Default value Units Value range Enabled True — True, False Iterations — [1, 1e+009] Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] False — True, False Determines if the seed is automatically defined and unique Random seed index User-defined seed index for bit generation Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration Technical background This model generates a sequence of N bits: where N = T w B r NG = N – nl – nt Tw is the global parameter Time window and Br is the parameter Bit rate. The number of bits generated is the Number of trailing zeros. N G . n l and n t are the Number of leading zeros and Operation mode controls the algorithm used to generate the bit sequence: 210 • Probability: Random number generator is used, with parameter Mark probability specifying the probability of ones in the sequence • Order: PRBS generator[1] with Order k is used to generate a sequence with period of 2k-1 • Alternate: Alternate sequence of ones and zeros is generated • Ones: A sequence of ones is generated • Zeros: A sequence of zeros is generated PSEUDO-RANDOM BIT SEQUENCE GENERATOR References [1] Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., Numerical Recipes in C. Cambridge University Press, (1991). 211 PSEUDO-RANDOM BIT SEQUENCE GENERATOR Notes: 212 USER-DEFINED BIT SEQUENCE GENERATOR User-Defined Bit Sequence Generator Generates a bit sequence that is user-defined. Ports Name and description Port type Signal type Bit sequence Output Binary Parameters Main Name and description Default value Units Value range Bit rate Bit rate Bits/s [0,+INF[ MBits/s GBits/s Load from file False — True, False Sequence.dat — Filename 0101101110 — String Number of leading zeros (Time window * 3 / 100) * Bit rate — [0, 1000] Number of trailing zeros (Time window * 3 / 100) * Bit rate — [0, 1000] Determines whether or not the component will load the bit sequence from the file Filename File with the bit sequence Bit sequence User-defined bit sequence 213 USER-DEFINED BIT SEQUENCE GENERATOR Simulation Name and description Default value Units Value range Enabled True — True, False 1 — [1, 1e+009] Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Technical background You can enter the string Bit sequence or choose Load from file. In this, case the parameter Filename is enabled. All bit files are formatted containing one bit per line, e.g. the bit file representing the sequence "01011..." has the following form: 0 1 0 1 1 The sequence length is defined by: N = TwBr Tw is the global parameter Time window and Br is the parameter Bit rate. If the userdefined sequence is shorter than the N, the sequence will be repeated until the length is equal to N. 214 USER-DEFINED BIT SEQUENCE GENERATOR Transmitters Library - Electrical Pulse & Symbol Generators • Duobinary Pulse Generator • Electrical Jitter • Noise Source • RZ Pulse Generator • NRZ Pulse Generator • Gaussian Pulse Generator • Hyperbolic-Secant Pulse Generator • Sine Generator • Triangle Pulse Generator • Saw-Up Pulse Generator • Saw-Down Pulse Generator • Impulse Generator • Raised Cosine Pulse Generator • Sine Pulse Generator • Measured Pulse • Measured Pulse Sequence • Bias Generator • M-ary Pulse Generator • M-ary Raised Cosine Pulse Generator • Predistortion • PAM Pulse Generator • QAM Pulse Generator • PSK Pulse Generator • DPSK Pulse Generator • OQPSK Pulse Generator • MSK Pulse Generator 215 USER-DEFINED BIT SEQUENCE GENERATOR Notes: 216 DUOBINARY PULSE GENERATOR Duobinary Pulse Generator Used for duobinary modulation schemes. It is equivalent to a subsystem based on an electrical delay and adder. It can be used together with any electrical pulse generator. Ports Name and description Port type Signal type Input Input Electrical Clock Input Binary Output Output Electrical Parameters Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled 217 DUOBINARY PULSE GENERATOR Technical background The equivalent subsystem is: Figure 1 Duobinary Pulse Generator subsystem 218 ELECTRICAL JITTER Electrical Jitter Inserts jitter in the input signal. Ports Name and description Port type Signal type Input Input Electrical Clock Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Units Value range Frequency 100 MHz Hz, MHz, GHz, THz [0,+INF[ 0.1 UI - [0,+INF[ 0 UI - [0,+INF[ Name and description Default value Units Value range Enabled True - True, False Jitter frequency Jitter amplitude Jitter amplitude range Random jitter amplitude rms Random jitter Simulation Determines whether or not the component is enabled 219 ELECTRICAL JITTER Technical background The jitter is a short-term, non-cumulative variation of the significant instants of a digital signal from their positions in time. Jitter amplitude is measured in unit intervals (UI), where 1 UI is the phase deviation of one clock period. The peak-to-peak UI deviation of the phase function with respect to time is referred as jitter amplitude. The output signal is: A E out t = E in t + tr + ------- sin 2ft 2B where A is the deterministic jitter amplitude, B is the signal bit rate, and f is the jitter frequency. And tr is the random jitter that has a Gaussian probability distribution with zero mean and standard deviation defined by the parameter Random jitter amplitude (rms value). 220 NOISE SOURCE Noise Source Source of thermal noise. Ports Name and description Port type Signal type Output Output Electrical Parameters Main Name and description Default value Default unit Units Value range PSD True — — True, False –60 dBm W, mW, dBm ]-INF,+INF[ Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether the power is defined as PSD or as the average power in time Noise Power Value of the PSD or the average power Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window 221 NOISE SOURCE Noise Name and description Default value Units Value range Add noise to signal False — True, False Name and description Default value Units Value range Generate random seed True — True, False 0 — [0, 4999] Determines whether the noise will propagate separately from the signal or will be added to the signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The average output Power or Power spectral density are parameters that you specify. This model generates electrical sampled signals or electrical sampled noise according to: E out = x t + jy t P 2 A Gaussian distribution describes the probability density function for the real and imaginary part of E. P is the average power when PSD parameter is false, if PSD is true then P is calculated from the power spectral density multiplied by the Sample rate. 222 RZ PULSE GENERATOR RZ Pulse Generator Generates a Return to Zero (RZ) coded signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Rectangle shape Exponential — Exponential, Gaussian, Linear, Sine Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Determines the shape for the edges of the pulse Format for pulse range Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. 223 RZ PULSE GENERATOR Name and description Default value Default unit Value range Duty cycle 0.5 bit [0,1] 0 bit [-1, 1] 0.05 bit [0,1] 0.05 bit [0,1] Time duration of the high level bit, starting at the beginning of the bit period and defined as the ratio of the bit period. Position Relative position of pulse stream (ratio of bit period). For example if Position = 0.5, the pulse stream is shifted by 50% of the bit period. Rise time Defined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude Fall time Defined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background According to the parameter Rectangle shape, this model can produce pulses with different edge shapes: Exponential – t cr ,0 t t 1 1 – e 1 t 1 t t 2 Et = e – t cf ,t t t 2 c 0 t c t T 224 RZ PULSE GENERATOR Gaussian – t cr ,0 t t 1 1 – e 1 t 1 t t 2 Et = 2 e – t c f ,t t t 2 c 0 t c t T 2 Linear t c r ,0 t t 1 1 t 1 t t 2 Et = t c f ,t 2 t t c 0 t c t T Sine sin .t c r ,0 t t 1 1 ,t 1 t t 2 Et = sin .t c f ,t 2 t t c 0 ,t c t T where cr is the rise time coefficient and cf is the fall time coefficient. t1 and t2, together with cr and cf, are numerically determinate to generate pulses with the exact values of the parameters Rise time and Fall time. tc is the duty cycle duration, and T is the bit period. 225 RZ PULSE GENERATOR Figure 1 Example range settings for RZ Pulse Generator with Input Bit Stream = [1111] (Amplitude = 1, DC Bias = 0, Duty cycle = 0.25, Position = 0) Amplitude = 1 DC Bias = 0 Duty cycle (0.25) – Measured from start of “ON” bit 226 NRZ PULSE GENERATOR NRZ Pulse Generator Generates a Non Return to Zero (NRZ) coded signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Rectangle shape Exponential — Exponential, Gaussian, Linear, Sine Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Determines the shape for the edges of the pulse Format for pulse range Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. 227 NRZ PULSE GENERATOR Name and description Default value Default unit Value range Position 0 bit 0.05 bit [0,1] 0.05 bit [0,1] Relative position of start of pulse (ratio of bit period). For example if Position = 0.5, the pulse stream is shifted by 50% of the bit period. Rise time Defined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude Fall time Defined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 228 NRZ PULSE GENERATOR Technical background The NRZ Pulse Generator component produces rectangular non-return to zero (NRZ) electrical pulses with the following edge shapes: Exponential – t cr ,0 t t 1 1 – e 1 ,t 1 t t 2 Et = – t c f e ,t 2 t T Gaussian – t cr 2 ,0 t t 1 e 1 ,t 1 t t 2 Et = 2 e – t cf , t t T 2 Linear t c r ,0 t t 1 E t = 1 t 1 t t 2 t c f ,t 2 t T Sine sin .t c r ,0 t t 1 1 ,t 1 t t 2 Et = sin .t c f ,t 2 t T where cr is the rise time coefficient and cf is the fall time coefficient and T is the bit period. The time points t1 and t2, together with cr and cf, are numerically set to generate pulses that align with the values of the parameters Rise time and Fall time The range of the pulse amplitude is determined from either the Minimum and Maximum parameters or the DC Bias and Peak Amplitude parameters. Example settings for each parameter set are shown in Figures 1 and 2. 229 NRZ PULSE GENERATOR Figure 1 Example settings for NRZ Pulse Generator with Input Bit Stream = [0101] (Min/Max) Max = 2.5 Min = ‐0.5 Figure 2 Example settings for NRZ Pulse Generator with Input Bit Stream = [0101] (DC Bias & Amplitude) Amplitude = 2 DC Bias = 1 Amplitude = 2 230 GAUSSIAN PULSE GENERATOR Gaussian Pulse Generator Generates an electrical Gaussian-pulsed signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ 0.5 bit [0,1] Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. Width FWHM of the pulse amplitude. 231 GAUSSIAN PULSE GENERATOR Name and description Default value Default unit Value range Position 0 bit 1 — [1,100] False — True, False Relative position of pulse stream (ratio of bit period). For example if Position = 0.5, the pulse stream is shifted by 50% of the bit period. When Position = 0, the center of the Gaussian pulse is located at the middle of the bit period (0.5) Order Order of the function Truncated Determines whether or not the pulses overlap with each other Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background This model generates Gaussian or super-Gaussian electrical pulses according to the bit sequence at the input. For each bit 2N 1 t.k – --- ---------------- 2 T FWHM E t = B. A p .e + A bias where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width TFWHM, and N is the Order of the Gaussian (N=1) or super-Gaussian pulses (N>1). 232 GAUSSIAN PULSE GENERATOR Figure 1 Example range settings for Gaussian Pulse Generator with Input Bit Stream = [1111] (Amplitude = 1, DC Bias = 0, Width = 0.25, Position = 0)) Amplitude = 1 DC Bias = 0 Width (0.25 bit) – Measured at FWHM Amplitude = 1 233 GAUSSIAN PULSE GENERATOR 234 HYPERBOLIC-SECANT PULSE GENERATOR Hyperbolic-Secant Pulse Generator Generates a hyperbolic-secant pulsed signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. 235 HYPERBOLIC-SECANT PULSE GENERATOR Name and description Default value Default unit Value range Width 0.5 bit [0,1] 0 bit False — True, False FWHM of the pulse amplitude Position Relative position of pulse stream (ratio of bit period). For example if Position = 0.5, the pulse stream is shifted by 50% of the bit period. When Position = 0, the center of the Gaussian pulse is located at the middle of the bit period (0.5) Truncated Defines whether or not the pulses overlap with each other Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background This model generates electrical pulses according to the bit sequence at the input. For each bit: t.k 2 E t = B. A p cosh ----------------- + A bias T FWHM where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM. 236 HYPERBOLIC-SECANT PULSE GENERATOR Figure 1 Example range settings for Hyperbolic-Secant Pulse Generator with Input Bit Stream = [1111] (Max = 1, Mi = 0, Width = 0.2, Position = 0)) Max = 1 Width (0.2 bit) – Measured at FWHM Min = 0 237 HYPERBOLIC-SECANT PULSE GENERATOR 238 SINE GENERATOR Sine Generator Generates an electrical sine waveform signal. Ports Name and description Port type Signal type Output Output Electrical Parameters Main Name and description Default value Default unit Units Value range Frequency 32 GHz Hz, MHz, GHz, THz ]0,+INF[ 1 a.u. — ]-INF,+INF[ 0 a.u. — ]-INF,+INF[ 0 deg — ]-INF,+INF[ Frequency simulation window Amplitude Amplitude of the pulse (with respect to DC Bias) Bias DC Offset of the pulse Phase Initial phase of the signal 239 SINE GENERATOR Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window Figure 1 Example settings for Sine Generator (Amplitude = 2, Bias = 0.5) Amplitude = 2 DC Bias = 0.5 240 TRIANGLE PULSE GENERATOR Triangle Pulse Generator Generates an electrical triangle-pulsed signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. 241 TRIANGLE PULSE GENERATOR Name and description Default value Default unit Value range Width 0.5 bit [0,1] 0 bit False — True, False FWHM of the pulse amplitude Position When Position = 0, the apex of the triangular pulse is centered at the middle of the bit period (0.5) If the Position is a non-zero value, the pulse stream will be shifted accordingly. For example if Position = 0.5, all the pulses in the stream will be shifted by 50% of the bit period Truncated Determines whether or not the pulses overlap with each other Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 242 TRIANGLE PULSE GENERATOR Figure 1 Example settings for Triangular Pulse Generator with Input Bit Stream = [1111] (Amplitude = 1, DC Bias = 1, Width = 0.5 bit & Position = 0.25 bit_ Amplitude = 1 DC Bias = 1 Width (0.5 bit) ‐ FWHM Position (0.25 bit) – Shift is applied to entire pulse stream 243 TRIANGLE PULSE GENERATOR 244 SAW-UP PULSE GENERATOR Saw-Up Pulse Generator Generates a saw-up signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. 245 SAW-UP PULSE GENERATOR Name and description Default value Default unit Value range Width 0.5 bit [0,1] 0 bit [-1, 1] False — True, False Full width of pulse (ratio of bit period). Position When Position = 0, the half maximum rise point of the saw up pulse determines the center of the pulse and is positioned at the middle of the bit period (0.5) If the Position is a non-zero value, the pulse stream will be shifted accordingly. For example if Position = 0.5, all the pulses in the stream will be shifted by 50% of the bit period Truncated Determines whether or not the pulses overlap with each other Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 246 SAW-UP PULSE GENERATOR Figure 1 Example settings for Saw Up Pulse Generator with Input Bit Stream = [1111] (Amplitude = 1, DC Bias = 1, Width = 0.5 bit & Position = 0 bit) Amplitude = 1 DC Bias = 1 Width (0.5 bit) – Measured from base of pulse When Position = 0, the half maximum rise point of the saw up pulse determines the center of the pulse and is positioned at the middle of the bit period (0.5). If the Position is a non‐zero value, the pulse stream will be shifted accordingly. For example if Position = 0.5, all the pulses in the stream will be shifted by 50% of the bit period. In this example Position = 0. 247 SAW-UP PULSE GENERATOR 248 SAW-DOWN PULSE GENERATOR Saw-Down Pulse Generator Generates a saw-down pulsed signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. 249 SAW-DOWN PULSE GENERATOR Name and description Default value Default unit Value range Width 0.5 bit [0,1] 0 bit [-1, 1] False — True, False Full width of pulse (ratio of bit period). Position When Position = 0, the half maximum rise point of the saw up pulse determines the center of the pulse and is positioned at the middle of the bit period (0.5) If the Position is a non-zero value, the pulse stream will be shifted accordingly. For example if Position = 0.5, all the pulses in the stream will be shifted by 50% of the bit period Truncated Determines whether or not the pulses overlap with each other Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 250 SAW-DOWN PULSE GENERATOR Figure 1 Example settings for Saw Down Pulse Generator with Input Bit Stream = [1111] (Amplitude = 1, DC Bias = 1, Width = 0.5 bit & Position = 0 bit) Amplitude = 1 DC Bias = 1 Width (0.5 bit) – Measured from base of pulse When Position = 0, the half maximum fall point of the saw down pulse determines the center of the pulse and is positioned at the middle of the bit period (0.5). If the Position is a non‐zero value, the pulse stream will be shifted accordingly. For example if Position = 0.5, all the pulses in the stream will be shifted by 50% of the bit period. In this example Position = 0. 251 SAW-DOWN PULSE GENERATOR 252 IMPULSE GENERATOR Impulse Generator Generates an electrical signal composed by a sequence of Impulses. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. 253 IMPULSE GENERATOR Name and description Default value Default unit Value range Amplitude (wrt DC) 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ 0.5 bit [0,1] Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. Position When Position = 0, the impulse is set to the last sampled data point for the bit period If the Position is a non-zero value, the pulse stream will be shifted accordingly. For example if Position = 0.5, all the pulses in the stream will be shifted by 50% of the bit period. Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 254 IMPULSE GENERATOR Figure 1 Example settings for Impulse Generator with Input Bit Stream = [1111] (Max = 1, Min = 0, Position = 0 bit) Max = 1 The impulse is set as the last sampled data point for the bit period (when Bit = “On” and Position = 0) Min = 0 255 IMPULSE GENERATOR 256 RAISED COSINE PULSE GENERATOR Raised Cosine Pulse Generator Generates a raised-cosine pulsed signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ 0.5 bit [0,1] Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. Width FWHM of the pulse amplitude 257 RAISED COSINE PULSE GENERATOR Name and description Default value Default unit Position 0 bit Value range Relative position of pulse stream (ratio of bit period). For example if Position = 0.5, the pulse stream is shifted by 50% of the bit period. When Position = 0, the center of the Raised Cosine pulse is set to the beginning of the bit period where Bit = “On” Truncation length Samples per bit * Sequence length Roll off factor 1 Square root False — [0,1] True, False Simulation Name and description Default value Default unit Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background This model generates electrical pulses according to the bit sequence at the input. For each bit: t.k 2 E t = B. A p . cos ----------------- + A bias T FWHM where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM. 258 RAISED COSINE PULSE GENERATOR Figure 1 Example settings for Raised Cosine Pulse Generator (Max = 1, Min = 0, Width = 0.2, Position = 0, Truncation length = 2048) Max = 1 Bit sequence: 00000000000000000100000000000000 Truncation length = 2048, Width (FWHM) = 0.2 Min = 0 259 RAISED COSINE PULSE GENERATOR 260 SINE PULSE GENERATOR Sine Pulse Generator Generates a sine-pulsed signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. DC bias DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. 261 SINE PULSE GENERATOR Name and description Default value Default unit Value range Width 0.5 bit [0,1] 0 bit False — True, False FWHM of the pulse amplitude Position Relative position of pulse stream (ratio of bit period). For example if Position = 0.5, the pulse stream is shifted by 50% of the bit period. When Position = 0, the center of the Sine pulse is located at the middle of the bit period (0.5) Truncated Determines whether or not the pulses overlap with each other Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background This model generates electrical pulses according to the bit sequence at the input. For each bit: t.k E t = B. A p . cos ----------------- + A bias T FWHM where Ap is the parameter peak-to-peak Amplitude, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient numerically determinate to generate pulses with the exact values of the parameter Width TFWHM. 262 SINE PULSE GENERATOR Figure 1 Example settings for Sine Pulse Generator with Input Bit Stream = [1111] (Max = 1, Min = 0, Width = 0.5, Position = 0 bit) Max = 1 Width (0.5 bit) – Measured at FWHM Min = 0 263 SINE PULSE GENERATOR 264 MEASURED PULSE Measured Pulse Generates an electrical pulse based on measurements according to the bit sequence at the input port. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Format for pulse range Min/Max — Min/Max, DC Bias/Peak Amplitude a.u. ]-INF,+INF[ Determines whether to use “Min/Max” values or “DC Bias/Amplitude” Maximum 1 Maximum value of the pulse. Used when Format for pulse range = “Min/Max”. Minimum 0 Minimum value of the pulse. Used when Format for pulse range = “Min/Max”. Amplitude (wrt DC) 1 Amplitude of the pulse (relative to DC bias). Used when Format for pulse range = “DC Bias/Amplitude”. 265 MEASURED PULSE Name and description Default value Default unit Value range DC bias 0 a.u. ]-INF,+INF[ 0 bit Pulse.dat — — Name and description Default value Units Value range Interpolation Linear — Linear, Cubic DC offset of the pulse. Used when Format for pulse range = “DC Bias/Amplitude”. Position Relative position of start of pulse (ratio of bit period). For example if Position = 0.5, the pulse stream is shifted by 50% of the bit period Filename Filename with the measured data (must contain a minimum of 5 time-amplitude data samples Numerical Determines the interpolation algorithm for the measured data Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Graphs Name and description X Title Y Title Measured data Time period (a.u.) Amplitude (a.u.) 266 MEASURED PULSE Technical background This model generates electrical signal loading measurements from a file. The input file is formatted containing two values per line, the time in seconds and signal amplitude in arbitrary units. The time scale is normalized to fit in one bit period - the duration of the pulse. For example, the file representing one measurement has the following form: 0 0 1e-6 0.5 2e-6 0.5 3e-6 0 ... Note: The measurement file must contain a minimum of 5 data samples to be successfully loaded into the Measured Pulse component. 267 MEASURED PULSE 268 MEASURED PULSE SEQUENCE Measured Pulse Sequence Generates an electrical signal based on measurements. Ports Name and description Port type Signal type Output Output Electrical Parameters Main Name and description Default value Default unit Value range Scale 1 a.u. ]-INF,+INF[ 0 s [0,+INF[ Sequence.dat — — Name and description Default value Units Value range Interpolation Linear — Linear, Cubic Factor to scale the signal amplitude Start time Initial part of the signal to be skipped Filename Filename with the measured data Numerical Determines the interpolation algorithm for the measured data 269 MEASURED PULSE SEQUENCE Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window Graphs Name and description X Title Y Title Measured data Time (s) Amplitude (a.u.) Technical background This model generates electrical signal loading measurements from a file. The input file is formatted containing two values per line, the time in seconds and signal amplitude in arbitrary units. For example, the file representing one measurement has the following form: 0 0 1e-6 0.5 2e-6 0.5 3e-6 0 ... 270 BIAS GENERATOR Bias Generator A d.c. source. Ports Name and description Port type Signal type Output Output Electrical Parameters Main Name and description Default value Units Value range Amplitude 1 a.u. ]-INF,+INF[ Amplitude of the signal output Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window 271 BIAS GENERATOR Notes: 272 M-ARY PULSE GENERATOR M-ary Pulse Generator Generates multilevel pulses according to the M-ary signal input. Ports Name and description Port type Signal type Input Input M-ary Output Output Electrical Parameters Main Name and description Default value Gain 0 Units Value range ]-INF,+INF[ Linear gain to be applied to the signal input Bias 1 a.u. ]-INF,+INF[ DC Offset of the pulse Duty cycle 1 [0,1] 0 [0,1] Ratio of pulse width (signal is active) to symbol period. For example if Duty cycle = 0.5, the signal is active for the first 50% of the symbol period Position Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period Rise time 0.05 bit Fall time 0.05 bit 273 M-ARY PULSE GENERATOR Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 274 M-ARY PULSE GENERATOR Technical background This model generates pulses according to: b 0 t t 1 v out t = av in t + b t 1 t t 1 + t c b t 1 + t c t T where v in is the input M-ary signal, a is the linear gain, and b is the parameter Bias. T is the bit period, t c is the duty cycle, and t 1 is the pulse position. 275 M-ARY PULSE GENERATOR 276 M-ARY RAISED COSINE PULSE GENERATOR M-ary Raised Cosine Pulse Generator Generates multilevel raised cosine pulses according to the M-ary signal input. Ports Name and description Port type Signal type Input Input M-ary Output Output Electrical Parameters Main Name and description Default value Gain 0 Units Value range ]-INF,+INF[ Linear gain to be applied to the signal input Bias 1 a.u. ]-INF,+INF[ DC offset of the pulse Width 1 [0,1] 0 [0,1] Ratio of pulse width (signal is active) to symbol period. For example if Duty cycle = 0.5, the signal is active for 50% of the symbol period Position Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period Truncation length Samples per bit * Sequence length Roll off factor 1 [0,1] False True, False The raised cosine roll off factor Square root Determines whether or not the square root is enabled 277 M-ARY RAISED COSINE PULSE GENERATOR Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background This model generates pulses according to: b 0 t t 1 v out t = ah t + b t 1 t t 1 + w b t 1 + w t T where v in is the input M-ary signal, a is the linear gain, and b is the parameter Bias. T is the bit period, w is the pulse width, and t 1 is the pulse position. h is given by: sin t ----- cos t --------- T T - h t = -----------------------------------------2 2t t - 1 – -------- --- T T If parameter Square root is enable, h is given by: t sin ----- 1 + T t cos ----- 1 + + ------------------------------------T 4t --------T h t = 4 --------------------------------------------------------------------------------2 4t T 1 – --------- T 278 PREDISTORTION Predistortion Apply predistortion to electrical signals. The component can inversely model an optical modulator's amplitude and phase characteristics. Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Main Name and description Default value Predistortion Arcsin Units Arcsin, Polynomial Predistortion type Coefficients 1 Value range a.u. ]-INF,+INF[ Coefficients for Polynomial predistortion type Gain 1 ]-INF,+INF[ Linear gain to be applied to the signal Bias 0 a.u. ]-INF,+INF[ DC Offset of the signal Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Determines whether or not the component is enabled 279 PREDISTORTION Technical background If parameter Predistortion is Arcsin, the function applied to the input signal is: 1 v out t = --- arc sin v in t a + b where v in is the input signal, a is the linear gain, and b is the bias. If parameter Predistortion is Polynomial, the function applied to the input signal is: v out t = c 0 + c 1 v in t + c 2 v t where 280 N 2 in + + c N v t in a + b c i is the polynomial coefficient of index i. PAM PULSE GENERATOR PAM Pulse Generator Generates a M-ary electrical signal from binary signals using pulse amplitude modulation (PAM). Ports Name and description Port type Signal type Bit sequence Input Binary PAM Pulses Output Electrical Parameters Main Name and description Default value Units Value range Bits per symbol 2 [0,100] 1 [0,1] 0 [0,1] False True, False False True, False Number of bits per symbol used in the coding Duty cycle Ratio of pulse width (signal is active) to symbol period. For example if Duty cycle = 0.5, the signal is active for 50% of the symbol period Position Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period Gray code Defines whether or not to use Gray code User-defined PAM map Defines whether to calculate PAM values based on user-defined values PAM amplitudes (a.u.) 4x2 PAM amplitudes file name PAM_IQ.dat Name of file that contains initial PAM values 281 PAM PULSE GENERATOR Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background When transmitting information, we can vary the amplitude of a signal according to the source symbols. The amplitude values are taken from the set of amplitudes [1]: a i = 2i – 1 – M i = 1 2 ...M where to: M is the number of possible sequences of binary digits, calculated according M = 2 where h h is the number of bits per symbol. Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. This model generates pulses according to: v k – out 0 0 t t 1 = a k t 1 t t 1 + t c 0 t 1 + t c t T where a k is the amplitude of the signal and t 1 is the pulse position. k , T is the bit period, t c is the duty cycle, Figure 1 shows the block diagram of this component. 282 PAM PULSE GENERATOR Figure 1 PAM Pulse Generator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 283 PAM PULSE GENERATOR 284 QAM PULSE GENERATOR QAM Pulse Generator Generates two parallel M-ary electrical signals from binary signals using quadrature amplitude modulation (QAM). Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output Electrical Output - Q Output Electrical Parameters Main Name and description Default value Units Value range Bits per symbol 2 [0,100] 1 [0,1] 0 [0,1] False True, False Number of bits per symbol used in the coding Duty cycle Ratio of pulse width (signal is active) to symbol period. For example if Duty cycle = 0.5, the signal is active for 50% of the symbol period Position Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period Gray code Defines whether or not to use Gray code 285 QAM PULSE GENERATOR Name and description Default value User-defined I-Q map False Units Value range True, False Defines whether to calculate IQ values based on user-defined values I-Q amplitudes (a.u.) 64x3 I-Q amplitudes file name QAM_IQ.dat Name of file that contains initial I-Q values Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background With the QAM sequence generator, the bit sequence is split into two parallel subsequences, each transmitted in two quadrature carriers when building a QAM modulator. This is done by using a serial to parallel converter. When transmitting information, we can vary the amplitude of a signal according to the source symbols. For each output port, the value of the amplitude takes value from the set of amplitudes [1] a 1 = 2i – 1 – M i = 1 2 ..., M where M is the number of possible sequence of binary digits, calculated according to: M = 2 h2 where h is the number of bits per symbol. The equivalent QAM set is given by the square of M . This means: If h = QAM. 2 , M = 2 , then we have a 4-QAM. If h = 4 , M = 4 , then we have a 16- If h = 6 , 256-QAM. 286 M = 8 , then we have a 64-QAM. If h = 8 , M = 16 , then we have a QAM PULSE GENERATOR Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. This model generates pulses according to : 0 0 t t 1 v k – out t = a k t 1 t t 1 + t c 0 t 1 + t c t T where a k is the amplitude of the signal and t 1 is the pulse position. k , T is the bit period, t c is the duty cycle, Figure 1 represents the block diagram of this component. Figure 1 QAM Pulse Generator block diagram 287 QAM PULSE GENERATOR References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 288 PSK PULSE GENERATOR PSK Pulse Generator Generates two parallel M-ary electrical signals from binary signals using phase shift keying modulation (PSK). Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output Electrical Output - Q Output Electrical Parameters Main Name and description Default value Bits per symbol 2 Units Value range [0,100] Number of bits per symbol used in the coding Phase offset 45 deg, rad ]-INF,+INF[ Initial phase offset Gray code False True, False Defines whether or not to use Gray code Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 289 PSK PULSE GENERATOR Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1]: 2 i = ------ i – 1 + i = 1 2 ...M M where M is the number of possible sequence of binary digits, calculated according to: M = 2 h where h is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to: I i = cos i i = 1 2 ...M Q i = sin i i = 1 2 ...M Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. This model generates pulses according to: I k – out t = I k 0 t T Q k – out t = Q k 0 t T where I k and Q k are the amplitudes of the output signals k and T is the bit period. Figure 1 shows the block diagram of this component. Figure 1 PSK Pulse Generator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 290 DPSK PULSE GENERATOR DPSK Pulse Generator Generates two parallel M-ary electrical signals from binary signals using differential phase shift keying modulation (DPSK). Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output Electrical Output - Q Output Electrical Parameters Main Name and description Default value Bits per symbol 2 Units Value range [0,100] Number of bits per symbol used in the coding Phase offset 45 deg, rad ]-INF,+INF[ Initial phase offset Gray code False True, False Defines whether or not to use Gray code Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window 291 DPSK PULSE GENERATOR Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1], [2]: 2 ki = k – 1 + ------ i – 1 + i = 1 2 ...M M where ki is the phase value for the current symbol, and k – 1 is the phase value for the previous symbol. M is the number of possible sequence of binary digits, calculated according to: M = 2 h where h is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to: I ki = cos ki i = 1 2 ...M Q ki = sin ki i = 1 2 ...M This model generates pulses according to: I k – out t = I k 0 t T Q k – out t = Q k 0 t T where I k period. and Q k are the amplitudes of the output signals k and T is the bit Figure 1 shows the block diagram of this component. Figure 1 DPSK Pulse Generator block diagram 292 DPSK PULSE GENERATOR References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] Pawula, R.F., “On M-ary DPSK Transmission Over Terrestrial and Satellite Channels”, IEEE Trans. on Commun. COM-32, 752-761, (July 1984). 293 DPSK PULSE GENERATOR 294 OQPSK PULSE GENERATOR OQPSK Pulse Generator Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output Electrical Output - Q Output Electrical Parameters Main Name and description Default value Units Value range Phase offset Initial phase offset 45 deg, rad ]-INF,+INF[ Gray code Defines whether or not to use Gray code False True, False Simulation Name and description Default value Default units Unit Value range Enabled Determines whether or not the component is enabled True — — True, False Sample rate Frequency simulation window Sample rate Hz Hz, GHz, THz ]0,+INF[ 295 OQPSK PULSE GENERATOR Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values take the values in the set of angles [1]: 2 i = ------ i – 1 + i = 1 2 ...M M where M is the number of possible sequence of binary digits, when using quadrature phase shift keying (QPSK), this number is equal to 4, and is the phase offset. A reduction of the signal fluctuations is possible by delaying the Q channel by one bit period. The bit period is calculated from the input binary signal. The in-phase and the quadrature-channel will have amplitudes according to: I i = cos i i = 1 2 ...M Q i = sin i i = 1 2 ...M Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. This model generates pulses according to: I k – out t = I k 0 t T Q k – out t = Q k Ts t T + Ts where k is the amplitude of the signal I , T is the bit period, and Ts is the input bit period. Figure 1 shows the block diagram of this component. Figure 1 OQPSK Pulse Generator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 296 MSK PULSE GENERATOR MSK Pulse Generator Generates two parallel M-ary symbol sequences from binary signals using minimum shift keying modulation (MSK). Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output Electrical Output - Q Output Electrical Parameters Main Name and description Default value Units Value range Phase offset Initial phase offset 45 deg, rad ]-INF,+INF[ Gray code Defines whether or not to use Gray code False True, False Simulation Name and description Default value Default units Unit Value range Enabled Determines whether or not the component is enabled True — — True, False Sample rate Frequency simulation window Sample rate Hz Hz, GHz, THz ]0,+INF[ 297 MSK PULSE GENERATOR Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values take the values in the set of angles []: 2 i = ------ i – 1 + i = 1 2 ...M M where M is the number of possible sequence of binary digits, when using quadrature phase shift keying (QPSK), this number is equal to 4, and is the phase offset. A reduction of the signal fluctuations is possible by delaying the Q channel by one bit period. The bit period is calculated from the input binary signal. The MSK is a special case of OQPSK in which a sinusoidal pulse replaces the rectangular waveform. The in-phase and the quadrature-channel will have amplitudes according to: I i = cos i i = 1 2 ...M Q i = sin i i = 1 2 ...M Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. This model generates pulses according to: t I k – out t = I k sin --------- 0 t T 2Ts t Q k – out t = Q k cos --------- Ts t T + Ts 2Ts where k is the amplitude of the signal I , T is the bit period, and Ts is the input bit period. Figure 1 shows the block diagram of this component. 298 MSK PULSE GENERATOR Figure 1 MSK Pulse Generator block diagram 299 MSK PULSE GENERATOR References Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 300 MSK PULSE GENERATOR Transmitters Library - Electrical Electrical Modulators • Electrical Amplitude Modulator (AM) • Electrical Frequency Modulator (FM) • Electrical Phase Modulator (PM) • Quadrature Modulator • PAM Modulator • QAM Modulator • PSK Modulator • DPSK Modulator • OQPSK Modulator • MSK Modulator • FSK Modulator • CPFSK Modulator • OFDM Modulation (OS12) • OFDM Modulator Measured • OFDM Modulation • Burst Modulator 301 MSK PULSE GENERATOR Notes: 302 ELECTRICAL AMPLITUDE MODULATOR (AM) Electrical Amplitude Modulator (AM) Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 1 a.u. ]-INF,+INF[ Frequency of the input signal carrier Bias DC Offset of the pulse Gain 1 ]-INF,+INF[ Linear gain to be applied to the signal input Phase 0 deg,rad ]-INF,+INF[ Phase of the input signal carrier Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled 303 ELECTRICAL AMPLITUDE MODULATOR (AM) Technical background The Electrical Amplitude Modulator implements an analog amplitude modulator. The output signal is modulated according to: v out t = Gv in t cos 2f c t + c + b v in is the input electrical signal, G is the parameter gain, b is the bias, f c is the carrier frequency, and c is the phase of the carrier. where Figure 1 shows the block diagram of this component. Figure 1 Electrical Amplitude Modulator block diagram 304 ELECTRICAL FREQUENCY MODULATOR (FM) Electrical Frequency Modulator (FM) Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 1 a.u. ]-INF,+INF[ 1 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ 1 Hz, kHz, Mhz, GHz ]-INF,+INF[ Frequency of the input signal carrier Amplitude Peak-to-peak amplitude of the pulse Bias DC Offset of the pulse Phase Phase of the input signal carrier Modulation constant Frequency change relative to the input signal amplitude Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled 305 ELECTRICAL FREQUENCY MODULATOR (FM) Technical background The Electrical Frequency Modulator implements an analog frequency modulator. The output signal is modulated according to: v out t = A cos 2 f c t + 2 m v in t dt + c + b v in is the input electrical signal, m is the modulation constant, A is the parameter Amplitude, b is the Bias, f c is the carrier frequency, and c is the where phase of the carrier. 306 ELECTRICAL PHASE MODULATOR (PM) Electrical Phase Modulator (PM) Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 1 a.u. ]-INF,+INF[ 1 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ 1 deg, rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Peak-to-peak amplitude of the pulse Bias DC Offset of the pulse Phase Phase of the input signal carrier Modulation constant Phase change relative to the input signal amplitude Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled 307 ELECTRICAL PHASE MODULATOR (PM) Technical background The Electrical Phase Modulator implements an analog phase modulator. The output signal is modulated according to: v out t = A cos 2f c t + mv in t + c + b v in is the input electrical signal, m is the modulation constant, A is the parameter Amplitude, b is the Bias, f c is the carrier frequency, and c is the phase where of the carrier. 308 QUADRATURE MODULATOR Quadrature Modulator Ports Name and description Port type Signal type Input-I Input Electrical Input-Q Input Electrical Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 1 a.u. ]-INF,+INF[ Frequency of the input signal carrier Bias DC Offset of the pulse Gain 1 ]-INF,+INF[ Linear gain to be applied to the signal input Phase 0 deg,rad ]-INF,+INF[ Phase of the input signal carrier Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled 309 QUADRATURE MODULATOR Technical background The Quadrature Modulator implements a quadrature analog amplitude modulator. The output signal is modulated according to: v out t = G I t cos 2f c t + c – Q t sin 2f c t + c + b where I and Q are the input electrical signals, G is the parameter Gain, Bias, f c is the carrier frequency, and c is the phase of the carrier. b is the Figure 1 shows the block diagram of this component. Figure 1 Quadrature Modulator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 310 PAM MODULATOR PAM Modulator Encodes and modulates binary signal to an electrical signal using pulse amplitude modulation (PAM). Ports Name and description Port type Signal type Bit Sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ Amplitude 1 a.u. ]-INF,+INF[ Bias 1 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ Frequency of the input signal carrier DC Offset of the pulse Phase Phase of the input signal carrier Bits per symbol 2 [0,100] 0.5 [0,1] 0 [0,1] Number of bits per symbol used in the coding Duty cycle Ratio of pulse width (signal is active) to symbol period. For example if Duty cycle = 0.5, the signal is active for the first 50% of the symbol period Position Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period 311 PAM MODULATOR Name and description Default value Default unit Value range Gray code False True, False False True, False Defines whether or not to use Gray code User-defined PAM map Defines whether to calculate PAM values based on user-defined values PAM amplitudes (a.u.) 4x2 PAM amplitudes file name PAM_IQ.dat Name of file that contains initial PAM values Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background The PAM Modulator implements a PAM modulator [1]. Figure 1 shows a block diagram of the component. Figure 1 PAM Modulator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 312 QAM MODULATOR QAM Modulator Encodes and modulates a binary signal to an electrical signal using quadrature amplitude modulation (QAM). Ports Name and description Port type Signal type Bit Sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Bias DC Offset of the pulse Phase Phase of the input signal carrier Bits per symbol 2 [0,100] 0.5 [0,1] 0 [0,1] Number of bits per symbol used in the coding Duty cycle Ratio of pulse width (signal is active) to symbol period. For example if Duty cycle = 0.5, the signal is active for the first 50% of the symbol period Position Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period 313 QAM MODULATOR Name and description Default value Default unit Value range Gray code False True, False False True, False Defines whether or not to use Gray code User-defined I-Q map Defines whether to calculate IQ values based on user-defined values I-Q amplitudes (a.u.) 64x3 I-Q amplitudes file name QAM_IQ.dat Name of file that contains initial I-Q values Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background The QAM Modulator implements a QAM Modulator [1]. Figure 1 shows a block diagram of this component. Figure 1 QAM Modulator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 314 PSK MODULATOR PSK Modulator Encodes and modulates a binary signal to an electrical signal using phase shift keying modulation (PSK). Ports Name and description Port type Signal type Bit Sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Bias DC Offset of the pulse Phase Phase of the input signal carrier Bits per symbol 2 [0,100] Number of bits per symbol used in the coding Phase offset 45 deg, rad ]-INF,+INF[ Defines whether to use Gray coding or not Gray code False True, False Defines whether or not to use Gray code 315 PSK MODULATOR Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background The PSK Modulator implements a PSK modulator [1]. Figure 1 shows a block diagram of this component. Figure 1 PSK Modulator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 316 DPSK MODULATOR DPSK Modulator Encodes and modulates a binary signal to an electrical signal using differential phase shift keying modulation (DPSK). Ports Name and description Port type Signal type Bit Sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Bias DC Offset of the pulse Phase Phase of the input signal carrier Bits per symbol 2 [0,100] Number of bits per symbol used in the coding 317 DPSK MODULATOR Name and description Default value Default unit Value range Phase offset 45 deg, rad ]-INF,+INF[ Defines whether to use Gray coding or not Position 0 [0,1] False True, False Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period Gray code Defines whether or not to use Gray code Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background Figure 1 shows a block diagram of the DPSK modulator [1]: Figure 1 DPSK Modulator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 318 OQPSK MODULATOR OQPSK Modulator Encodes and modulates a binary signal to an electrical signal using offset quadrature phase shift keying modulation (OQPSK). Ports Name and description Port type Signal type Bit Sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ 45 deg, rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Bias DC Offset of the pulse Phase Phase of the input signal carrier Phase offset Defines whether to use Gray coding or not Gray code False True, False Defines whether or not to use Gray code 319 OQPSK MODULATOR Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background Figure 1 shows a block diagram of the OQPSK modulator [1]: Figure 1 OQPSK Modulator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 320 MSK MODULATOR MSK Modulator Encodes and modulates a binary signal to an electrical signal using minimum shift keying modulation (MSK). Ports Name and description Port type Signal type Bit Sequence Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ 45 deg, rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Bias DC Offset of the pulse Phase Phase of the input signal carrier Phase offset Defines whether to use Gray coding or not Gray code False True, False Defines whether or not to use Gray code 321 MSK MODULATOR Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background Figure 1 shows a block diagram of the MSK modulator [1]: Figure 1 MSK Modulator block diagram References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 322 FSK MODULATOR FSK Modulator Encodes and modulates a binary signal to an electrical signal using frequency shift keying modulation (FSK). Ports Name and description Port type Signal type Input Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Bias DC Offset of the pulse Phase Phase of the input signal carrier Bits per symbol 2 [0,100] Number of bits per symbol used in the coding Frequency separation 1 Frequency separation between symbols Gray code False Hz, MHz, GHz, THz [0,+INF[ True, False Defines whether or not to use Gray code 323 FSK MODULATOR Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background The FSK Modulator implements a FSK modulator [1]. When transmitting information, we can vary the frequency of a signal according to the source symbols. The frequency values takes information from the set of amplitudes [1]: a i = f s 2i – 1 – M i = 1 2 ...M where f s is the frequency separation, binary digits, calculated according to: M = 2 where M is the number of possible sequences of h h is the number of bits per symbol. v out t = A cos 2f c t + 2a i + c + b where A is the parameter amplitude, c is the phase of the carrier. b is the bias, f c is the carrier frequency, and References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 324 CPFSK MODULATOR CPFSK Modulator Encodes and modulates a binary signal to an electrical signal using continuous phase frequency shift keying modulation (CPFSK). Ports Name and description Port type Signal type Input Input Binary Output Output Electrical Parameters Main Name and description Default value Default unit Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 a.u. ]-INF,+INF[ 0 deg,rad ]-INF,+INF[ Frequency of the input signal carrier Amplitude Bias DC Offset of the pulse Phase Phase of the input signal carrier Bits per symbol 2 [0,100] Number of bits per symbol used in the coding 325 CPFSK MODULATOR Name and description Default value Default unit Value range Frequency separation 1 Hz, MHz, GHz, THz [0,+INF[ Frequency separation between symbols Position 0 [0,1] False True, False Relative position of start of pulse (ratio of symbol period). For example if Position = 0.5, the entire pulse stream is shifted by 50% of a symbol period Gray code Defines whether or not to use Gray code Simulation Name and description Default value Default units Unit Value range Enabled True — — True, False Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Sample rate Frequency simulation window Technical background The CPFSK Modulator implements a CPFSK modulator [1]. When transmitting information, we can vary the frequency of a signal according to the source symbols. The frequency values takes information from the set of amplitudes [1]: a i = f s 2i – 1 – M i = 1 2 ...M where f s is the frequency separation, binary digits, calculated according to: M = 2 where M is the number of possible sequences of h h is the number of bits per symbol. v out t = A cos 2f c t + 2a i + c + b where A is the parameter amplitude, c is the phase of the carrier. b is the bias, f c is the carrier frequency, and In this model, because the phase transitions are constant, a single oscillator with a modulated frequency modulated is used. The absence of abrupt phase transitions results in a narrower spectrum. 326 CPFSK MODULATOR References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987) 327 CPFSK MODULATOR 328 OFDM MODULATION (OS12) OFDM Modulation (OS12) This component modulates a digital signal into multiple orthogonal sub-carriers. Ports Name and description Port type Signal type Input - I 1 Input M-ary Input - Q 1 Input M-ary Output - I Output Electrical Output - Q Output Electrical Parameters Main Name and description Default value Default unit Value range Number of input ports 1 - [1,1000] 4 - [1,100e6] False - True, False 0 - [0,100e6] 64 - [1,100e6] Define the number of Users for the OFDM modulator Number of subcarriers Number of subcarriers used for transmission by each user User defined position If True each user can define the position of its initial subcarrier Position array Array containing the initial subcarrier positions for each user Number of IFFT points Number of points used in the IFFT 329 OFDM MODULATION (OS12) Name and description Default value Default unit Value range Symmetric spectrum False - True, False Symbol extension - Symbol extension, Zero values 0 - [0,100e6] Defines if the input vector to the IFFT is constrained to have hermetian symmetry Cyclic prefix Defines which guard period will be used Number of prefix points Defines the number of points used in the guard period DAC Name and description Default value Default units Unit Value range Interpolation Cubic - - Linear, Cubic, Step False - - True, False Name and description Default value Default units Unit Value range Sample rate Sample rate Hz Hz, GHz, THz [0,+INF[ True - - True, False Defines the type of interpolation that will be used Smoothing filter Determines whether or not the smoothing filter is enabled Simulation Frequency simulation window Enabled Determines whether or not the component is enabled Graphs Name and description X Title Y Title OFDM FFT Frequency (Hz) Amplitude (a.u.) Technical background Orthogonal Frequency Division Multiplexing [1] is a multi-carrier transmission technique, which divides the available spectrum into many carriers, each one being modulated by a low rate data stream. The following diagram describes the different parts of the OFDM modulator component. 330 OFDM MODULATION (OS12) Figure 1 OFDM modulator diagram The input data can be in different modulations formats, for example: BPSK, QPSK, QAM, etc. This input serial symbol stream is shifted into a parallel format. Then the data is transmitted in parallel by assigning each symbol to one carrier in the transmission. After mapping the spectrum, an inverse Fourier transform is used to find the corresponding time waveform. The cyclic prefix (guard period) can then be added to start each symbol. The component allows the introduction of a cyclic extension of the symbol transmitted or a guard time with zero transmission. The parameter Number of prefix points will define how many points will be used in the guard period. Different interpolation techniques (Step, Linear, and Cubic) can be used to function as the digital-to-analog converter. After the DAC, the parallel data is shifted back into the serial symbol stream. An internal smoothing filer is applied depending on whether the parameter “Smoothing filter” is enabled or not. The figure below presents an example of OFDM transmitter using the OFDM modulator. 331 OFDM MODULATION (OS12) Figure 2 OFDM transmitter - System configuration Figure 2 shows the coding of 10 Gbps data to 4-QAM symbols. The 4-QAM symbols are then mapped to 4 subcarriers defined in the OFDM modulator. Finally, I and Q generated analog waveforms are converted to real-valued waveforms by mixing with a RF carrier. In this example, the OFDM modulator presents the following parameters: Number of users = 1; Number of subcarriers = 4; Initial Position of the subcarriers in the spectrum = 17; Number of IFFT points = 32; Number of prefix points = 0; The subcarrier frequencies are integer multiples of 1/Tsymbol, where Tsymbol is the duration of an OFDM symbol, and in this case the frequency is 1.25 GHz. Since the initial position defined by the OFDM modulator is 17 (position “Number of IFFT points / 2 = 16“ stands for a subcarrier frequency of 0), the initial subcarrier will be allocated at 1.25 GHz, and the subsequent subcarriers will be at 2.5 GHz, 3.75 GHz, and 5 GHz, respectively. The allocation of subcarriers, as shown in Figure 3, can also be visualized from the “Graphs“ property of OFDM Modulator in project browser. Figure 4 shows the spectrum of the In-phase signal at the OFDM output as well as the upconverted OFDM signal spectrum. 332 OFDM MODULATION (OS12) Figure 3 Allocation of OFDM subcarriers Figure 4 (a) OFDM output (In-phase) (b) Up-converted OFDM output (a) (b) The time-domain In-phase signal at the OFDM output is shown in Figure 5, with “Interpolation” set to Step, Linear, and Cubic, respectively. 333 OFDM MODULATION (OS12) Figure 5 OFDM time-domain output (In-phase) with “Interpolation” set to (a) Step, (b) Linear, and (c) Cubic, respectively. (a) (b) (c) In the simulation results presented above, no guard period was added to the simulation. In the next simulation, the OFDM transmitter used was the same as presented above, however, different guard periods (no guard period, symbol extension with 16 points, and zero transmission guard time with 16 points) were added to the OFDM symbol. The time-domain In-phase signal at the OFDM output is presented in Figure 6. BER Analysis When performing the BER analysis of OFDM systems it is important to consider that when prefixes are added by the OFDM modulator, the time window (or sequence length) of the simulation is temporarily extended beyond that defined by the global parameter settings. When the same prefixes are then removed at the OFDM demodualtion stage, the original sequence length is re-established, however a portion of the information from the original data stream is lost. To avoid including this portion of the bit stream within the BER calculation it is required to ignore a certain portion of the trailing bits from the orginal bit sequence. Within the BER Analyzer this can be set within the parameter Ignore end bits using the following formula: n FFT S Bits ignore = S – int -------------------------------------------------------------------------------- n Sub Bits Sym n Sub Bits Sym n FFT + n Prefix where S is the Sequence length, nFFT is the number of FFT points, nSub is the number of subcarriers, and nPrefix is the number of prefix points 334 OFDM MODULATION (OS12) Figure 6 Time-domain In-phase signal at the OFDM output with different type of guard periods No guard period Symbol extension guard period Zero transmission guard period 335 OFDM MODULATION (OS12) References [1] Armstrong, J. , “OFDM for Optical Communications”, J. Lightwave Technology, vol. 27, pp. 189204, Feb 2009. 336 OFDM MODULATOR MEASURED OFDM Modulator Measured This is an OFDM Modulator Measured component which modulates a digital signal into multiple orthogonal sub-carriers. Ports Name and description Port type Signal type Supported Modes Input - I 1 Input M-Ary - Input - Q 1 Input M-Ary - Output - I Output Electrical - Output - Q Output Electrical - Parameters Main Name and description Default value Default unit Units Value range Maximum possible sub-carriers 64 - - - False - - [True, False] Symbol extension - - Symbol extension, Zero values 0 - - [ 0, 1e+008 ] Table with the subcarrier index data Symmetric spectrum Defines if the input vector to the IFFT is constrained to have hermetian symmetry Cyclic prefix Defines which guard period will be used Number of prefix points Defines the number of points used in the guard period 337 OFDM MODULATOR MEASURED DAC Name and description Default value Default unit Units Value range Interpolation Cubic - - Linear, Cubic, Step False - - [True, False] Name and description Default value Default unit Units Value range Sample rate Sample rate Hz Hz, GHz, THz [ 1, 1e+100 ] True - - [True, False] Defines the type of interpolation that will be used Smoothing filter Determines whether or not the smoothing filter is enabled Simulation Frequency simulation window Enabled Determines whether or not the component is enabled Graphs Name and description X Title Y Title OFDM FFT Frequency (Hz) Amplitude (a.u.) 338 OFDM MODULATOR MEASURED Technical Background Orthogonal Frequency Division Multiplexing [1] is a multi-carrier transmission technique, which divides the available spectrum into many carriers, each one being modulated by a low rate data stream. The following diagram describes the different parts of the OFDM Modulator Measured component. Figure 1 OFDM modulator diagram The input data can be in different modulations formats, for example: BPSK, QPSK, QAM, etc. This input serial symbol stream is shifted into a parallel format. Then the data is transmitted in parallel by assigning each symbol to one carrier in the transmission. After mapping the spectrum, an inverse Fourier transform is used to find the corresponding time waveform. The cyclic prefix (guard period) can then be added to start each symbol. The component allows the introduction of a cyclic extension of the symbol transmitted or a guard time with zero transmission. The parameter Number of prefix points defines how many points will be used in the guard period. Different interpolation techniques (Step, Linear, and Cubic) can be used to function as the digital-to-analog converter. After the DAC, the parallel data is shifted back into the serial symbol stream. An internal smoothing filer is applied depending on whether the parameter “Smoothing filter” is enabled or not. The figure below presents an example of OFDM transmitter using the OFDM Modulator Measured. 339 OFDM MODULATOR MEASURED Figure 2 OFDM transmitter - System configuration Figure 2 shows the coding of 10 Gbps data to 4-QAM symbols. The 4-QAM symbols are then mapped to 4 subcarriers defined in the OFDM Modulator Measured. Finally, I and Q generated analog waveforms are converted to real-valued waveforms by mixing with a RF carrier. In this example, the Number of prefix points = 0, and the subcarrier information are defined by the parameter “Subcarrier index”, which uses a N x 1 table. The data in the tabel is visualized in Figure 3(a), with x-axis representing the row number of the table, and y-axis representing the values in the corresponding table cells. The table has 32 rows, which means “Number of IFFT points = 32“. For the table cell values, there are four “1”s (all other are “0”s), which means “Number of subcarriers = 4”. Once we know the number of subcarriers, we can calculate the subcarrier frequencies. The subcarrier frequencies are integer multiples of 1/Tsymbol, where Tsymbol is the duration of an OFDM symbol, and in this case the frequency is 1.25 GHz. For the position of subcarriers, the definition here is slightly different from the component “OFDM Modulator”. Since the numbering of rows starts from 1, not 0, here row number “Number of IFFT points / 2 + 1 = 17“ stands for a subcarrier frequency of 0. In the table, the value of the cells located at row 18, 19, 20, and 21 is “1”, so the subcarriers are located at 1.25 GHz, 2.5 GHz, 3.75 GHz, and 5 GHz, respectively. 340 OFDM MODULATOR MEASURED Figure 3 (a) Loaded table data (b) Allocation of OFDM subcarriers (a) (b) The allocation of subcarriers, as shown in Figure 3(b), can be visualized from the “Graphs“ property of OFDM Modulator Measured in project browser. Figure 4 shows the spectrum of the In-phase signal at the OFDM output as well as the up-converted OFDM signal spectrum. The time-domain In-phase signal at the OFDM output is shown in Figure 5, with “Interpolation” set to Step, Linear, and Cubic, respectively. 341 OFDM MODULATOR MEASURED Figure 4 (a) OFDM output (In-phase) (b) Up-converted OFDM output (a) (b) Figure 5 OFDM time-domain output (In-phase) with “Interpolation” set to (a) Step, (b) Linear, and (c) Cubic, respectively. (a) (b) (c) In the next simulation, the OFDM transmitter used was the same as presented before, however, different guard periods (no guard period, symbol extension with 16 points, and zero transmission guard time with 16 points) were added to the OFDM symbol. The time-domain In-phase signal at the OFDM output is presented in Figure 6. 342 OFDM MODULATOR MEASURED Figure 6 Time-domain In-phase signal at the OFDM output with different type of guard periods No guard period Symbol extension guard period Zero transmission guard period 343 OFDM MODULATOR MEASURED The format of the file for the loaded sub-carrier index data can be seen as follows: Figure 7 Example of the file for the loaded sub-carrier index data References [1] Armstrong, J. , “OFDM for Optical Communications”, J. Lightwave Technology, vol. 27, pp. 189204, Feb 2009. 344 OFDM MODULATION OFDM Modulation This component modulates a digital signal into multiple orthogonal sub-carriers. Ports Name and description Port type Signal type Input - I 1 Input M-ary Input - Q 1 Input M-ary Output - I Output Electrical Output - Q Output Electrical Output - Training Output Electrical Parameters Main Name and description Default value Default unit Value range Maximum possible sub-carriers 64 - - False - - Table with the sub-carrier index data Symmetric spectrum Defines if the input vector to the IFFT is constrained to have hermitian symmetry Cyclic prefix Defines which guard period will be used Number of prefix points Symbol extension Symbol extension, Zero values 0 - - 0 dBm W, mW, dBm 1 - - Defines the number of points used in the guard period Average OFDM power Input port parameters Number of input ports (users) 345 OFDM MODULATION Name and description Default value Default unit Value range Number of sub-carriers per port 1 Sub-carrier locations 1 Equalize port powers TRUE TRUE, FALSE Dual polarization FALSE TRUE, FALSE Polarization X X, Y Number of training symbols 0 Parameters for dual polarization system DAC Name and description Default value Default units Unit Value range Interpolation Cubic - - Linear, Cubic, Step False - - True, False Name and description Default value Default units Unit Value range Sample rate Sample rate Hz Hz, GHz, THz [0,+INF[ True - - True, False Defines the type of interpolation that will be used Smoothing filter Determines whether or not the smoothing filter is enabled Simulation Frequency simulation window Enabled Determines whether or not the component is enabled Graphs Name and description X Title Y Title OFDM FFT Frequency (Hz) Amplitude (a.u.) Technical background Orthogonal frequency division multiplexing (OFDM) is a multi-carrier transmission technique[1], which divides the available spectrum into many orthogonal subcarriers, each one being modulated by a low rate data stream. The purpose of this format is to 346 OFDM MODULATION significantly reduce inter-carrier and inter-symbol interference (ICI and ISI). Figure 1 shows a schematic of the OptiSystem OFDM Modulation component Figure 1 OFDM modulator diagram Coded data in The input data is a serial stream of coded symbols. The available formats for the OFDM demodulation component are: BPSK, QPSK, 8PSK, 16PSK, 4QAM, 16QAM, 64QAM. It is possible to use multiple users/ports at different modulation formats. However, care must be taken to ensure each user sends their data at the same symbol rate (see Example #2). Serial to Parallel The purpose of this block is two-fold: • It copies the input data onto an output channel that can be directly read in by the demodulation component. Since these are the known initial symbols, the demodulator can use these for training (preamble) and pilot symbols. If you are going to perform dual polarization analysis, then some of the initial training symbols will have to be modified for the demodulator (see Example #3 for details). • It converts the input serial data stream into a parallel stream of OFDM symbols as pictorially represented in Figure 2. 347 OFDM MODULATION Figure 2 Serial to parallel block IFFT After the data has been placed into a number of OFDM symbols, OFDM symbols are allocated to subcarriers which correspond to orthogonal frequencies (0 ISI) for the system. To transmit this data along an optical carrier, each OFDM symbol must be converted from the frequency domain to the time domain. This is accomplished by applying an inverse Fourier transform on each OFDM symbol. Add Cyclic Prefix We now have all OFDM symbols in the frequency domain. Due to the dispersive nature of the optical channels (such as a fiber), it is desirable to add a guard extension or, preferably, a cyclic prefix to each OFDM time-domain symbol to reduce the ISI and ICI [1]. This is represented in Figure 3. Figure 3 Cyclic prefix Parallel to Serial, DAC and Filtering Each time-domain OFDM symbol is now placed into a serial stream. Different interpolation techniques (Step, Linear and Cubic) can be used to function as the digital-to-analog converter. An internal smoothing filter is applied if the parameter Smoothing filter is selected. 348 OFDM MODULATION Important considerations Symbol and bit rates It is crucial to correctly set the symbol and bit rates. This applies not only to the global values but to the settings within the bit stream generators associated with the OFDM system. Within one OFDM symbol period, all the individual symbols required for that OFDM symbol must be sent with: OFDM symbol period = Individual symbol period * Total number of sub-carriers possible Two examples follow for an QPSK system. In these examples the global bit rate is 40Gbit/s. Since this is an QPSK modulation (2 bits per symbol), the symbol rate will be 20Gsym/s. In both cases there are a total of 128 sub-carriers available such that: OFDM symbol period = Symbol period * 128 = 128/(Symbol rate) = 2 * 128 /Global bit rate. In the first case (see Figure 4) we are using all 128 subcarriers. Thus to fill up an entire OFDM symbol in the OFDM symbol period, the generating PRBS bit rate is set to the Global bit rate (Bit rate *128 / 128 = Bit rate). In the second case, we only need to fill up 80 of the sub-carriers (the others will be set to zero automatically) in one OFDM symbol period. Therefore the PRBS will generate bits at a slower rate than the global bit rate (Bit rate * 80 /128) Figure 4 QPSK Example In the next example (see Figure 5), we have a similar situation except that the symbol rate is now ¼ of the bit rate due to the 16QAM modulation. For these two examples, the bit rate of the PRBS generator does not depend on the modulation format, but rather on the total number of subcarriers available and the amount actually used. 349 OFDM MODULATION Figure 5 QAM Example When using multiple ports and mixed modulations, the situation becomes more complicated. However, the principle that all relevant symbols must be filled into their respective sub-carriers still holds. See Example #2 for the case of two ports and mixed modulations. Sub-carrier locations The OFDM Modulation component provides you with a number of options to specify the locations of the subcarriers being used. Examples of the notation used include: Notation Sub-carrier allocation 1, 5, 10 Sub-carriers placed at positions 1, 5, and 10 1,5,10,21-30 Sub-carriers placed at positions 1, 5, 10 and 21 to 30 1,5,10,21-30x2 Sub-carriers placed at positions 1, 5, 10, 21, 23, 25, 27, 29 “x2” means that positions are skipped by two locations 1#4x3 Sub-carriers placed at positions 1, 4, 7, and 10 “#” represents the number of sub-carriers to be positioned 1,5,10;31,35,40 Port 1 has positions 1, 5, and 10 Port 2 has positions 31, 35 and 40 Semi-colons are used to separate the sub-carriers by port number Example #1: Single polarization one port. In this example, an QPSK sequence is sent to the OFDM modulation component. There are 128 possible subcarriers available. Of these, 80 are used and placed at locations 25 to 104. (Note: setting the subcarrier locations as 25#80 will give the same results). 350 OFDM MODULATION Figure 6 Example of single polarization QPSK system and a representation of the sub-carrier locations Of particular importance are the settings for the various Symbol rates and Bit rates. Note these properties in the global layout The global Bit rate is 40 Gbit/s. Since this is QPSK modulation, the time-domain OFDM symbols will be transmitted at the Symbol rate of 20 Gsym/s. The serial to parallel OFDM symbol generator works by first collecting enough serial symbols to fill an OFDM symbol. These then undergo an IFFT and are prefixed. The serialization is repeated again until all input serial symbols are processed. If we wish to fill all 128 of the sub-carriers, then the PRBS generator must be set to produce bits at a rate of the global Bit rate. However, in this case we only need to produce 80 symbols in the time it takes to create one OFDM symbol. Thus, the PRBS is set at a rate of Bit rate*80/128. 351 OFDM MODULATION Example #2: Single polarization, two ports. In this example the total number of subcarriers available is again 128. The subcarriers for the first port are located at 25 to 64 (we can use 25-64 or 25#40). The subcarriers for the second port are located at 65 to 104 (we can use 65-104 or 65#40). This creates a total of 80 subcarriers. Figure 7 An example of a mixed modulation single polarization OFDM modulation system and a representation of the sub-carrier locations The port parameters are separated by a semicolon. The parameter Equalize port powers is checked which means that each port will be normalized to the same average power over their subcarriers. Again, particular attention must be paid to the Bit rates of the PRBS, especially when using mixed modulation to make sure the symbols are transmitted to the modulator at the correct rate. In this case the output time domain signal will be transmitted at the 16QAM Symbol rate = Bit rate / 4. 352 OFDM MODULATION During the time that the OFDM symbol will be filled only 40 QPSK symbols and 40 16QAM symbols need to be sent to the modulator. In addition, QPSK has a symbol rate twice that of the 16QAM thus the bit rate of the PRBS into the QPSK coder is Bit rate / 2*40/128 and that of the PRBS into the 16QAM coder is Bit rate*40 /128. Example #3: Dual polarization, two ports. This example is similar to Example #2, except that we must have a modulator for the X and the Y polarization (only the X polarization component is shown in Figure 8). Please refer to the sample files in “OptiSystem 13 Samples/Advanced modulation systems/OFDM systems” for full dual polarization examples. Figure 8 An example of a mixed modulation single polarization OFDM modulation system and a representation of the sub-carrier locations In the case of the modulator being used in a single polarization system, it is unnecessary to specify the polarization or number of training symbols. However if we are using the OFDM Demodulation Dual Polarization component it is necessary to set the correct training symbols to account for any polarization mixing. 353 OFDM MODULATION In the OFDM Demodulation Dual Polarization component, the training symbols must follow the format: tk i = t X k i t X k i NT NT t k i + ------ = i = 1 ----- 2 2 t Y k i – t Y k i where k is the sub-carrier index, i is the training symbol index and NT is the number of training symbols. Choosing Dual polarization “X” or “Y” ensures that the X and Y polarization symbols are respectively set correctly. References [1] X. Liu, F. Buchali, and R. W. Tkach, “Improving the nonlinear tolerance of polarization-DivisionMultiplexed CO-OFDM in long-haul fiber transmission,” J. Lightw. Tech., vol. 27, no. 16, pp. 36223640, 2009. [2] X. Liu and F. Buchali, “A novel channel estimation method for PDM-OFDM enabling improved tolerance to WDM nonlinearity,” presented at the OFC'09, paper OWW5 354 BURST MODULATOR Burst Modulator This component modulates an input signal into a signal with multiple bursts, modulated by a control signal. Ports Name and description Port type Signal type Input Input Electrical Control Input Electrical Output Output Electrical Parameters Main Name and description Default value Units Value range Threshold 0.5 - ]-INF, +INF[ Name and description Default value Units Value range Enabled True - True, False Control signal threshold value Simulation Determines whether or not the component is enabled Technical background This component modulates an input signal into a signal with multiple bursts, and the time slots for the bursts are determined by the control signal. Figure 1 is an example showing how to connect this component. 355 BURST MODULATOR Figure 1 Burst modulator - Layout The basic principle of the Burst Modulator is illustrated in Figure 2. As we can see, for each time slot when the control signal is above the threshold level, the input signal will be transmitted to the output as bursts. Figure 2 Burst modulator - Principle Input Signal Control Signal Output Signal 356 BURST MODULATOR Transmitters Library - Electrical Carrier Generators • Carrier Generator • Carrier Generator Measured 357 BURST MODULATOR Notes: 358 CARRIER GENERATOR Carrier Generator This component generates a user-defined number of carriers. The output is a sum of sinusoidal electrical signals with constant amplitude. The phase can be constant or random. Ports Name and description Port type Signal type Output Output Electrical Parameters Main Name and description Default value Units Value range Number of channels 2 — [1,+INF[ 50 Hz, MHz, GHz [0,+INF[ 3.5 Hz, MHz, GHz [0,+INF[ 1 a.u. ]-INF,+INF[ 0 a.u. ]-INF,+INF[ Yes — True, false 0 deg ]-INF,+INF[ Number of output signal carriers Frequency Frequency of the first carrier Frequency spacing Spacing between adjacent carriers Amplitude Output signal amplitude of each carrier Bias DC bias Random phase Defines whether the phase of the output carriers will be random or user defined Phase Constant phase 359 CARRIER GENERATOR Name and description Default value Units Value range Disable channels False — True, false — — Defines whether disable channels or not List of channels List of channels that should be disabled Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background This component generates a sum of sinusoidal carriers with the same zero peak amplitude according to: N v out = vi t + vbias , where v i is the signal for each carrier, i=1 parameter Number of channels and vbias is the parameter Bias. 360 N is the CARRIER GENERATOR Each carrier is defined by: v i = A sin 2f i + i , where f i is the frequency of each carrier. The phase can be defined as random, or user-defined. The user-defined phase is the same for all the carriers. The user can remove carriers from the sum by selecting Disable channels parameter and providing the list of channels or carriers. 361 CARRIER GENERATOR Notes: 362 CARRIER GENERATOR MEASURED Carrier Generator Measured This component loads a file with the list of frequency, amplitude and phase of each carrier, and generates a sum of sinusoidal electrical signals. Ports Name and description Port type Signal type Output Output Electrical Parameters Main Name and description Default value Units Frequency amplitude phase (Hz a.u. deg) 50e6 1 0 Hz, a.u., deg Table with the carrier data Amplitude and phase file name 58e6 1 0 Value range Carriers.dat — — 1 — ]-INF,+INF[ 0 a.u. ]-INF,+INF[ False — True, false 0 deg ]-INF,+INF[ False — True, false File name with the list of carriers. Gain Carrier data gain Bias DC bias Random phase Defines whether the phase of the output carriers will be random or user defined Phase Constant phase Disable channels Defines whether disable channels or not 363 CARRIER GENERATOR MEASURED Name and description Default value List of channels Units Value range — — List of channels that should be disabled Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window Technical background This component generates a sum of sinusoidal carriers according to: N v out = G v i t + v bias , i=1 where v i is the signal for each carrier, N is the number of channels, G is the parameter Gain, and Vbias is the parameter Bias. Each carrier is defined by: v i = A i sin 2f i t + i , where A i , f i , and i are the amplitude, frequency and phase of each carrier.The phase can be defined as random, or user-defined. The user-defined phase is the same for all the carriers. The user can remove carriers from the sum by selecting Disable channels parameter and providing the list of channels or carriers. The user can provide the measurements in the parameter Frequency amplitude phase (Hz a.u. deg); alternatively the measurements can be loaded from a file using the parameter Amplitude and phase file name. The amplitude and phase curves must be provided in the file containing three columns, where the first one refers to the frequency specified in [Hz] units; the second one gives the amplitude curve in [a.u.] units, and the last one gives the phase in [deg] units. Standard broadcast files (NTSC, PAL GB and L) are available under the folder \Components\Data\Broadcast Standards. 364 CARRIER GENERATOR MEASURED Transmitters Library - Electrical Sequence generators • PAM Sequence Generator • QAM Sequence Generator • PSK Sequence Generator • DPSK Sequence Generator • PPM Sequence Generator • DPIM Sequence Generator • 4B5B Sequence Generator • NRZI Sequence Generator • AMI Sequence Generator • Manchester Sequence Generator • 4B3T Sequence Generator • 8B10B Sequence Generator • Duobinary Precoder • 4-DPSK Precoder 365 CARRIER GENERATOR MEASURED Notes: 366 PAM SEQUENCE GENERATOR PAM Sequence Generator Generates a M-ary symbol sequence from binary signals using pulse amplitude modulation (PAM). Ports Name and description Port type Signal type Bit sequence Input Binary PAM sequence Output M-ary Parameters Main Name and description Default value Units Value range Bits per symbol 2 [0,100] False True, False False True, False Number of bits per symbol used in the coding Gray code Defines whether to use Gray coding or not User-defined PAM map Defines whether to calculate PAM values based on userdefined values PAM amplitudes (a.u.) 4x2 PAM amplitudes file name PAM_IQ.dat Name of file that contains initial PAM values Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled 367 PAM SEQUENCE GENERATOR Technical background When transmitting information, we can vary the amplitude of a signal according to the source symbols. The value of the amplitude takes value from the set of amplitudes [1]: a 1 = 2i – 1 – M i = 1 2 ..., M where M is the number of possible sequence of binary digits, calculated according to: M = 2 where h h is the number of bits per symbol. If bits per symbol ( h ) equals 2, M is equal to 8, and values of a and i will be: Bit sequence i ai 00 1 -3 01 2 -1 10 3 1 11 4 3 If bits per symbol ( h ) equals 3, M is equal to 8, and values of a and i will be: Bit sequence i ai 000 1 -7 001 2 -5 010 3 -3 011 4 -1 100 5 1 101 6 3 110 7 5 111 8 7 Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. 368 PAM SEQUENCE GENERATOR In the case of bits per symbol ( h ) equals 3, values of a will be: Bit sequence ai 000 -7 001 -5 101 -3 100 -1 110 1 111 3 011 5 010 7 M is equal to 8, with Gray code, and the When User-defined PAM map is selected, the component will allocate the PAM amplitudes based on the PAM amplitudes contained in the PAM amplitudes MxN parameters array. Note: The Gray code feature is disabled when User-defined I-Q map is selected. PAM data, and associated source symbols, can be loaded initially from a data file (the default is otherwise PAM4). The required format is two tab-delimited, or spaced, columns as follows (example here is for PAM8): 000 -7 001 -5 010 -3 011 -1 100 1 101 3 110 5 111 7 References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 369 PAM SEQUENCE GENERATOR 370 QAM SEQUENCE GENERATOR QAM Sequence Generator Generates two parallel M-ary symbol sequences from binary signals using quadrature amplitude modulation (QAM). Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output M-ary Output - Q Output M-ary Parameters Main Name and description Default value Units Value range Bits per symbol (b/sym) 4 bits [0,100] Square - Square, Star, Circular - - - Number of bits per symbol used in the coding Constellation map Defines the type of QAM constellation map to be coded. If set to Star or Circular the symbols are arranged evenly onto concentric circles with radii defined by the parameter Star and cicular level radii Star and circular level radii Defines the amplitude of the radius for each concentric circle. The format is r1 r2 ...rN (space delimited). For example if set to “1”, all symbols will be placed along a concentic circle of radius = 1. If set to “1 2”, symbols will be allocated evenly onto two concentric circles of radii 1 and 2. NOTE: The number of radii must be set to a power of 2 value (2, 4, 8, ...) to ensure an even distribution of symbols for all concentric circles. Also, no more than 16 symbols can be placed on any concentric circle. 371 QAM SEQUENCE GENERATOR Name and description Default value Units Value range Gray code False True, False False True, False False True, False Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used Differential encoding Defines whether to use Differential encoding. If Differential encoding is selected, Gray coding cannot be used User-defined I-Q map Defines whether to calculate IQ values based on userdefined values I-Q amplitudes (a.u.) 64x3 I-Q amplitudes file name QAM_IQ.dat Name of file that contains initial I-Q values Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled Technical background With the QAM sequence generator, the bit sequence is split into two parallel subsequences, each can be transmitted in two quadrature carriers when building a QAM modulator. This is achieved by using a serial to parallel converter. Square QAM maps When transmitting information, we can vary the amplitude of a signal according to the source symbols. For each output port, the amplitude takes one of the values from the set of amplitudes [1]: a 1 = 2i – 1 – M i = 1 2 ..., M where M is the number of possible sequence of binary digits, calculated according to: M = 2 h2 where h is the number of bits per symbol. The equivalent QAM set is given by the square of M . This means: 372 QAM SEQUENCE GENERATOR If h = QAM. 2 , M = 2 , then we have a 4-QAM. If h = 4 , M = 4 , then we have a 16- If h = 6 , 256-QAM. M = 8 , then we have a 64-QAM. If h = 8 , M = 16 , then we have a If bits per symbol ( h ) are equal to 4, we have a 16-QAM that requires 2 consecutive bits from the input sequence for each sub-sequence: Seq. Subseq. I/i a Subseq. Q / i a 0000 00 / 1 -3 00 / 1 -3 0001 00 / 1 -3 01 / 2 -1 0010 00 / 1 -3 10 / 3 1 0011 00 / 1 -3 11 / 4 3 0100 01 / 2 -1 00 / 1 -3 0101 01 / 2 -1 01 / 2 -1 0110 01 / 2 -1 10 / 3 1 0111 01 / 2 -1 11 / 4 3 1000 10 / 3 1 00 / 1 -3 1001 10 / 3 1 01 / 2 -1 1010 10 / 3 1 10 / 3 1 1011 10 / 3 1 11 / 4 3 1100 11 / 4 3 00 / 1 -3 1101 11 / 4 3 01 / 2 -1 1110 11 / 4 3 10 / 3 1 1111 11 / 4 3 11 / 4 3 Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. Star and Circular QAM maps Star and Circular constellations can also be produced by the QAM sequence generator. These are defined with the Constellation map and Star and circular level radii parameters. For example (Fig 1) to create a 16-QAM star constellation with two orbital levels of radii 1 and 2, set the parameters Bits per symbol (b/sym) = 4, Constellation map = Star and Star and circular level radii = 1 2 (the format is r1 r2....rN - space delimited). 373 QAM SEQUENCE GENERATOR NOTE: The number of radii must be set to a power of 2 value (1, 2, 4, 8,...) to ensure an even distribution of symbols along all the concentric circles (orbitals). Also, no more than 16 symbols can be placed on any concentric circle. Figure 1 16-QAM star with two orbital levels (2 amplitudes and 8 phases) User Defined QAM maps When User-defined I-Q map is selected, the component will allocate the I-Q amplitudes based on the I and Q amplitudes contained in the I-Q amplitudes MxN parameters array. When this feature is selected, the user will be able to define both even and odd bits per symbol settings. Note: The Gray code feature is disabled when User-defined I-Q map is selected. I-Q data, and associated source symbols, can be loaded initially from a data file (the default is otherwise 16-QAM). The required format is three tab-delimited, or spaced, columns as follows (example here is for 16-QAM): 374 Sequence I Q 0000 -3 -3 0001 -3 -1 0010 -3 1 0011 -3 3 0100 -1 -3 0101 -1 -1 0110 -1 1 0111 -1 3 QAM SEQUENCE GENERATOR Sequence I Q 1000 1 -3 1001 1 -1 1010 1 1 1011 1 3 1100 3 -3 1101 3 -1 1110 3 1 1111 3 3 Please refer to the “Advanced modulation formats/QAM systems” folder in the “Samples” directory for example data files for 4-QAM, 8-QAM, 16-QAM, 32-QAM and 64-QAM I-Q maps Differential coding [2, 3] Differential encoding/decoding is used to resolve phase ambiguity problems with mQAM and mPSK modulation formats. Note: The Differential coding feature is disabled when User-defined I-Q map is selected For 32-QAM and 128-QAM square constellations a look up table based on Ref 3 is used. For all other constellations the technique defined in Ref 2 is used For example for 16-QAM differential encoding, a group of 4 bits is mapped into one of the 24 possible transitions between two consecutive complex symbols S(i-1) and S(i). The transition can be expressed in terms of two differential angles { }, where is determined by the first dibit (one of four patterns from two consecutive bits: 00, 01, 10, 11) of the QAM symbol and is determined by the second dibit. The dibit to the differential angle mapping is as follows: Dibit Differential angle 00 0 01 /2 11 01 3/2 The complex symbol S(i) represents the summation of the quadrant center C(i) and a displacement D(i): Si = Ci + Di (1) 375 QAM SEQUENCE GENERATOR The differential 16-QAM encoding rule can be described as two recursive updating formulas:: Si = Ci – 1 e j 1 i Di = Di – 1 e j 2 i (2) The initial symbol S(0) is set be letting C(0) = Re j/4 and D(0) = re j/4, with: R = 2 2 r = (3) 2 where R denotes the distance between the origin and the quadrant center, and r denotes the distance between the quadrant center and the constellation point. All the symbols can be expressed as: S i = a i + jb i where a b { 1, 3} (4) References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] J.-K. Hwang, Y.-L. Chiu, and C.-S. Liao, "Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system," Int. J. Commun. Syst., vol. 21, no. 6, pp. 631-641, 2008. [3] Wei, Ruey Y, “Differential encoding by a look-up table for quadrature-amplitude modulation”, IEEE Transactions on Communications, V59 2011, pp 84-94 376 PSK SEQUENCE GENERATOR PSK Sequence Generator Generates two parallel M-ary symbol sequences from binary signals using phase shift keying modulation (PSK). Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output M-ary Output - Q Output M-ary Parameters Main Name and description Default value Units Value range Bits per symbol (b/sym) 2 bits [0,100] 45 deg, rad ]-INF, +INF[ Number of bits per symbol used in the coding Phase offset Initial phase offset Gray code False True, False False True, False Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used Differential encoding (2 b/sym only) Defines whether to use Differential encoding. This feature is disabled if bits/symbol is not equal to 2.If Differential encoding is selected, Graycoding cannot be used 377 PSK SEQUENCE GENERATOR Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1]: 2 i = ------ i – 1 + i = 1 2 ...M M where M is the number of possible sequence of binary digits, calculated according to: M = 2 h where h is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to: I i = cos i i = 1 2 ...M Q i = sin i i = 1 2 ...M Assuming Q will be: = 0 , if bits per symbol ( h ) equals 2, M equals 4, the values of I and Bit sequence I Q 00 1 0 01 0 1 10 -1 0 11 0 -1 378 PSK SEQUENCE GENERATOR Assuming Q will be: = 0 , if bits per symbol ( h ) equals 3, M equals 8, the values of I and Bit sequence I Q 000 1 0 001 ------22 ------22 010 0 1 011 2 – ------2 100 -1 ------22 0 101 2 – ------2 110 0 2 – ------2 -1 111 ------22 2 – ------2 Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. Differential encoding (QPSK) [2] For QPSK differential encoding, a group of 4 bits is mapped into one of the 22 possible transitions between two consecutive complex symbols S(i-1) and S(i). The transition can be expressed in terms of the differential angle . The dibit to the differential angle mapping is as follows: Dibit Differential angle 00 0 01 /2 11 01 3/2 379 PSK SEQUENCE GENERATOR The differential QPSK encoding rule can be described as an updating formula: Si = Si – 1 e j i (5) The initial symbol S(0) is set be letting S(0) = re j/4, with: r = 2 (6) where r denotes the distance between the origin center and the constellation point. All the symbols can be expressed as: S i = a i + jb i where a b 1 (7) References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] J.-K. Hwang, Y.-L. Chiu, and C.-S. Liao, "Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system," Int. J. Commun. Syst., vol. 21, no. 6, pp. 631-641, 2008.\ 380 DPSK SEQUENCE GENERATOR DPSK Sequence Generator Generates two parallel M-ary symbol sequences from binary signals using differential phase shift keying modulation (DPSK). Ports Name and description Port type Signal type Bit sequence Input Binary Output - I Output M-ary Output - Q Output M-ary Parameters Main Name and description Default value Bits per symbol 2 Units Value range [0,100] Number of bits per symbol used in the coding Phase offset 45 deg, rad ]-INF, +INF[ Initial phase offset Gray code False True, False Defines whether to use Gray coding or not Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled 381 DPSK SEQUENCE GENERATOR Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1, 2] 2 ki = k – 1 + ------ i – 1 + i = 1 2 ...M M where ki is the phase value for the current symbol, and k – 1 is phase value for the previous symbol. M is the number of possible sequence of binary digits, calculated according to: M = 2 h where h is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to: I ki = cos ki i = 1 2 ...M Q ki = sin ki i = 1 2 ...M Assuming Q will be: = 0 , if bits per symbol ( h ) equals 2, M equals 4, the values of I and k Bit sequence I Q 0 00 1 0 1 01 0 1 2 10 -1 0 3 11 0 -1 Assuming Q will be: = 0 , if bits per symbol ( h ) equals 3, M equals 8, the values of I and k Bit sequence I Q 0 000 1 0 1 001 ------22 2 382 010 0 ------22 1 DPSK SEQUENCE GENERATOR k Bit sequence 3 011 I Q 2 – ------2 ------22 4 100 5 101 -1 0 2 – ------2 6 110 7 111 0 2 – ------2 -1 ------22 2 – ------2 Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. 383 DPSK SEQUENCE GENERATOR References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] Pawula, R.F., “On M-ary DPSK Transmission Over Terrestrial and Satellite Channels”, IEEE Trans. on Commun. COM-32, 752-761, (July 1984). 384 PPM SEQUENCE GENERATOR PPM Sequence Generator Generates a sequence of bits using pulse position modulation (PPM). Ports Name and description Port type Signal type Bit sequence Input Binary PPM Sequence Output Binary Parameters Main Name and description Default value Units Value range Bits per symbol 2 - [0,100] Number of bits per symbol used in the coding Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background With the PPM sequence generator, the signal is split up into one of N possible symbols, with L bits per symbol, where N = 2 L [1]. The position of the symbol varies depending on what the original bit sequence was, which is mapped to it. 385 PPM SEQUENCE GENERATOR For instance, given the sequence 00011011 and 2 bits per symbol, there will be 2 2 2 3 possible symbols, and the bits will be mapped as follows: Bit sequence Decimal Value N 00 0 1000 01 1 0100 10 2 0010 11 3 0001 For the sequence 101 011 110 111 000 and 3 bits per symbol, there will be possible symbols, and the bits will be mapped as follows: Bit sequence Decimal Value N 101 5 0000 0100 011 3 0001 0000 110 6 0000 0010 111 7 0000 0001 000 0 1000 0000 References [1] Z. Ghassemlooy, A. R. Hayes, “Digital pulse interval modulation for IR communication systems-a review”, Int. J. Commun. Syst, vol 13, pp 519-536, Nov 2000. 386 DPIM SEQUENCE GENERATOR DPIM Sequence Generator Generates a sequence of bits using digital pulse interval modulation (DPIM). Ports Name and description Port type Signal type Bit sequence Input Binary DPIM Sequence Output Binary Parameters Main Name and description Default value Units Value range Bits per symbol 2 - [0,100] Number of bits per symbol used in the coding Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background In each PPM symbol, the empty slots following a pulse are essentially redundant, and it is this redundancy which is removed when adopting digital pulse interval modulation (DPIM). In DPIM, information is encoded by varying the number of empty slots between adjacent pulses [1]. 387 DPIM SEQUENCE GENERATOR For instance, given the sequence 00011011 and 2 bits per symbol, the encoded sequence is: Bit sequence Decimal Value N 00 0 10 01 1 100 10 2 1000 11 3 10000 For the sequence 101 110 001 010 111 and 3 bits per symbol, the encoded sequence is: Bit sequence Decimal Value N 101 5 1000000 110 6 10000000 001 1 100 010 2 1000 111 7 100000000 References [1] Z. Ghassemlooy, A. R. Hayes, “Digital pulse interval modulation for IR communication systems-a review”, Int. J. Commun. Syst, vol 13, pp 519-536, Nov 2000. 388 4B5B SEQUENCE GENERATOR 4B5B Sequence Generator Generates a sequence of bits by mapping 4-bit symbols to specific 5-bit symbols (4B5B). Ports Name and description Port type Signal type Bit sequence Input Binary 4B5B Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background With the 4B/5B sequence generator, the signal is split up into 4-Bit symbols. The symbols are then mapped to specific 5-Bit symbols, so that there are never more than 3 consecutive 0’s (the 5-Bit symbols do not have more than 1 leading 0 and more than 2 trailing 0’s) [1]. The table of symbols for the 16 possible 4-bit combinations is: 4-Bit Symbol Decimal Value 5-Bit Symbol 0000 0 11110 0001 1 01001 0010 2 10100 0011 3 10101 389 4B5B SEQUENCE GENERATOR 4-Bit Symbol Decimal Value 5-Bit Symbol 0100 4 01010 0101 5 01011 0110 6 01110 0111 7 01111 1000 8 10010 1001 9 10011 1010 10 10110 1011 11 10111 1100 12 11010 1101 13 11011 1110 14 11100 1111 15 11101 References [1] B. A. Forouzan, Data Communications and Networking, McGraw-Hill Science, 2003. 390 NRZI SEQUENCE GENERATOR NRZI Sequence Generator Generates a sequence of bits using non-return-to-zero inverted encoding (NRZI). Ports Name and description Port type Signal type Bit sequence Input Binary NRZI Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background With the NRZI [1] sequence generator, the signal is mapped in such a way that a logical ‘1’ represents a transition, and a logical ‘0’ does not. For instance, for the sequence 10010110101101, the NRZI encoded sequence is 11100100110110. References [1] B. A. Forouzan, Data Communications and Networking, McGraw-Hill Science, 2003. 391 NRZI SEQUENCE GENERATOR Notes: 392 AMI SEQUENCE GENERATOR AMI Sequence Generator Generates an m-ary symbol sequence from binary signals using alternate mark inversion (AMI). Ports Name and description Port type Signal type Bit sequence Input Binary AMI Sequence Output M-ary Parameters Main Name and description Default value Units Value range Encoding type Bipolar - Bipolar, B8ZS, B6ZS, B3ZS, HDB3 Name and description Default value Units Value range Enabled True - True, False Simulation Determines whether or not the component is enabled Technical background With the AMI code is generated by inverting alternate 1s or marks [1] [2], This process removes the DC component. Different encoding types are available: 393 AMI SEQUENCE GENERATOR Bipolar This is the default AMI mode. For every mark in the original sequence, it alternates between positive and negative values, starting with the positive, for the modified sequence. Sequence Bipolar AMI sequence 100111101 +00-+-+0- 011001111 0+-00+-+- B8ZS This mode of the AMI scans the original code and looks for eight consecutive zeros, when it finds them it replaces them with 000-+0+- or 000+-0-+ depending on the bit right before the eight zeros. Sequence Bipolar AMI sequence Value of preceding bit B8ZS AMI sequence 10100000000110 +0-00000000+-0 - +0-000-+0+-+-0 10000000011011 +00000000-+0-+ + +000+-0-+-+0-+ B6ZS This mode of the AMI is the exact same as the B8ZS, except it looks for six consecutive zeros, and the patterns are 0-+0+- and 0+-0-+. Sequence Bipolar AMI sequence Value of preceding bit B6ZS AMI sequence 101000000110 +0-000000+-0 - +0-0-+0+-+-0 100000011011 +000000-+0-+ + +0+-0-+-+0-+ 394 AMI SEQUENCE GENERATOR B3ZS This mode scans for three consecutive zeros, however the pattern it replaces them with depends not only on the preceding bit, but also on the number of non-zero bits there were since the last substitution (without counting the first bit of the sequence), the possible patterns are: 00-, 00+, -0-, +0+. . Sequence Bipolar AMI sequence Value of preceding bit for first substitution Sequence after first substitution Value of preceding bit for second substitution B3ZS AMI sequence 1010001101000 +0-000+-0+000 -, ODD +0-00-+-0+000 +, ODD +0-00-+-0+00+ 101100011000 +0-+000+-000 +, EVEN +0-+-0-+-000 -, EVEN +0-+-0-+-+0+ HDB3 This mode is the exact same as the B3ZS, except it searches for four consecutive zeros, and the patters are: 000-, 000+, +00+, -00-.. Sequence Bipolar AMI sequence Value of preceding bit for first substitution Sequence after first substitution Value of preceding bit for second substitution B3ZS AMI sequence 101000011010000 +0-0000+-0+000 -, ODD +0-000-+-0+0000 +, ODD +0-000-+-0+000+ 10110000110000 +0-+0000+-0000 +, EVEN +0-+-00-+-0000 -, EVEN +0-+-00-+-+00+ References [1] W. Stallings, Data and Computer Communications, Prentice Hall, 2006. [2] D. R. Smith, Digital Transmission Systems, Springer, 2003. 395 AMI SEQUENCE GENERATOR 396 MANCHESTER SEQUENCE GENERATOR Manchester Sequence Generator Generates a sequence of bits using Manchester encoding. Ports Name and description Port type Signal type Bit sequence Input Binary Manchester Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background The Manchester sequence generator encodes a signal by generating a 1->0 transition for a 1 symbol and a 0->1 transition for a 0 symbol [1] . The bandwidth of the encoded signal is two times the original bandwidth. Sequence Manchester sequence 10011011 1001011010011010 11011110 1010011010101001 References [1] B. A. Forouzan, Data Communications and Networking, McGraw-Hill Science, 2003. 397 MANCHESTER SEQUENCE GENERATOR Notes: 398 4B3T SEQUENCE GENERATOR 4B3T Sequence Generator Generates a sequence of bits by mapping 4-bit symbols to specific 3-bit ternary symbols (4B3T). Ports Name and description Port type Signal type Bit sequence Input Binary 4B3T Sequence Output Binary Parameters Main Name and description Default value Units Value range Zero padding False - True, False Name and description Default value Units Value range Enabled True - True, False Determines whether or not to add zeroes at the end of the sequence Simulation Determines whether or not the component is enabled Technical background This mapping from 4 bits to 3 ternary states is given in a table known as Modified Monitoring State 43 (MMS43) [1] [2]. 399 4B3T SEQUENCE GENERATOR References [1] D. J. Morris, Pulse Code Formats for Fiber Optical Data Communication, CRC, 1983. [2] D. R. Smith, Digital Transmission Systems, Springer, 2003. 400 8B10B SEQUENCE GENERATOR 8B10B Sequence Generator Generates a sequence of bits by mapping a 8-bits symbol to a specific 10-bits symbol (8B10B). Ports Name and description Port type Signal type Bit sequence Input Binary 8B10B Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background Described in [1] in detail, 8B10B coding decomposes each 8-bits into two blocks of 5 bits and 3 bits, converting them to 6-bit and 4-bit equivalents, respectively. Each consecutive blocks exhibit a total average of zero (DC-balanced). References [1] A. X. Widmer, P. A. Franaszek, “A DC-Balanced, Partitioned-Block, 8B/10B Transmission Code”, IBM Journal of Research and Development, Vol 27, No 5, pp 440, 1983. 401 8B10B SEQUENCE GENERATOR 402 DUOBINARY PRECODER Duobinary Precoder This component simulates a precoder generally utilized in a duobinary modulation. Ports Name and description Port type Signal type Input1 Input Binary Output1 Output Binary Parameters Main Name and description Default value Units Value range Delay 1 bits [1, +INF] Name and description Default value Units Value range Enabled True — True, False Delay to apply to the signal input Simulation Determines whether or not the component is enabled Technical background Normally, an optical duobinary system requires a precoder in order to avoid recursive decoding in the receiver, error propagation and reduce hardware complexity. The precoder is composed on an exclusive-or gate with a delayed feedback path. The precoding rule for this is: bk = dk bk – d d k is the transmitted binary data sequence, b k is the precoded binary sequence, d is the number of delayed bits, and represents the logic instruction where 403 DUOBINARY PRECODER exclusive-or “XOR”. Due to the use of the precoder in a transmitter, decoding in the receiver is simple. Figure 2 shows a diagram detailing the precoder. You can specify the number of bits delayed in the feedback path. When Figure 2 404 k – d 0 , then b k – d = 1 . Duobinary precoder 4-DPSK PRECODER 4-DPSK Precoder This component simulates a precoder for 4-DPSK modulation utilized for serial or parallel transmitter configuration Ports Name and description Port type Signal type Input1 Input Binary Output1 Output Binary Output2 Output Binary Parameters Main Name and description Default value Units Value range Transmitter configuration Serial - Serial, Parallel Name and description Default value Units Value range Enabled True — True, False Determines if the precoder will be used in a serial or parallel transmitter configuration Simulation Determines whether or not the component is enabled Technical background Normally, an optical 4-DPSK system requires a precoder in order to avoid recursive decoding in the receiver, error propagating and to reduce hardware complexity. Figure 1 shows a diagram detailing the precoder. Mathematically, the precoder operation can be described by the following set of equations: Serial configuration 405 4-DPSK PRECODER Ii = Qi – 1 Ii – 1 di Ii – 1 + Qi – 1 Ii – 1 gi Ii – 1 Qi = Qi – 1 Ii – 1 gi Ii – 1 + Qi – 1 Ii – 1 di Ii – 1 Parallel configuration Ii = di gi gi Ii – 1 + di gi gi Qi – 1 Qi = di gi gi Qi – 1 + di gi gi Ii – 1 Figure 1 4-DPSK precoder 406 Transmitters Library - Optical Optical Sources • CW Laser • Ideal Single Mode Laser • Laser Measured • Fabry Perot Laser • LED • White Light Source • Pump Laser • Pump Laser Array • Controlled Pump Laser • CW Laser Array • CW Laser Array ES • CW Laser Measured • Directly Modulated Laser Measured • VCSEL Laser • VCSEL Laser Measured • DFB Laser • Empirical Laser Measured • Spectral Light Source • Set OSNR 407 408 CW LASER CW Laser Generates a continuous wave (CW) optical signal. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz,THz, nm [0,+INF[ Power 0 dBm W, mW, dBm ]-INF,+INF[ Linewidth 10 MHz — [0,+INF[ Initial phase 0 deg — ]-INF,+INF[ Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Emission frequency Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization 409 CW LASER Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Parameterized Parameterized — — Sampled, Parameterized Sample rate Sample rate Hz Hz, GHz, THz ]0,+INF[ Name and description Default value Default unit Units Value range Noise bandwidth 0 THz Hz, THz, nm [0,+INF[ –100 dB — ]-INF,+INF[ 3 dB — ]-INF,+INF[ Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Frequency simulation window Noise Bandwidth to create noise bins Noise threshold Minimum value for adaptation of noise bins Noise dynamic Threshold ratio for adaptation of noise bins Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 410 CW LASER Technical background In the CW case, the average output Power is a parameter that you specify. The laser phase noise is modeled using the probability density function: 2 1 f = ---------------------- e 2 fdt where – ----------------4fdt is the phase difference between two successive time instants and dt is the time discretization. A Gaussian random variable for the phase difference between two successive time instants with zero mean and a variance equal to assumed, with f 2 f has been as the laser line-width (which is equivalent to the full width half maximum (FWHM) of the laser power spectrum) The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j where the power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as follows: 2 k 1 – k cos tan 2 = -------------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 411 CW LASER 412 IDEAL SINGLE MODE LASER Ideal Single Mode Laser Utilizes the rate equations to simulate the modulation dynamics of an ideal single mode laser with no internal cavity losses. Ports Name and description Port type Signal type Modulation Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Unit Value range Frequency 193.1 THz Hz, THz, nm [30,3e5] True — — True, False 10 dBm W, mW, dBm [-1e100, 1e100] 0 dBm W, mW, dBm [-1e100, 1e100] 38 mA — [0, 1000] Emission frequency of the laser Calculate current Defines whether to estimate the input bias and peak current to achieve the user defined output power level Power The output power at constant peak current Power at bias current The output power at constant bias current Bias current Input bias current 413 IDEAL SINGLE MODE LASER Name and description Default value Default unit Unit Value range Modulation peak current 23 mA — [0, 1000] 33.4572 mA — [0, 1000] 0.0155558 mW — [0, 1000] Name and description Default value Default unit Value range Active layer volume 1.5e-010 cm3 0, 1e-3 Quantum efficiency 0.4 — 0, 1 Group velocity 8.5e+009 cm/s 0, 100e9 Differential gain coefficient 2.5e-016 cm2 0, 50e-16 Carrier density at transparency 1e+018 cm-3 0, 100e18 Mode confinement factor 0.4 — 0, 1 Recombination model Lifetime — Lifetime, Coefficients Carrier lifetime 1e-009 s 0, 50e-9 Recombination coefficient A 100000000 1/s 0, 1e15 3e-029 cm^3/s 0, 1e-7 1e-009 cm^6/s 0, 1e-7 Photon lifetime 3e-012 s 0, 50e-9 Spontaneous emission factor 3e-005 — 2e-5, 20e-5 Gain compression coefficient 1e-017 cm3 0.5e-17, 10e17 Linewidth enhancement factor 5 — –20, 20 Input modulation peak current Threshold current The threshold current, calculated from the laser physical parameters Threshold power The threshold power, calculated from the laser physical parameters Physical The internal quantum efficiency of the laser (also called slope efficiency) Linear recombination coefficient Recombination coefficient B Bimolecular recombination coefficient Recombination coefficient C Auger recombination coefficient 414 IDEAL SINGLE MODE LASER Numerical Name and description Default value Units Value range Adaptive step False — True, False 1000000 — [1e3,10e6] 0.0001 — — Name and description Default value Units Value range Calculate graphs False True, False 20 [5, 100e6] Defines whether to use adaptive step or not Max. number of steps The maximum number of steps Relative error Relative integration error Graphs Defines whether to calculate graphs or not Number of points Number of points for the graphs From 0 mA [0, +INF] 40 mA [0, +INF] Name and description Default value Units Value range Enabled True — True, False Parameterized Parameterized — — Name and description Default value Units Value range Include noise True — True, False Include phase noise True — True, False Current lower limit for the graphs To Current upper limit for the graphs Simulation Noise 415 IDEAL SINGLE MODE LASER Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The modulation dynamics of the laser are modeled by coupled rate equations which describe the relation between the carrier density N t , photon density S t , and optical phase t 1 dN t It Nt ------------= ----------- – ---------- – v g g N t – N t ------------------------------- S t 1 + St dt qV n (1) 1 S t N t dS t - -----------= v g g N t – N t ------------------------------- S t – --------- + -------------------------1 + St p dt n (2) d t 1 1 -----------= --- v g g N t – N t – ----dt 2 p where, g vg Nt V p n 416 is the differential gain coefficient is the group velocity is the gain compression factor is the carrier density at transparency is the spontaneous emission factor is the mode confinement factor is the active layer volume is the photon lifetime is the carrier lifetime is the line-width enhancement factor (3) IDEAL SINGLE MODE LASER The chirp (), is defined by 1 d v = ---------- -----2 dt (4) where, v h is the optical frequency is the Planck’s constant If the “Lifetime” recombination model is chosen, then: 1 ----- = A + B N + C N 2 n (5) where A, B, and C are the recombination coefficients. Note: The spontaneous emission rate BN (also called Rsp) is sometimes used in lieu of 1/2n in the last term of equation (3). Either form is acceptable but it is important that the spontaneous emission factor is selected accordingly. The optical power and chirp response of the semiconductor laser to a current waveform I t is determined by equations 1-4. Parameters Bias current and Modulation peak current are scale factors applied to the input electrical signal. The internal current I t is given by: (6) I t = I DC + I in t I Pk Where I in t is the input signal current, I DC is the parameter Bias Current and I Pk is the parameter Modulation peak current. If parameter Bias Current and Modulation peak current have zero values, the internal current is given by I in t only. A Runge-Kutta algorithm is used to numerically integrate the coupled first order differential equations (1-3). If parameters Include noise and Include phase noise are disabled, these equations apply to a noiseless laser oscillating in a single longitudinal mode above threshold. The photon and electron densities within the active region of the laser are assumed to be uniform. If parameter Include noise is enabled, the Langevin noise terms for photon and electron densities are included in the model[2]. If Include phase noise is enabled, the Langevin noise term for the phase is included in the model. The line-width enhancement factor and the nonlinear gain compression parameter are taken to be constant for a given structure. 417 IDEAL SINGLE MODE LASER In this model we assume that there are no internal losses. Therefore the escape rate (per unit time) for each mirror is assumed to be equal to 1/2p. Due to this assumption, the output optical power is given by: S V int h v P = --------------------------------------2 p where (7) int is the internal quantum efficiency The Laser Rate Equations supports individual samples for time-driven simulation. References [1] J. C. Cartledge and G. S. Burley, “The Effect of the Laser Chirping on Lightwave System Performance”, J. Lightwave Technology, vol. 7, pp. 568-573, March 1989. [2] Agrawal GP, Dutta NK. Semiconductor lasers, 2nd ed. New York: Van Nostrand Reinhold, 1993. 418 LASER MEASURED Laser Measured Extracts values of the rate equation parameters using measurements and simulates the modulation dynamics of a laser. Ports Name and description Port type Signal type Modulation Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [30,3e5] True — — True, False 10 dBm W, mW, dBm [-1e100, 1e100] 0 dBm W, mW, dBm [-1e100, 1e100] 23 mA — [0, 1000] 28 mA — [0, 1000] Emission frequency of the laser Calculate current Defines whether to estimate the input bias and peak current to achieve the user defined output power level Power The output power at constant peak current Power at bias current The output power at constant bias current Bias current Input bias current Modulation peak current Input modulation peak current 419 LASER MEASURED Measurements Name and description Default value Default unit Units Value range Frequency response data type Parameters — — Parameters, From file 10.28 1e9s-1 — ]0, 1000] 6.43 1e20 Hz2 — ]0, 1000] 6.43 1e20 Hz2 — ]0, 1000] 18 mA — [0, 1000] 23 mA — [0, 1000] True — — True, False 0.3 mW/mA — [1e-100, 1e100] 1.5 mW W, mW, dBm [1e-100, 1e100] False — — True, False 10 MHz — [1,200] False — — True, False 0.5 ns — [1e-5, 100] Defines whether the frequency response data is provided by the damping factor and resonance frequency factor parameters or by the subtracted IM response curve Damping factor The measured damping factor of the laser Resonance frequency factor The measured resonance frequency factor of the laser Subtracted IM response filename File containing the subtracted IM response curve Threshold current The measured threshold current of the laser Reference current The reference current used to estimate the measured output power Slope efficiency data Defines whether to use slope efficiency or power to estimate the LI curve Slope efficiency The measured slope efficiency of the laser Power at reference current The laser power at the reference current Linewidth data Determines whether the line-width will be part of the parameter extraction procedure Linewidth Specifies the laser line-width for the steady-state condition Turn-on delay data Determines whether the turn-on delay will be part of the parameter extraction procedure Turn-on delay Specifies the laser turn-on delay 420 LASER MEASURED Name and description Default value Default unit Units Value range Average RIN data False — — True, False 0.2 GHz — [0.01,20] 15 GHz — [0.01,20] -140 dB/Hz — [-500, -50] Determines whether the average RIN in a specified bandwidth will be part of the parameter extraction procedure RIN start Specifies the initial frequency of the frequency range where the average RIN is calculated RIN stop Specifies the final frequency of the frequency range where the average RIN is calculated Average RIN Specifies the average RIN value for the steadystate condition over the frequency bandwidth defined by the values of RIN start and stop. Initial estimate Name and description Default value Default unit Value range Group velocity 8.5e+009 cm/s 0, 100e9 Calculate parameters True — Linewidth enhancement factor 5 — –20, 20 Active layer volume estimation 2e-011 cm3 0, 1e-3 Quantum efficiency estimation 0.2 — 0, 1 Carrier density at transparency estimation 1e+018 cm-3 0, 100e18 Differential gain coefficient estimation 1.765e-016 cm2 0, 50e-16 Mode confinement factor estimation 0.2 — 0, 1 Recombination model Lifetime — Lifetime, Coefficients Recombination coefficient A estimation 1e-009 s 0, 50e-9 100000000 1/s 0, 50e-9 3e-029 cm^3/s 0, 50e-9 Defines whether to optimize the laser physical parameters to achieve the target measurement or not. Linear recombination coefficient Recombination coefficient B estimation Bimolecular recombination coefficient Recombination coefficient C estimation Auger recombination coefficient 421 LASER MEASURED Name and description Default value Default unit Value range Auger recombination coefficient estimation 1e-009 cm^6/s 0, 50e-9 Photon lifetime estimation 1e-012 s 0, 50e-9 Spontaneous emission factor estimation 0.0001 — 2e-5, 20e-5 Gain compression coefficient estimation 1.5e-017 cm3 0.5e-17, 10e-17 Numerical Name and description Default value Units Value range Adaptive step False — True, False 1000000 — [1e3,10e6] 0.0001 — — Name and description Default value Units Value range Calculate graphs False True, False 20 [5, 100e6] Defines whether to use adaptive step or not Max. number of steps The maximum number of steps Relative error Relative integration error Graphs Defines whether to calculate graphs or not Number of points Number of points for the graphs From 0 mA [0, +INF] 40 mA [0, +INF] Current lower limit for the graphs To Current upper limit for the graphs Simulation Name and description Default value Units Value range Enabled True — True, False Parameterized — — Determines whether or not the component is enabled Parameterized 422 LASER MEASURED Noise Name and description Default value Units Value range Include noise True — True, False Include phase noise True — True, False Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The laser measured model extracts values of the rate equation parameters using measurements of the threshold current, optical power, resonance frequency, and damping factor to simulate a DFB laser. Based on the results featured in [1], the values of the rate equation parameters are calculated in a way that parameters simultaneously yield the measured values of Y (damping factor), Z (resonance frequency factor), Ith (threshold current), and P (Power bias). The parameter extraction procedure is based on minimization of the sum of squared errors between the measured values of (Y, Z, Ith, P) and values calculated from rate equation parameters. The minimization is over the values of the rate equation parameters which are: Damping factor S 1 1 1 Y = g 0 ------------------------ + ----- – v g g N – N t --------------------------2 + ----p 1 + S n 1 + S Resonance frequency factor g0 S 1 1 1 Z = v g g ------------------------ ----- + – 1 ----- N – N t --------------------------2 + -------------n p n 1 + S p 1 + S Threshold current q V 1 + Nt vg g p I th = ----------- ---------------------------------------------------n vg g p 423 LASER MEASURED Power bias S V int h v P = --------------------------------------2 p where g is the differential gain coefficient is the gain compression factor Nt int is the carrier density at transparency V p n is the active layer volume NandS are the steady-state values of the carrier and photon densities corresponding to the bias current of the laser v vg h is the unmodulated optical frequency is the spontaneous emission factor is the mode confinement factor is the internal quantum efficiency is the photon lifetime is the electron lifetime is the group velocity is the Planck’s constant The minimization routine finds a local minimum for the equation 2 2 2 Func = Y mea – Y cal + z mea – z cal + P mea – P cal + I mea – I cal 2 where Y mea Z mea ,P mea ,I mea are the measured values and Y cal Z cal ,P cal ,I cal are the calculated values using the initial estimates of the rate equation parameters. The parameters available in the main tab allow the user to enter the values for current, or for power in steady state. Using these numbers, the model will estimate the values of the current. Note: It is recommended to enter the values for current, rather than power, when using the measured laser (as this is the realistic case). The parameters in the measured tab are used to extract the physical/geometrical properties of the laser. This extraction is completely independent of the parameters in the main tab (current/power). After finding the rate equation parameters, the laser measured works similarly to the laser rate equations model. RIN is calculated according to [2][3]. 424 LASER MEASURED The internal current I t is given by: I t = I DC + I in t I Pk (1) Where I in t is the input signal current, I DC is the parameter Bias Current and I Pk is the parameter Modulation peak current. If parameter Bias Current and Modulation peak current have zero values, the internal current is given by I in t only. The user can also calculate the subtracted IM response from the measured IM response curves (Figure1) and load a file with this information into the component. This will allow a pre-optimization step, where the component fits the parameters Z and Y to the measured results. Figure 1 Measured IM responses The file format for the subtracted IM response data is the following: Frequency0 SubtractedIM0 Frequency1 SubtractedIM1 Frequency2 SubtractedIM2 ... FrequencyN SubtractedIMN 425 LASER MEASURED The units are GHz and dB respectively. The laser measured can also include the turn-on delay parameter in the optimization process. In this case, the turn-on delay value specified defines the time needed for the carrier density to reach the threshold carrier density when the laser current rises to the reference current. The calculation of the turn-on delay is based on the definition find in [1].The laser line-width parameter can be included in the optimization process by defining the line-width value for the laser when the bias current is the reference current parameter [4]. The RIN is calculated according to [2][3] and the user has to define the average RIN value in the defined frequency range. If parameter Include noise is enabled, the Langevin noise terms for photon and electron densities are included in the model[4]. If Include phase noise is enabled, the Langevin noise term for the phase is included in the model. The Laser Measured supports individual samples for time-driven simulation. References [1] Cartledge, J. C. and Srinivasan, R. C. “Extraction of DFB laser rate equation parameters for system simulation purposes”, J. Light. Techn., 15, 852-860, (1997). [2] Yamada, M. "Variation of intensity noise and frequency noise with the spontaneous emission factor in semiconductor lasers". IEEE Journal of Quantum Electronics. Volume 30, Issue 7, July 1994 Page(s):1511 - 1519. [3] Agrawal, G.P., Fiber-Optic Communication Systems, Second edition. John Wiley & Sons, Inc., N.Y., (1997). [4] Agrawal GP, Dutta NK. Semiconductor lasers, 2nd ed. New York: Van Nostrand Reinhold, 1993. [5] K.Petermann, Laser Diode Modulation and Noise, Kluwer Academic Publishers,1988 426 FABRY PEROT LASER Fabry Perot Laser The Fabry Perot laser component simulates the modulation dynamics of a FabryPerot laser cavity using either the multi-mode rate equations or the transmission line laser model (TLLM). It also allows for an external optical signal to be injected into the active layer. Ports Name and description Port type Signal type Modulation Input Electrical Input Input Optical Output Optical Optical injection port. Connect an optical null signal when not being used. Output Parameters Main Name and description Default value Default unit Unit Value range Frequency 193.1 THz Hz, THz, nm [30,3e5] 27 mA — [0, 1000] 10 mA — [0, 1000] 0.01 — — [0, 1] Emission frequency of the laser Bias current Input bias current Modulation peak current Input modulation peak current Front facet reflectivity The threshold current, calculated from the laser physical parameters 427 FABRY PEROT LASER Name and description Default value Default unit Unit Value range Rear facet reflectivity 0.3 — — [0, 1] mA — — — Spatially averaged multimode, Transmission line Default value Default unit Value range Active length 0.06 cm3 ]0, 1000] Active layer width 0.00015 cm3 ]0,1000] Active layer depth 20e-006 cm3 ]0, 1000] Group index 3.5 — [1, 5] Quantum efficiency 0.4 — [0, 1] Differential gain coefficient 1e-016 cm2 [0, 50e-16] Gain bandwidth 5 THz [0.1, 20] Carrier density at transparency 1e+018 cm-3 [0, 100e18] Mode confinement factor 0.4 — [0, 1] Recombination model Lifetime — Lifetime, Coefficients Carrier lifetime 1.86e-009 s [0, 50e-9] Recombination coefficient A 100e+006 1/s [0, 1e15] 0.2e-009 cm3/s [0, 1e-7] The threshold power, calculated from the laser physical parameters Threshold current Automatically calculated Laser model Determines which laser model to use to solve the rate equations Spatially averaged multimode Physical Name and description Active layer parameters Internal quantum efficiency of the device. Also called slope efficiency. Carrier parameters Linear recombination coefficient Recombination coefficient B Bimolecular recombination coefficient 428 FABRY PEROT LASER Name and description Default value Default unit Value range Recombination coefficient C 40e-030 cm6/s [0, 1e-7] Spontaneous emission factor 0.004 — [2e-5, 20e-5] Gain compression coefficient 36e-018 cm3 [0.5e-17, 10e17] Linewidth enhancement factor 5 — [–20, 20] Loss 10 cm-1 [0, 1e10] Two photon absorption False — True, False 25e-027 m4/GW [0, 1e10] Name and description Default value Units Value range Number of side modes 1 Auger recombination coefficient Loss parameters When selected “Two photon absorption” is modeled Two photon absorption coefficient Side Modes [0,10] Only applies to Spatially averaged multimode model. Up to 10 side modes are supported (when set to 0, no side modes are created single mode laser) Mode spacing model The mode spacing can be Defined explicitly or Calculated from the cavity length Separation Defined explicitly - Defined explicitly, Calculated from cavity length 71.4 GHz [0.01, 500] Defines the frequency separation between the side modes (enabled when Mode spacing model = Defined explicitly 429 FABRY PEROT LASER Numerical Name and description Default value Units Value range Adaptive step False — True, False 100000 — [1e3,10e6] 0.001 — — 50 — [0, 200] Name and description Default value Units Value range Enabled True — True, False Parameterized Parameterized — — Name and description Default value Units Value range Include noise True — True, False Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Defines whether to use adaptive step or not. Applies only to Spatially averaged multimode model Max. number of steps The maximum number of steps. Applies only to Spatially averaged multimode model Relative error Relative integration error. Applies only to Spatially averaged multimode model Number of cavity sections Number of cavity sections defined for the TLMM model Simulation Noise When selected includes carrier/photon density noise and phase noise Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 430 FABRY PEROT LASER Technical background Two methods can be employed to model the dynamics of the Fabry Perot laser: Spatially Averaged Multimode or Transmission Line. These can be selected from the Laser model properties field in the “Main” tab of the Fabry Perot Laser Properties dialog box. The response of the multi-mode laser to a current waveform I(t) is determined by equations 1-5 below. The parameters Bias current and Modulation peak current are scale factors applied to the input electrical signal. The internal current I(t) is given by: I t = I DC + I in t I Pk Where Iin(t) is the input signal current, IDC is the parameter Bias Current and IPk is the parameter Modulation peak current. If the parameter Bias Current and Modulation peak current have zero values, the internal current is given by Iin(t) only. Spatially averaged multimode The Spatially averaged multimode model does not consider the spatial distribution of the field within the cavity (i.e. it is “spatially averaged”). It uses the standard multimode rate equations. Due to its averaged nature, it cannot model effects such as spatial hole burning. However, it is computationally faster than the transmission line model. The modulation dynamics of the FP laser are modeled by the coupled rate equations which describe the relation between the carrier density N(t), photon densities Si(t), and optical phases i(t): dN t It Nt 1 -------------- = ----------- – ---------- – G i N t – N t ---------------------------------------- S i t dt qV n i 1 + S j t j (1) dS i t 1 t ------------- = G i N t – N t ------------------------------------------------------- S i t – p S i t + N + K c S ext t dt n 1 + S t (2) i d i t -------------- = 1--- G i N t – N t – p dt 2 (3) where the gain (Gi) and the chirp (), for each mode i, are defined by: G i = v g g --------------------------------------------- 2i f i – f o 2 1 + --------------------- f (4) (5) 1 d i t i = ---------- -------------dt 2 431 FABRY PEROT LASER g vg is the differential gain coefficient is the group velocity fi is the frequency of the laser mode i fo is the laser central frequency f is the 3dB gain bandwidth is the gain compression factor Nt is the carrier density at transparency V is the active layer volume p is the cavity loss n Sext(t) Kc is the spontaneous emission factor is the mode confinement factor is the carrier lifetime is the line-width enhancement factor is the optically injected signal is the photon density coupling factor for the injected optical signal If the “Lifetime” recombination model is chosen, then: 1---= A + B N + C N2 n (6) where A, B, and C are the recombination coefficients. Note: The spontaneous emission rate BN (also called Rsp) is sometimes used in lieu of 1/2n in the last term of equation (3). Either form is acceptable but it is important that the spontaneous emission factor is selected accordingly. A Runge-Kutta algorithm is used to numerically integrate the coupled first order differential equations (1-3). If parameters Include noise and Include phase noise are disabled, these equations apply to a noiseless laser oscillating in a multi longitudinal modes above threshold. The photon and carrier densities within the active region of the laser are assumed to be uniform. If parameter Include noise is enabled, the Langevin noise terms for photon and carrier densities are included in the model [1] as well as the noise term for phase. The line-width enhancement factor and the nonlinear gain compression parameter are taken to be constant for a given structure. The number of longitudinal modes considered in the simulation is defined by the parameter Number of side modes (number of modes = 2*Number of side modes + 1) 432 FABRY PEROT LASER The electrical field at the laser output is given by: Et = P i exp j i t + i i with int h v i m v g V S i P i = -------------------------------------------------------------- where int v is the internal quantum efficiency is the optical frequency m is the mirror loss h is the Planck’s constant The component also allows injection of external light coupled into the longitudinal modes. The coupling constant is given by: vg K c = ----------------L Rf where L is the cavity length and Rf is the reflectivity of the facet through which the external optical signal is injected. Transmission line model The Transmission Line Laser Model (TLLM), is more computationally time consuming than the Spatially Averaged Multimode model. However, since it is discretized in both time and the longitudinal direction, it has the ability to model non-linear and fast transient effects. It is recommended to use this model if one needs to consider such effects as spatial hole burning and two-photon absorption [2,3]. The TLLM uses the rate equations for the interaction between the Field and the Carriers, and therefore uses many of the same parameters described in the previous section. However, as opposed to the multimode rate equations where the rate equations are discretized in wavelength, here they are discretized in time. The model follows the field as it propagates in time though the laser cavity. Unlike the traveling wave model, which solves directly for this field at each cavity section, the TLLM model makes an analogy to the standard Transmission Line Model (TLM). The field is modeled as a “voltage” and all elements in the laser cavity are modeled by “impedances” [2]. The laser cavity is broken into multiple sections. The sections are connected by nodes at which the field (“voltage”) scatters forwards and backwards. The gain and loss of the field are modeled in the time-domain by an RLC filter at each section where the effective R, L and C values are determined from the differential gain, damping, 3dB 433 FABRY PEROT LASER frequency and attenuation in the active layer assuming a Lorentzian line-width. The carrier rate equation is also modeled using the TLM. Frequency chirping is incorporated in the model with extra impedances connected to circulators [3]. External optical injection is incorporated by adding the injected field at each time-point to the left-most element, using the same coupling constant as the Spatially Average Multimode model. For reasons of computational efficiency, it is not recommended to use more than 50 sections (see Number of cavity sections in the “Numerical” tab), it is preferable to use 20-30 sections if the results are sufficiently accurate. The output field of the laser is simply the field at the right-most laser cavity X (1 - reflectivity). References [1] Agrawal GP, Dutta NK. Semiconductor lasers, 2nd ed. New York: Van Nostrand Reinhold, 1993. [2] A. Lowery, “New dynamic semiconductor laser model based on the transmission-line modelling method”, IEE Proceedings J Optoelectronics, V 134, pp281 (1987). [3] A. Lowery, "New dynamic model for multimode chirp in DFB semiconductor lasers", IEE Proceedings, V 137, pp293 (1990) 434 LED LED Simulates a modulated LED. Ports Name and description Port type Signal type Modulation Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [30,3e5] Electron lifetime 1e-009 s — ]0, 1] RC constant 1e-009 s — ]0, 1] Power calculation method Use slope efficiency Slope efficiency 0.5 W/A W/A Quantum efficiency 0.05 — — Spectral line profile Gaussian Bandwidth 6 THz Hz, THz, nm ]0, INF] File frequency unit Hz - - Hz, GHz, THz, nm, m Power — - Power-Phase, Real-Imag, Power, Phase Use sloped efficiency, Use quantum efficiency Gaussian, Defined Determines the frequency unit of the file with the measurements File format Determines the format of the file with the measurements ]0, 1] 435 LED Name and description Default value Default unit Units Value range Linear scale True — - True, False Filter.dat — — Defines whether the measured data is in linear scale or not Spectral line shape filename Filename with the measured data Interpolation Linear — Linear, Cubic Simulation Name and description Default value Units Value range Enabled True — True, False Parameterized Parameterized — — Iterations Iterations — [1, 1e+009] Name and description Default value Units Value range Generate random seed Yes — True, False 0 — [0,4999] Determines whether or not the component is enabled Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background In this model, the mean of the optical power is a function of the modulation current (input signal). The conversion of the current into optical power is described by the responsivity of the LED: it P = h f -------q where h f q 436 is the quantum efficiency is the Planck’s constant is the emission frequency is the electron charge LED i t is the modulation current signal The modulated characteristics depend of the electron lifetime and the device of the diode, and are modeled by the transfer function applied to the current: 1 H f = -----------------------------------------------------------1 + j 2 f n + rc where n is the Electron life time and rc is the RC constant. If the parameter Parameterized is selected, the output consist of a single value representing the average LED output at the frequency output. Note: The noise bins signals are not produced by this modulator. 437 LED 438 WHITE LIGHT SOURCE White Light Source Generates a Gaussian distributed optical white noise. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [0,+INF[ True — — True, False –30 dBm W, mW, dBm ]-INF,+INF[ Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Emission frequency PSD Determines whether the Power is the PSD (/Hz) or the average power Power Average output powers Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window 439 WHITE LIGHT SOURCE Noise Name and description Default value Default unit Units Value range Noise bins spacing 10 GHz Hz, GHz, THz, nm [1, 100000] Convert noise bins Convert noise bins — — — Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the generated noise bins are incorporated into the signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The average output Power or Power spectral density and Frequency are parameters that you specify. This model generates noise bins or sampled signals at the output according to: Ex t Ey t = x x t + jy x t r v x y t + j yy t P4 A Gaussian distribution has been assumed to describe the probability density function for the real and imaginary part of Ex and Ey. P is the average power when PSD parameter is false. If PSD is true, then P is calculated from the power spectral density multiplied by the Sample rate. 440 PUMP LASER Pump Laser Generates an optical parameterized signal to be used for optical amplifier pumping. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 980 nm Hz, THz, nm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Emission frequency Power Average output powers Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization 441 PUMP LASER Simulation Name and description Default value Units Value range Enabled True — True, False Iterations — [1, 1e+009] Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Technical background In the CW Laser case, average output Power is a parameter that you specify. This model generates only parameterized signal at the output. The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P E Y t ke j where the power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as follows: 2 k 1 – k cos tan 2 = -------------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 442 PUMP LASER ARRAY Pump Laser Array An array of pump lasers. Ports Name and description Port type Signal type Output 1 Output Optical Output 2 Output Optical Output 3 Output Optical Output 4 Output Optical Output 5 Output Optical Output 6 Output Optical Output 7 Output Optical Output 8 Output Optical Parameters Main Name and description Default value Units Value range Number of output ports 8 — [1, 1000] Frequency Name and description Default value Default unit Units Value range Frequency[0] 1405 nm Hz, THz, nm [100, 2000] 1412.5 nm Hz, THz, nm [100, 2000] Center frequency for pump 0 Frequency[1] Center frequency for pump 1 443 PUMP LASER ARRAY Name and description Default value Default unit Units Value range Frequency[2] 1420 nm Hz, THz, nm [100, 2000] 1427.5 nm Hz, THz, nm [100, 2000] 1435 nm Hz, THz, nm [100, 2000] 1442.5 nm Hz, THz, nm [100, 2000] 1450 nm Hz, THz, nm [100, 2000] 1457.5 nm Hz, THz, nm [100, 2000] Name and description Default value Default unit Units Value range Power[0] 100 mW W, mW, dBm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ 100 mW W, mW, dBm [0,+INF[ Center frequency for pump 2 Frequency[3] Center frequency for pump 3 Frequency[4] Center frequency for pump 4 Frequency[5] Center frequency for pump 5 Frequency[6] Center frequency for pump 6 Frequency[7] Center frequency for pump 7 Power Output power for pump 0 Power[1] Output power for pump 1 Power[2] Output power for pump 2 Power[3] Output power for pump 3 Power[4] Output power for pump 4 Power[5] Output power for pump 5 Power[6] Output power for pump 6 Power[7] Output power for pump 7 444 PUMP LASER ARRAY Polarization Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Name and description Default value Units Value range Enabled True — True, False Iterations — [1, 1e+009] Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation 445 PUMP LASER ARRAY Notes: 446 CONTROLLED PUMP LASER Controlled Pump Laser This component is a pump laser that can be controlled by an electrical analog signal. It allows the design and simulation of automatic gain control schemes for optical amplifiers, such as control loops for the pump laser current. Ports Name and description Port type Signal type Input Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 980 nm Hz, THz, nm [0,+INF[ 20 mA — [0,+INF[ 0.5 W/A — [0,+INF[ 300 mA — [0,1000] 0 deg — ]-INF,+INF[ Emission frequency Threshold current Lasing begins and optical output sharply rises when current supplied exceeds the threshold current Slope efficiency The increase in optical output power divided by the increase in electrical input current Maximum current If the input current is above this value the output power is constant Initial phase Laser initial phase 447 CONTROLLED PUMP LASER Control Name and description Default value Units Value range Gain 1 — ]-INF,+INF[ 0 — ]-INF,+INF[ Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Name and description Default value Units Value range Enabled True — True, False Parameterized — True, False The electrical signal is multiplied by this parameter before the laser stage Bias The electrical signal is biased by this parameter before the laser stage Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled Parameterized Determines whether the output signal is parameterized or not Technical background The controlled pump laser designed for analog control of the output pump power. The input signal is first scaled by the parameters Gain and Bias. If the value of the scaled signal is less than the Maximum input current and greater than the Threshold current the current is multiplied by the Slope efficiency. The model supports individual samples for time driven simulation 448 CW LASER ARRAY CW Laser Array This component is an array of CW lasers. Ports Name and description Port type Signal type Output 1 Output Optical Output 2 Output Optical Output 3 Output Optical Output 4 Output Optical Output 5 Output Optical Output 6 Output Optical Output 7 Output Optical Output 8 Output Optical Parameters Main Name and description Default value Default Unit Value range Number of output ports 8 — [1, 1000] Linewidth 10 MHz [0, 1e+009[ Initial phase 0 deg [-1e+100,1e+100] 449 CW LASER ARRAY Frequency Name and description Default value Default unit Units Value range Frequency[0] 193.1 THz Hz, THz, nm [30, 300000] 193.2 THz Hz, THz, nm [30, 300000] 193.3 THz Hz, THz, nm [30, 300000] 193.4 THz Hz, THz, nm [30, 300000] 193.5 THz Hz, THz, nm [30, 300000] 193.6 THz Hz, THz, nm [30, 300000] 193.7 THz Hz, THz, nm [30, 300000] 193.8 THz Hz, THz, nm [30, 300000] Name and description Default value Default unit Units Value range Power[0] 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ Center frequency for laser 0 Frequency[1] Center frequency for laser 1 Frequency[2] Center frequency for laser 2 Frequency[3] Center frequency for laser 3 Frequency[4] Center frequency for laser 4 Frequency[5] Center frequency for laser 5 Frequency[6] Center frequency for laser 6 Frequency[7] Center frequency for laser 7 Power Output power for laser 0 Power[1] Output power for laser 1 Power[2] Output power for laser 2 Power[3] Output power for laser 3 Power[4] Output power for laser 4 Power[5] Output power for laser 5 450 CW LASER ARRAY Name and description Default value Default unit Units Value range Power[6] 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Output power for laser 6 Power[7] Output power for laser 7 Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Parameterized Parameterized — — — Sample rate Sample rate Hz Hz, GHz, THz ]0,+INF[ Name and description Default value Default unit Units Value range Noise bandwidth 0 THz Hz, THz, nm [0,+INF[ –100 dB — ]-INF,+INF[ 3 dB — ]-INF,+INF[ Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Frequency simulation window Noise Bandwidth to create noise bins Noise threshold Minimum value for adaptation of noise bins Noise dynamic Threshold ratio for adaptation of noise bins 451 CW LASER ARRAY Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 452 CW LASER ARRAY ES CW Laser Array ES This component is an array of CW lasers. The emission frequencies are equally spaced (ES). Ports Name and description Port type Signal type Output 1 Output Optical Output 2 Output Optical Output 3 Output Optical Output 4 Output Optical Output 5 Output Optical Output 6 Output Optical Output 7 Output Optical Output 8 Output Optical Parameters Main Name and description Default value Default Unit Value range Number of output ports 8 — [1, 1000] Frequency 193.1 THz, Hz, nm [30,+INF[ 100 GHz, THZ, Hz, nm ]-INF,+INF[ Linewidth 10 MHz [0, 1e+009[ Initial phase 0 deg [-1e+100,1e+100] Emission frequency of the first laser Frequency spacing Frequency spacing between adjacent lasers 453 CW LASER ARRAY ES Power Name and description Default value Default unit Units Value range Power[0] 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Output power for laser 0 Power[1] Output power for laser 1 Power[2] Output power for laser 2 Power[3] Output power for laser 3 Power[4] Output power for laser 4 Power[5] Output power for laser 5 Power[6] Output power for laser 6 Power[7] Output power for laser 7 Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization 454 CW LASER ARRAY ES Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Parameterized Parameterized — — — Sample rate Sample rate Hz Hz, GHz, THz ]0,+INF[ Name and description Default value Default unit Units Value range Noise bandwidth 0 THz Hz, THz, nm [0,+INF[ –100 dB — ]-INF,+INF[ 3 dB — ]-INF,+INF[ Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Frequency simulation window Noise Bandwidth to create noise bins Noise threshold Minimum value for adaptation of noise bins Noise dynamic Threshold ratio for adaptation of noise bins Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The CW Laser Array ES is equivalent to the conventional CW Laser Array component. However, The CW Laser Array ES model is easier to set up for WDM systems, because it only requires the initial laser emission frequency and the spacing. The signal output power is the same for all the output signals. 455 CW LASER ARRAY ES Notes: 456 CW LASER MEASURED CW Laser Measured Generates a continuous wave (CW) optical signal based on measurements. You can enter parameters such as linewidth, side mode suppression, and relative intensity noise (RIN). Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz,THz, nm [0,+INF[ Power 0 dBm W, mW, dBm ]-INF,+INF[ Linewidth 10 MHz — [0,+INF[ Initial phase 0 deg — ]-INF,+INF[ Emission frequency 457 CW LASER MEASURED Side Mode Name and description Default value Default unit Units Value range Calculate side mode False — — — 1 — — [1, 100000] 75 GHz Hz, GHz, THz, nm [0,+INF[ 30 dB — [0,+INF[ False — — — Name and description Default value Default unit Units Value range RIN –130 dB/Hz — ]-INF,+INF[ False — — True, False 10 dBm W. mW, dBm ]-INF,+INF[ Determines if the signal output will have one side mode Number of side modes Number of side modes if running as a Fabry-Perot laser. Separation Mode frequency separation from the laser center frequency Suppression ratio Attenuation of the side mode relative to the output power Independent side mode When enabled, the side mode has an independent power value that can change the total average power RIN Relative intensity noise value Include RIN Determines if the RIN will be added to the output signal Measured power Value of the power during the measurement of RIN 458 CW LASER MEASURED Polarization Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] None — None, Polarization X, Polarization Y Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Polarization filter Determines the polarization of the filter Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Parameterized Parameterized — — — Sample rate Sample rate Hz Hz, GHz, THz ]0,+INF[ Name and description Default value Default unit Units Value range Noise bandwidth 1 THz Hz, THz, nm [1e-100, 1e100] 100 GHz Hz, GHz, THz, nm [1, 1000] Convert noise bins — — [0, 0] Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Frequency simulation window Noise Bandwidth to increase noise bins Noise bins spacing Determines noise bins spacing Convert noise bins Determines if the generated noise bins are incorporated into the signal 459 CW LASER MEASURED Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 460 CW LASER MEASURED Technical background This model is similar to the CW Laser — however, it includes additional effects, such as multiple side modes and RIN. If the you enable the parameter Calculate side mode, the side mode will be generated according to: E out t = j P 1 + s cos 2 f t + s cos – 2 f t e where P is laser output power, s is the parameter Suppression ratio in linear scale, and f is defined by the parameter Separation. If the parameter Independent side mode is enabled, the average signal power will be greater than P, since it includes the contribution from the side mode. If this parameter is disabled, the output power will be P. This means that the signal will be scaled in order to give the same average power. The signal phase and polarization is calculated in the same way as the CW laser. The model can also works as a Fabry-Perot laser; in this case, the parameter Number of side modes defines the number of modes of the laser. The normalized power for each mode is calculated based on the power of the central mode and the power of the first side mode [1], according to: 1 P n = ------------------------------------------21 n 1 + ----- – 1 ----- P s M M is the parameter Number of side modes, n is the index of each side mode pair, and P s is calculated from the power of the first side mode: where 1 P s = --------------------------------- 1--- – 1 M 2 + 1 s If the parameter Include RIN is enabled, the model generates noise bins with bandwidth and spacing that you define. The parameter RIN is the ratio of the meansquare optical intensity noise to the square of the average power [2][3]: 2 P RIN = --------------dB Hz 2 Pm 2 where P is the mean-square optical intensity fluctuation at a specific frequency 2 2 and P m is the parameter Measured power. This models estimates P based on the parameters RIN and Measured power. The signal phase and polarization is calculated in the same way as the CW laser, where the laser phase noise is modeled using a Gaussian random variable for the 461 CW LASER MEASURED phase difference between two successive time instants with zero mean and a variance equal to 2 f , where f is the laser Linewidth. The probability density function is: 1 f = ---------------------- e 2 fdt 2 – -----------------4fdt where is the phase difference between two successive time instants and dt is the time discretization. The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j The power splitting k and the phase difference Azimuth and Ellipticity : are calculated from the parameters k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin References [1] Agrawal, G.P. and Dutta, N.K., “Semiconductor Laser”, 2nd Edition, Van Nostrand Reinhold, New York, N.Y., (1993). [2] Lau, K. Y. and Yariv, A., "Ultra-High Speed Semiconductor Laser", J. Quant. Elect., 21, 121-136, (1985). [3] Agrawal, G.P., Fiber-Optic Communication Systems, Second edition. John Wiley & Sons, Inc., N.Y., (1997). 462 DIRECTLY MODULATED LASER MEASURED Directly Modulated Laser Measured Directly modulated laser that allows you to specify the dynamic of the laser based on measured parameters. You can also enter parameters such as linewidth, chirp, side mode, suppression and relative intensity noise (RIN). Ports Name and description Port type Signal type Modulation Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz,THz, nm [0,+INF[ Digital — — Digital, Analog 10 dBm W, mW, dBm ]-INF,+INF[ 10 dB — [0,+INF[ 20 mA — [0,+INF[ Emission frequency Configuration Defines whether the laser will work in analog or digital configuration Power Laser output power Extinction ratio Steady state power ratio between marks and spaces Threshold current Lasing begins and optical output sharply rises when current supplied exceeds the threshold current 463 DIRECTLY MODULATED LASER MEASURED Name and description Default value Default unit Units Value range Slope efficiency 0.4 W/A — [0,+INF[ Linewidth 10 MHz — [0,+INF[ Initial phase 0 deg — ]-INF,+INF[ The increase in optical output power divided by the increase in electrical input current Measurements Name and description Default value Default unit Units Value range Overshoot 30 % — [0,+INF[ 30 % — [0,+INF[ 1/(Bit rate) * 0.05 s s, ms, ns, ps [0,+INF[ 1/(Bit rate) * 0.05 s s, ms, ns, ps [0,+INF[ 1/(Bit rate) * 0.5 s s, ms, ns, ps [0,+INF[ 1/(Bit rate) * 0.5 s s, ms, ns, ps [0,+INF[ (Bit rate) * 5 Hz Hz, MHz, GHz, THz [0,+INF[ (Bit rate) * 5 Hz Hz, MHz, GHz, THz [0,+INF[ Percentage of overshoot during the transition from 0 to 1 relative to the steady state power Undershoot Percentage of undershoot during the transition from 0 to 1 relative to the steady state power Rise time Defined as the time from when the rising edges reaches 0% of the amplitude to the time it reaches 100% of the amplitude Fall time Defined as the time from when the falling edges reaches 100% of the amplitude to the time it reaches 0% of the amplitude Damping time leading edge Relaxation time when the signal overshoot reaches 1/e of the max value during the transition from 0 to 1 Damping time trailing edge Relaxation time when the signal undershoot reaches 1/e of the min value during the transition from 1 to 0 Resonant frequency leading edge Frequency of the oscillations in the transition from 0 to 1 Resonant frequency trailing edge Frequency of the oscillations in the transition from 1 to 0 464 DIRECTLY MODULATED LASER MEASURED Side Mode Name and description Default value Default unit Units Value range Calculate side mode False — — True, False 1 — — [1, 100000] 75 GHz Hz, GHz, THz, nm [0,+INF[ 30 dB — [0,+INF[ Name and description Default value Default unit Units Value range RIN –130 dB/Hz — ]-INF,+INF[ False — — — 10 dBm W, mW, dBm ]-INF,+INF[ Name and description Default value Default unit Value range Alpha parameter 0 — [-100, 100] Adiabatic chirp 0 1/(W.s) ]-INF,+INF[ Determines if the signal output will have one side mode Number of side modes Number of side modes if running as a Fabry-Perot laser. Separation Mode frequency separation from the laser center frequency Suppression ratio Attenuation of the side mode relative to the output power RIN Relative intensity noise value Include RIN Determines if the RIN will be added to the output signal Measured power Value of the power during the measurement of RIN Chirp Results from changes in the steady state carrier densities 465 DIRECTLY MODULATED LASER MEASURED Polarization Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] None — None, Polarization X, Polarization Y Name and description Default value Units Value range Enabled True — True, False Parameterized — [1,+INF[ Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Polarization filter Determines the polarization of the filter Simulation Determines whether or not the component is enabled Parameterized Noise Name and description Default value Default unit Units Value range Noise bandwidth 1 THz Hz, THz, nm [1e-100, 1e100] 100 GHz Hz, GHz, THz, nm [1, 1000] Convert noise bins — — [0, 0] Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Bandwidth to increase noise bins Noise bins spacing Determines noise bins spacing Convert noise bins Determines if the generated noise bins are incorporated into the signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 466 DIRECTLY MODULATED LASER MEASURED Technical background This model is a different from the Laser Measured, where you can enter measured parameters and the model calculates the rate equation parameter by using sophisticated optimization routines. Here you can enter measured parameters that describe the laser dynamics by building the laser output signal. If the parameter Configuration is Digital, the range of the amplitude of the signal input is normalized between 0 and 1. This means that this model converts the input signal to a sequence of squared pulses. The parameter Power is the steady state value of the output power at the 1 level. The steady-state value for the power at the 0 level is calculated from the parameter Extinction ratio: Er = 10 log P 1 P 0 where P1 is the parameter Power, Er is the parameter Extinction ratio, and P0 is the steady-state power at the 0 level. The measured parameters will be used to build P(t) (see Figure 1). Figure 1 Measured parameters used to build P(t) 467 DIRECTLY MODULATED LASER MEASURED If you enable the parameter Calculate side mode, the side mode is generated according to: E out t = j P t 1 + s cos 2 f t + s cos – 2 f t e where P is laser output power, s is the parameter Suppression ratio in linear scale, and f is defined by the parameter Separation. The model can also works as a Fabry-Perot laser; in this case, the parameter Number of side modes defines the number of modes of the laser. The normalized power for each mode is calculated based on the power of the central mode and the power of the first side mode [1], according to: 1 P n = ------------------------------------------2n 1 1 + ----- – 1 ----- P s M M is the parameter Number of side modes, n is the index of each side mode pair, and P s is calculated from the power of the first side mode: where 1 P s = --------------------------------- 1--- – 1 M 2 + 1 s If the parameter Configuration is Analog, the model will use the parameters Threshold current and Slope efficiency to scale the input signal, without normalization.Different from the Digital, the Analog configuration supports individual samples for time driven simulation. If the parameter Include RIN is enabled, the model will generate noise bins with bandwidth and spacing that you define. The parameter RIN is the ratio of the meansquare optical intensity noise to the square of the average power [2][3]: 2 P RIN = --------------dB Hz 2 Pm 2 where P is the mean-square optical intensity fluctuation at a specific frequency 2 and P m is the parameter Measured power. 2 This model estimates P based on the parameters RIN and Measured power. 468 DIRECTLY MODULATED LASER MEASURED The chirp is modeled using: d d ------ = -----e- ----- InP t + P t 2 dt dt where is the signal phase, e is the parameter Alpha parameter or linewidth enhancement factor, and is the parameter Adiabatic chirp. The signal phase and polarization is calculated in the same way as the CW laser, where the laser phase noise is modeled using a Gaussian random variable for the phase difference between two successive time instants with zero mean and a variance equal to 2 f , where f is the laser Linewidth. The probability density function is: 2 – -----------------1 4fdt f = ---------------------- e 2 fdt where is the phase difference between two successive time instants and dt is the time discretization. The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j The power splitting k and the phase difference Azimuth and Ellipticity : is calculated from the parameters k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin References [1] Agrawal, G.P. and Dutta, N.K., “Semiconductor Laser”, 2nd Edition, Van Nostrand Reinhold, New York, N.Y., (1993). [2] Lau, K. Y. and Yariv, A., "Ultra-High Speed Semiconductor Laser", J. Quant. Elect., 21, 121-136, (1985). [3] Agrawal, G.P., Fiber-Optic Communication Systems, Second edition. John Wiley & Sons, Inc., N.Y., (1997). 469 DIRECTLY MODULATED LASER MEASURED Notes: 470 VCSEL LASER VCSEL Laser This component is a vertical-cavity surface emitting laser (VCSEL). It includes thermal effects and parameter fitting based on measured LI and IV curves. Ports Name and description Port type Signal type Input Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Unit Value range Frequency 193.1 THz Hz, THz, nm [30, 3e5] 38 mA [0, 1000] 28 mA [0, 1000] Laser emission frequency Bias current Input bias current Modulation peak current Input modulation peak current Thermal Name and description Default value Thermal effects True Units Value range [True, False] Defines whether thermal effects are included in the calculation Temperature 20 C, K [-INF, +INF] 2600 C/W [0, +INF] The ambient temperature Thermal impedance Related to the temperature changes to the power dissipated as heat 471 VCSEL LASER Name and description Default value Units Value range Thermal time constant 1e-6 s [0, +INF] Name and description Default value Units Value range Reduce parameters True Response time of the device temperature Physical [True, False] Defines if the user can enter a reduced number of physical parameters Active layer volume 1.5e-010 cm3 [0, 1e-3] Group velocity 8.5e+009 cm/s [0, 100e9] Quantum efficiency 0.4 Differential gain coefficient 2.5e-016 cm2 [0, 50e-16] Carrier density at transparency 1e+018 cm-3 [0, 100e18] Mode confinement factor 0.4 Scaling factor 2.6e-008 W [0, +INF] 16000 1/s [0, +INF] [0, 1] [0, 1] Factor accounting for the output coupling efficiency Gain coefficient Coefficient in 1/s Carrier number at transparency 19400000 Carrier lifetime 1e-009 s [0, 50e-9] Photon lifetime 3e-012 s [0, 50e-9] Spontaneous emission factor 3e-005 Gain compression coefficient 1e-017 Line-width enhancement factor 5 [-20, 20] Injection efficiency 1 [0, +INF] [0, +INF] [2e-5, 20e-5] cm3 [0.5e-17, 10e-17] Current injection efficiency Meaurements Name and description Default value Units Value range Max input current 40 mA [0, +INF] The maximum value for the signal input current. It should match the maximum value of the measurements 472 VCSEL LASER Name and description Default value Units Value range a- Ioff(T) 1.246e-3 - a0=A, [-INF, +INF] Coefficients for the polynomial function of temperature for the offset current curve 2.545e-5 a1=A/C, 2.908e-7 - a2=A/C2, 2.531e-10 a3=A/C3… 1.022e-12 b- V(T) 1 b0=V1/2, [-INF, +INF] b1= V1/2/C, Coefficients for the polynomial function of temperature for the current-voltage curve b2= V1/2/C2, b3= V1/2/C3… c- V(I) Coefficients for the polynomial function of current for the current-voltage curve 1.721 275 2.439e4 c0=V1/2, c1= V 1/2 [-INF, +INF] /A, V1/2/A2, 1.338e6 - c2= 4.154e7 c3= V1/2/A3… 6.683e8 4.296e9 Parameter fitting True [True, False] Defines if the component will fit the parameters using the measurements LI curves filename The filename with the measurements of the LI curves, including the temperature dependence IV curves filename The filename with the measurements of the IV curves, including the temperature dependence LI curves at different temperatures (ACW) LI Temperature.dat IV Temperature.dat 183x3 array The values loaded from the LI curves filename IV curves at different temperatures (ACV) The values loaded from the IV curves filename 78x3 array Col 1: A Col 1: [0,+INF] Col 2: C Col 2: [-INF,+INF] Col 3: W Col 3: [0,+INF] Col 1: A Col 1: [0,+INF] Col 2: C Col 2: [-INF,+INF] Col 3: V Col 3: [0,+INF] 473 VCSEL LASER Numerical Name and description Default value Units Value range Adaptive step False — True, False 1000000 — [1e3,10e6] 0.0001 — — Defines whether to use adaptive step or not Max. number of steps The maximum number of steps Relative error Relative integration error Graphs Name and description Default value Units Value range Calculate graphs False True, False 20 [5, 100e6] Defines whether to calculate graphs or not Number of points Number of points for the graphs From 0 mA [0, +INF] 40 mA [0, +INF] Current lower limit for the graphs To Current upper limit for the graphs Simulation Name and description Default value Enabled True Parameterized Parameterized Units Value range [True, False] Noise Name and description Default value Include noise True [True, False] Include phase noise True [True, False] 474 Units Value range VCSEL LASER Random numbers Name and description Default value Units Value range Generate random seed True [True, False] 0 [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Graphs Name and description X Title Y Title IV curve Current (A) Voltage (V) LI curve Current (A) Power (W) Measured IV curve Current (A) Voltage (V) Measured LI curve Current (A) Power (W) Results Name and description Units Output power at bias current mW Voltage at bias current V Ioff(thermal) at bias current mA Device temp at bias current C Output power at peak current mW Voltage at peak current V Ioff(thermal) at peak current mA Device temperature at peak current C Max device temperature over time window C Thermal impedance C/W Active layer volume cm^3 Quantum efficiency Gain coefficient 1/s Scaling factor W Carrier number at transparency 475 VCSEL LASER Name and description Units Current at max. voltage A a0 A a1 A/C a2 A/C^2 a3 A/C^3 a4 A/C^4 a5 A/C^5 a6 A/C^6 a7 A/C^7 a8 A/C^8 a9 A/C^9 b0 V^.5 b1 V^.5/C b2 V^.5/C^2 b3 V^.5/C^3 b4 V^.5/C^4 b5 V^.5/C^5 b6 V^.5/C^6 b7 V^.5/C^7 b8 V^.5/C^8 b9 V^.5/C^9 c0 V^.5 c1 V^.5/A c2 V^.5/A^2 c3 V^.5/A^3 c4 V^.5/A^4 c5 V^.5/A^5 c6 V^.5/A^6 c7 V^.5/A^7 c8 V^.5/A^8 c9 V^.5/A^9 476 VCSEL LASER Technical Background The modulation dynamics of the laser are modeled by coupled rate equations that describe the relationship between the carrier density N(t), photon density S(t), and between the optical phase t and temperature T(t)[1][2]. i I t – I off t N t 1 dN t ------------= ------------------------------------- – ---------- – v g g N t – N t ------------------------------- S t 1 + St dt qV n (1) 1 S t Nt dS t - -----------= v g g N t – N t ------------------------------- S t – --------- + -------------------------1 + St p dt n d t 1 1 ------------- = --- v g g Nt – N t – ----dt 2 p dT t - 1 -----------= ------ T 0 + IV (I,T) – P 0 R th – T dt th (2) (3) (4) where, g is the differential gain coefficient v g is the group velocity is the gain compression factor N t is the carrier density at transparency is the spontaneous emission factor is the mode confinement factor V is the active layer volume p is the photon lifetime n is the carrier lifetime is the line-width enhancement factor i is the injection efficiency T 0 is the ambient temperature P O is the output power R th is the thermal impedance th is the thermal time constant 477 VCSEL LASER The time variations for the optical and laser chirp are given by [1] S V int h v P 0 = --------------------------------------2 p 1 d v = ---------- -----2 dt (5) (6) where int is the internal quantum efficiency v is the optical frequency h is Planck’s constant By enabling the parameter Reduce parameters, the user can enter the alternative parameters that will be used to calculate N t , int and g according to: N0 N t = ------ (7) V G0 V g = ---------- (8) vg 2k p o = ----------- (9) hv where N o is the carrier number at transparency G 0 is the gain coefficient k is the scaling factor, with P O = kSV The offset current is given by a polynomial function of temperature [2]. 2 3 4 5 6 7 8 I off T = a 0 + a 1 T + a 2 T + a 3 T + a 4 T + a 5 T + a 6 T + a 7 T + a 8 T + a 9 T where the coefficients 478 a 0 to a 9 are given by the parameter a – Ioff T . 9 VCSEL LASER The current-voltage (IV) relationship is modeled using a polynomial function of temperature and current [2]: · 9 9 V (T,I) = b 0 + b 1 T + + b 9 T c 0 + c 1 I + + c 9 I where · 9 b 0 + b 1 T + + b 9 T is · 5 2 3 4 6 7 8 9 b0 + b1 T + b2 T + b3 T + b4 T + b5 T + b6 T + b7 T + b8 T + b9 T 9 c 0 + c 1 I + + c 9 I is 2 3 4 5 6 7 8 9 c0 + c1 I + c2 I + c3 I + c4 I + c5 I + c6 I + c7 I + c8 I + c9 I where the coefficients and c – V I . b 0 to b 9 and c 0 to c 9 are given by the parameter b – V T When the parameter Parameter fitting is disabled, the component will calculate using user-defined parameters. In this case, the user should provide all the parameters, including the coefficient for the polynomial functions. The measured LI and IV curves will not be used in the calculation. When the parameter Parameter fitting is enabled, the component will calculate new parameters using the current parameters as a first guess, including the number and the initial values for the polynomial coefficients. The new parameters can be seen in the component results. First the component will calculate the coefficients for the IV curve, and then it will calculate the coefficients for the offset current, the thermal impedance and the new slope efficiency. The maximum value of the input current is calculated from the current derivative of the IV curve. However, the user should provide this value as an input parameter. The parameters will be adjusted to reflect the new slope efficiency. The affected parameters are the active layer volume and the quantum efficiency. For each calculation, the component will also generate the peak power and voltage results based on the bias and modulation peak current. These values can be used for external parameter fitting if the user intends to use a different fitting engine. The file format for the LI curve data is the following: Current0 Temperature0 Power0 Current1 Temperature1 Power1 Current2 Temperature2 Power2 The units are ampere, Celsius and watt. 479 VCSEL LASER The file format for the IV curve data is the following: Current0 Temperature0 Voltage0 Current1 Temperature1 Voltage 1 Current2 Temperature2 Voltage 2 The units are ampere, Celsius and volt. The range for the current value should be the same for both files. If the range is not the same, the parameter-fitting engine will not converge to an optimum fitting. For example, if the LI curve is provided from 0 to 40 mA, the IV curve must be also provided from 0 to 40 mA. The default parameters of the VCSEL are the same as in [2]. If the parameter Thermal effects is disabled, the calculation will perform using the same equations as in [1], without the thermal effects and the parameter fitting. Parameters Bias current and Modulation peak current are scale factors applied to the input electrical signal. 480 VCSEL LASER The internal current I t is given by: I t = I DC + I in t I Pk (4) Where I in t is the input signal current, I DC is the parameter Bias Current and I Pk is the parameter Modulation peak current. If parameter Bias Current and Modulation peak current have zero values, the internal current is given by I in t only. The VCSEL Laser supports individual samples for time-driven simulation. References [1] J. C. Cartledge and G. S. Burley, "The Effect of the Laser Chirping on Lightwave System Performance", J. Lightwave Technology, vol. 7, pp. 568-573, March 1989. [2] P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton and K. W. Wyatt, "A Simple Rate-EquationBased Thermal VCSEL Model", J. Lightwave Technology, vol. 17, pp. 865-872, May 1999. 481 VCSEL LASER Notes: 482 VCSEL LASER MEASURED VCSEL Laser Measured This component is a vertical-cavity surface emitting laser (VCSEL). It includes thermal effects and parameter fitting based on measured LI and IV curves.The VCSEL Laser Measured component is a vertical-cavity surface emitting laser (VCSEL) model which allows for the extraction of laser rate equation parameters using measurements of the threshold current, optical power, resonance frequency, and damping factor. Once achieved, thermal effects be optionally modeled; including parameter fitting based on measured LI and IV curves. Ports Name and description Port type Signal type Input Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Unit Value range Frequency 193.1 THz Hz, THz, nm [30, 3e5] 38 mA [0, 1000] 28 mA [0, 1000] Laser emission frequency Bias current Input bias current Modulation peak current Input modulation peak current Thermal Name and description Default value Thermal effects True Units Value range [True, False] Defines whether thermal effects are included in the calculation 483 VCSEL LASER MEASURED Name and description Default value Units Value range Temperature (Test) 20 C, K [-INF, +INF] 20 C, K [-INF, +INF] 2600 C/W [0, +INF] 1e-6 s [0, +INF] Name and description Default value Units Value range Optimize device parameters True The ambient temperature at which the simulation is run Temperature (Ref) The ambient temperature specified with the measured data Thermal impedance Related to the temperature changes to the power dissipated as heat Thermal time constant Response time of the device temperature Physical [True, False] When enabled (TRUE) the parameters specified below are optimized with measured data Active layer volume 10e-012 cm3 [0, 1e-3] Group velocity 8.5e+009 cm/s [0, 100e9] Quantum efficiency 0.4 Differential gain coefficient 2.5e-016 cm2 [0, 50e-16] Carrier density at transparency 1e+018 cm-3 [0, 100e18] Mode confinement factor 1 Carrier lifetime 5e-009 s [0, 50e-9] Photon lifetime 2.28e-012 s [0, 50e-9] Spontaneous emission factor 1e-006 Gain compression coefficient 1e-017 Linewidth enhancement factor 5 [-20, 20] Injection efficiency 1 [0, +INF] Current injection efficiency 484 [0, 1] [0, 1] [2e-5, 20e-5] cm3 [0.5e-17, 10e-17] VCSEL LASER MEASURED Meaurements Name and description Default value Default unit Units Value range Frequency response data type Parameters — — Parameters, From file 10.28 1e9s-1 — ]0, 1000] True — — True, False 6.43 1e20 Hz2 — ]0, 1000] 3.87 GHz — ]0, 1000] 6.43 1e20 Hz2 — ]0, 1000] 18 mA — [0, 1000] 23 mA — [0, 1000] True — — True, False 0.3 mW/mA — [1e-100, 1e100] 1.5 mW W, mW, dBm [1e-100, 1e100] False — — True, False 10 MHz — [1,200] Defines whether the frequency response data is provided by the damping factor and resonance frequency factor parameters or by the subtracted IM response curve Damping factor The measured damping factor of the laser Resonance frequency data Defines whether to use the resonance frequency or the resonance frequency factor for calculations Resonance frequency factor The measured resonance frequency factor of the laser Resonance frequency The measured resonance frequency of the laser Subtracted IM response filename File containing the subtracted IM response curve Threshold current The measured threshold current of the laser Reference current The reference current used to estimate the measured output power Slope efficiency data Defines whether to use slope efficiency or power to estimate the LI curve Slope efficiency The measured slope efficiency of the laser Power at reference current The laser power at the reference current Linewidth data Determines whether the line-width will be part of the parameter extraction procedure Linewidth Specifies the laser line-width for the steady-state condition 485 VCSEL LASER MEASURED Name and description Default value Default unit Units Value range Average RIN data False — — True, False 0.2 GHz — [0.01,20] 15 GHz — [0.01,20] -140 dB/Hz — [-500, -50] 40 mA — [0, +INF] a- Ioff(T) 1.246e-3 - a0=A, mA [-INF, +INF] Coefficients for the polynomial function of temperature for the offset current curve 2.545e-5 a1=A/C, 2.908e-7 - a2=A/C2, 2.531e-10 a3=A/C3… — [-INF, +INF] — [-INF, +INF] — — Determines whether the average RIN in a specified bandwidth will be part of the parameter extraction procedure RIN start Specifies the initial frequency of the frequency range where the average RIN is calculated RIN stop Specifies the final frequency of the frequency range where the average RIN is calculated Average RIN Specifies the average RIN value for the steadystate condition over the frequency bandwidth defined by the values of RIN start and stop. Max input current The maximum value for the signal input current. It should match the maximum value of the measurements 1.022e-12 b- V(T) 1 b0=V1/2, b1= V Coefficients for the polynomial function of temperature for the current-voltage curve 1/2 /C, b2= V1/2/C2, b3= V1/2/C3… c- V(I) 1.721 275 - c0=V1/2, Coefficients for the polynomial function of current for the current-voltage curve 2.439e4 c1= V1/2/A, 1.338e6 - c2= V1/2/A2, 4.154e7 c3= V1/2/A3… 6.683e8 4.296e9 Parameter fitting Defines if the component will fit the parameters using the measurements 486 True — VCSEL LASER MEASURED Name and description Default value Default unit Units Value range LI curves filename LI Temperature.dat — — — IV Temperature.dat — — — 183x3 array Col 1: A — C1: [0,+INF] The filename with the measurements of the LI curves, including the temperature dependence IV curves filename The filename with the measurements of the IV curves, including the temperature dependence LI curves at different temperatures (ACW) The values loaded from the LI curves filename IV curves at different temperatures (ACV) 78x3 array Col 2: C C2:[-INF,+INF] Col 3: W C3: [0,+INF] Col 1: A The values loaded from the IV curves filename — C1: [0,+INF] Col 2: C C2: [-INF,+INF] Col 3: V C3: [0,+INF] Numerical Name and description Default value Units Value range Adaptive step False — True, False 1000000 — [1e3,10e6] 0.0001 — — Defines whether to use adaptive step or not Max. number of steps The maximum number of steps Relative error Relative integration error Graphs Name and description Default value Units Value range Calculate graphs False True, False 20 [5, 100e6] Defines whether to calculate graphs or not Number of points Number of points for the graphs From 0 mA [0, +INF] 40 mA [0, +INF] Current lower limit for the graphs To Current upper limit for the graphs 487 VCSEL LASER MEASURED Simulation Name and description Default value Enabled True Parameterized Parameterized Units Value range [True, False] Noise Name and description Default value Units Value range Include noise True [True, False] Include phase noise True [True, False] Random numbers Name and description Default value Units Value range Generate random seed True [True, False] 0 [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 488 VCSEL LASER MEASURED Graphs Name and description X Title Y Title IV curve Current (A) Voltage (V) LI curve Current (A) Power (W) Measured IV curve Current (A) Voltage (V) Measured LI curve Current (A) Power (W) Normalized IM Response IM Response (dB) Modulation frequency (GHz) Response subtraction curve Response Subtraction (dB) Modulation frequency (GHz) Response subtraction curve fitted Response Subtraction (dB) Modulation frequency (GHz) Results Name and description Units Output power at bias current mW Voltage at bias current V Ioff(thermal) at bias current mA Device temp at bias current C Output power at peak current mW Voltage at peak current V Ioff(thermal) at peak current mA Device temp at peak current C Max device temp over time window C Thermal offset correction mA Quantum efficiency Active layer volume 10-11 cm3 Spontaneous emission factor Gain compression coefficient 10-17 cm3 Carrier density at transparency 1018 cm-3 Differential gain coefficient 10-16 cm2 Linewidth enhancement factor Mode confinement factor Carrier lifetime ns 489 VCSEL LASER MEASURED Name and description Units Photon lifetime ps Slope efficiency - fitted mW/mA Thermal impedance - fitted C/W Quantum efficiency - fitted Active layer volume - fitted 10-12 Z0 1020 Hz2 Z1 1020 Hz2 Y0 109 s-1 Y1 109 s-1 Threshold current at reference mA Slope efficiency at reference mW/mA Power at reference mW Resonance freq. factor 1020 Hz2 Resonance frequency GHz Average RIN dB/Hz Linewidth MHz Current at max. voltage A a0 A a1 A/C a2 A/C^2 a3 A/C^3 a4 A/C^4 a5 A/C^5 a6 A/C^6 a7 A/C^7 a8 A/C^8 a9 A/C^9 b0 V^.5 b1 V^.5/C b2 V^.5/C^2 b3 V^.5/C^3 490 VCSEL LASER MEASURED Name and description Units b4 V^.5/C^4 b5 V^.5/C^5 b6 V^.5/C^6 b7 V^.5/C^7 b8 V^.5/C^8 b9 V^.5/C^9 c0 V^.5 c1 V^.5/A c2 V^.5/A^2 c3 V^.5/A^3 c4 V^.5/A^4 c5 V^.5/A^5 c6 V^.5/A^6 c7 V^.5/A^7 c8 V^.5/A^8 c9 V^.5/A^9 Technical Background The VCSEL Laser Measured model simulation process includes the following linked features: • The input of measurement data from VCSEL manufacturer data sheets or experimental results • Laser rate equations physical parameter extraction based on certain of these measurement data • The modeling of VCSEL steady state and transient performance (including characterization of thermal effects) • Detailed results and graphs representing the device’s performance under transient and non-transient conditions Measurement data The VCSEL Laser Measured model extracts values of the rate equation parameters using measurements of Y (damping factor), Z (resonance frequency factor), Ith (threshold current), and P (Power bias) [1]. The parameter extraction procedure is based on minimization of the sum of squared errors between the measured values of (Y, Z, Ith, P) and values calculated from rate 491 VCSEL LASER MEASURED equation parameters. The minimization is over the values of the rate equation parameters which are included in the following equations: Damping factor S 1 1 1 Y = v g g ------------------------ + ----- – v g g N – N t --------------------------2 + ----p 1 + S n 1 + S Resonance frequency factor vg g S 1 1 1 Z = v g g ------------------------ ----- + – 1 --------------- N – N t --------------------------2 + -------------n p n 1 + S p 1 + S Threshold current q V 1 + Nt vg g p I th = ----------- ---------------------------------------------------n vg g p Power bias S V int h v P = --------------------------------------2 p where, g is the gain compression factor Nt int is the carrier density at transparency V is the active layer volume p n 492 is the differential gain coefficient is the spontaneous emission factor is the mode confinement factor is the internal quantum efficiency is the photon lifetime is the carrier lifetime NandS are the steady-state values of the carrier and photon densities corresponding to the bias current of the laser v vg h is the unmodulated optical frequency is the group velocity is the Planck’s constant VCSEL LASER MEASURED The minimization routine finds a local minimum for the equation 2 2 2 Func = Y mea – Y cal + z mea – z cal + P mea – P cal + I mea – I cal 2 where Y mea Z mea ,P mea ,I mea are the measured values and Y cal Z cal ,P cal ,I cal are the calculated values using the initial estimates of the rate equation parameters. The laser linewidth parameter can be included in the optimization process (when “Linewidth data parameter” is selected) by defining the linewidth value for the laser when the bias current is the reference current parameter [4]. Similarly, when “Average RIN data” is selected, the average RIN value is included in the optimization process (the user has to define the average RIN value in the defined frequency range; see [2][3] for details on how RIN is calculated. The user can also calculate the subtracted IM response from the measured IM response curves (Figure 1) and load a file with this information into the component. This will allow for a pre-optimization step, where the component fits the parameters Z and Y to the measured results. Figure 1 Measured IM responses The file format for the subtracted IM response data is the following: Frequency0 SubtractedIM0 Frequency1 SubtractedIM1 Frequency2 SubtractedIM2 ... FrequencyN SubtractedIMN The units are GHz and dB respectively. 493 VCSEL LASER MEASURED Main tab (bias and modulation current settings) The extraction of rate equation parameters is independent of the parameters in the main tab (frequency and current settings). The internal current I t is given by: I t = I DC + I in t I Pk (1) Where I in t is the input signal current, I DC is the parameter Bias Current and I Pk is the parameter Modulation peak current. If parameter Bias Current and Modulation peak current have zero values, the internal current is given by I in t only. Physical parameters (laser rate model) When Optimize device parameters is selected within the Physical parameters tab, the laser rate equation device parameters are optimized (and thus subject to change) to align with measurement data as defined in the previous section. When not selected, the parameter settings defined in the Physical parameters tab will be used The modulation dynamics of the laser are modeled by coupled rate equations that describe the relationship between the carrier density N(t), photon density S(t), and between the optical phase t and temperature T(t) [6][7]. i I t – I off t N t dN t 1 ------------= ------------------------------------- – ---------- – v g g N t – N t ------------------------------- S t qV n dt 1 + S t dS t - 1 S t N t -----------= v g g N t – N t ------------------------------- S t – --------- + -------------------------dt n 1 + St p d t 1 1 -----------= --- v g g Nt – N t – ----dt 2 p dT t 1 -----------= ------ T 0 + IV (I,T) – P 0 R th – T dt th 494 (3) (4) (1) (2) VCSEL LASER MEASURED where, g is the differential gain coefficient v g is the group velocity is the gain compression factor N t is the carrier density at transparency is the spontaneous emission factor is the mode confinement factor V is the active layer volume p is the photon lifetime n is the carrier lifetime is the line-width enhancement factor i is the injection efficiency T 0 is the ambient temperature P O is the output power R th is the thermal impedance th is the thermal time constant The time variations for the optical and laser chips are given by [6] S V int h v P 0 = --------------------------------------2 p 1 d v = ---------- -----2 dt (5) (6) where int is the internal quantum efficiency v is the optical frequency h is Planck’s constant Thermal tab (thermal modeling) When Thermal effects is selected, the parameters defined in the Thermal parameters tab are used as inputs to the laser rate equations thermal model. The parameter Temperature (Test) represents the ambient temperature at which the simulation is to 495 VCSEL LASER MEASURED be run. The parameter Temperature (Ref) represents the ambient temperature at which the Measured data was obtained (for example the settings for Power at reference current, Slope efficiency or Threshold current are normally associated with an ambient test temperature). The laser rate equations for thermal modeling differ mainly from the non-thermal laser rate equations through the addition of a thermal offset current within the dN(t)/dt carrier density relationship. This offset current is given by a polynomial function of temperature (= Temperature (Test)) [7] The offset current is given by a polynomial function of temperature [7]. 2 3 4 5 6 7 8 I off T = a 0 + a 1 T + a 2 T + a 3 T + a 4 T + a 5 T + a 6 T + a 7 T + a 8 T + a 9 T where the coefficients 9 a 0 to a 9 are given by the parameter a – Ioff T The current-voltage (IV) relationship is modeled using a polynomial function of temperature and current [7]: · 9 9 V (T,I) = b 0 + b 1 T + + b 9 T c 0 + c 1 I + + c 9 I where the coefficients and c – V I . b 0 to b 9 and c 0 to c 9 are given by the parameter b – V T When the parameter Parameter fitting is disabled (see the Measurements tab), the component will calculate using user-defined parameters. In this case, the user should provide all the parameters, including the coefficient for the polynomial functions. The measured LI and IV curves will not be used in the calculation. When the parameter Parameter fitting is enabled, the component will calculate new parameters using the current parameters as a first guess, including the number and the initial values for the polynomial coefficients. First the component will calculate the coefficients for the IV curve, and then it will calculate the coefficients for the offset current, the thermal impedance and the new slope efficiency. The parameters will be adjusted to reflect the new slope efficiency. The affected parameters are the active layer volume and the quantum efficiency. The maximum value of the input current is calculated from the current derivative of the IV curve. However, the user should provide this value as an input parameter. For each calculation, the component will also generate the peak power and voltage results based on the bias and modulation peak current. These values can be used for external parameter fitting if the user intends to use a different fitting engine. The file format for the LI curve data is the following: Current0 Temperature0 Power0 Current1 Temperature1 Power1 Current2 Temperature2 Power2 The units are ampere, Celsius and watt. 496 VCSEL LASER MEASURED The file format for the IV curve data is the following: Current0 Temperature0 Voltage0 Current1 Temperature1 Voltage 1 Current2 Temperature2 Voltage 2 The units are ampere, Celsius and volt. The range for the current value should be the same for both files. If the range is not the same, the parameter-fitting engine will not converge to an optimum fitting. For example, if the LI curve is provided from 0 to 40 mA, the IV curve must be also provided from 0 to 40 mA. The default parameters of the VCSEL are the same as in [7]. If the parameter Thermal effects is disabled, the calculation will perform using the same equations as in [6], without the thermal effects and the parameter fitting. If parameter Include noise is enabled, the Langevin noise terms for photon and electron densities are included in the model[4]. If Include phase noise is enabled, the Langevin noise term for the phase is included in the model. Component results An extensive list of component results is included with the VCSEL Laser Measured component and includes the following: • Output power calculations at bias and peak current conditions • Steady state and transient thermal data (thermal offset current, device junction temperatures, thermal voltage) at bias and peak current conditions • Device physical parameters results (after Measured data fitting) • Adjustments to Slope efficiency, Thermal impedance, Quantum efficiency, and Active layer volume following measured LI and IV curve parameter fitting • Device measured data results • Thermal coefficient (a, b, c) values References [1] Cartledge, J. C. and Srinivasan, R. C. “Extraction of DFB laser rate equation parameters for system simulation purposes”, J. Light. Techn., 15, 852-860, (1997). [2] Yamada, M. "Variation of intensity noise and frequency noise with the spontaneous emission factor in semiconductor lasers". IEEE Journal of Quantum Electronics. Volume 30, Issue 7, July 1994 Page(s):1511 - 1519. [3] Agrawal, G.P., Fiber-Optic Communication Systems, Second edition. John Wiley & Sons, Inc., N.Y., (1997). [4] Agrawal GP, Dutta NK. Semiconductor lasers, 2nd ed. New York: Van Nostrand Reinhold, 1993. [5] K.Petermann, Laser Diode Modulation and Noise, Kluwer Academic Publishers,1988 497 VCSEL LASER MEASURED [6] J. C. Cartledge and G. S. Burley, "The Effect of the Laser Chirping on Lightwave System Performance", J. Lightwave Technology, vol. 7, pp. 568-573, March 1989. [7] P. V. Mena, J. J. Morikuni, S. M. Kang, A. V. Harton and K. W. Wyatt, "A Simple Rate-EquationBased Thermal VCSEL Model", J. Lightwave Technology, vol. 17, pp. 865-872, May 1999. 498 DFB LASER DFB Laser The distributed feedback (DFB) laser component simulates the modulation dynamics of a DFB laser cavity using either the multi-mode rate equations or the transmission line laser model (TLLM). It also allows for an external optical signal to be injected into the active layer. Ports Name and description Port type Signal type Modulation Input Electrical Output Output Optical Input Input Optical Optical injection port. Connect an optical null signal when not being used. Parameters Main Name and description Default value Default unit Unit Value range Bias current 27 mA — [0, 1000] 10 mA — [0, 1000] 0.001 — — [0, 1] Input bias current Modulation peak current Input modulation peak current Front facet reflectivity The threshold current, calculated from the laser physical parameters 499 DFB LASER Name and description Default value Default unit Unit Value range Rear facet reflectivity 0.3 — — [0, 1] mA — — — Spatially averaged multimode, Transmission line Default value Default unit Value range Active length 0.06 cm 0, 1e-3 Active layer width 0.00015 cm 0, 1e-3 Active layer depth 20e-006 cm 0, 1e-3 Group index 20e-006 cm 0, 1e-3 Quantum efficiency 3.5 — Group velocity 8.5e+009 cm/s 0, 100e9 Differential gain coefficient 1e-016 cm2 0, 50e-16 Gain bandwidth 5 THz Carrier density at transparency 1e+018 cm-3 0, 100e18 Mode confinement factor 0.4 — 0, 1 Recombination model Lifetime — Lifetime, Coefficients Carrier lifetime 1.86e-009 s [0, 50e-9] Recombination coefficient A 100e+006 1/s [0, 1e15] The threshold power, calculated from the laser physical parameters Threshold current Automatically calculated Laser model Determines which laser model to use to solve the rate equations Spatially averaged multimode Physical Name and description Active layer parameters The internal quantum efficiency of the laser (also called slope efficiency) Carrier parameters Linear recombination coefficient 500 DFB LASER Name and description Default value Default unit Value range Recombination coefficient B 0.2e-009 cm3/s [0, 1e-7] 40e-030 cm6/s [0, 1e-7] Spontaneous emission factor 0.004 — [2e-5, 20e-5] Gain compression coefficient 36e-018 cm3 [0.5e-17, 10e17] Linewidth enhancement factor 5 — [–20, 20] Loss 10 cm-1 [0, 1e10] Two photon absorption False — True, False 25e-027 m4/GW [0, 1e10] Name and description Default value Units Value range Grating index difference 0.005 — [0, 1] Grating order 1 — — Grating period 221.42857 nm — Bragg wavelength 1550 Hz, THz, nm — Quarter wave shift at center False Bimolecular recombination coefficient Recombination coefficient C Auger recombination coefficient Loss parameters When selected “Two photon absorption” is modeled Two photon absorption coefficient Grating True, False 501 DFB LASER Numerical Name and description Default value Units Value range Adaptive step False — True, False 100000 — [1e3,10e6] 0.001 — — 50 — [0, 200] Name and description Default value Units Value range Calculate graphs False True, False 20 [5, 100e6] Defines whether to use adaptive step or not. Applies only to Spatially averaged multimode model Max. number of steps The maximum number of steps. Applies only to Spatially averaged multimode model Relative error Relative integration error. Applies only to Spatially averaged multimode model Number of cavity sections Number of cavity sections defined for the TLMM model Graphs Defines whether to calculate graphs or not Number of points Number of points for the graphs From 0 mA [0, +INF] 40 mA [0, +INF] Name and description Default value Units Value range Enabled True Parameterized Parameterized Current lower limit for the graphs To Current upper limit for the graphs Simulation 502 [True, False] DFB LASER Noise Name and description Default value Units Value range Include noise True — True, False Include phase noise True — True, False Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The DFB laser essentially consists of a Fabry Perot laser with a Bragg grating above the active layer. It is schematically represented in the following figure: Figure 1 DFB Schematic (quarter wave shift not enabled). The “Grating” tab provides the parameters for the Bragg grating. When Quarter wave shift at center is not enabled the DFB is configured as per Figure 1. In this case, there will be two dominant modes on either side of the Bragg wavelength at equal distances (note that due to imperfections in real DFB lasers, generally one of these modes will be more dominant). When Quarter wave shift at center is enabled the laser is as represented in Figure 2 (in this case, there will be one dominant mode exactly at the Bragg wavelength.) 503 DFB LASER Figure 2 DFB Schematic (quarter wave shift enabled) Two methods can be used to model the dynamics of the DFB laser: Spatially averaged multimode and Transmission line. These models are accessed from the Laser model drop down menu field within the “Main” tab of the DFB Laser Properties dialog box The response of the multi-mode laser to a current waveform I(t) is determined by equations 1-5. The parameters Bias current and Modulation peak current are scale factors applied to the input electrical signal. The internal current I(t) is given by: I t = I DC + I in t I Pk Where Iin(t) is the input signal current, IDC is the parameter Bias Current and IPk is the parameter Modulation peak current. If the parameter Bias Current and Modulation peak current have zero values, the internal current is given by Iin(t) only. Spatially averaged multimode The Spatially averaged multimode model does not consider the spatial distribution of the field within the cavity (i.e. it is “spatially averaged”). It uses the standard multimode rate equations. Due to its averaged nature, it cannot model effects such as spatial hole burning. However, it is computationally faster than the transmission line model. The multimode rate equations used for the DFB laser model are similar to those used for the “Spatially averaged” Fabry Perot model, with the following exceptions: 504 • The modes are either the two dominant modes of the non-quarter wave shifted laser or the single mode at the Bragg wavelength of the quarter wave shifted laser. All other modes in the system are ignored, which is usually a good approximation. • The mirror reflectivities are replaced by effective reflectivities [1] which depend on the modes of the DFB structure. The DFB modes are calculated using coupled mode theory. Intuitively this should seem reasonable as the Bragg grating will cause back-scattering that is wavelength dependent. These modes depend on the actual mirror reflectivities, size of cavity, and coupling strength (calculated from the “Grating index difference”) [1]. DFB LASER • The photon lifetime is replaced by an effective photon lifetime [2] (or as implemented here, cavity loss) also mode dependent. From this, one can calculate the threshold current. The modulation dynamics of the DFB laser are modeled by the multimode rate equations which describe the relation between the carrier density N(t), photon densities Si(t), and optical phases i(t): dN t I t N t 1 -------------- = ----------- – ---------- – G i N t – N t ---------------------------------------- S i t dt qV n i 1 + S j t j (1) dS i t 1 N t ------------- = G i N t – N t ---------------------------------------- S i t – p S i t + ------------------ + K c S ext t n dt 1 + S t (2) i d i t -------------- = 1--- G i N t – N t – p dt 2 (3) where the gain (Gi) and the chirp (), for each mode i, are defined by: G i = v g g --------------------------------------------- 2i f i – f o 2 1 + --------------------- f (4) (5) 1 d i t i = ---------- -------------2 dt g vg is the differential gain coefficient is the group velocity fi is the frequency of the laser mode i fo is the laser central frequency f is the 3dB gain bandwidth is the gain compression factor Nt V is the carrier density at transparency p is the cavity loss n Sext(t) is the spontaneous emission factor is the mode confinement factor is the active layer volume is the carrier lifetime is the line-width enhancement factor is the optically injected signal 505 DFB LASER Kc is the photon density coupling factor for the injected optical signal If the “Lifetime” recombination model is chosen, then: 1---= A + B N + C N2 n (8) where A, B, and C are the recombination coefficients. Note: The spontaneous emission rate BN (also called Rsp) is sometimes used in lieu of 1/2n in the last term of equation (3). Either form is acceptable but it is important that the spontaneous emission factor is selected accordingly. A Runge-Kutta algorithm is used to numerically integrate the coupled first order differential equations. If parameters Include noise and Include phase noise are disabled, these equations apply to a noiseless laser oscillating in a multi longitudinal modes above threshold. The photon and carrier densities within the active region of the laser are assumed to be uniform. If parameter Include noise is enabled, the Langevin noise terms for photon and carrier densities are included in the model [1] as well as the noise term for phase. The line-width enhancement factor and the nonlinear gain compression parameter are taken to be constant for a given structure. The number of longitudinal modes considered in the simulation is defined by the parameter Number of side modes (number of modes = 2*Number of side modes + 1) The electrical field at the laser output is given by: Et = P i exp j i t + i i with int h v i m v g V S i P i = -------------------------------------------------------------- where int v 506 is the internal quantum efficiency is the optical frequency m is the mirror loss h is the Planck’s constant DFB LASER The component also allows injection of external light coupled into the longitudinal modes. The coupling constant is given by: vg K c = ----------------L Rf where L is the cavity length and Rf is the reflectivity of the facet through which the external optical signal is injected. Transmission line model The Transmission Line Laser Model (TLLM), is more computationally time consuming than the Spatially Averaged Multimode model. However, since it is discretized in both time and the longitudinal direction, it has the ability to model non-linear and fast transient effects. It is recommended to use this model if one needs to consider such effects as spatial hole burning and two-photon absorption [3,4].This method also makes no approximation on the longitudinal modes in the laser. Thus, while one will have the same dominant modes as with the above model, there is also an inter-play with the higher order DFB modes and the Fabry Perot modes. These effects are especially pronounced for weak grating coupling The TLLM uses the rate equations for the interaction between the Field and the Carriers, and therefore uses many of the same parameters described in the previous section. However, as opposed to the multimode rate equations where the rate equations are discretized in wavelength, here they are discretized in time. The model follows the field as it propagates in time though the laser cavity. Unlike the traveling wave model, which solves directly for this field at each cavity section, the TLLM model makes an analogy to the standard Transmission Line Model (TLM). The field is modeled as a “voltage” and all elements in the laser cavity are modeled by “impedances” [3]. The laser cavity is broken into multiple sections. The sections are connected by nodes at which the field (“voltage”) scatters forwards and backwards. The gain and loss of the field are modeled in the time-domain by an RLC filter at each section where the effective R, L and C values are determined from the differential gain, damping, 3dB frequency and attenuation in the active layer assuming a Lorentzian line-width. The carrier rate equation is also modeled using the TLM.Spontaneous emission is modeled by adding a stochastic voltage term in each section The DFB structure is modeled by alternating each transmission line section with “high” or “low” impedances (for the quarter wave shift, the two most central layers will have the same impedance) which will generate corresponding scattering matrices at each node. It can be shown that this can model the real DFB grating modes as some of the higher harmonics of these alternating impedance structures will correspond to the DFB modes [4] Frequency chirping is incorporated in the model with extra impedances connected to circulators [4]. External optical injection is incorporated by adding the injected field at each time-point to the left-most element, using the same coupling constant as the Spatially Average Multimode model. 507 DFB LASER For reasons of computational efficiency, it is not recommended to use more than 50 sections (see Number of cavity sections in the “Numerical” tab), it is preferable to use 20-30 sections if the results are sufficiently accurate. The output field of the laser is simply the field at the right-most laser cavity X (1 - reflectivity). References [1] Shun Lien Chuang, “Physics of Photonic Devices”, 2nd ed. Wiley, 2009. [2] W. Zheng and G. W.Taylor, “Determination of the Photon Lifetime for DFB Lasers”, IEEE Journal of Quantum Electronics, V 43, pp 295 (2007) [3] A. Lowery, “New dynamic semiconductor laser model based on the transmission-line modelling method”, IEE Proceedings J Optoelectronics, V 134, pp281 (1987). [4] A. Lowery, “New dynamic model for multimode chirp in DFB semiconductor lasers”, IEE Proceedings, V 137, pp293 (1990) 508 EMPIRICAL LASER MEASURED Empirical Laser Measured The Empirical Laser Measured component uses vendor-based or measured data to model the input current - light relationship (LI) and the transfer function (H(f)) of a semiconductor laser. Ports Name and description Port type Signal type Modulation Input Electrical Output Output Optical Parameters Main Name and description Default value Default unit Unit Value range Frequency 193.1 THz Hz, THz, nm [30,3e5] Linewidth 10 MHz — Initial phase 0 deg Temperature 25 C Emission frequency of the laser Temperature used for the analysis Use measured LI curve data False False, True Manufacturer specifications Temperature (reference) 25 C 0.75 mA The reference temperature at which the manufacturer data was measured/provided Threshold current (reference) Threshold current variation with T Slope efficiency (reference) — [0, 1000] — [0, 1000] %/C 0.4 W/A 509 EMPIRICAL LASER MEASURED Name and description Default value Slope efficiency variation with T Maximum current Default unit Unit Value range — [0, 1000] %/C 10 mA Measured LI curve data LI curves filename LI Temperature.dat LI curves at different temperatures LI Interpolation order 6 Transfer function model None None, Load coefficients, User-defined, From S21 data Use Butterworth filter True False, True Filter order 2 Load coefficient parameters Filename for load coefficients User defined parameters Current dependence False False, True Temperature dependence False False, True Resonant frequency 5 GHz 3 dB frequency 7.5 GHz Damping coefficient 1 1/ns Damping coefficient offset 0 1/ns Parasitic frequency cut-off 1000 GHz D factor GHz/sqrt(mA) K factor ns D factor change with temp 0 % K factor change with temp 0 % S21 data S21 data filename S21 information filename Maximum order in current 510 2 EMPIRICAL LASER MEASURED Name and description Default value Maximum order in temperature 2 Save coefficients False Default unit Unit Value range False, True Filename for saved coefficients Side Mode Name and description Default value Default unit Units Value range Calculate side mode False — — True, False 1 — — [1, 100000] 75 GHz Hz, GHz, THz, nm [0,+INF[ 30 dB — [0,+INF[ Name and description Default value Default unit Value range Alpha parameter 0 — [-100, 100] Adiabatic chirp 0 1/(W.s) ]-INF,+INF[ Determines if the signal output will have one side mode Number of side modes Number of side modes if running as a Fabry-Perot laser. Separation Mode frequency separation from the laser center frequency Suppression ratio Attenuation of the side mode relative to the output power Chirp Results from changes in the steady state carrier densities 511 EMPIRICAL LASER MEASURED Polarization Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] None — None, Polarization X, Polarization Y Name and description Default value Units Value range Enabled True — True, False Parameterized — [1,+INF[ Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Polarization filter Determines the polarization of the filter Simulation Determines whether or not the component is enabled Parameterized Noise Name and description Default value Default unit Units Value range RIN –130 dB/Hz — ]-INF,+INF[ False — — — 10 dBm W, mW, dBm ]-INF,+INF[ 1 THz Hz, THz, nm [1e-100, 1e100] 100 GHz Hz, GHz, THz, nm [1, 1000] Convert noise bins — — [0, 0] Relative intensity noise value Include RIN Determines if the RIN will be added to the output signal Measured power Value of the power during the measurement of RIN Noise bandwidth Bandwidth to increase noise bins Noise bins spacing Determines noise bins spacing Convert noise bins Determines if the generated noise bins are incorporated into the signal 512 EMPIRICAL LASER MEASURED Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Name and description Default value Units Value range Adaptive step False — True, False 1000000 — [1e3,10e6] 0.0001 — — Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Numerical Defines whether to use adaptive step or not Max. number of steps The maximum number of steps Relative error Relative integration error Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The Empirical Laser Measured model takes LI data (from either manufacturer specifications or measured data), functionally represented by L(t) =L(I(t)), and transfer function data (from either user defined parameters or measured S21 data), functionally represented by H(...), and calculates the response directly as:: –1 E t = F Ef (1) E f = Hf Lf L f = F L t 513 EMPIRICAL LASER MEASURED where F is the Fourier transform. This model is designed such that it can be used over a range of currents and temperatures, depending on the coefficients or experimental data used. LI Curve The LI curve has two purposes. The first is to provide a relation between the power and current at any required temperature. The second is to estimate the threshold current at the required temperature, which is needed to calculate the transfer function in the following section. When using manufacturer specifications, it is only required to input the appropriate Temperature, Threshold current, Threshold current variation with temp, Slope efficiency and Slope efficiency variation with temp as found under the Main tab to characterize the LI curve at any temperature. Alternatively, one can use experimental LI curves at various temperatures. From this data, with appropriate interpolations, the LI curve and threshold current can be determined over a range of temperatures. LI data format The format for the data is in three columns as follows (the current must be in mA, temperature in C and power in mW) First curve data Second curve data Nth curve data Current (mA) Temperature (C) Power (mW) I1(1) T1 P1(1) I1(2) T1 P1(2) I1(3) T1 P1(3) ... ... ... I2(1) T2 P2(1) I2(2) T2 P2(2) I2(3) T2 P2(3) ... ... ... IM(1) TM PM(1) IM(2) TM PM(2) IM(3) TM PM(3) ... ... ... For example, if we have three sets of LI data at 10, 20 and 30 C (each at currents of 1,2,3, and 4 mA), the data should be formatted as follows: 514 1 10 0.1 2 10 3 EMPIRICAL LASER MEASURED 3 10 5 4 10 9 1 20 0.1 2 20 2 3 20 4 4 20 6 1 30 0.01 2 30 1 3 30 2 4 30 3 Each one of the LI curves is fitted with a polynomial (default Order = 6) to allow for the calculation of the optical power at any current. For temperatures not exactly at the experimental data temperatures, a linear interpolation is performed by using the two closest experimental curves. Estimating the threshold current Qualitatively, we can estimate the threshold current as being the point at which the LI curve quickly changes slope as shown schematically in Fig 1. In this model, the threshold current is found from the inflection point of the second derivative of the LI curve. Figure 1 Threshold current inflection point for a semiconductor laser 515 EMPIRICAL LASER MEASURED Transfer function The transfer function of this component is based on a small-signal response function multiplied by a parasitic element and, optionally, a Butterworth filter. f r2 1 - H b f f 3dB H f = ------------------------------------------------------- --------------------------------1/2 2 1/2 2 2 2 2 2 f fr – f + f 1 + ---- f p (2) Where fr is the resonant frequency, is the damping coefficient, fp is the parasitic frequency, f3dB is the 3dB bandwidth and Hb is the Butterworth filter transfer function. Once these terms are determined, a transfer function can be constructed. There are three options for getting these terms: • Direct input. See the appropriate values in “User defined parameters” in the Transfer function tab. In this case there is no current or temperature dependence assumed. • User K and D factors. Assuming fp is a constant, and estimating a 3 dB frequency; find fr and from the K and D factors as follows: f r = D 1 – D T – T ref I – I th 1 / 2 (3) = K 1 – K T – T ref f r2 + o where D, K and are the D factor change with temperature, K factor change with temperature and Damping coefficient offset; respectively • Use experimental S21 data. From the known temperature and currents of each experimental curve; fp, f3dB, fr, and are approximated using non-linear curve fitting. Once these values have been found for each temperature and current, a further polynomial fit is performed to extract coefficients for later interpolation (as follows) f r I T = an m I – I th 1/2 n T – T ref m n m f 3dB I T = bn m I – Ith 1/2 n T – T ref m n· m I T = 1/2 n cn m I – Ith T – Tref m n· m f p I T = dn m I – I th 1/2 n T – T ref m n· m where an,m dn,m are extracted coefficients. In this way we can find, at each temperature and current, the various parameters and then the transfer function. Note: The threshold current Ith is determined from the LI curve. 516 (4) EMPIRICAL LASER MEASURED Note: The transfer function is not built with the instantaneous current, but rather the average current (I), which is a reasonable approximation as it is already assumed we are operating in the small-signal regime S21 data format Two files must be read when using S21 data. The first is called S21 data filename which holds the raw response (assumed to be based on power transmission response) versus frequency data and the second S21 information filename holds the temperature, current, and initial guesses of certain values for each curve. The data and information formats are represented schematically as follows: Frequency Response Frequency Response Frequency Response f1(1) tr1(1) f2(1) tr2(1) fN(1) trN(1) f1(2) tr1(2) f2(2) tr2(2) fN(2) trN(2) f1(3) tr1(3) f2(3) tr2(3) fN(3) trN(3) ... ... ... ... ... Current Temperature Guess for resonance f Guess for Damping coeff. Guess for 3 dB bandwidth of Butterworth filter I1 T1 f1 Damp. C1 f(3dB)1 I2 T2 f2 Damp. C2 f(3dB)2 I3 T3 f3 Damp. C3 f(3dB)3 ... ... ... ... ... IN TN fN Damp. CN f(3dB)N All frequencies must be in Hz, the temperature in degrees C, the current in mA and the damping coefficient in ns-1 For example, consider the case when we have three experimental S21 curves. The first is at 1 mA and 10 C. It has a response of 0.1 at 1E8 Hz, 0.4 at 1E9 Hz, 1 at 2E9 Hz and 0.01 at 3E9 Hz. The second is at 2 mA and 20 C. It has a response of 0.2 at 2E8 Hz, 0.5 at 1E9 Hz and 0.1 at 2E9 Hz. The third is at 3 mA and 50 C. It has a response of 0.1 at 2E8 Hz, 0.8 at 5E8 Hz and 0.01 at 1E9 Hz. The data file will thus be formatted as follows: 1E8 0.1 2E8 0.2 2E8 0.1 1E9 0.4 1E9 0.5 5E8 0.8 2E9 1 2E9 0.1 1E9 0.01 3E9 0.01 -1 0 -1 0 Please note the placement of frequencies “-1” and response “0”. This is because the table must be completely full for the software to load and read the file correctly. The 517 EMPIRICAL LASER MEASURED last two data sets only have 3 values. Any values with frequency “-1” will be ignored during the calculation. The information file will have the format: 1 10 2E9 1 4E9 2 20 1E9 1 2E9 3 50 5E8 1 1E9 The guess for the damping coefficient is not as critical, however it is important to have a good guess for the resonant frequency. A sufficient guess it to look at each curve and estimate the frequency of peak transmission response. Generally, a good 3 dB frequency guess is about twice the resonant frequency. For convenience, we have include the option Save coefficients under the Transfer function tab. This saves the calculated an,m dn,m coefficients into a data file, which can then be read in again later by selecting the option Load coefficients from the Transfer function model drop-down box. References [1] F. Hopfer, A. Mutig, G. Fiol, P. Moser, D. Arsenijevic, V. A. Shchukin, N. N. Ledentsov, S. S. Mikhrin, I. L. Krestnikov, D. A. Livshits, A. R. Kovsh, M. Kuntz, D. Bimberg, ‘‘120°C 20 Gbit/s operation of 980 nm VCSEL based on sub-monolayer growth,’’ Vertical-Cavity Surface-Emitting Lasers XIII, Photonics West 2009, 24–29 January 2009, San Jose, California, USA, Proceedings of SPIE, Vol. 7229, 72290C, 6th February 2009. [2] Muller, M.; Hofmann, W.; Grundl, T.; Horn, M.; Wolf, P.; Nagel, R.D.; Ronneberg, E.; Bohm, G.; Bimberg, D.; Amann, Markus-Christian, “1550-nm High-Speed Short-Cavity VCSELs,” Selected Topics in Quantum Electronics, IEEE Journal of, vol.17, no.5, pp.1158,1166, Sept.-Oct. 2011 [3] Amann, Markus-Christian; Hofmann, W., “InP-Based Long-Wavelength VCSELs and VCSEL Arrays,” Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, no.3, pp.861-868, MayJune 2009. 518 SPECTRAL LIGHT SOURCE Spectral Light Source The Spectral Light Source applies a spectral line profile to a white noise source. Either a Lorentzian, Gaussian or file-based (user-defined) spectral profile can be defined. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz,THz, nm [0,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ 10 MHz — [0,+INF[ 0 — — None, Lorentzian, Gaussian, Defined 10 MHz Hz, kHz, MHz, GHz, THz, um, nm ]0,+INF[ Hz - - Hz, GHz, THz, nm, m Power — - Power-Phase, Real-Imag, Power, Phase Emission frequency PSD Power spectral density. When selected Power Emission frequency Spectral line profile Determines which type of spectral profile to be applied to the white light source Linewidth FWHM (power) of spectral line shape. Applies to Gaussian and Lorentzian profiles File frequency unit Determines the frequency unit of the file with the measurements File format Determines the format of the file with the measurements 519 SPECTRAL LIGHT SOURCE Name and description Default value Default unit Units Value range Linear scale True — - True, False Filter.dat — — Defines whether the measured data is in linear scale or not Spectral line shape filename Filename with the measured data Interpolation Linear Azimuth 0 — Linear, Cubic deg — ]-90,90] 0 deg — [-45,45] Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Sample rate Hz Hz, GHz, THz ]0,+INF[ Name and description Default value Default unit Units Value range Noise bins spacing 10 GHz Hz, GHz, THz, nm [0,+INF[ Convert noise bins — — — Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Sample rate Frequency simulation window Noise Width (frequency) of noise bins Convert noise bins When selected 520 SPECTRAL LIGHT SOURCE Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The Spectral Light Source applies a spectral line profile to a white noise source. Either a Lorentzian, Gaussian or file-based (user-defined) spectral profile can be defined. 521 SPECTRAL LIGHT SOURCE 522 SET OSNR Set OSNR The Set OSNR component is used to add a defined noise floor level to a signal. Ports Name and description Port type Signal type Input 1 Input Optical Output 1 Output Optical Parameters Main Name and description Default value Default unit Unit Value range Signal Frequency 1550 nm Hz, THz, nm [30,3e5] 2*Symbol rate — Hz 18 — — — Iterations Iterations — — — Sample rate 5*Sample rate Hz — — Convert noise bins mA — — Center frequency of the white light source Signal bandwidth The signal bandwidth for measuring the signal power Set OSNR The OSNR level at which the input signal will be set The frequency bandwidth of the noise source Convert noise bins Technical background The Set OSNR component is used to add a defined noise floor level to an optical signal. A White Light Source with a large bandwidth (default setting = 5*sample rate) 523 SET OSNR is used as the noise source. The noise is level is set based on the following OSNR calculation: P s mW OSNR dB = 10 log -------------------------- P n0.1 mW where Ps is the total signal power within the signal bandwidth (2 x Symbol rate) and Pn0.1 is the noise power measured within a 0.1 nm bandwidth window Note: As the noise is added to the signal using a power combiner there is a 3 dB transmission loss applied to both the signal and noise source (the OSNR level is not affected). Figure 1 Set OSNR compound component 524 SET OSNR Transmitters Library - Optical Optical Pulse Generators • Optical Gaussian Pulse Generator • Optical Sech Pulse Generator • Optical Impulse Generator • Measured Optical Pulse • Measured Optical Pulse Sequence • Time Resolve Chirp (TRC) Measurement Data 525 SET OSNR 526 OPTICAL GAUSSIAN PULSE GENERATOR Optical Gaussian Pulse Generator Generates a Gaussian-pulsed optical signal. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [0,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ –100 dBm W, mW, dBm ]-INF,+INF[ 0.5 bit — [0,1] Position 0 bit — Order 1 — — [1,100] False — — True, False Emission frequency Power Peak-to-peak power of the pulse Bias DC Offset of the pulse Width FWHM of the pulse amplitude Order of the function Truncated Determines whether or not the pulses overlap with each other 527 OPTICAL GAUSSIAN PULSE GENERATOR Chirp Name and description Default value Default unit Value range Chirp definition Linear — Linear, Measured Chirp factor 0 rad/s Alpha parameter 0 rad/W Adiabatic chirp 0 1/s [0,1] Name and description Default value Default unit Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Results from changes in the steady state carrier densities Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Parameterized Parameterized — — Sample rate Sample rate Hz Hz, GHz, THz Determines whether or not the component is enabled Frequency simulation window 528 ]0,+INF[ OPTICAL GAUSSIAN PULSE GENERATOR Technical background This model generates Gaussian or super-Gaussian optical pulses according to the bit sequence at the input. For each bit, the output optical power is: 2N 1 t.k – --- ---------------- 2 T FWHM P t = B. A p .e + A bias where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM, and N is Order of the Gaussian (N=1) or super-Gaussian pulses (N>1). The chirp is modeled using: d d ------ = -----e- ---- ln P t + P t dt 2 dt where is the signal phase, eis the parameter Linewidth enhancement factor, and is the parameter Adiabatic chirp. The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j where the power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as: k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 529 OPTICAL GAUSSIAN PULSE GENERATOR Notes: 530 OPTICAL SECH PULSE GENERATOR Optical Sech Pulse Generator Generates a hyperbolic-secant pulsed optical signal. Ports Name and description Port type Signal type Bit sequences Input Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [0,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ –100 dBm W, mW, dBm ]-INF,+INF[ 0.5 bit — [0,1] Position 0 bit — Truncated False — — Emission frequency Power Peak-to-peak power of the pulse Bias DC Offset of the pulse Width FWHM of the pulse amplitude True, False Determines whether or not the pulses overlap with each other 531 OPTICAL SECH PULSE GENERATOR Chirp Name and description Default value Default unit Value range Chirp definition Linear — Linear, Measured Chirp factor 0 rad/s Alpha parameter 0 rad/W Adiabatic chirp 0 1/s [0,1] Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Results from changes in the steady state carrier densities Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Parameterized Parameterized — — Sample rate Sample rate Hz Hz, GHz, THz Determines whether or not the component is enabled Frequency simulation window 532 ]0,+INF[ OPTICAL SECH PULSE GENERATOR Technical background This model generates optical pulses according to the bit sequence at the input. For each bit, the output optical power is: t.k P t = B. A p cosh ------------- + A bias T FWHM where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. k is the fitting coefficient determined numerically to generate pulses with the exact values of the parameter Width, TFWHM. The chirp is modeled using: d d ------ = -----e- ---- ln P t + P t dt 2 dt where is the signal phase, eis the parameter Linewidth enhancement factor, and is the parameter Adiabatic chirp. The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j The power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as: k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 533 OPTICAL SECH PULSE GENERATOR Notes: 534 OPTICAL IMPULSE GENERATOR Optical Impulse Generator Generates an optical signal composed by a sequence of Impulses. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [0,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ –100 dBm W, mW, dBm ]-INF,+INF[ 0 bit Emission frequency Power Peak-to-peak power of the pulse Bias DC Offset of the pulse Position [0,1] Relative position of the impulse Chirp Name and description Default value Units Alpha parameter 0 rad/W Adiabatic chirp 0 1/s Value range [0,1] Results from changes in the steady state carrier densities 535 OPTICAL IMPULSE GENERATOR Polarization Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Parameterized Parameterized — — Sample rate Sample rate Hz Hz, GHz, THz Determines whether or not the component is enabled Frequency simulation window 536 ]0,+INF[ OPTICAL IMPULSE GENERATOR Technical background This model generates optical pulses according to the bit sequence at the input. For each bit, the output optical power is: P t = B. A p t – t p + A bias where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. is the impulse function and tP is the parameter Pulse position. The chirp is modeled using: d d ------ = -----e- ---- ln P t + P t dt 2 dt where is the signal phase, eis the parameter Linewidth enhancement factor, and is the parameter Adiabatic chirp. The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j The power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as: k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 537 OPTICAL IMPULSE GENERATOR Notes: 538 MEASURED OPTICAL PULSE Measured Optical Pulse Generates a pulse based on measurements. Ports Name and description Port type Signal type Bit sequence Input Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [0,+INF[ 0 dBm W, mW, dBm ]-INF,+INF[ –100 dBm W, mW, dBm ]-INF,+INF[ Position 0 bit — Filename Optical pulse.dat — — — Power — — Power, Power Phase, Real Imag, Phase Emission frequency Power Peak-to-peak power of the pulse Bias DC Offset of the pulse Filename with the measured data File format Determines the format of the file with the measurements 539 MEASURED OPTICAL PULSE Polarization Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Name and description Default value Units Value range Interpolation Linear — Linear, Cubic Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Numerical Determines the interpolation algorithm for the measured data Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Parameterized Parameterized — — Sample rate Sample rate Hz Hz, GHz, THz Determines whether or not the component is enabled Frequency simulation window Graphs Name and description X Title Y Title Measured magnitude data Time period (a.u.) Amplitude (V) Measured phase data Time period (a.u.) Phase (rad) 540 ]0,+INF[ MEASURED OPTICAL PULSE Technical background The input file is formatted containing two items per line — the time in seconds and the signal measurement (Power in watts, Phase in radians, Real and Imag in Volts). The time scale is normalized to fit in one bit period - the duration of the pulse. According to the parameter File format, the second item can be one value (Power or Phase), or two values (Power and Phase or Real and Imag). Power (Phase will be set to zero) 0 0 1e-6 0.5 2e-6 0.5 3e-6 0 ... Power Phase 0 0 0 1e-6 0.5 3.14 2e-6 0.5 3.14 3e-6 0 0 0 0 0 1e-6 –0.5 7.9e-4 2e-6 –0.5 7.9e-4 3e-6 0 0 ... Real Imag ... 541 MEASURED OPTICAL PULSE Phase (Power will be set to one) 0 0 1e-6 3.14 2e-6 3.14 3e-6 0 ... This model generates optical pulses according to the bit sequence at the input. For each bit, the output optical power is: P t = B. A p M t + A bias where Ap is the parameter peak-to-peak Power, and Abias is the parameter Bias. B is the bit value (1 or 0) and depends on the input bit sequence. M is the measured data. The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j The power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as: k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 542 MEASURED OPTICAL PULSE SEQUENCE Measured Optical Pulse Sequence Generates an optical signal based on measurements. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [0,+INF[ 1 a.u. — ]-INF,+INF[ 0 s — [0,+INF[ Sequence.dat — — — Power — — Power, Power Phase, Real Imag, Phase Name and description Default value Units Value range Azimuth 0 deg ]-90,90] Emission frequency Scale Factor to scale the signal amplitude Start time Initial part of the signal to be skipped Filename Filename with the measured data File format Determines the format of the file with the measurements Polarization Azimuth angle of output polarization 543 MEASURED OPTICAL PULSE SEQUENCE Name and description Default value Units Value range Ellipticity 0 deg [-45,45] Name and description Default value Units Value range Interpolation Linear — Linear, Cubic Ellipticity angle of output polarization Numerical Determines the interpolation algorithm for the measured data Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Parameterized Parameterized — — Sampled, Parameterized Sample rate Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Frequency simulation window Graphs Name and description X Title Y Title Measured magnitude data Time (s) Amplitude (V) Measured phase data Time (s) Phase (rad) 544 MEASURED OPTICAL PULSE SEQUENCE Technical background This model generates optical signal loading measurements from a file. The input file is formatted containing two items per line — the time in seconds and signal measurement (Power in watts, Phase in radians, Real and Imag in Volts). According to the parameter File format, the second item can be one value (Power or Phase) or two values (Power and Phase or Real and Imag). Power (Phase will be set to zero) 0 0 1e-6 0.5 2e-6 0.5 3e-6 0 ... Power Phase 0 0 0 1e-6 0.5 3.14 2e-6 0.5 3.14 3e-6 0 0 0 0 0 1e-6 –0.5 7.9e-4 2e-6 –0.5 7.9e-4 3e-6 0 0 ... Real Imag ... 545 MEASURED OPTICAL PULSE SEQUENCE Phase (Power will be set to one) 0 0 1e-6 3.14 2e-6 3.14 3e-6 0 ... The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j The power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as: k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 546 TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA Time Resolve Chirp (TRC) Measurement Data This component is an interface between OptiSystem and time resolve chirp (TRC) [1] measurement instruments, such as the OSA Agilent 86146B with TRC option. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [0,+INF[ 1 a.u. — ]-INF,+INF[ 0 s — [0,+INF[ Sequence.dat — — — Name and description Default value Units Value range Azimuth 0 deg ]-90,90] 0 deg [-45,45] Emission frequency Scale Factor to scale the signal amplitude Start time Initial part of the signal to be skipped Filename Filename with the measured data Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization 547 TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA Numerical Name and description Default value Units Value range Interpolation Linear — Linear, Cubic Determines the interpolation algorithm for the measured data Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Iterations — — [1,+INF[ Parameterized Parameterized — — Sampled, Parameterized Sample rate Sample rate Hz Hz, GHz, THz ]0,+INF[ Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Frequency simulation window Graphs Name and description X Title Y Title Measured power data Time (s) Power (W) BER measured chirp data Time (s) Chirp (Hz) Technical background This component generates optical signal loading measurements from a file. These measurements are TRC data that describe the power and chirp evolution of the optical signal in time [1]. TRC provides frequency vs. time information about a modulated lightwave signal. Also called dynamic chirp, the TRC graph provides useful information on the ability of a modulated signal to propagate over long distances in optical fiber. Using measurement equipment such as the Agilent 86146B, with the filter mode capability, Agilent 86100 Infinium Digital Communications Analyzer (DCA) dedicated software (86146B Option TRL), and a personal computer, the time resolved chirp (TRC) of a modulated laser can be calculated. From the measurement, a file with the TRC data is generated. OptiSystem can load this file and the effect of laser chirp on a wide variety of system performance metrics 548 TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA - such as the effect on the performance of a long-haul dense wavelength division multiplexed (DWDM) system with EDFA and Raman optical amplification and dispersion compensation - can be studied across an unlimited range of system designs. The input file is formatted containing three items per line - the time in seconds, the signal power is Watt (Linear scale) or dBm, and the signal chirp (Hz). Time Signal power (W or dBm) Signal chirp 0 1.27617e-006 -7.80425e+009 6.25e-012 1.139e-006 -4.94806e+009 1.25e-011 1.46161e-006 -6.57706e+009 1.875e-011 1.33136e-006 -6.10874e+009 2.5e-011 1.54705e-006 -2.89844e+009 3.125e-011 1.03595e-006 -7.38826e+009 ... ... ... The output is multiplied with a complex vector considering the state of polarization: E X t = 1 – k P t E Y t ke j The power splitting k and the phase difference are related to the parameters Azimuth and Ellipticity as: k 1 – k cos tan 2 = 2 ----------------------------------------1 – 2.k sin 2 = 2 k 1 – k sin 549 TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA References [1] Agilent Technologies, “Making Time-Resolved Chirp Measurements Using the Optical Spectrum Analyzer and Digital Communications Analyzer”, Agilent Application Note 1550-7, 2002. 550 TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA Transmitters Library - Optical Optical Modulators • MZ Modulator Analytical • EA Modulator Analytical • Amplitude Modulator • Phase Modulator • Frequency Modulator • Dual Drive MZ Absorption-Phase • EA Modulator Measured • Single Drive MZ Modulator Absorption-Phase • Dual Port Dual Drive MZ Modulator Absorption-Phase • Dual Port MZ Modulator Measured 551 TIME RESOLVE CHIRP (TRC) MEASUREMENT DATA 552 MZ MODULATOR ANALYTICAL MZ Modulator Analytical Simulates a Mach-Zehnder modulator using an analytical model. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Value range Extinction ratio 30 dB [0,+INF[ Negative signal chirp False — True, False Symmetry factor –1 — [-1,1[ Name and description Default value Units Value range Enabled True — True, False Simulation Determines whether or not the component is enabled Technical background The Mach-Zehnder modulator is an intensity modulator based on an interferometric principle. It consists of two 3 dB couplers which are connected by two waveguides of equal length (see Figure 1). By means of an electro-optic effect, an externally applied voltage can be used to vary the refractive indices in the waveguide branches. 553 MZ MODULATOR ANALYTICAL The different paths can lead to constructive and destructive interference at the output, depending on the applied voltage. Then the output intensity can be modulated according to the voltage. Figure 1 Mach-Zehnder modulator The equations that describe the behavior of the MZ modulator are: E out t = E in t cos t exp j t where is the phase difference between the two branches and is defined as: t = --- 0.5 – ER Modulation t – 0.5 2 with 4 1 ER = 1 – --- arc tan ------------------- extrat and is the signal phase change defined as: t = SC t 1 + SF 1 – SF where the parameter SC is –1 if negative signal chirp is true, or 1 if negative signal chirp is false. extract is the extinction ratio, SF is the symmetry factor, and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1. For parameterized and noise bins signals, the average power is calculated according to the above. 554 EA MODULATOR ANALYTICAL EA Modulator Analytical Simulates an Electro-absorption modulator using an analytical model. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Units Value range Modulation index 0.95 — [0,1[ Chirp factor 0 — ]-INF, +INF[ Name and description Default value Units Value range Enabled True — True, False Simulation Determines whether or not the component is enabled 555 EA MODULATOR ANALYTICAL Technical background In this model, the optical carrier is modulated externally by the electrical modulation signal, (see Figure 1). Figure 1 EA modulator Assuming that the optical input signal is Ein, the following equation describes the behavior of the model: E out t = E in t Mod t exp j --- ln Mod t 2 where Eout(t) is the output optical signal, is the chirp factor, and Mod(t) is defined as Mod t = 1 – MI + MI modulation t where MI is the modulation index and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1. For parameterized and noise bins signals, the average power is calculated according to the above. 556 AMPLITUDE MODULATOR Amplitude Modulator Simulates an ideal amplitude modulator. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Units Value range Modulation index 1 — [0,1] Name and description Default value Units Value range Enabled Yes — True, False Simulation Determines whether or not the component is enabled 557 AMPLITUDE MODULATOR Technical background In this model, the optical carrier is modulated externally by the electrical modulation signal. Assuming that the optical input signal is Ein, the following equations describe the behavior of the model: E out t = E in t Mod t where Eout(t) is the output optical signal and Mod(t) is defined as Mod t = 1 – MI + MI modulation t where MI is the modulation index and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1. For parameterized and noise bins signals, the average power is calculated according to the above. 558 PHASE MODULATOR Phase Modulator Simulates an ideal phase modulator. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Units Value range Normalize electrical signal True — True, False 90 deg ]-INF,+INF[ Name and description Default value Units Value range Enabled True — True, False Defines if the electrical input signal will be normalized between 0 and 1 Phase deviation Simulation Determines whether or not the component is enabled 559 PHASE MODULATOR Technical background In this model, the electrical modulation signal imposes a phase modulation on an optical carrier. Assuming that the optical input signal is Ein, the following equation describes the behavior of the model. E out t = E in t exp j modulation t where Eout(t) is the output optical signal, is the phase deviation, and modulation(t) is the electrical input signal. The electrical input signal is normalized between 0 and 1. The parameterized and noise bins signals are not affected by this modulator. 560 FREQUENCY MODULATOR Frequency Modulator Simulates an ideal frequency modulator. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Unit Value range Frequency deviation 10 GHz Hz, GHz, THz [0,+INF[ Name and description Default value Units Value range Enabled True — True, False Simulation Determines whether or not the component is enabled 561 FREQUENCY MODULATOR Technical background In this model, the electrical modulation signal imposes a frequency modulation on an optical carrier. Assuming that the optical input signal is Ein, the following equation describes the behavior of the model: t E out t = E in t exp j 2 f modulation – 0.5 d 0 where Eout(t) is the output optical signal, f is the frequency deviation, and modulation is the electrical input signal. The electrical input signal is normalized between 0 and 1. The parameterized and noise bins signals are not affected by this modulator. 562 DUAL DRIVE MZ ABSORPTION-PHASE Dual Drive MZ Absorption-Phase Simulates a Mach-Zehnder modulator with dual-drive modulation using measured parameters. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Value range Splitting Ratio 1.3 — [0,10000] Modulator Type Phase-Shift — Conventional, Phase-Shift Bias Voltage 1 –2.8 V ]-INF, +INF[ Bias Voltage 2 –1.1 V ]-INF, +INF[ Normalize electrical signal True — True, False Modulation Voltage12 1.2 V [0, +INF[ Absorption / Phase Filename AbsorptionPhase. dat — — Name and description Default value Units Value range Enabled True — True, False File with the measured absorption and phase Simulation Determines whether or not the component is enabled 563 DUAL DRIVE MZ ABSORPTION-PHASE Graphs Name and description X Title Y Title Measured absorption Voltage (V) Absorption (dB) Measured phase Voltage (V) Phase (radians) Technical background In this model, you can specify the dependence of the measured absorption and phase on applied voltage for a Mach-Zehnder modulator. You can use the default characteristics curves or choose to load from Filename. For a modulator with the same input and output Y-branch splitting ratios, the output signal is: a V 1 E0 a V 2 E V 1 ,V 2 = ---------------- SR exp – --------------------- + j V 1 L + exp – --------------------- + j V 2 L – j 0 2 2 1 + SR E V 1 ,V 2 I V 1 ,V 2 exp j V 1 ,V 2 where SR = P1/P2 is the Y-branch power splitting ratio a 2 L 0 V1 , V2 I is the attenuation constant is the phase constant is the interaction length of the modulator arm is 0 radians for a conventional modulator and radians for phase-shift modulator are voltages applied to arms 1 and 2, respectively is the intensity of the optical signal is the phase V i i = 1 2 is defined as: V i t = V bi + V mod12 v t for the normalized case where V bi is the bias voltage, V mod12 is the peak-to-peak voltage, and v t is the normalized modulation waveform with a peak-to-peak amplitude of 1 and an average value of 0. The electrical input signal can be normalized between 0.5 and -0.5. V i t = V bi V mod t for the non-normalized case. The model utilizes a Dual drive (push and pull) modulation ( V 1 564 = – V 2 . DUAL DRIVE MZ ABSORPTION-PHASE The model has stored default curves characteristics of a Mach-Zehnder modulator. The dependence of the measured absorption and phase of the optical signal on applied voltage for each arm of a modulator is illustrated in Figure 1. Figure 1 Default characteristics of absorption and phase in the Dual Mach-Zehnder model 565 DUAL DRIVE MZ ABSORPTION-PHASE References [1] Cartledge, J. C., “Combining self-phase modulation and optimum modulation conditions to improve performance of 10 Gb/s transmission systems using MQW Mach-Zehnder modulators”, J. Light. Techn., 18, 647-654, (2000). 566 EA MODULATOR MEASURED EA Modulator Measured Simulates an Electro-absorption modulator using measured parameters. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Value range Bias voltage –1 V ]-INF, +INF[ Normalize electrical signal True — True, False Modulation voltage (peak-to-peak) 2 V [0, +INF[ Absorption / Alpha Filename AbsorptionAlpha.dat — — File with the measured absorption and -parameter m Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled 567 EA MODULATOR MEASURED Graphs Name and description X Title Y Title Measured absorption Voltage (V) Absorption (dB) Measured alpha-parameter Voltage (V) Alpha-parameter Calculated alpha-parameter Voltage (V) Alpha-parameter Technical background In this model, you can specify the dependence of the measured absorption and parameter- m on the applied voltage for an EA modulator. You can use the default characteristic curves or choose to load from file. In this case, the parameter Filename is enabled. In the case of the EA modulator, the output signal response to an applied voltage is: E V = 1 I V exp j --- m V d ln I V 2 (1) where IV is the voltage-dependent intensity of the signal. While Equation 1 is an accurate result, it is not in the most convenient form for simulation purposes when empirical equations for m V and I V are obtained from a fitting to measured results. The determination of the argument of the exponential function in Equation 1 requires function evaluation and integration. The modulator output signal given by Equation 1 can also be written in the convenient 1 + j 2 form I using a voltage-dependent parameter r V as: EV = IV 1 + j r V 2 (2) A comparison of the phase terms in Equation and Equation 2 yields 1 r V = ----------- m V d V V (3) Equation 3 shows how the attenuation constant V and -parameter- m V jointly combine to determine r V . Using Equation 2, with r V determined from measurements of m V and I V , the evaluation of the argument of the exponent only requires function evaluation. 568 EA MODULATOR MEASURED The default characteristics curves stored in the component, the dependence of the measured absorption, and -parameter- m V on applied voltage, is illustrated in Figure 1. Figure 1 Dependence of the absorption and m on the applied voltage for an MQW-EAM For this component, the electrical input signal can be normalized between 0.5 and -0.5. Then, the voltage applied to the modulator is given by: (4) V t = V b + V mod v t where Vb is the bias voltage, Vmod is the peak-to-peak voltage, and v(t) is the normalized modulation waveform (electrical input signal) with a peak-to-peak amplitude of 1 and an average value of 0. 569 EA MODULATOR MEASURED Notes: 570 SINGLE DRIVE MZ MODULATOR ABSORPTION-PHASE Single Drive MZ Modulator Absorption-Phase Simulates a Mach-Zehnder modulator with single drive modulation using measured parameters. Ports Name and description Port type Signal type Modulation Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Value range Splitting Ratio 1.3 — [0,10000] Modulator Type Phase-Shift — Conventional, Phase-Shift Bias Voltage 1 –2.8 V ]-INF, +INF[ Bias Voltage 2 –1.1 V ]-INF, +INF[ Normalize electrical signal True — True, False Modulation Voltage 1.5 V [0, +INF[ Operation mode Change in V2 = 0 — Change in V1 = 0, Change in V2 = 0 Absorption / Phase Filename AbsorptionPhase.dat — — File with the measured absorption and phase 571 SINGLE DRIVE MZ MODULATOR ABSORPTION-PHASE Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled Graphs Name and description X Title Y Title Measured absorption Voltage (V) Absorption (dB) Measured phase Voltage (V) Phase (radians) Technical background In this model, you can specify the dependence of the measured absorption and phase on applied voltage for a Mach-Zehnder modulator. You can use the default characteristics curves or choose to load from Filename. For a modulator with the same input and output Y-branch splitting ratios, the output signal is: a V 1 E0 a V 2 E V 1 ,V 2 = ---------------- SR exp – --------------------- + j V 1 L + exp – --------------------- + j V 2 L – j 0 2 2 1 + SR E V 1 ,V 2 I V 1 ,V 2 exp j V 1 ,V 2 where SR = P1/P2 is the Y-branch power splitting ratio a 2 L 0 V1 , V2 I is the attenuation constant is the phase constant is the interaction length of the modulator arm is 0 radians for a conventional modulator and radians for phase-shift modulator are voltages applied to arms 1 and 2, respectively is the intensity of the optical signal is the phase Vi(i=1,2) is defined as: V i t = V bi + V modi v t for the normalized case where Vbi is the bias voltage, Vmodi is the peak-to-peak voltage, v(t) is the normalized modulation waveform with a peak-to-peak amplitude of 1 and an average value of 0. The electrical input signal is normalized between 0.5 and -0.5. 572 SINGLE DRIVE MZ MODULATOR ABSORPTION-PHASE V i t = V bi V mod t for the non-normalized case The model utilizes a single drive modulation, i.e., V mod is 0 in one of the arms. The model has stored default curves characteristics of a Mach-Zehnder modulator. The dependence of the measured absorption and phase of the optical signal on applied voltage for each arm of a modulator is illustrated in Figure 1. Figure 1 Default characteristics of absorption and phase in the Single Mach-Zehnder mode 573 SINGLE DRIVE MZ MODULATOR ABSORPTION-PHASE References [1] Cartledge, J. C., “Combining self-phase modulation and optimum modulation conditions to improve performance of 10 Gb/s transmission systems using MQW Mach-Zehnder modulators”, J. Light. Techn., 18, 647-654, (2000). 574 DUAL PORT DUAL DRIVE MZ MODULATOR ABSORPTION-PHASE Dual Port Dual Drive MZ Modulator AbsorptionPhase Simulates a Mach-Zehnder modulator with dual-drive modulation using two ports with measured parameters. Ports Name and description Port type Signal type Modulation 1 Input Electrical Modulation 1 Input Electrical Carrier Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Value range Splitting Ratio 1.3 — [0,10000] Modulator Type Phase-Shift — Conventional, Phase-Shift, Bias Voltage 1 –2.8 V ]-INF, +INF[ Bias Voltage 2 –1.1 V ]-INF, +INF[ Normalize electrical signal True — True, False Modulation Voltage12 1.2 V [0, +INF[ Absorption / Phase Filename AbsorptionPhase.dat — — File with the measured absorption and phase 575 DUAL PORT DUAL DRIVE MZ MODULATOR ABSORPTION-PHASE Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled Graphs Name and description X Title Y Title Measured absorption Voltage (V) Absorption (dB) Measured phase Voltage (V) Phase (radians) Technical background In this model, you can specify the dependence of the measured absorption and phase on applied voltage for a Mach-Zehnder modulator. You can use the default characteristics curves or choose to load from Filename. For a modulator with the same input and output Y-branch splitting ratios, the output signal is: E0 a V 2 a V 1 E V 1 ,V 2 = ---------------- SR exp – --------------------- + j V 1 L + exp – --------------------- + j V 2 L – j 0 1 + SR 2 2 E V 1 ,V 2 I V 1 ,V 2 exp j V 1 ,V 2 where SR = P 1 P 2 is the Y-branch power splitting ratio a 2 L 0 V1 , V2 I is the attenuation constant is the phase constant is the interaction length of the modulator arm is 0 radians for a conventional modulator and radians for phase-shift modulator are voltages applied to arms 1 and 2, respectively is the intensity of the optical signal is the phase V i i = 1 2 is defined as: V i t = V bi V modi v t for the normalized case where V bi is the bias voltage, V modi is the peak-to-peak voltage, and v t is the normalized modulation waveform with a peak-to-peak amplitude of 1 and an average value of 0. The electrical input signal is normalized between 0.5 and -0.5. 576 DUAL PORT DUAL DRIVE MZ MODULATOR ABSORPTION-PHASE V i t = V bi V modi t for the non-normalized case. The model utilizes a Dual drive (push and pull) modulation: V 1 = – V 2 . The model has stored default curves characteristics of a Mach-Zehnder modulator. The dependence of the measured absorption and phase of the optical signal on applied voltage for each arm of a modulator is illustrated in Figure 1. Figure 1 Default characteristics of absorption and phase in the Dual Mach-Zehnder model 577 DUAL PORT DUAL DRIVE MZ MODULATOR ABSORPTION-PHASE References [1] Cartledge, J. C., “Combining self-phase modulation and optimum modulation conditions to improve performance of 10 Gb/s transmission systems using MQW Mach-Zehnder modulators”, J. Light. Techn., 18, 647-654, (2000). 578 DUAL PORT MZ MODULATOR MEASURED Dual Port MZ Modulator Measured This component simulates a Lithium Niobate Mach-Zehnder modulator based on measured parameters. Ports Name and description Port type Signal type Input 1 Input Optical Input 2 Input Electrical Input 3 Input Electrical Output 1 Output Optical Parameters Main Name and description Default value Default unit Value range Extinction ratio 20 dB [0,+INF[ Switching bias voltage 4 V [0,+INF[ 4 V ]-INF,+INF[ 5 dB [0,+INF[ Bias voltage1 0 V ]-INF,+INF[ Bias voltage2 0 V ]-INF,+INF[ Normalize electrical signal False — True, False Modulation voltage1 2 V ]-INF,+INF[ Main settings DC voltage required to turn the modulator from the OFF state to the ON state, or vice versa Switching RF voltage RF voltage required to turn the modulator from the OFF state to the ON state, or vice versa Insertion loss Voltage settings 579 DUAL PORT MZ MODULATOR MEASURED Name and description Default value Default unit Value range Modulation voltage2 -2 V ]-INF,+INF[ Name and description Default value Units Value range Load transfer function False — True, False Hz — Hz, THz Power — Power; Phase; Power Phase; Real, Imag. True — True, False Filter.dat — — Name and description Default value Units Value range Enabled True — True, False False — True, False Bandwidth Response Determines whether you want to load a modulator transfer function or use an ideal one. File frequency unit Determines the frequency unit of the file. File format Determines the format of the file. Linear scale Determines whether or not the data is in linear scale. HF filename File with the transfer function (S21) Simulation Determines whether or not the component is enabled Used for individual samples Digital filter Digital filter order Technical background The Mach-Zehnder structure consists of an input optical branch, which splits the incoming light into two arms, followed by two independent optical arms, which are subsequently recombined by the output optical branch. Application of an electrical signal to one of the optical arms controls the degree of interference at the output optical branch and therefore controls the output intensity. 580 DUAL PORT MZ MODULATOR MEASURED The output optical field is determined as follows: E in t jv t V RF + jv bias2 V DC jv 1 t V RF + jv bias1 V DC - e 2 E O t = -------------------+ 1 – e IL 20 10 where: • • • Ein(t) is the input (optical) signal IL is the parameter Insertion loss v1(t) and v2(t) are the input electrical voltages for the upper (1) and lower (2) modulator arms • • • • vbias1(t) and vbias2(t) are the settings for Bias voltage1 and Bias voltage2 VRF is the Switching modulation voltage VDC is the Switching bias voltage denotes the power splitting ratio of both Y-branch waveguides (assumed to be symmetrical), and is given by: 1 = 1 – -------- 2 r = 10 ExtRatio 10 r where ExtRatio is linked to the parameter Extinction ratio Typical settings Mach-Zehnder modulators are typically operated at three bias points: Peak, Null and Quadrature (see Fig 1) Figure 1 MZ modulator transmittance function Peak Imax ‐ Quadrature + Quadrature Null Imin V 2V V1‐V2 581 DUAL PORT MZ MODULATOR MEASURED For the Null setting, the operating bias (V1 - V2) should be set to V. For the Peak setting, the operating bias (V1 - V2) should be set to 0. For the positive or negative Quadrature settings, the operating bias (V1 - V2) should be set to 0.5V or 1.5V,respectively. Thus, assuming a Vof 4V, the following operating point settings can be used: Table 1 Typical settings for Null, Peak and Neg Quadrature operating points Parameter Null Peak Neg Quadrature Switching bias voltage 4 4 4 Switching RF voltage 4 4 4 Bias voltage1 -2 0 1 Bias voltage2 2 0 -1 Optionally, the settings for Bias voltage1 and Bias voltage2 can be set to 0 and the biases can be applied directly to the input electrical waveform. Example configurations are displayed in Figure 2. These examples can also be found in OptiSystem 13 samples/Transmitter design and analysis/LiNb_Modulator_Settings.osd Normalization When Normalize electrical signal is selected, the external electrical signals (for the upper (1) and lower (2) modulator arms) are normalized between -0.5 and 0.5 and then multiplied by Modulation voltage1 and Modulation voltage2, respectively. The resulting settings for v1(t) and v2(t) will thus be: v1(t)= Normalized electrical signal * Modulation voltage1 v2(t)= Normalized electrical signal * Modulation voltage2 Note: To setup the modulator operating bias point you must use the parameters Bias voltage1 and Bias voltage2. Any bias settings contained within the input electrical signals will be lost due to the normalization 582 DUAL PORT MZ MODULATOR MEASURED Figure 2 MZ modulator transmittance function Modulation transfer function The modulator transfer function relates the effective drive voltage to the applied drive voltage. When Load transfer function is selected/enabled, a transfer function will be applied to the drive voltage (otherwise it will be assumed to be ideal). The file should be formated with two items per line, the frequency and filter measurement. The parameter File frequency unit determines the frequency unit of the first item; it can be Hz or THz. The parameter File format, determines the data format for the second item. It can be one value (Power or Phase) or two values (Power & Phase or Real & Imag). Sample file formats follow. 583 DUAL PORT MZ MODULATOR MEASURED Power (Phase is set to zero, assuming frequency units THz) 193.10 0 193.11 0.5 193.12 0.5 193.13 0 Power & Phase 193.14 0 0 193.15 0.5 3.14 193.16 0.5 3.14 193.17 0 0 193.18 0 0 193.19 -0.5 7.9-e-4 193.20 -0.5 7.9-e-4 193.21 0 0 Real & Imag Phase (Power is set to one) 193.22 0 193.23 3.14 193.24 3.14 193.253 0 When the Normalize electrical signal parameter is True, the electrical signals of port1 and port2 are normalized between -0.5 and 0.5. In this case, the amplitude of each RF electrical signal considered in v 1 t and v 2 t will be the values in the modulation voltage parameters divided by 2. References [1] Cartledge, J. C., Rolland, C., Lemerle, S., and Solheim, A., “Theoretical performance of 10 Gb/s lightwave systems using a III-V semiconductor Mach-Zehnder modulator.”, IEEE Phot. Techn. Letters., 6, 282-284, (1994). [2] Cartledge, J.C., "Performance of 10 Gb/s lightwave systems based on lithium niobate MachZehnder modulators with asymmetric Y-branch waveguides". IEEE Phot. Techn. Letters., 7, 1090 -1092, (1995). 584 DUAL PORT MZ MODULATOR MEASURED Transmitters Library - Optical Optical Transmitters • WDM Transmitter • Optical Transmitter • Optical Duobinary Transmitter • Optical DPSK Transmitter • Optical CSRZ Transmitter • Optical QPSK Transmitter • Optical DP-QPSK Transmitter • 16-QAM Transmitter • Optical DP-16-QAM Transmitter 585 DUAL PORT MZ MODULATOR MEASURED Notes: 586 WDM TRANSMITTER WDM Transmitter This component is a WDM transmitter. Ports Name and description Port type Signal type Output 1 Output Optical Output 2 Output Optical Output 3 Output Optical Output 4 Output Optical Output 5 Output Optical Output 6 Output Optical Output 7 Output Optical Output 8 Output Optical Parameters Main Name and description Default value Default Unit Value range Number of output ports 8 — [1, 1000] Frequency 193.1 THz, Hz, nm [30,+INF[ 100 GHz, THZ, Hz, nm ]-INF,+INF[ Power 0 dBm W, mW, dBm Extinction ratio 10 dB [0,1000] Linewidth 10 MHz [0, 1e+009[ Initial phase 0 deg [-1e+100,1e+100] Emission frequency of the first laser Frequency spacing Frequency spacing between adjacent lasers 587 WDM TRANSMITTER PRBS Name and description Default value Default unit Value range Bit rate Bit rate Bits/s [0, 1e+012] MBits/s GBits/s Order log(Sequence length)/log(2) - [2,30] Number of leading zeros 1 - [0,+INF[ Number of trailing zeros 1 - [0,+INF[ Name and description Default value Default unit Value range Modulation type NRZ - Off, NRZ, RZ 0.5 bit [0, 1] 0 bit [-1, 1] 1 / (Bit rate) * 0.05 s, ms, ns, ps [0, 1e100] 1 / (Bit rate) * 0.05 s, ms, ns, ps [0, 1e100] Order of the PRBS generator Coding Defines the signal modulation type Duty cycle Duration of the high level bit Position The relative position of the bit Rise time Defined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude Fall time Defined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude 588 WDM TRANSMITTER Enhanced Name and description Default value Default unit Value range Transmitter type EML - EML, DML Overshoot 30 % - 30 % - 1/(Bit rate) * 0.5 s s, ms, ns, ps 1/(Bit rate) * 0.5 s s, ms, ns, ps (Bit rate) * 5 Hz Hz, MHz, GHz, THz (Bit rate) * 5 Hz Hz, MHz, GHz, THz Percentage of overshoot during the transition from 0 to 1 relative to the steady state power Undershoot Percentage of undershoot during the transition from 1 to 0 relative to the steady state power Damping time leading edge Relaxation time when the signal overshoot reaches 1/e of the max value during the transition from 0 to 1 Damping time trailing edge Relaxation time when the signal undershoot reaches 1/e of the min value during the transition from 1 to 0 Resonant frequency leading edge Frequency of the oscillations in the transition from 0 to 1 Resonant frequency trailing edge Frequency of the oscillations in the transition from 1 to 0 Side Mode Name and description Default value Default unit Units Value range Calculate side mode False - - True, False 1 - - [1, 100000] 75 GHz Hz, GHz, THz, nm [0,+INF[ 30 dB - [0,+INF[ Determines if the signal output will have one side mode Number of side modes Number of side modes if running as a Fabry-Perot laser. Separation Mode frequency separation from the laser center frequency Suppression ratio Attenuation of the side mode relative to the output power 589 WDM TRANSMITTER RIN Name and description Default value Default unit Units Value range RIN -130 dB/Hz - ]-INF,+INF[ False - - True, False 10 dBm W, mW, dBm ]-INF,+INF[ Name and description Default value Default unit Value range Alpha parameter 0 rad/W [-1000, 1000] Adiabatic chirp 0 1/(W.s) [-1000, 1000] Name and description Default value Units Value range Azimuth 0 deg [-90,90] 0 deg [-45,45] None - None, Polarization X, Polarization Y Relative intensity noise value Include RIN Determines if the RIN will be added to the output signal Measured power Value of the power during the measurement of RIN Chirp Results from changes in the steady state carrier densities Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Polarization filter Determines the polarization of the filter 590 WDM TRANSMITTER Simulation Name and description Default value Default unit Units Value range Enabled True - - True, False Iterations - - [1, +INF[ Parameterized Parameterized - - True, False Sample rate Sample rate Hz Hz, GHz, THz ]0, +INF[ Name and description Default value Units Value range Noise bandwidth Sample rate Hz, GHz, THz, nm - Sample rate Hz, GHz, THz, nm - Convert noise bins - True, False Name and description Default value Units Value range Generate random seed True - True, False 0 - [0,4999] False - True, False Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Frequency simulation window Noise Bandwidth of the noise bins Noise bins spacing Determines noise bins spacing Convert noise bins Determines if the generated noise bins are incorporated into the signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration 591 WDM TRANSMITTER Technical background WDM systems require multiple transmitters and different parameters for each one of them. In addition, they also require different modulation schemes and formats. By using multiple components, users can customize designs, but it is time consuming. The WDM Transmitter encapsulates different components, allowing users to select different modulation formats and schemes for multiple channels in one single component. It is a transmitter array that allows for different modulation types and schemes. The block diagram for each WDM channel transmitter is shown below: The first stage is the PRBS; the same engine used in the Pseudo-Random Bit Sequence Generator component is used in this stage. Parameters Bit rate, Order, Number of leading and trailing zeros are used in the internal Pseudo-Random Bit Sequence Generator. A different seed will be used for each bit sequence for each WDM channel. The operation and parameters of the PRBS component is described in the technical background of the Pseudo-Random Bit Sequence Generator. The second stage is the Coding/Modulation; the parameter Modulation type has three options: RZ, NRZ and Off. RZ and NRZ coding is generated by the engines of the RZ Pulse Generator and NRZ Pulse Generator respectively. A CW operation of the 592 WDM TRANSMITTER transmitter is possible by selecting Off as modulation type. The Duty cycle parameter is used when modulation type RZ is selected. The operations and parameters of the electrical pulse generators are described in the technical background of the RZ and NRZ Pulse Generators. The last stage is the optical source and modulation scheme; by using the parameter Transmitter type the user can select between a external modulated laser scheme (EML) or a directly modulated laser scheme (DML). The laser engine used in this stage is the same used in the Directly Modulated Laser Measured component. The operation and parameters of this component are described in the technical background of the Directly Modulated Laser Measured. By using 3R regenerators, it is possible to recover the original bit sequence and electrical signals for all the WDM channels: 593 WDM TRANSMITTER Notes: 594 OPTICAL TRANSMITTER Optical Transmitter The optical transmitter is a single channel version of the WDM Transmitter component. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 10 dB - [0, 1000] 10 MHz - [0, 1e+009] 0 deg Emission frequency Power Output power Extinction ratio Steady-state power ratio between high and low level bits Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal [-1e+100, 1e+100] 595 OPTICAL TRANSMITTER PRBS Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 1 - - [0, 1000] Name and description Default value Default unit Units Value range Modulation type NRZ - - [Off, NRZ, RZ] 0.5 bit - [0, 1] 0 bit - [-1, 1] 1/(Bit rate)*0.05 s s, ms, ns, ps [0, 1e+100] 1/(Bit rate)*0.05 - s, ms, ns, ps [0, 1e+100] Name and description Default value Default unit Units Value range Transmitter type EML - - EML, DML Determines whether or not the PRBS signal is defined by an external PRBS generator. Order of the PRBS Coding Defines the modulation type Duty cycle Duration of the high level bit Position The relative position of the bit Rise time Defined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude Fall time Defined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude Enhanced Defines whether the transmitter uses an external modulated laser (EML) or a directly modulated laser (DML) 596 OPTICAL TRANSMITTER Name and description Default value Default unit Units Value range Overshoot 30 % - [0, 100] 30 % - [0, 100] 1/(Bit rate)*0.5 s s, ms, ns, ps [0, 1e+100] 1/(Bit rate)*0.5 s s, ms, ns, ps [0, 1e+100] (Bit rate)*5 Hz Hz, MHz, GHz, THz [0, 3e+015] (Bit rate)*5 Hz Hz, MHz, GHz, THz [0, 3e+015] Name and description Default value Default unit Units Value range Calculate side mode False - - True, False 1 - - [1, 100000] 75 GHz Hz, GHz, THz, nm [0, 3e+012] 30 dB - [0, 1e+009] Percentage of overshoot during the transition from low level to high level relative to the steady-state power Undershoot Percentage of undershoot during the transition from high level to low level relative to the steady-state power Damping time leading edge Relaxation time when the signal overshoot reaches 1/e of the max. value during the transition from low level to high level Damping time trailing edge Relaxation time when the signal undershoot reaches 1/e of the max. value during the transition from high level to low level Resonant frequency leading edge Frequency of the oscillations in the transition from low level to high level Resonant frequency trailing edge Frequency of the oscillations in the transition from high level to low level Side Mode Determines if the signal output will have side modes Number of side modes Number of side modes if running as a Fabry-Perot laser Separation Mode frequency separation from the laser center frequency Suppression ratio Attenuation of the side modes relative to the output power 597 OPTICAL TRANSMITTER RIN Name and description Default value Default unit Units Value range Include RIN False - - True, False -130 dB/Hz - [-1e+100, 0] 10 dBm W, mW, dBm [-1000, 1000] Name and description Default value Default unit Units Value range Alpha parameter 0 - - [-100, 100] Adiabatic chirp 0 1/(W.s) - [-1e+100, 1e+100] Name and description Default value Default unit Units Value range Azimuth 0 deg - [-90, 90] 0 deg - [-45, 45] None - - [None, Polarization X, Polarization Y] Name and description Default value Default unit Units Value range Enabled True - - True, False Iterations - - [1, 1e+009] Determines if RIN will be added to the output signal RIN Relative intensity noise value Measured power Value of power during the measurement of RIN Chirp Results from changes in the steadystate carrier densities Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Polarization filter Determines the type of polarization filter Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation 598 OPTICAL TRANSMITTER Name and description Default value Default unit Units Value range Parameterized Parameterized - - True, False Sample rate Hz Hz, GHz, THz [1, 1e+100] Name and description Default value Default unit Units Value range Noise bandwidth Sample rate Hz Hz, GHz, THz, nm [0, 1e+100] Noise bins spacing Sample rate Hz Hz, GHz, THz, nm [0, 1e+100] Convert noise bins Convert noise bins - - - Defines whether or not the output signal is parameterized Sample rate Frequency simulation window Noise Determines the noise bandwidth Determines if the generated noise bins are incorporated into the signal Random numbers Name and description Default value Units Value range Generate random seed True - True, False 0 - [0, 4999] 0 - [0, 4999] False - True, False Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Random seed index PRBS User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration Technical Background Refer to WDM Transmitter for the technical background. 599 OPTICAL TRANSMITTER Notes: 600 OPTICAL DUOBINARY TRANSMITTER Optical Duobinary Transmitter This component simulates a single channel optical transmitter with a duobinary modulated signal. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 10 MHz - [0, 1e+009] 0 deg - [-1e+100, 1e+100] Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Emission frequency Power Output power Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal PRBS Determines whether or not the PRBS signal is defined by an external PRBS generator. Bit rate 601 OPTICAL DUOBINARY TRANSMITTER Name and description Default value Default unit Units Value range Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 3 - - [0, 1000] Name and description Default value Default unit Units Value range Amplitude 2 a.u. - [-1e+100, 1e+100] -2 a.u. - [-1e+100, 1e+100] 0 bit - [-1, 1] 0.05 bit - [0, 1] 0.05 bit - [0, 1] Name and description Default value Default unit Units Value range Filter type Bessel - - [Butterworth, Bessel] 0.25 * Bit rate Hz - - 0 dB - [0, 1e+100] 100 dB - [0, 1e+100] Order of the PRBS Coding Peak-to-peak amplitude of the NRZ pulse generator Bias DC offset of the NRZ pulse generator Position The relative position of the bit Rise time Defined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude Fall time Defined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude Filter Defines the filter type Cutoff frequency 3 dB cutoff frequency of the filter Filter insertion loss Insertion loss of the filter Depth Maximum attenuation value of the filter 602 OPTICAL DUOBINARY TRANSMITTER Name and description Default value Default unit Units Value range Order 4 - - [1, 100] Name and description Default value Default unit Value range Extinction ratio 20 dB [0,+INF[ Switching bias voltage 4 V [0,+INF[ 4 V ]-INF,+INF[ Insertion loss 0 dB [0,+INF[ Bias voltage1 0 V ]-INF,+INF[ Bias voltage2 4 V ]-INF,+INF[ Order of the function Modulator DC voltage required to turn the modulator from the OFF state to the ON state, or vice versa Switching RF voltage RF voltage required to turn the modulator from the OFF state to the ON state, or vice versa Polarization Name and description Default value Default unit Units Value range Azimuth 0 deg - [-90, 90] 0 deg - [-45, 45] Name and description Default value Default unit Units Value range Enabled True - True, False Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled Iterations Iterations - - [1, 1e+009] Parameterized - - True, False Number of times to repeat the calculation Parameterized Determines whether the output signal is parameterized or not 603 OPTICAL DUOBINARY TRANSMITTER Name and description Default value Default unit Units Value range Sample rate Sample rate Hz Hz, GHz, THz [1, 1e+100] Frequency simulation window Random numbers Name and description Default value Units Value range Generate random seed True - True, False 0 - [0, 4999] 0 - [0, 4999] False - True, False Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Random seed index PRBS User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration Technical Background The layout representing the duobinary transmitter component is shown in Figure 1. To generate the optical duobinary signal a CW laser source, a Mach-Zehnder modulator driven in a push-pull configuration to get a chirp free transmission, and a NRZ pulse pattern generator were used. The NRZ duobinary signal was created using a low pass Bessel/Butterworth filter; this signal then drives the MZ modulator. In order to avoid recursive decoding in the receiver, a duobinary precoder was also used. The duobinary precoder was composed of an exclusive-or gate with a delayed feedback path. 604 OPTICAL DUOBINARY TRANSMITTER Figure 1 Duobinary optical transmitter equivalent layout. 605 OPTICAL DUOBINARY TRANSMITTER Notes: 606 OPTICAL DPSK TRANSMITTER Optical DPSK Transmitter This component simulates a single channel optical transmitter with Differential PhaseShift Keying modulation. Ports Name and description Port type Signal type Bit Sequence Output Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 20 dB - [0, 1000] 10 MHz - [0, 1e+009] 0 deg - [-1e+100, 1e+100] Emission frequency Power Output power Extinction ratio Steady-state power ratio between high and low level bits Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal 607 OPTICAL DPSK TRANSMITTER PRBS Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 1 - - [0, 1000] Name and description Default value Default unit Units Value range Duty cycle RZ-33% - - RZ-33%, RZ50%, RZ-66%, NRZ Name and description Default value Default unit Units Value range Azimuth 0 deg - [-90, 90] 0 deg - [-45, 45] Name and description Default value Default unit Units Value range Enabled True - - True, False Iterations - - [1, 1e+009] Determines whether or not the PRBS signal is defined by an external PRBS generator. Order of the PRBS Coding Duration of the high level bit Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation 608 OPTICAL DPSK TRANSMITTER Name and description Default value Default unit Units Value range Parameterized Parameterized - - True, False Sample rate Hz Hz, GHz, THz [1, 1e+100] Determines whether the output signal is parameterized or not Sample rate Frequency simulation window Random numbers Name and description Default value Units Value range Generate random seed True - True, False 0 - [0, 4999] 0 - [0, 4999] False - True, False Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Random seed index PRBS User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration Technical Background The layout representing the Differential Phase-Shift Keying transmitter component is shown at Figure 1. The RZ-DPSK transmitter includes two modulators: one for phase modulation of the data and one for amplitude modulation of the clock for RZ pulse carving. 609 OPTICAL DPSK TRANSMITTER Figure 1 DPSK optical transmitter equivalent layout. The transmitter can simulate 3 DPSK signals: with 33%-duty-cycle RZ pulses, with 50%-duty-cycle RZ pulses, and with 66%-duty-cycle RZ pulses. Figure 2 (a), (b) and (c) shows the correspondent spectra and time domain pulses respectively. Figure 2 Spectra and time domain DPSK signals for (a) 33%-duty-cycle, (b) 50%-duty-cycle and (c) 66%duty-cycle. (a) 610 OPTICAL DPSK TRANSMITTER (b) (c) 611 OPTICAL DPSK TRANSMITTER Notes: 612 OPTICAL CSRZ TRANSMITTER Optical CSRZ Transmitter This component simulates a single channel optical transmitter with an optical carriersuppressed RZ signal. Ports Name and description Port type Signal type Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Frequency 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 10 MHz - [0, 1e+009] 0 deg - [-1e+100, 1e+100] Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Emission frequency Power Output power Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal PRBS Determines whether or not the PRBS signal is defined by an external PRBS generator. Bit rate 613 OPTICAL CSRZ TRANSMITTER Name and description Default value Default unit Units Value range Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 1 - - [0, 1000] Name and description Default value Default unit Units Value range Amplitude 1 a.u. - [-1e+100, 1e+100] -1 a.u. - [-1e+100, 1e+100] 0.5 bit - [0, 1] 0.25 bit - [-1, 1] 0.05 bit - [0, 1] 0.05 bit - [0, 1] Name and description Default value Default unit Value range Extinction ratio 30 dB [0,+INF[ Switching bias voltage 4 V [0,+INF[ 4 V ]-INF,+INF[ Order of the PRBS Coding Peak-to-peak amplitude of the RZ pulse generator Bias DC offset of the RZ pulse generator Duty cycle Duration of the high level bit Position The relative position of the bit Rise time Defined as the time from when the rising edge reaches 10% of the amplitude to the time it reaches 90% of the amplitude Fall time Defined as the time from when the falling edge reaches 90% of the amplitude to the time it reaches 10% of the amplitude Modulator DC voltage required to turn the modulator from the OFF state to the ON state, or vice versa Switching RF voltage RF voltage required to turn the modulator from the OFF state to the ON state, or vice versa 614 OPTICAL CSRZ TRANSMITTER Name and description Default value Default unit Value range Insertion loss 0 dB [0,+INF[ Bias voltage1 0 V ]-INF,+INF[ Bias voltage2 2 V ]-INF,+INF[ Modulator insertion loss Polarization Name and description Default value Default unit Units Value range Azimuth 0 deg - [-90, 90] 0 deg - [-45, 45] Name and description Default value Default unit Units Value range Enabled True - - True, False Iterations - - [1, 1e+009] Parameterized - - True, False Sample rate Hz Hz, GHz, THz [1, 1e+100] Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Parameterized Determines whether the output signal is parameterized or not Sample rate Frequency simulation window Random numbers Name and description Default value Units Value range Generate random seed True - True, False 0 - [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 615 OPTICAL CSRZ TRANSMITTER Name and description Default value Units Value range Random seed index PRBS 0 - [0, 4999] False - True, False User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration Technical Background The layout representing the CSRZ transmitter component is shown at the figure below. The CSRZ signal is generated using a MZ modulator concatenated with a phase modulator. The first modulator generates a RZ optical signal, and then a NRZ electrical signal is applied to the phase modulator to generate an alternated phase in the RZ signal. Figure 1 CSRZ optical transmitter equivalent layout. 616 OPTICAL QPSK TRANSMITTER Optical QPSK Transmitter This component simulates a single channel optical coherent transmitter with an optical QPSK signal. Ports Name and description Port type Signal type Bit sequence Output Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range External laser False - - True, False 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 0.01 MHz [0, 1e+009] 0 deg [-1e+100, 1e+100] Determines whether or not the local oscillator laser is defined by an external source Frequency Emission frequency Power Output power Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal 617 OPTICAL QPSK TRANSMITTER PRBS Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 1 - - [0, 1000] Name and description Default value Default unit Units Value range Gray code False - - True, False False - - True, False Name and description Default value Default unit Units Value range Azimuth 0 deg - [-90, 90] 0 deg - [-45, 45] Name and description Default value Default unit Units Value range Enabled True - - True, False Determines whether or not the PRBS signal is defined by an external PRBS generator. Order of the PRBS Coding Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used Differential coding Defines whether to use Differential coding. If Differential encoding is selected, Graycoding cannot be used Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled 618 OPTICAL QPSK TRANSMITTER Name and description Default value Default unit Units Value range Iterations Iterations - - [1, 1e+009] Parameterized - - True, False Sample rate Hz Hz, GHz, THz [1, 1e+100] Number of times to repeat the calculation Parameterized Determines whether the output signal is parameterized or not Sample rate Frequency simulation window Random numbers Name and description Default value Generate random seed True Units Value range True, False Determines if the seed is automatically defined and unique Random seed index 0 - [0, 4999] 0 - [0, 4999] False - True, False User-defined seed index for noise generation Random seed index PRBS User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration Technical Background The layout representing the optical coherent QPSK transmitter component is shown in the figure below. The QPSK signal is generated by using MZ modulators to encode the QPSK symbols onto an optical carrier. Each modulator branch modulates the inphase (I) and quadrature components (Q) of a carrier. 619 OPTICAL QPSK TRANSMITTER Figure 1 Coherent optical QPSK transmitter equivalent layout. 620 OPTICAL DP-QPSK TRANSMITTER Optical DP-QPSK Transmitter This component simulates a single channel optical coherent transmitter with an optical dual-polarization QPSK signal. Ports Name and description Port type Signal type Bit sequence Output Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range External laser False - - True, False 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 0.01 MHz - [0, 1e+009] 0 deg - [-1e+100, 1e+100] Determines whether or not the local oscillator laser is defined by an external source Frequency Emission frequency Power Output power Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal 621 OPTICAL DP-QPSK TRANSMITTER PRBS Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 1 - - [0, 1000] Name and description Default value Default unit Units Value range Gray code False - - True, False False - - True, False Name and description Default value Default unit Units Value range Enabled True - - True, False Iterations - - [1, 1e+009] Parameterized - - True, False Sample rate Hz Hz, GHz, THz [1, 1e+100] Determines whether or not the PRBS signal is defined by an external PRBS generator. Order of the PRBS Coding Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used Differential coding Defines whether to use Differential coding. If Differential encoding is selected, Graycoding cannot be used Simulation Determines whether or not the component is enabled Iterations Number of times to repeat the calculation Parameterized Determines whether the output signal is parameterized or not Sample rate Frequency simulation window 622 OPTICAL DP-QPSK TRANSMITTER Random numbers Name and description Default value Units Value range Generate random seed True - [True, False] 0 - [0, 4999] 0 - [0, 4999] False - True, False Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Random seed index PRBS User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration 623 OPTICAL DP-QPSK TRANSMITTER Technical Background The layout representing the optical coherent dual-polarization QPSK transmitter component is shown in the figure below. In this case, polarization multiplexing is used, the laser output is split into two othogonal polarization components, which are modulated separately by QPSK modulators (similar to the one shown in the QPSK transmitter layout) and then combined using a polarization beam splitter (PBS). Figure 1 Optical dual-polarization QPSK transmitter equivalent layout. 624 16-QAM TRANSMITTER 16-QAM Transmitter This component simulates a single channel optical transmitter with 16-QAM modulation. Ports Name and description Port type Signal type Bit sequence Output Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range External laser False - - True, False 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 0.01 MHz - [0, 1e+009] 0 deg - [-1e+100, 1e+100] Determines whether or not the local oscillator laser is defined by an external source Frequency Emission frequency Power Output power Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal 625 16-QAM TRANSMITTER PRBS Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 1 - - [0, 1000] Name and description Default value Default unit Units Value range Gray code False - - True, False False - - True, False Name and description Default value Default unit Units Value range Azimuth 0 deg - [-90, 90] 0 deg - [-45, 45] Name and description Default value Default unit Units Value range Enabled True - - True, False Determines whether or not the PRBS signal is defined by an external PRBS generator. Order of the PRBS Coding Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used Differential coding Defines whether to use Differential coding. If Differential encoding is selected, Graycoding cannot be used Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled 626 16-QAM TRANSMITTER Name and description Default value Default unit Units Value range Iterations Iterations - - [1, 1e+009] Parameterized - - True, False Sample rate Hz Hz, GHz, THz [1, 1e+100] Number of times to repeat the calculation Parameterized Determines whether the output signal is parameterized or not Sample rate Frequency simulation window Random numbers Name and description Default value Units Value range Generate random seed True - [True, False] 0 - [0, 4999] 0 - [0, 4999] False - True, False Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Random seed index PRBS User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration 627 16-QAM TRANSMITTER Technical Background The layout representing the optical 16-QAM transmitter component is shown in the figure below. The 16-QAM signal is generated by using MZ modulators to encode the QAM symbols onto an optical carrier. Each modulator branch modulates the in-phase (I) and quadrature components (Q) of a carrier. Figure 1 Optical 16-QAM transmitter layout 628 OPTICAL DP-16-QAM TRANSMITTER Optical DP-16-QAM Transmitter This component simulates a single channel optical transmitter with dual polarization16-QAM modulation format. Ports Name and description Port type Signal type Bit sequence Output Binary Output Output Optical Parameters Main Name and description Default value Default unit Units Value range External laser False - - True, False 193.1 THz Hz, THz, nm [1, 10000] 0 dBm W, mW, dBm [-1000, 1000] 0.01 MHz - [0, 1e+009] 0 deg - [-1e+100, 1e+100] Determines whether or not the local oscillator laser is defined by an external source Frequency Emission frequency Power Output power Linewidth Laser linewidth Initial phase Defines the initial phase of the output signal 629 OPTICAL DP-16-QAM TRANSMITTER PRBS Name and description Default value Default unit Units Value range External PRBS False - - True, False Bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Order log(Sequence length)/log(2) - - [0, 30] Number of leading zeros 1 - - [0, 1000] Number of trailing zeros 1 - - [0, 1000] Name and description Default value Default unit Units Value range Gray code False - - True, False False - - True, False Name and description Default value Default unit Units Value range Azimuth 0 deg - [-90, 90] 0 deg - [-45, 45] Name and description Default value Default unit Units Value range Enabled True - - True, False Determines whether or not the PRBS signal is defined by an external PRBS generator. Order of the PRBS Coding Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used Differential coding Defines whether to use Differential coding. If Differential encoding is selected, Graycoding cannot be used Polarization Azimuth angle of output polarization Ellipticity Ellipticity angle of output polarization Simulation Determines whether or not the component is enabled 630 OPTICAL DP-16-QAM TRANSMITTER Name and description Default value Default unit Units Value range Iterations Iterations - - [1, 1e+009] Parameterized - - True, False Sample rate Hz Hz, GHz, THz [1, 1e+100] Number of times to repeat the calculation Parameterized Determines whether the output signal is parameterized or not Sample rate Frequency simulation window Random numbers Name and description Default value Units Value range Generate random seed True - [True, False] 0 - [0, 4999] 0 - [0, 4999] False - True, False Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Random seed index PRBS User-defined seed index for the internal PRBS generator Different each iteration Determines if the seed is automatically defined and unique for each calculation iteration 631 OPTICAL DP-16-QAM TRANSMITTER Technical Background The layout representing the optical coherent dual-polarization 16-QAM transmitter component is shown in the figure below. Polarization multiplexing is used to split the laser output signal into two orthogonal polarization components, which are modulated separately by 16-QAM modulators and then combined using a polarization beam splitter (PBS). Figure 1 Optical DP-16-QAM transmitter layout.Notes: [3] 632 Optical Fibers Library • Optical fiber • Optical fiber CWDM • Bidirectional Optical Fiber • Nonlinear Dispersive Fiber (Obsolete) 633 634 OPTICAL FIBER Optical fiber The optical fiber component simulates the propagation of an optical field in a singlemode fiber with the dispersive and nonlinear effects taken into account by a direct numerical integration of the modified nonlinear Schrödinger (NLS) equation (when the scalar case is considered) and a system of two, coupled NLS equations when the polarization state of the signal is arbitrary. The optical sampled signals reside in a single frequency band, hence the name total field [1]. The parameterized signals and noise bins are only attenuated. Ports Name and description Port type Signal type Input Input Optical Output Output Optical Parameters Main Name and description Symbol Default value Default unit Value range TRUE — TRUE/FALSE 0 1550 nm [100, 2000] L 50 km [0, 100,000] — TRUE — TRUE/FALSE User defined reference wavelength If TRUE, frequency value of “Reference wavelength” is used internally as ‘zero’ (or reference) frequency in spectrum of signal envelope. Values of parameters (attenuation, dispersion) are assumed to correspond to this frequency. If parameters are wavelengthdependent (from files), they are evaluated at this frequency. If FALSE, central frequency of simulated band is used. Reference wavelength Value of user defined/specified reference wavelength. Length Fiber length Attenuation effect If TRUE, attenuation effect is enabled. 635 OPTICAL FIBER Name and description Symbol Default value Default unit Value range Attenuation data type — Constant — Constant/ From File 0.2 dB/km [0, 1010] — — — — Defines the attenuation as a fixed constant value or as a wavelength dependent curve taken from a file. If ‘constant’, value from “Attenuation” tab in component is used. Attenuation Specified value is used if “Attenuation data type” is set to ‘constant’. If ‘from file’, the value is ignored. Attenuation vs. wavelength Defines the attenuation as a wavelength dependent curve in a file. Dispersion Name and description Symbol Default value Default unit Value range Group velocity dispersion — TRUE — TRUE/FALSE — TRUE — TRUE/FALSE Constant — Constant/ From File 2 -20 ps2/km [-10100, 10100] 3 -20 ps3/km [-10100, 10100] D 16.75 — [-10100, 10100] — 0.075 If TRUE, the GVD effect is enabled. Third order dispersion If TRUE, the TOD effect is enabled. Frequency domain parameters Defines domain in which dispersion parameters are specified. If TRUE, frequency domain is used and dispersion effect is specified in terms of 2 and 3 . Otherwise, wavelength domain is used ( D and S ). Dispersion data type Defines if dispersion parameter values are read from component tabs, or taken from a file Beta 2 Value of the GVD parameter in the frequency domain Beta 3 Value of the GVD parameter in the frequency domain Dispersion ps ----------------------- nm km Value of the GVD parameter in the wavelength domain Dispersion slope Value of dispersion slope parameter. 636 [-10100, 10100] ps -------------------------2 nm km OPTICAL FIBER Name and description Symbol Default value Default unit Value range Dispersion file format — Dispersion vs wavelength — Dispersion vs wavelength/ Group delay vs wavelength — — — — Determines contents of dispersion file: group delay or dispersion vs. wavelength. If “Dispersion vs. wavelength” and “Frequency domain parameters” are selected, it is assumed that file contains 2 . If “Frequency domain parameters” is disabled, component assumes that file contains D . If “Group delay vs wavelength”, the file contains 1 . Dispersion file name Specifies file containing dispersion data The parameter “Frequency domain parameters” refers to the alternative definitions: 1 D D = --------- S = ------- (wavelength domain definition) and 1 2 2 = --------- 3 = --------- (frequency domain definition) of the dispersion parameters, but not to the argument of these functions, which is always assumed to be the wavelength. All the parameters in the component 2 and 3 ) are given as functions of wavelength (not frequency). This is also the case when 1 or 2 are specified from a file - the first column of the file contains wavelength values ( ) and the second column - the corresponding values of 1 or 2 . (including PMD Name and description Symbol Default value Default unit Value range Birefringence type — Deterministic — Deterministic/ Stochastic d----- d 0.2 ps-----km [-10100, 10100] Defines the birefringence. If “Deterministic”, both the strength of birefringence and principal axes are assumed constant, hence random mode coupling is disabled. If “Stochastic”, random mode coupling is enabled. Differential group delay If Birefringence type is “Deterministic”, this is the value of the differential group delay. If “Stochastic”, parameter is disabled. 637 OPTICAL FIBER Name and description Symbol Default value Default unit Value range PMD coefficient Dp 0.5 ps ---------km [0,10100] L scatt 500 m [0,10100] scatt 100 m [0,10100] Polarization mode dispersion coefficient. If Birefringence type is “Stochastic”, this is the value of the PMD parameter. If “Deterministic”, parameter is disabled. Mean scattering section length Averaged value of fiber length at which the polarization state of the signal is randomized by applying the scattering matrix. Scattering section dispersion Dispersion of the scattering section length. Nonlinearities Name and description Symbol Default value Default unit Value range Self-phase modulation — TRUE — TRUE/FALSE Constant — Constant/ From File Determines if the self-phase modulation (SPM) effect will be taken into account. If FALSE all the nonlinear effects self-steepening, SRS - are disabled. In the vector case enabling this effect enables also the cross-phase modulation between the orthogonal polarization components. Effective area data type Defines is effective area parameter value is read from the component tab or from a file. If “Constant”, the value from the component is used. Effective area Defines the value of the effective area parameter. This value is used if “Effective area data type” is set to “Constant”. Otherwise, the value is ignored. Effective area vs. wavelength [0,1010] A eff 80 — — — — — Constant — Constant/ From File n2 2.6 X 10-20 m 2 If “Effective area data type” is “From file”, this tab specifies the file containing the effective area data. n2 data type Determines if n 2 parameter (nonlinear index of refraction) value is read from the component tab or from a file. If “Constant”, value is taken from component. n2 The value of the n 2 parameter (nonlinear index of refraction). If data type is set to “Constant”, this value is used, otherwise the value is ignored. 638 2 m -----W [0,10100] OPTICAL FIBER Name and description Symbol Default value Default unit Value range Self-steepening — FALSE — FALSE/TRUE — FALSE — FALSE/TRUE — FALSE — FALSE/TRUE R1 14.2 fs [0,10100] R2 3 fs [0,10100] 0.18 — [0, 1] f 0.75 — [0, 1] Specifies whether self-steepening effect is taken into account. Can be enabled only after enabling the SPM, and is taken into account only in the scalar case (if Model type is set to Scalar), and if Full Raman response parameter is FALSE. Full Raman response Defines the stimulated Raman scattering (SRS) effect representation in the model. If TRUE, SRS is represented through the convolution integrals of the fields with the Raman susceptibilities [6, 18-21]. Intrapulse Raman scattering is disabled. Intrapulse Raman scattering Defines the stimulated Raman scattering (SRS) for [1921]. Can be enabled if Full Raman response is FALSE. If both Full Raman response and Intrapulse Raman scattering are FALSE, SRS effect is not taken into account in the simulation. Raman self-shift time 1 Value of the Raman self-shift time parameter associated with the parallel SRS effect R1 = dIm 1111 d = 0 Units are such that Re 1111 = 0 = 1 [19-21]. Raman self-shift time 2 R2 = dIm 1122 d = 0 Units are such that 21]. Re 1111 = 0 = 1 [18, 20, Fractional Raman contribution Fraction of the nonlinear polarization, related to the stimulated Raman scattering effect [2]. Orthogonal Raman factor f = Re 1122 = 0 Units are such that Re 1111 = 0 = 1 . 639 OPTICAL FIBER Numerical Name and description Symbol Default value Default unit Value range Model type — Scalar — Scalar/Vect or Exponential — Exponential RungeKutta 4th order Defines model type used for simulation. Depends on polarization state of signal. If “Vector” selected, signal can have arbitrary polarization state and a system of two coupled equations (17) is solved. If “Scalar” selected, the signal preserves its polarization state and a single equation is solved (1). In the following cases, vector simulation is performed regardless of value of model type parameter: • • Two polarization components are detected at fiber input PMD effect is “Stochastic”. Propagator type Method used to apply nonlinear propagator in the split-step Fourier method. “Exponential” corresponds to standard implementation [2], “Runge-Kutta 4th (2nd) order” uses Runge-Kutta 4th (2nd) order (see [3]) to apply nonlinearity operator. Exponential cannot be used when Model type is set to Vector, and SRS effect is enabled. The default selection is Runge-Kutta 2nd order. Calculation type Exponential RungeKutta 2nd order — Iterative — Iterative/ Noniterative 2 — [2, 1010] Variable — Variable/ Constant 3.14 mrad [0,10100] Specifies implementation of split-step Fourier method [2, 4] when Propagator type is “Exponential”. Number of iterations Switch On/Off the dispersion slope (the third-order dispersion) Step Size — Specifies whether variable or fixed step-size simulation is used. If “Variable”, step size is adaptively changed depending on value of “Max. nonlinear phase shift” parameter, and solution itself. If “Constant”, step size is evaluated once at the beginning of simulation. In some cases, the fixed step size calculation executes faster, due to the smaller number of calculations per step, but the variable step size calculation is more flexible and can be faster if the peak power of the waveform varies considerably in z (for example, in the presence of strong attenuation). Max. Nonlinear phase shift Maximum (over the time window) phase shift induced by the self-phase modulation effect per step. 640 NL max OPTICAL FIBER Name and description Symbol Default value Default unit Value range Boundary conditions — Periodic — Periodic/ Absorbing — 0.5 — [0,10100] — [1400, 1700] nm [100, 2000] Specifies type of boundary conditions used in simulation. Filter steepness If “Boundary conditions” option is set to “Absorbing”, the “Filter steepness” parameter determines the absorption/reflection properties of the time window boundaries. Lower/Upper calculation limit Set the spectral range in which the simulation is performed. Any spectral components outside the range is ignored. Graphs Name and description Symbol Default value Default unit Value range Calculate graph — FALSE — FALSE/TRUE — 200 — [1, 100000000] — 200 — [1, 100000000] — TRUE — TRUE/FALSE Enables/disables 3D graphs. If disabled, no graphs are plotted and no data are stored. Number of distance steps Number of snapshots used to construct a 3D plot. If this value is increased, the fidelity of the plot is improved only if the value is below the number of actual steps in z . The number of snapshots stored cannot be bigger than the number of steps in z taken by the simulation to obtain the solution. The latter is determined by the maximum nonlinear phase-shift parameter (numerical tab). Number of wavelength/time steps Number of stored points per snapshot. If this value is increased, the fidelity of the plot is improved only if the value is below the actual number of points in the time (frequency) domain used by the simulation to obtain the solution. The latter is related to the number of samples, which is a global parameter. Linear scale Determines axis type (linear or logarithmic) for the dependent variable. If TRUE, the axis type is linear. Note: The rest of the parameters in the Graphs tab of the component determine which graphs are plotted after the simulation is complete. 641 OPTICAL FIBER Simulation Name and description Symbol Default value Default unit Value range Enabled — TRUE — TRUE/FALSE Name and description Symbol Default value Default unit Value range Convert noise bins — FALSE — FALSE/TRUE Name and description Symbol Default value Default unit Value range Generate random seed — TRUE — TRUE/FALSE — 0 — [0, 4999] Determines whether or not the component is enabled. If FALSE, all input signals reach the output port of the component without any changes. Noise If TRUE, each noise bin within the bandwidth of the signal is converted to a Gaussian white noise, with the correct power spectral density, and the noise is added to the signal. Random numbers Determines how random number generator is initialized (seeded). If TRUE, the seed index used for the initialization is the random number itself. Otherwise, a user specified number is used. Random seed index If “Generate random seed” is FALSE, this value specifies the seed index. The generated pseudorandom sequence is the same if the seed index is not changed. The value of the “Random seed index” is ignored if “Generate random seed” is TRUE. 642 OPTICAL FIBER Technical Background Scalar approach Basic equation When the optical field is assumed to maintain its polarization along the fiber length, the evolution of a slowly varying electric field envelope can be described by a single nonlinear Schrödinger (NLS) [2] equation (the scalar approach, Model type parameter from the "Numerical" tab is set to "Scalar") of the form: 2 2 0 2 E 3 0 3 E E i E ------ + E + i ---------------- --------- – ----------------- --------- = i E 2 E + ------ ------ E 2 E – R1 E ------------ z 2 T 2 6 T 3 0 T T In Equation 2, (1) E = E z T is the electric field envelope. A frame moving at the group velocity ( T = t – z vg t – 1 z The derivatives of the propagation constant of the fiber mode ) is assumed. , ( c is the mode effective index), with respect to frequency n 0 n = ------------------- n = 1 2 3 . n 2 and 3 are the first and the second group velocity dispersion (GVD) parameters, respectively, and 0 is the reference frequency of the signal, related to the parameter "Reference wavelength" ("Main" category of the components tool-box) through o = 2c/o with c being the light speed in vacuum. The physical meaning of the terms in Equation 2 is the following. The first term takes into account the slow changes of the electric field along the fiber length. The second term takes into account the linear losses of optical fiber. The third term represents the (first-order) group velocity dispersion. This is the effect responsible for the pulse broadening. (See "Group velocity dispersion" in the Tutorials). The next term is the second-order GVD, known also as third-order dispersion (TOD). This effect becomes important for a signal with a broad spectrum (e.g. femtosecond pulses or WDM systems with many channels). The pulse shape becomes asymmetric due to the effect of TOD. (See "Third order dispersion" from the Tutorials). The parameters and 2 3 are denoted as "frequency domain parameters" in the interface of the component (see the "Dispersion" category in the Parameters table). The following 643 OPTICAL FIBER relations are used internally to convert between them and the commonly used wavelength domain parameters D (dispersion) and S (dispersion slope). d 1 2c D = --------- = – -------2 2 d (2) 2 2 dD 3 = --------- S + 2D S = ------ 2c d The parameter is given by: 0 n2 = -----------cA eff (3) In Equation 3, n 2 is the nonlinear refractive index coefficient and A eff is the fiber effective area. The first term in the right-hand side in Equation 1 accounts for the selfphase modulation effect. It is responsible for the broadening of the pulse spectra and, in the presence of anomalous GVD, for the formation of optical solitons (See "Selfphase modulation" and "Self-phase modulation and group velocity dispersion" from the Tutorials). The second term in the right-hand side of Equation 1 takes into account the self-steepening effect. It leads to an asymmetry in the SPM-broadened spectra of ultrashort (femtosecond) pulses [2] and is responsible for the formation of optical shocks (see "Self-steepening" in the Tutorials). This effect will be taken into account only if the "Full Raman response" parameter is set to False. The last term in Equation 1 accounts for the intra-pulse Raman scattering effect with the parameter R1 being the parallel Raman self-shift time. The intra-pulse Raman scattering is an approximation to the actual Raman response of the material which is valid provided that signal spectrum is narrow compared to the Raman-gain spectrum. The R parameter is related to the slope of the imaginary part of the Raman susceptibility Im 1111 at zero frequency offset [2]. The parameter is the fractional contribution of the delayed response of the material to the total nonlinearity [2]. The intra-pulse Raman scattering effect is responsible for the self-frequency shift i.e. energy transfer from higher to lower spectral components. It leads to a decay of higher order solitons into its constituents (see "Intrapulse Raman scattering" in the Tutorials). The intra-pulse Raman scattering plays the most important role among the higher order nonlinear effects [2]. In a WDM system, the stimulated Raman scattering is responsible for an energy transfer from higher to lower frequency channels (crosstalk). The Raman induced crosstalk can be neglected when the following relation is satisfied [5]: P TOT B TOT L E 9mWTHzMm 644 (4) OPTICAL FIBER L E z L amp is the total effective length, is the fiber loss, L amp is the amplifier spacing, z the link length, P TOT is the total optical power, and B TOT is the where total optical bandwidth. Full Raman response By selecting the option "Full Raman response" from the Numerical tab, the component can simulate the SRS effect even if the signal spectrum is much narrower than the Raman gain spectrum. In this case Equation 1 is replaced by: i 2 0 2 E 3 0 3 E E ------ + E + ------------------ --------- – ----------------- --------- = 2 z 2 6 T 3 T (4a) 2 2 i 1 – E E + E h 1111 s E T – s ds 0 Contained within Equation (4a) is h 1111 t which is the (time-domain) Raman response function [2], [20]. It is the Fourier-transform of the of the Raman susceptibility 1111 . In this case the self-steeping effect is neglected. Numerical solution In dimensionless form, Equation 1 reduces to: 2 3 2 U U U U 2 2 i ------- + D 2 --------+ N 1 U U = iD 3 --------+ N 2 U ------------- – iN 3 ---- U U – iAU , 2 3 t t t t (5) where the coefficients are given by: sign 2 L D sign 3 LD LD LD D 2 = ---------------------- D 3 = ----------------------------- N 1 = ------ N 2 = ------ R' , N 3 = --------- s . 2 L D' L NL L NL L NL (6) The new quantities are introduced according to: 2 LD 3 T0 T0 1 1 = -------- L NL = -------- L D' = -------- s = -----------0 T0 2 P 0 3 R R' = ----- E = To (7) P 0 U T = T 0 t z = L D . 645 OPTICAL FIBER T 0 is the time window size and P 0 is the maximum (over the time 2 window) of the electric field intensity E z = 0 T . In Equation 7, The symmetrized split-step Fourier method [2, 4] is used to solve Equation 5. The to + h ( h is the step-size, related to the value of the 2 NL Max. nonlinear phase shift parameter max = max U h ) according to: solution is advanced from + h h--- h U + h t = exp D̂ exp N̂ ' d' exp --- D̂ U t , 2 2 where the dispersion (8) D̂ and nonlinearity N̂ operators are given by: 2 3 D̂ = iD 2 ------2- + D 3 ------3- – A t t (9) and 2 2 U U U 2 N̂ = iN 1 U – iN 2 ------------- – N 3 ------------- + U ------- t t t (10) The different options available from the "Numerical" tab specify the details of the implementation of Equation 8 and Equation 10 (see Figure 1). The simplest (and the fastest) implementation corresponds to "Propagator type" set to "Exponential" and "Calculation type" set to "Noniterative". In this case, the following approximation is used: +h 646 N̂ ' dz' hN̂ exp h 2 D̂ U t . (11) OPTICAL FIBER Figure 1 Component “Numerical" tab According to Equation 11, the half-step propagated field, with the nonlinear effects ignored, is used in turn to evaluate the nonlinearity operator. The dispersion operator is evaluated in the frequency domain according to: h h –1 Ũ D + --- = FFT exp --- D̂ i FFT U t , 2 2 (12) where FFT means fast Fourier transform. If, in addition the "Step size" option is set to "Constant" ("Propagator type", "Exponential", and "Calculation type" are set to "Noniterative"), the number of operations per step decreases because the first and the last Fourier transform for each step cancels each other out (dispersion operators combine) (see Equation 13). + h + h h h h h U + 2h t = exp --- D̂ exp N̂ ' d' exp --- D̂ exp --- D̂ exp N̂ ' d' exp --- D̂ U t = 2 2 2 2 h exp --- D̂ exp 2 + h N̂ ' d' exp hD̂ exp + h (13) h N̂ ' d' exp --- D̂ U t 2 647 OPTICAL FIBER When the "Propagator Type" is set to "Runge-Kutta 4th order" (or "Runge-Kutta 2nd order") (RK4 or RK2), the exponent with the nonlinearity operator in Equation 8 is replaced by the direct integration of the following system of coupled ordinary differential equations: U ------- = N̂U z NL (14) by means of the standard RK4 (or RK2) routine (see example in [3]). The application of the dispersion operator is the same. Note: The Runge-Kutta (2nd or 4th order) implementations in the fiber component enable modeling the stimulated Raman scattering effect with the optical signal having an arbitrary polarization ("Model type" parameter set to "Vector"). However, due to the larger number of operations per step, they are executed slower and are not recommended otherwise (in "scalar" simulations or when the Raman effect is not included in a vector simulation) because the "Exponential" implementation of the nonlinearity provides faster execution. If the "Propagator type" is set to "Exponential" and "Calculation type" to "Iterative", Equation 11 is replaced by [2], [4]: +h h N̂ ' d' --- N + N + h 2 (15) N̂ means N̂ E . Since N̂ + h is unknown at + h 2 , it is necessary to follow an iterative procedure that is initiated by replacing N̂ + h by N̂ (see [2], [4] for the details). Working with two iterations gives a reasonable The symbol combination between accuracy and speed, as recommended in [2]. 648 OPTICAL FIBER Figure 2 Evolution of E t = 0 2 for N=3 soliton over 15 soliton periods with different calculation modes Note: In the three cases presented, NL max = 27.6mrad , constant step size. A comparison between the "Iterative" and "Noniterative" approaches is presented in Figure 2. Evolution of N=3 soliton over 15 soliton periods is presented. The "Step size" is kept "Constant" with the "Max. nonlinear phase shift" parameter is equal to 27.6. mrad. The noniterative approach is the fastest but not accurate enough at this step size. The development of spurious, numerical instability, which breaks the periodicity of the soliton evolution [2], is evident at the end of the run. For the same step size the iterative implementation of the split-step Fourier method suppresses the instability, thus improving the quality of the results, however this improvement is at the expense of increased computation time. h in the component is determined through the value of the parameter 2 = max E h . In the case of the constant step size calculation, it is The step size NL max calculated once, using the input signal to obtain the maximum value of the intensity. In the case of variable step size calculation such an evaluation is performed at each step. 649 OPTICAL FIBER Figure 3 Variable step size, value of NL max is NL max = 50mrad In Figure 3, the calculation presented in Figure 2 is repeated using variable step size. This calculation takes longer in comparison to the "Noniterative" case presented in Figure 2, but less than in the case where two iterations are used. Depending on the behavior of the solution, variable step size calculation can take less time compared to the constant step size, although the fixed step size calculation performs a smaller number of operations per step (see Equation 13). In the presence of considerable attenuation, the importance of nonlinear effects decreases along the fiber length, which would permit the use of a larger step size. In this case, the use of variable step size will reduce the computation time. The variable step size calculation is more NL flexible, because different tasks can be handled keeping the value of max constant. For the case presented in Figure 3, this value is double the size of the one used in Figure 2, but the results are even better (refer to compare with Figure 2, "Noniterative"). The split-step scheme used in the model is locally second order accurate which 3 means that the local error is proportional to the h . However, the global error (after N 3 2 steps) is proportional to Nh = Lh [22]. Thus, increasing the fiber length might require decrease of the step size to maintain the same accuracy. The use of FFT implies periodic boundary conditions. In some cases a part of the pulse energy may spread eventually hitting the time window boundaries. When the energy reaches one of the edges of the time window it automatically reenters from the other edge perturbing the solution. This can be avoided using the absorbing type of boundary conditions. To achieve this at each step the optical field is multiplied in the time domain [10] by: t = 1 – sech FilterSteepnes t – t edge , (16) where t edge indicates the nearest edge. The effect of periodic and absorbing boundary conditions is shown in Figure 4 where the results presented in Figure 3 from "Birefringence and solitons" (propagation distance is equal to 1262.34km) are displayed. However here the time window is reduced to show the effect of the periodic 650 OPTICAL FIBER boundary conditions. The oscillatory tail developed by the solution in the case when periodic boundary conditions are used is an unphysical effect, resulting from the interference of the radiation that has reentered the time window and the solution. In the case when absorbing boundary conditions are used the radiation that has separated from the solution is removed. The smaller the value of the filter steepness parameter the better the time window boundaries absorb (and do not reflect), however the larger part of the time window becomes absorbing (see Equation 16. Figure 4 Periodic (left plot) and absorbing with filter steepness 0.05 (right plot) boundary conditions 651 OPTICAL FIBER Vector approach When the polarization state of the incident light is not preserved during its propagation inside an optical fiber the scalar approach is no longer applicable and Equation 1 is replaced by [2], [6] - [10]: 2 3 i E E E X E --------- + 1X ---------X + ------2- -----------X- – ----3- -----------X- = i 1 – E X 2 + 2--- E Y 2 E X z t 2 t 2 6 t 3 3 + iE X 2 h1111 s EX t – s 2 ds + h 1122 s E Y t – s ds 0 0 + iE Y h 1212 s E X t – s E Y t – s ds 0 (17) 2 3 E Y E i E E --------- + 1X --------Y- + -------2 -----------Y- – ----3- -----------Y- = i 1 – E Y 2 + 2--- E X 2 E Y z t 2 t 2 6 t 3 3 + iE Y h1111 s E t – s 0 2 2 ds + h 1122 s E X t – s ds 0 + iE X h 1212 s E t – s E X t – s ds 0 Equation 17, h ijkl t contains the Raman response functions [6], [18]. Their Fourier transformations and Raman susceptibilities ijkl v , are shown in Figure 4.1. The convolution integrals in Equation 17 are evaluated in the frequency domain, by multiplying the spectra of the electric fields with the Raman susceptibilities and then performing the inverse FFT. 652 OPTICAL FIBER Figure 4.1 Raman susceptibilities for fused quartz [6, 18] The SRS effect is represented by "Intrapulse Raman scattering" (Equation 17) is replaced by [20]: 2 3 E E i E E ---------X- + 1X ---------X- + -------2 -----------X- – -----3 -----------X- = z t 2 t 2 6 t 3 2 2 EX EY 1 +f 2 2 2 i E X + --- 1 – + -------------- E Y – R1 --------------- – R2 --------------- E X 3 2 t t R1 – R2 E X E Y – i ---------------------- ------------------------ E Y 2 t (17a) 2 3 E E E i E ---------Y + 1Y ---------Y + -------2 -----------Y- – -----3 -----------Y- = z t 2 t 2 6 t 3 2 2 2 EY EX 1 +f 2 2 i E Y + --- 1 – + -------------- E X – R1 --------------- – R2 --------------- E Y 3 2 t t R1 – R2 E Y E X – i ---------------------- ------------------------ E X 2 t Note: In the case of Equation 17 or Equation 17a, due to the orthogonal Raman gain terms (the last sections in Equation 17 or Equation 17a), the "Exponential" option for the "Propagator type" is not applicable. The component automatically selects "Runge Kutta 2nd order" when the model type is set to "Vector", and the Raman effect ("Intrapulse Raman scattering" or "Full Raman response" options are selected. Due to the increased number of convolutions performed at each step the fiber component can be slow when solving Equation 17. 653 OPTICAL FIBER In normalized units and when the SRS effect is neglected ( reads as: 2 3 2 3 = 0 ) Equation 17 u u u u 2 2 2 i ------ + ------ + D 2 --------2 – iD 3 -------3- + N 1 u + --- v u = 0 t 3 (18) v v v v 2 2 2 i ------ + ----- + D 2 -------2- – iD 3 -------3- + N 1 v + --- u v = 0 t 3 The quantities 1X and 1Y are the inverse group velocities for the polarization components respectively. X and Y Figure 5 Optical fiber as a concatenation of trunks Note: The arrows represent the principal axes. The parameter is given by = 1X – 1Y T 0 2 2 , where 1X – 1Y is the value of the differential group delay parameter entered from the "PMD" tab, in the case where "Deterministic" mode is selected for the birefringence effect (see "Birefringence and solitons" from the Tutorials). The effects of four-wave mixing between the orthogonal polarization components are not taken into account due to their negligible contribution for typical values of the birefringence [9], [10]. The is introduced according to = t – 1 z T 0 where 1 = 1X + 1Y 2 . All the other parameters have the same meaning as in the normalized time scalar case. The "coarse-step method" [11] is used to simulate the PMD effects in the "Stochastic" mode. The fiber is represented by a concatenation of trunks and the propagation of light in each trunk is simulated by the split-step Fourier method described in the previous section. The lengths of the trunks are random numbers with a Gaussian distribution [12]. The average and the dispersion of this distribution are the "Scattering section length" L scatt and "Scattering section dispersion" scatt parameters: i f L scatt 654 i 2 – L scatt – L scatt 1 = ------------------------ exp -----------------------------------------2 2 scatt 2 scatt (19) OPTICAL FIBER It is recommended [12] that the dispersion is 20% of the average value. The birefringence of each trunk is given by [11] (see the related PMD examples in the tutorials): DP d----- = ----------------d i L scatt (20) where D PMD is the PMD coefficient. The principal axes of the trunks are randomly oriented with respect to each other (see Figure 4). To simulate the random mode coupling at the end of each trunk the following transformation is applied [11], [13]: E X' E Y' In Equation 20, 0 2 . = cos sin exp i E X – sin exp – i cos EY (21) and are random numbers uniformly distributed in the interval Wavelength dependent parameters The file that specifies the wavelength dependence of the parameters consists of two columns with the left column being the wavelength in nanometers and the right column containing the corresponding values of the parameters (see Table 1 ). The sampling interval is not necessarily be constant. The parameter values must be given in the units specified in the "Units" tab of the table. Table 1 Wavelength dependence of the attenuation parameter nm dB km 1400 0.31405 1402.5 0.30246 1405 0.29276 1407.5 0.28457 1410 0.27757 1412.5 0.27153 The values of the parameters in Equation 1 and Equation 17 are evaluated at the reference wavelength. Note: The reference wavelength must be within the wavelength interval covered by the files for all the wavelength dependent parameters specified. The reference wavelength can be either user-specified or "automatic". In the last case the wavelength corresponding to the central frequency of the spectrum of the signal 655 OPTICAL FIBER is assumed by the component to be the reference wavelength. Linear interpolation is used to calculate the values of the attenuation, effective area and n 2 parameters at this wavelength. For the dispersion parameters the following procedure is used. The wavelength dependence specified by the file is fitted internally using the five-term Sellmeier formula [14]. The higher-order dispersion parameters are then obtained by analytically differentiating this expression. If the option frequency domain parameter is unchecked, the file may give either the group delay 1 or dispersion D (depending on the choice made in the "Dispersion file format" tab), and if the frequency domain parameters option is selected, either 1 or 2 can be supplied, again determined by the value of the "Dispersion file format" parameter. If the wavelength dependence of the group delay is given by the user, two successive differentiations are applied to its Sellmeier fit. Differentiating the analytical fit instead of using a direct numerical differentiation of the data provides the advantage of being able to produce reasonable results even in the case where the supplied data is noisy (see Appendix 1). Note: The accuracy of the Sellmeier fit depends on the type of the fiber. This is shown in Figure 6, where the results obtained for dispersion flattened and dispersion shifted fibers are shown. Figure 6 Comparison between the original dispersion data and their fits for two fiber types Guidelines for using the component for WDM simulations Periodic boundary conditions are required for simulating the propagation of long bit sequences at different carrier wavelengths, which is the case when WDM systems are designed. To avoid the aliasing phenomena (see e.g. [3]), the sample rate is chosen to be at least three times bigger (Figure 7) than the bandwidth occupied by the simulated channels (see e.g. [15]). 656 OPTICAL FIBER Figure 7 WDM channels and their four-wave mixing products Any frequency component outside the frequency range (Fc-SR/2, Fc+SR/2), where SR is the sample rate and Fc is the reference frequency is falsely translated (aliased) into that range by the very act of discrete sampling [3]. If the sample rate is bigger than the bandwidth occupied by the WDM channels (so it can accommodate all the channels) but less than three times that value in the presence of nonlinear effect the four-wave mixing products resulting from the nonlinear interaction between the channels (spurious waves [16]) will be aliased. In [16], to minimize the amount of aliased power the requirement that the value of the power spectrum at the boundary of the available spectral range be -40 dB of its peak value is used. The longitudinal step size depends on the importance of the nonlinear effects for the particular simulation. If all the nonlinear effects are disabled step size equal to the fiber length will be used. The increase of the impact of nonlinearity will require decrease of the step size (decrease of the value of the max. nonlinear phase shift parameter) to maintain the same accuracy. 657 OPTICAL FIBER Figure 8 Output spectra corresponding to NL NL max = 50mrad and max = 3mrad Note: The propagation distance is 100km. Input configuration is given in "Crossphase modulation" in the Tutorials. Values in the order of a few milliradians (one [15] and three [17])) are used with this parameter in a WDM system simulation. The effect of an improperly chosen step size is shown in Figure 8, where the output spectra corresponding to an interaction of two Gaussian pulses with carrier wavelengths one nm spaced are shown (see "Crossphase modulation" from the Tutorials). While the correct result that the four-wave mixing products (or spurious waves) should disappear when the pulses are no longer over-lapped (in the absence of any loss and gain [16]) is reached when the step-size is small enough, in the opposite case, the spurious frequencies present in the output spectra are still evident. The improperly chosen step size (too big) tends to exaggerate the four wave mixing products (see [22] and references therein). To increase the accuracy, you can switch from a "Noniterative" to an "Iterative" calculation type, keeping the step size the same (with the same step size, the "Iterative" implementation is more accurate, (see Figure 2), or alternatively, to keep working in the "Noniterative" mode and decrease the step size, or the value of the "Max. nonlinear phase shift" parameter. With respect to saving computational time, the latter strategy is better. It should be noted that computational time will not be saved by simultaneously increasing the number of iterations and the step size. 658 OPTICAL FIBER Appendix 1 Dispersion fitting according to the Sellmeier formula When the option "Dispersion from file” is selected, the dispersion data are internally fitted according to the five-term Sellmeier formula [14], namely: = c1 where –4 + c2 –2 2 + c3 + c4 + c5 (1) 4 is the group delay (per unit fiber length) or, respectively: d –5 –3 3 D = ------ = c 1' + c 2' + c 4' + c 5' d (2) where D is the dispersion [ps/nm/km]. The user supplies data either for the dispersion or the group delay that are then fitted according to Equation 2A or Equation 1A, and the slope and/or dispersion are calculated by differentiating Equation 1A and Equation 2A analytically. The least-square fitting associated with Equation 2A amounts to minimizing: N Q = –5 c1 i –3 3 2 + c 2 i + c 4 i + c 5 i – D i = min (3) i=1 where N is the number of points. Using: Q ------- = 0 i = 14 , c i (4) 659 OPTICAL FIBER the following linear system is obtained: – 10 –8 –4 –2 i i i i –8 –6 –2 i i i N –4 –2 2 4 i i i i –2 4 6 i N i i –5 C1 C2 C4 = C5 Di i –3 Di i Di i 3 Di i (5) which is solved by LU-decomposition [3]. In the case when the user supplies a group delay data file, Equation 1A is used and Equation 5A transforms into Equation 6A. The fitting procedure is useful when/if noisy data is supplied by the user, as the following example shows. Figure 1A shows dispersion-versus-wavelength dependence of SMF-28 and the corresponding "exact" results for dispersion parameters are displayed below the graph. –8 –6 –4 –2 i i i i –6 –4 –2 i i i N –4 –2 2 i i N i –2 2 4 i N i i 2 4 6 N i i i 660 –4 N 2 i 4 i 6 i 8 i C1 C2 C3 = C4 C5 i i –2 i i i 2 i i 4 i i (6) OPTICAL FIBER Figure 1A Lambda = 1550.75nm beta2=-2.08625e-026 s2/m beta3=1.27246e-040 s3/m D= 1.63411e-005 s/m2 S= 56.9931 s/m3 To assess the influence of noise on the results from the calculation some noise is added to the data presented in Figure 1A with the resulting graph presented in Figure 2A. Supplying the data from Figure 2A to the Nonlinear Dispersive Fiber Total Field component gives the results for the dispersion parameters presented under Figure 2A. 661 OPTICAL FIBER Figure 2A Lambda = 1550.75nm beta2=-2.10115e-026 s2/m beta3=1.32966e-040 s3/m D= 1.64578e-005 s/m2 S= 60.3521 s/m3 662 OPTICAL FIBER Appendix 2 Optical fiber data SMF-28 The SMF-28 model used in OptiSystem has the following characteristics: Figure 1 Attenuation Figure 2 Group Velocity Dispersion 663 OPTICAL FIBER Figure 3 Effective Area Figure 4 Group Delay Attenuation curve shows a minimum of GVD curve reveals a dispersion of 2 slope of 0.05 ps/nm km . Effective area at Group delay is 0.185 dBm for a wavelength of 1550 nm . 16.5 ps/nm/km at 1550 nm with a dispersion 2 1550 nm is 76.5 m . 4897650 ps/km . This model can be varied in any way because you have the ability to change any particular parameter. Create a new file and then load it into the appropriate section, or just set the parameter to 'Constant' and enter a value. The Nonlinear Fiber model is very flexible, because it has the ability to model practically every manufactured fiber that exists on the market today. 664 OPTICAL FIBER +D NZDSF model The +D NZDSF model used in OptiSystem has the following characteristics: Figure 5 Attenuation Figure 6 Group Velocity Dispersion 665 OPTICAL FIBER Figure 7 Effective Area Figure 8 Group Delay Attenuation curve shows a minimum of GVD curve reveals a dispersion of 2 slope of 0.01 ps/nm km . The effective area at Group delay is 666 0.185 dBm for a wavelength of 1550 nm . 4.5 ps/nm/km at 1550 nm with a dispersion 2 1550 nm is 71.5 m . 4895870 ps/km . OPTICAL FIBER -D NZDSF model The -D NZDSF model used in OptiSystem has the following characteristics: Figure 9 Attenuation Figure 10 Group Velocity Dispersion 667 OPTICAL FIBER Figure 11 Effective Area Figure 12 Group Delay Attenuation curve shows a minimum of 0.185 dBm for a wavelength of 1550 nm. GVD curve reveals a dispersion of -7.5 ps/nm/km at 1550 nm with a dispersion slope of 0.18 ps/nm2/km. Effective area at 1550 nm is 92 m2. Group delay is 4890750 ps/km. 668 OPTICAL FIBER CDF (Standard) The DCF model used in OptiSystem has the following characteristics: Figure 13 Attenuation Figure 14 Group Velocity Dispersion 669 OPTICAL FIBER Figure 15 Effective Area Figure 16 Group Delay Attenuation curve shows a minimum of 0.3 dBm for a wavelength of 1600 nm. GVD curve reveals a dispersion of -82 ps/nm/km at 1550 nm with a dispersion slope of 4.5 ps/nm2/km. Effective area at 1550 nm is 32 m2. Group delay is 4914000 ps/km. 670 OPTICAL FIBER References [1] G. P. Agrawal, "Applications of nonlinear fiber optics", Academic press, 3rd edition, 2001. [2] G. P. Agrawal, "Nonlinear fiber optics", Academic press, 3rd edition, 2001. [3] W. H. Press, et al., "Numerical Recipes: The Art of Scientific Computing", 2nd Edition, Cambridge University Press, 1992. [4] M. Lax, J. H. Batteh and G. P. Agrawal, Journ. Appl. Phys. 52 , 109, (1981). [5] F. Matera and M. Settembre, Journ. Lightwave Technol. 14, 1 (1996). [6] R. W. Hellwarth, Prog. Quant. Electr. 5, 1 (1977). [7] E. A. Golovchenko and A. N. Pilipetskii, JOSA B, 11, 92 (1994). [8] P. T. Dinda, G. Millot, and S. Wabnitz JOSA B, 15, 1433 (1998). [9] C. R. Menyuk, Opt. Lett., 12, p. 614 (1987). [10] C. R. Menyuk, JOSA B, 5, p. 392(1988). [11] D. Marcuse, C. R. Menyuk and P. K. A. Wai JLT, vol. 15, No. 9, pp. 1735 (1997). [12] C. H. Prola Jr., J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. Von der Weid, and N. Gisin IEEE Phot. Technol. Letters, 9, No. 6, 842 (1997). [13] P. K. A. Wai, C. R. Menyuk, and H. H. Chen , Opt. Lett. 16 1231 (1991). [14] L. G. Cohen, Journ. Lightwave Technol. 3, 958, (1985). [15] M. I. Hayee and A. E. Willner, IEEE Phot. Technol. Lett. 11, No. 8, (1999). [16] D. Marcuse, A. R. Chraplyvy, and R. W. Tkach, Journ. Lightwave Technol, 9, 121 (1991). [17] R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, Journ. Lightwave Technol, 13, 841 (1995). [18] P. Tchofo Dinda, G. Millot, and S. Wabnitz, JOSA B, 15, 1433, (1998). [19] R.H.Stolen, J.P.Gordon, W.J. Tomlinson and H.A. Haus, JOSA B, 6, 1159 (1989). [20] C.R.Menyuk, M.N.Islam and J.P.Gordon, Optics Letters, 16 566, (1991). [21] K.J. Blow and D. Wood, IEEE J. Quant. Electr., 25, 2665, (1989). [22] O. Sinkin, R. Holzlohner, J. Zweck and C. R. Menyuk, Journ Lightwave Technol. 21, 61 (2003). 671 OPTICAL FIBER Notes: 672 OPTICAL FIBER CWDM Optical fiber CWDM The component simulates the propagation of arbitrary configuration of optical signals in a single-mode fiber. Dispersive - first and second order group velocity dispersion (GVD) effects - and non- self-phase modulation (SPM), cross-phase modulation (XPM) and stimulated Raman scattering (SRS) effects - are taken into account. The evolution of each sampled signal is governed by a modified nonlinear Schrödinger (NLS) equation (when the signal is assumed to maintain its state of polarizing) or a system of two, coupled NLS equations (arbitrary polarization state of the signal). Raman interaction for an arbitrary configuration of sampled and parameterized signals is also considered. Noise bins also participate in the SRS effects, however their power is assumed much smaller than that of the parameterized and sampled signals, which means that the SRS interaction between noise bins and parameterized/sampled signals is considered as a pump-probe interaction. The component provides most of the functionality of the total field approach fiber model (excepting the simulation of the Raman effect in birefringent fibers) while at the same time, it can handle different signal representation to give more flexibility and speed up the calculations. Ports Name and description Port type Signal type Input Input Optical Output Output Optical 673 OPTICAL FIBER CWDM Parameters Main Name and description Symbol Default value Units Value range Merge sample bands — False — False, True — True — True, False 0 1550 nm [100, 2000] L 50 km [0, 100 000] — True — True, False — Constant — Constant, From File If TRUE all the sampled signals will be re-sampled and a single frequency band confining all the sampled signals will be formed. As a result the "Total field approach" (see the technical description of the total field fiber model for the details) will be implemented in the simulation. This will include the effects of four-wave mixing in the simulation and, besides the SRS effect will be represented through the convolution integral of the Raman response function and the field intensity. If FALSE all the channels will be treated separately - FWM effects will be disabled and SRS effects will be approximated through inter band Raman scattering [1, 2]. User defined reference wavelength If TRUE the frequency corresponding to the value entered under "Reference wavelength" is used internally as reference frequency.. The system of modified NLS equations governing the evolution of the signals is solved in a frame moving with the group velocity corresponding to that frequency. If FALSE the value of the reference frequency is calculated as the averaged of the central frequencies of all the sampled and parameterized signals. Reference wavelength The value of the user specified reference wavelength. Length Fiber length Attenuation effect If TRUE the attenuation effect is enabled, and vice versa. Attenuation data type Defines if the attenuation value will be read from the "Attenuation" tab or from a file. If "Constant" the value specified in the "attenuation" tab will be used for all sampled, parameterized signals and noise bins. If "From file" a separate value will be calculated for each noise bin, parameterized or sampled signal by interpolating the data file. 674 OPTICAL FIBER CWDM Name and description Symbol Default value Units Value range Attenuation 0.2 dB/km [0, 1010] — — — — Name and description Symbol Default value Units Value range Group velocity dispersion — True — True, False — True — True, False — False — True, False — Constant — Constant / FromFile The specified value will be used for all signals if "Attenuation data type" is set to "Constant". If "Attenuation data type" is set to "From file" the value will be ignored. Attenuation vs wavelength If "Attenuation data type" is set to "From file" this field specifies the file containing the attenuation data. In this case the attenuation effect is wavelength dependent for all types of signals values corresponding to the central frequency of each signal will be calculated by linear interpolation and used internally. Dispersion If TRUE the GVD effect is enabled. Third order dispersion If TRUE the TOD effect is enabled. Dispersion data type Defines if the dispersion parameter values will be read from the tabs or from a file. If "Constant" the values from the tabs will be used to calculate the relative group delay, and first order GVD for each sampled signal by Taylor expansion around the reference wavelength. Otherwise (parameter set to "From file") group delay, first- and second order GVD parameters corresponding to each sampled signal will be calculated from the user-specified file by Sellmeier fitting. While "Frequency domain parameters" is TRUE, "Dispersion data type" will remain "Constant" and cannot be changed. This is done since the only acceptable format for the file specifying the dispersion is group delay vs. wavelength. Frequency domain parameters Defines the domain in which the dispersion parameters are specified. If TRUE frequency domain is used and the dispersion effect is specified in terms of Beta2 and Beta3. Otherwise the wavelength domain is used (D and S). This parameter is meaningful (and, hence, enabled) only if "Dispersion data type" is set to "Constant". 675 OPTICAL FIBER CWDM Name and description Symbol Default value Dispersion 2 -20 3 0 D 16.75 Units Dispersion slope — [-10100, 10100] [-10100, 10100] 0.075 ps -------------------------2 nm km [-10100, 10100] — — — The value of the TOD parameter in the frequency domain. Dispersion file name 3 ps ----------------------- nm km The value of the GVD parameter in the frequency domain. Beta 3 [-10100, 10100] ps -------km The value of the dispersion slope parameter in the wavelength. Beta 2 2 ps -------km The value of the GVD parameter in the wavelength domain. Value range Specifies the file with the dispersion data. PMD The notation "Frequency domain parameters" refers to the alternative definitions 1 D D = --------- S = ------- (wavelength domain definition) and 1 2 2 = --------- 3 = --------- (frequency domain definition). However, the format of the file specifying the wavelength dependence of the dispersion is the following: the first column of the file contains wavelength values and the second column, the corresponding values of , 1 . Consequently, "Frequency domain parameters" is meaningless when the dispersion is specified from a file. Name and description Symbol Default value Units Value range Birefringence type — Deterministic — Deterministic /Stochastic Determines the type of birefringence. If "Deterministic" is selected both the strength of birefringence and principal axes are assumed constant, hence random mode coupling is disabled. If "Stochastic" is selected the random mode coupling is enabled. 676 OPTICAL FIBER CWDM Name and description Differential group delay If "Birefringence type" is set to "Deterministic" this is the value of the differential group delay. If "Birefringence type" is set to "Stochastic" the parameter is disabled. Symbol d----- d Default value 0.2 PMD Coefficient Dp 0.5 Mean scattering section length L scatt 500 scatt 100 The averaged value of the fiber length at which the polarization state of the signal is randomized by applying the scattering matrix. Scattering section dispersion The dispersion of the scattering section length. Units ps-----km ps ---------km Value range [-10100, 10100] [0, 10100] [0, 10100] m [0, 10100] m In the case when more than one sampled signal (separated channels) is propagating in the fiber, the PMD-induced penalties will be the same for all channels. Different penalties (and Q-factors) will be obtained if all the channels are merged (total field approach). Birefringence and random mode coupling does not affect parameterized signals and noise bins. Nonlinearities Name and description Symbol Default value Units Value range Self-phase modulation — True — True, False — True — True, False Determines if the self-phase modulation (SPM) effect will be taken into account. If FALSE, all the nonlinear effects - XPM, SRS - will be disabled. Cross-phase modulation Determines if the XPM effects are taken into account. The parameter is active provided that the SPM effects are enabled. In the scalar case XPM includes the interactions among all parameterized and sampled signals. In the vector case only interactions between sampled signals are considered and the XPM between orthogonal polarization components is also included. 677 OPTICAL FIBER CWDM Name and description Symbol Default value Units Value range Effective area data type — Constant — Constant/ FromFile A eff 80 — — — — — — — Constant/ FromFile n2 2.6x10-20 — — — — — False — True/False Defines if the effective area parameter value will be read from the tab or from a file. If "Constant" the value from the tab will be used. Otherwise the parameter is treated as wavelength dependent and a separate value corresponding to the center frequency of each sampled signal, parameterized signal and noise bin is calculated and used. Effective area The value of the effective area parameter. This value will be used if "Effective area data type" is set to "Constant". Otherwise the value will be ignored. Effective area vs wavelength m 2 [0, 1010] If the "Effective area data type" is set to "From file" then this tab specifies the file containing the effective area data. n2 data type Defines if the n2 parameter (nonlinear index of refraction) value will be read from the tab or from a file. If "Constant" the value from the tab will be used. n2 The value of the n2 parameter. If "n2 data type" is set to "Constant" this value will be used. Otherwise it will be ignored. n2 vs wavelength 2 m -----W [0, 10100] If the "n2 data type" is set to "From file" then this tab specifies the file containing the nonlinear index of refraction wavelength data. Inter-band Raman scattering One of the two possible alternative representations of the SRS effect in the model that leads to energy exchange between different frequency bands. Interactions among all sampled signals, parameterized signals and noise bins are considered. Noise bins are treated as a weak probe with respect to the sampled signals and parameterized signals the latter are treated as pumps. Inter-band Raman scattering [1-7] is an approximation to the full expression of the Raman polarization valid provided that the frequency separation of the interacting signals is much larger than their individual spectral bandwidths. SRS effect can be enabled only in the scalar case (fixed polarization state, "Model type" from the numerical tab should be set to "Scalar" to enable SRS). If this representation for the SRS effect is used the model runs faster. 678 OPTICAL FIBER CWDM Name and description Symbol Default value Units Value range Complete Raman response — False — True/False — False The other alternative representations for the SRS effect, leading to coupling of signals occupying different frequency bands. In this case no assumption about the ratio between the bandwidth of the sampled signals and their frequency separation is made. Convolution integrals are calculated to represent the interaction of sampled signals with sampled signals, with noise bins and parameterized signals and vice versa. This is a more accurate description however the speed of the calculations in this case is lower. The interaction of noise bins with parameterized signals is always represented through inter-band Raman scattering i.e. the individual bandwidth of noise bins and parameterized signals is always considered zero. The parameter "Complete Raman response" is responsible only for this part of the Raman polarization that leads to energy exchange between different frequency bands. It does not include the Raman contribution to XPM and SPM. In case only one sampled signal and zero noise bins and parameterized signals propagate in the fiber, the two alternative descriptions of the SRS effect become completely equivalent. This is the case when the model works in the "Total filed approach" mode. However if "Complete Raman response" is selected, the "Molecular SPM and XPM" should be set to TRUE to achieve this equivalence while this is done automatically if "Inter-band Raman scattering" is selected to represent the SRS effect and only one sampled signal propagates in the fiber. Both parameters "Molecular XPM and SPM" and "Complete Raman response" are enabled if "Model type" is set to Scalar. Molecular XPM and SPM True/False The contribution to SPM and XPM stemming from the delayed (Raman) nonlinear response. This effect is meaningful for sampled signals only, since no phase is considered for Noise bins and Parameterized signals. In the presence of one sampled signal only molecular XPM is zero and the effect is reduced to molecular SPM. Molecular SPM might me important (and should not be neglected) despite that the energy transfer between different frequency components of the only sampled band present due to SRS is negligible. The parameter "Molecular XPM and SPM" is disabled if "Inter-band Raman scattering" is selected to represent the SRS, since the delayed part of the SPM and XPM is automatically included in this case. Both parameters "Molecular XPM and SPM" and "Complete Raman response" are enabled if "Model type" is set to Scalar. 679 OPTICAL FIBER CWDM Name and description Symbol Fractional Raman contribution The fraction of the nonlinear polarization, related to the stimulated Raman scattering effect [1]. Default value Units Value range 0.18 — [0,1] Numerical Name and description Symbol Default value Units Value range Model type — Scalar — Scalar/Vector — Variable — Variable/ Constant Defines the model type used for the simulation depending on the polarization state of the signal. If "Vector" is selected the signal can have arbitrary polarization state and a system of two coupled equations, corresponding to each polarization component (x or y) of every sampled signal is solved. If "Scalar" is selected it means that all the signals preserve their polarization state and a single equation (1) is solved for each sampled band. Vector simulation will be performed, regardless of the value of the model type parameter, in the following two cases1)Two polarization components are detected at the fiber input. This will work for sampled noise, since the noise is unpolarized and x- and y-polarization components are stored independently in the memory. Sampled signals with well defined polarization state however might use a different method of storage in the memory and, consequently, this parameter should be set to "Vector" manually if the polarization evolution is to be considered. 2)The PMD effect is set to stochastic.Turning the "vector" on will disable SRS. Step size Specifies whether variable or fixed step-size simulation will be used. If "Variable" is selected the step size is adaptively changed depending on the value of the "Max. nonlinear phase shift" parameter and the behavior of solutions itself. Otherwise the step size is evaluated only once, at the beginning of the simulation. In some cases the fixed step size calculation executes faster, due to the smaller number of calculations per step, but the variable step size calculation is more flexible and can be faster in the presence of strong attenuation. 680 OPTICAL FIBER CWDM Name and description Max. nonlinear phase shift Maximum (over the time window) phase shift induced by the self-phase modulation effect per step is calculated for each sampled signal. SPM induced phase shifts are then calculated for each parameterized signal. Then the step size is calculated in such a way that the maximum (over the entire set of signals) SPM-induced phase shift is equal to the specified value. Boundary conditions Symbol NL max Default value Units [0,10100] 3 mrad — Periodic — Periodic/ Absorbing — 0.5 — [0,10100] Specifies the type of boundary conditions used for the simulation. Filter steepness Value range In case "Boundary conditions" option is set to "Absorbing" the "Filter steepness" parameter determines the absorption/reflection properties of the time window boundaries. The same absorbing boundary conditions are used for all sampled signals. Graphs. Name and description Symbol Default value Units Value range Calculate graphs — False — True/False — 200 — [1, 100000000] — 200 — [1, 100000000] — False — True/False Enable / disable the 3D graphs. If disabled, no graphs will be plotted and no data is stored. Graphs are plotted for sampled signals only. Number of distance steps The number of longitudinal (or in z) snapshots (slices) that will be used to construct a 3D plot. Increasing this value will make the 3D graph to look better. The number of snapshots that are stored cannot be bigger than the number of steps in z taken by the simulation to obtain the solution. The latter is determined by the maximum nonlinear phase-shift parameter (numerical tab). Number of wavelength/time steps The number of stored points (in t) per snapshot. Increasing this value will make the 3D graph to look better. Linear scale Determines the axis-type (linear or logarithmic) for the dependent variable. If TRUE the axis type is linear. 681 OPTICAL FIBER CWDM Name and description Symbol Default value Units Value range — Wavelength range — Wavelength range/One sampled signal The next six parameters in this tab determine which graphs will be plotted after the simulation is finished. Plot type Determines the type of the plot that will be created in either frequency or time domain. If the parameter is set to "Wavelength range" than a copy of each sampled signal residing in the specified wavelength range will be created, this copies will be up-sampled and merged in a single frequency band. This single frequency band, containing all the signals will be plotted in either frequency or time domain. The merging does not affect the signals but their copies only, so multiple sampled signals will be involved in the simulation. If the parameter is set to "Plot one sampled signal" a 3D graph presenting the sampled signal with central frequency given by "Signal center frequency" will be created. Simulation Name and description Symbol Default value Units Value range Enabled — True — True/False Determines whether the component is enabled. If FALSE, all the input signals reach the output port of the component without any change. Noise Name and description Symbol Default value Units Value range Convert noise bins — False — True/False If TRUE each noise bin within the bandwidth of the signal will be converted to a Gaussian white noise, with the correct power spectral density, and this noise will be added to the signal. 682 OPTICAL FIBER CWDM Random numbers Name and description Symbol Default value Units Value range Generate random seed — False — True/False — 0 — [0, 4999] Determines how the random number generator is initialized (seeded). If TRUE the seed index used for this initialization is a random number itself. Otherwise user specified number is used for this purpose. Random seed index If "Generate random seed" is set to TRUE this value specifies the seed index. The generated pseudorandom sequence is one and same provided the seed index is not changed. The value of "Random seed index" will be ignored if "Generate random seed" is set to TRUE. Technical Background Scalar approach Signal propagation equations with Inter-band Raman scattering When the optical field is assumed to maintain its polarization along the fiber length (so called scalar approach, Model type parameter from the "Numerical" tab is set to "Scalar") the evolution of the slowly varying electric field envelopes sampled signals (SS), powers powers E i of a set of P l of another set of parameterized signals (PS) and N m of a third set of noise bins (NB) is governed by the set (1) of equations. The subsystem (1a) consists of Number of SS (the total count of sampled signals) coupled nonlinear Schrödinger (NLS) [1], [2], (1b) contains Number of PS equations (the total count of PS) and (1c) - Number of NB (the total count of NB) equations. 683 OPTICAL FIBER CWDM 2 3 E i i 2 i E i 3 i E i E - ----------- – ---------------- ----------- = -------- + l i – l 0 --------i + i E i + ----------------2 2 6 T 3 z T T Number of SS 2 – Number of PS 2 2 k=1 Number of SS i i Ek – 1 – Ei + 2 – l=1 Number of PS SS R ik 2 Ek + k=1 PS R il (1a) + Ei Pl l=1 Number of PS PP P + R lh h dP l h=1 -------- = – 2 l P l + 2 l P l Im Number of SS Time window dz SP 1 2 -------------------------------E t d t R li i Time window i=l 0 Number of PS PP R mh P h + dN m ---------- = – 2 m N m + 2 m N m Im h = 1 Number of SS dz SN 1 ------------------------------- Rmi Time window i=l Time window 2 E t d t i 0 (1b) (1c) The Raman matrices are defined according to: SS R ik PS R il 684 R = 1111 f i – f k i k 1 i Number of SS, 1 k Number of SS 0, i=k R f – f f i f l 1 i Number of SS, 1 l Number of PS = 1111 i l 0, fi = fl (2a) (2b) OPTICAL FIBER CWDM PP R lh SP R li R = 1111 f l – f h l h 1 l Number of PS, 1 h Number of PS 0, l=h R f – f f l f i 1 l Number of PS, 1 i Number of SS = 1111 l i 0, fl = fi R mh R f – f f m f h 1 m Number of NB, 1 h Number of PS = 1111 m h 0, fm = fh SN R mi R f – f f m f i 1 m Number of NB, 1 h Number of SS = 1111 m i 0, fm = fi PN (2c) (2d) (2e) (2f) Raman susceptibility for fused quartz is shown in Figure 1. It should be noted that R R 1111 – = 1111 , where "*" means complex conjugation. Figure 1 Raman susceptibilities for fused silica [3, 4] E i = E i z T is the electric field envelope of the i -th sampled signal. A frame moving at the group velocity ( T = t – z v g t – 1 0 z ) corresponding to the reference frequency 0 is assumed. In Equation (1a), 685 OPTICAL FIBER CWDM The reference frequency is related to the parameter "Reference wavelength" ("Main" category of the component tool-box) through 2c 0 = --------- with c being the light speed in vacuum. 0 The derivatives of the propagation constant of the fiber mode ( c is the mode effective index). n n = 1 2 n = ----------------n are the first ( 2 ) and second order ( 3 ) group velocity dispersion (GVD) parameters and are evaluated at the center frequencies i of the sampled signals. With respect to frequency, The nonlinear coefficients for every SS, NB, or PS in (1) are defined according to: j n2 j j = ---------------------cA eff j (3) The meaning of the terms on the left-hand side of the subsystem (1a) is the same as in the total field approach fiber model (see the technical description of this component). The first two terms in the right hand side of (1a) give the SPM and XPM contributions of the remaining sampled signals. The third term is the XPM contribution of the PS. The fourth and the fifth term describe the SRS induced interactions between the i -th sampled signal and rest of the sampled signals and with the parameterized signals, respectively. Subsystems (1b) and (1c) describe the power balance of the set of PS and NB respectively. These are obtained by replacing the NLS equations for NB and PS with the time-averaged versions of their power conservation laws. In the absence of attenuation the total number of photons is conserved as (1) shows. The first terms in the right-hand sides of (1b) and (1c) take into account the attenuation effects. The second and the third terms in the right-hand side of (1b) describe the SRS induced power transfer between the l -th PS and the rest of the PS and between the l -th PS and the SS respectively. The second and the third terms in the right-hand side of (1c) are responsible for the SRS-induced interactions between noise bins and PS and noise bins and SS. Note that in describing the interactions through SRS between NB and SS and NB and PS the power of the noise bins is neglected with respect to that of PS and SS - i.e. all the NB are treated as a weak "probe". They change their power due to the interactions with SS and PS, however the amount of power transferred from SS and PS to NB is neglected with respect to the power of SS and NB. This approximation is valid, provided the power of NB remains much smaller compared to that of SS and NB. With multiple SS present in the fiber the SRS effect is represented through inter-band Raman scattering. This is an approximation to the full expression for the Raman polarization [1],[2] that is valid provided that the frequency separation between the interacting signals is large enough compared to their individual bandwidths. 686 OPTICAL FIBER CWDM In the opposite case (frequency separation between the signals comparable with their individual spectral bandwidth) total field approach can be implemented by turning on the option "Merge sampled bands". In this case the system (1a) is replaced by the following single NLS Equation 4 and (1b) and (1c) remain unchanged. In Equation 4, the Raman response function h 1111 t is the Fourier transform of the Raman susceptibilities shown in Figure 1. Total field approach however should be used with some care. At first, in this case, (single sampled band) XPM and four wave mixing effects are included automatically in the simulation and turning on or off the "XPM" parameter in the "Nonlinearities" tab will have no effect on the results. 2 i 2 0 E i 3 0 3 E E ------ + E + ------------------ ---------- – ----------------- --------- = 2 2 6 T 3 z T 2 1 – E 2 + h 1111 s E T – ds 0 i Number of PS PS + R 1l Pl l=1 + E (4) Figure 2 687 OPTICAL FIBER CWDM Figure 3 Total field approach implemented with improper choice of sample rate. The output probe power is 0.931 mW. Figure 4 The correct result is obtained when the bandwidth is high enough. Output probe power is 1.377mW. The slight difference in the output probe power could be attributed to FWM. The following example shows the importance of the proper choice of numerical parameters. Figure 2 shows the layout. The input consists of a strong (1 W power) pump wave at 193 THz and a weak (1 mW) probe wave at 192.5 THz. "Merge sampled bands" parameter of the optical fiber component is enabled, which means that total field approach will be used. Attenuation effect is disabled and we use "Constant" step size with the "Maximum nonlinear phase shift" parameter equal to 5 mrad. Raman effect is enabled The rest of the set-up of the optical fiber component is the default one. Since total field approach will be used enabling or disabling the "XPM" parameter will have no effect on the results. Figure 3 and Figure 4 show the obtained results together with the global parameters of the layout in each case. Figure 5 gives the result treating the two waves as separated channels - "Merge sampled bands" parameter is set to FALSE in the optical fiber component. In the case presented in Figure 3 the simulated bandwidth is too 688 OPTICAL FIBER CWDM small to accommodate the FWM mixing products of both waves and hence they are aliased (see e.g. [8]). This false translation of the frequency of the wave (known as aliasing) can put the a weak FWM product in the closed spectral vicinity of the pump which will trigger a strong FWM (or modulation instability since the signal wavelengths are in the anomalous GVD regime, which is also a kind of FWM) if the frequency separation is small, and consequently, the coherence length is large. The result is an entirely unphysical generation of new frequency components. Note that probe attenuation is obtained instead of probe amplification. Figure 4 gives the correct result since no aliasing occurs. This is achieved by having the simulated bandwidth (or equivalently the sample rate) high enough to accommodate the three times the input signal bandwidth. Figure 5 Simulation in which both signals are treated as separated channels. Output probe power is 1.371 mW. A comparison with Figure 5 (obtained treating the pump and the probe wave as two separate sampled bands) which gives the same output power for the probe wave as the total field approach with the sample rate correctly chosen shows that in this case FWM effects are quite small. Besides, treating the signals as separate frequency bands leads a significant reduction of the simulation time. It should be kept in mind however that while in the case of total field approach, all the parameters (dispersion, attenuation, etc.) are evaluated just once - at the reference frequency, here (when multiple SS are considered) a set of parameters is evaluated for each sampled signal - at the center frequency of the corresponding signal. The meaning of the reference frequency (and reference wavelength) is the following: The subsystem (1a) is written in a frame moving with group velocity corresponding to the reference wavelength - no other signal parameters are evaluated at this frequency. The reference wavelength can be either user-specified or "automatic", which corresponds to the averaged frequency of the center frequencies of all SS and PS. 689 OPTICAL FIBER CWDM If "Dispersion data type" is set to "Constant" the dispersion parameters specified in the tabs (D and S) or, respectively, 2 and 3 , are assumed to correspond to the reference wavelength. Hence, Taylor expansion is used in this case: 1 2 1 – 1 0 = 2 0 – 0 + --- 3 0 – 0 2 Evaluating Equation 5 and its first and second derivatives with respect to (5) at the 1 gives the sets of parameters: 2 1 – 1 0 2 i and 3 i . signal frequencies It should be kept in mind however that with multiple sampled signals present, specifying nonzero 2 and 3 (or D and S) and disabling in the same time the "Group velocity dispersion" and "Third order dispersion" will result in 2 i = 0 i 3 i = 0 i , but 1 i 1 j if i j , which means that no GVD induced pulse broadening will be observed but pulses with different center frequencies will propagate with different group velocities. In contrary, if all the sampled signals are merged to form a single frequency band disabling the GVD effects will not only disable pulse broadening, but also will set the group velocity constant for the entire sampled band considered. If "Dispersion data type" is set to "From file" the data set specified by the file is Sellmeier fitted than dispersion parameters are calculated by analytically differentiating the fit. The file specifying the dispersion data must provide the dependence of group delay [ps/km] on the wavelength [nm]. For this reason "Frequency domain parameters" is disabled when "Dispersion data type" is set to "From file". 690 OPTICAL FIBER CWDM Signal propagation equations with "Complete Raman response" When the SRS effect is represented through "Complete Raman response" the system (1) is replaced by: 2 3 E i E i 2 i E i 3 i E i - ----------- – ---------------- ----------- = -------- + l i – l 0 --------i + i E i + ----------------2 2 6 T 3 z T T Number of PS Number of SS 2 i i 2 – 2 Ek – 1 – Ei + 2 – Number of SS E k T h 1111 E i T – E k T – e k = 1 k i – i i – k d (6a) 0 Number of PS h1111 Ei T – e l=1 0 + i i Pl Ei l=1 k=1 + i i – i i – l d Number of SS + i i E i T h 1111 0 2 E k T – d k=1 Number of PS dP l PP -------- = – 2 l P l + 2 l P l Im R P lh h + dz h=1 2 l P l ---------------T.W. Number of SS T.W. i=1 0 Im E i t (6b) – i i – l d dt h1111 Ei t – e 0 Number of PS dN m PN ---------- = – 2 m N m + 2 m N m Im R mh P h + dz h=1 2 m N m -------------------T.W. Number of SS T.W. i=1 0 Im E i t (6c) – i i – m d dt h1111 Ei t – e 0 691 OPTICAL FIBER CWDM In Equation (6), the time window size is denoted by T.W., and the star symbol means complex conjugation. The first three terms in the R.H.S of Equation (6a) are the SPM and XPM caused by the rest of the sampled signals and the parameterized signals on the i -th sampled signal. The fourth term is responsible for the SRS induced energy exchange between the i -th sampled signal and all the other sampled signals. The fifth term takes into account the energy exchange between the i -th sampled signal and all the parameterized signals. The last (sixth) term describes the SPM and XPM stemming from the delayed nonlinear response of the material. This effects can be turned on and off by the "Molecular SPM and XPM" parameter. The fourth and fifth terms (responsible for the SRS induced energy exchange between the sampled signals and the parameterized signals, respectively, are simultaneously switched on by setting the "Complete Raman response" parameter to TRUE. The sets contained in Equations (6b) and (6c) describe the evolution with propagation of the parameterized signals powers and noise bins powers respectively. The physical meaning of the terms in the RHS of Equations (6b) and (6c) is the following: The first terms take into account the attenuation. The second terms describe the energy exchange with parameterized signals due to SRS effect. These two terms are included in the simulation by switching on the "Complete Raman response" parameter. The last terms in the sets of Equations (6b) and (6c) describe the interaction of parameterized signals with sampled signals and of that of noise bins with sampled signals respectively. E i do not change significantly over the characteristic Raman response time of the medium, E i t – can be replaced with E i t in the In case the field envelopes integrands in Equations (6a), (6b) and (6c). Using h 1111 i – m = h1111 e – i i – m d , 0 the set of Equations (6) reduces to its simplified version, the set of Equations (1). 692 OPTICAL FIBER CWDM Vector approach Signal propagation equations When the polarization state of the incident sampled signals is not preserved during its propagation inside the optical fiber the scalar approach is no longer applicable and (1) is replaced by ("Model type" parameter must set to "Vector"). 2 E iX E iX i 2 i E iX _ ----------- + 1X i – 1 0 ---------- + i E iX + ----------------- ------------2 z T 2 T 3 i 3 E iX --------------- ------------- = i i 2 3 6 T Number of SS 2 2 2 E kX – E iX + --3 k=1 (7a) Number of SS E kY 2 E iX k=1 2 E iY E iY i 2 i E iY _ - ---------------------- + 1Y i – 1 0 ---------- + i E iY + ----------------2 2 z T T 3 3 i E iY --------------- ------------- = i i 2 3 6 T Number of SS k=1 2 2 2 E kY – E iY + --3 (7b) Number of SS E kX 2 E iY k=1 SRS is disabled automatically when the vector model is selected and noise bins and PS are just attenuated. The nonlinear terms in (7a) and (7b) contain SPM, XPM between parallel polarization components, and XPM between orthogonal polarization components. If the parameter "XPM" is set to TRUE, both XPM contributions (between parallel and between orthogonal polarization components) will be included. If "XPM" is set to FALSE, only the nonlinear contributions of SPM will included in the model. Note that the group delays are different for the two polarization components of the same sampled band which takes into account the birefringence. The birefringence can be two types: "Deterministic" and "Stochastic". In the first case, the birefringence is assumed constant and no energy exchange between the two polarization components occurs. In the second case, ("Stochastic" birefringence) random mode coupling is also enabled, which gives the possibility to simulate PMD (see the technical description of Nonlinear Dispersive Fiber Total Field for the details of the 693 OPTICAL FIBER CWDM PMD simulator). It should be kept in mind however that when the signals are represented as multiple sampled bands PMD impairments will be identical for all WDM channels. To obtain the frequency dependence of the penalties (or Q-factors) total field approach must be implemented by setting "Merge sample bands" to true. Numerical solution The symmetrized non-iterative split-step Fourier method [1] (see the technical description of Nonlinear Dispersive Fiber Total Field) is used to solve Equations (1a), (6a), and (7a, b). These equations are first rewritten in normalized (dimensionless) quantities in the following way: The time variable is divided by the time window size. "Averaged" GVD coefficient is introduced by averaging over the entire set of sampled signals. This averaged GVD coefficient and the actual time window size are then used to define the characteristic dispersion length [1] and this value normalizes the longitudinal variable (z). The maximum peak power for SS is determined as the global maximum over the time window and the entire set of SS. This value is compared with the maximum power over the set of PS. The quantity that is bigger is used to normalize the waveforms of the SS and the powers of the PS. The characteristic nonlinear length is defined by the averaging the nonlinear lengths of all PS and SS. The solution is advanced from z to z + h . h is the step-size, determined from the value of the Max. nonlinear phase shift parameter according to: z + h h h E z + h T = exp --- D̂ exp N̂ z' dz' exp --- D̂ E z t 2 2 z where the (8) D̂ is the dispersion and N̂ are the nonlinearity operators [1],[9]. Dispersion operator is applied in the frequency domain using FFT. The approximation: z+h z 694 N̂ z' dz' hN̂ exp h 2 D̂ E z t (9) OPTICAL FIBER CWDM is used. When the "Step size" parameter is set to "Constant" (7) can be simplified according to: z + h z + h h--- h--- h h--- E z + 2h t = exp D̂ exp N̂ z' dz' exp D̂ exp D̂ N̂ z' dz' exp --- D̂ E z t = 2 2 2 2 z z h exp --- D̂ exp 2 z+h z N̂ z' dz' exp hD̂ exp z+h z (10) h N̂ z' dz' exp --- D̂ E z t 2 which is executed faster. In the presence of attenuation, however, the role of nonlinearity will decrease along the fiber length and "Variable" step size will be advantageous. When the system (6) is solved (the parameter "Complete Raman response" is set to TRUE), the second order Runge-Kutta scheme is used to apply the nonlinearity operator. References [1] G. P. Agrawal, "Applications of nonlinear fiber optics", Academic press, 3rd edition, 2001. [2] G. P. Agrawal, "Nonlinear fiber optics", Academic press, 3rd edition, 2001. [3] R. W. Hellwarth, Prog. Quant. Electr. 5, 1 (1977). [4] P. Tchofo Dinda, G. Millot, and S. Wabnitz, JOSA B, 15, 1433, (1998). [5] R.H.Stolen, J.P.Gordon, W.J. Tomlinson and H.A. Haus, JOSA B, 6, 1159 (1989). [6] C.R.Menyuk, M.N.Islam and J.P.Gordon, Optics Letters, 16 566, (1991). [7] K.J. Blow and D. Wood, IEEE J. Quant. Electr., 25, 2665, (1989). [8] W. H. Press, et al., "Numerical Recipes: The Art of Scientific Computing", 2nd Edition, Cambridge University Press, 1992. [9] M. Lax, J. H. Batteh and G. P. Agrawal, Journ. Appl. Phys. 52 , 109, (1981). 695 OPTICAL FIBER CWDM 696 BIDIRECTIONAL OPTICAL FIBER Bidirectional Optical Fiber The component simulates the bidirectional propagation of arbitrary configuration of optical signals in a single-mode fiber. Dispersive and nonlinear - self-phase modulation (SPM), cross-phase modulation (XPM), stimulated Raman (SRS) and Brillouin (SBS) scattering effects - are taken into account. Raman interaction for an arbitrary configuration of sampled and parameterized signals is also considered. The component provides most of the functionality of the total field approach fiber model (except for the simulation of the Raman effect in birefringent fibers). The four-wave mixing effect between multiple sampled signals is not considered. 697 BIDIRECTIONAL OPTICAL FIBER Ports Name and description Port type Signal type Input1 Input Optical Output 1 Output Optical Input 2 Input Optical Output 2 Output Optical Parameters Main Name and description Symbol User-defined reference wavelength Default value Units True Value range [True, False] If True, the frequency corresponding to the value entered under "Reference wavelength" is used internally as reference frequency. The system of modified NLS equations governing the evolution of the signals is solved in a frame moving with the group velocity corresponding to that frequency. If False, the value of the reference frequency is calculated as the averaged of the central frequencies of all the sampled and parameterized signals. Reference wavelength 0 1550 nm [100, 2000] L 50 km [0, 100000] The value of the user-specified reference wavelength Length Fiber length Attenuation effect True [True, False] Constant [Constant, From file] If True, the attenuation effect is enabled Attenuation data type Defines if the attenuation value will be read from the "Attenuation" tab or from a file. If "Constant", the value specified in the "attenuation" tab will be used for all sampled, parameterized signals and noise bins. If "From file", a separate value will be calculated for each noise bin, parameterized or sampled signal by interpolating the data file. 698 BIDIRECTIONAL OPTICAL FIBER Name and description Symbol Default value Units Value range Attenuation 0.2 dB/km [0, 1010] Symbol Default value Units Value range The specified value will be used for all signals if "Attenuation data type" is set to "Constant". If "Attenuation data type" is set to "From file", the value will be ignored. Attenuation vs. wavelength If "Attenuation data type" is set to "From file", this field specifies the file containing the attenuation data. In this case the attenuation effect is wavelength dependent for all types of signals. Values corresponding to the central frequency of each signal will be calculated by linear interpolation and used internally. Dispersion Name and description Group velocity dispersion True [True, False] True [True, False] If True, the GVD effect is enabled Third order dispersion If True, the TOD effect is enabled Dispersion data type Defines if the dispersion parameter values will be read from the tabs or from a file. If "Constant", the values from the tabs will be used to calculate the relative group delay and the first-order GVD for each sampled signal by Taylor expansion around the reference wavelength. If the parameter is set to "From file", the group delay, and the first- and second-order GVD parameters corresponding to each sampled signal will be calculated from the userspecified file by Sellmeier fitting. When "Frequency domain parameters" is True, "Dispersion data type" will remain "Constant" and cannot be changed. This is done because the only acceptable format for the file specifying the dispersion is group delay vs. wavelength. Constant [Constant, From file] 699 BIDIRECTIONAL OPTICAL FIBER Name and description Symbol Frequency domain parameters Default value Units False Value range [True, False] Defines the domain in which the dispersion parameters are specified. If True, the frequency domain is used and the dispersion effect is specified in terms of 2 and 3 . Otherwise the wavelength domain is used (D and S). This parameter is meaningful (that is, enabled) only if "Dispersion data type" is set to "Constant". D Beta 2 16.75 ps/[(nm)(km)] [-10100, 10100] 0.75 ps/[(nm)2(km)] [-10100, 10100] 2 -20 ps2/km [-10100, 10100] 3 0 ps3/km [-10100, 10100] The value of the GVD parameter in the frequency domain Beta 3 The value of the TOD parameter in the frequency domain Dispersion The value of the GVD parameter in the wavelength domain Dispersion slope The value of the dispersion slope parameter in the wavelength Dispersion file name Specifies the file with the dispersion data Note: The notation "Frequency domain parameters" refers to these alternative definitions: Wavelength domain definition: 1 D D = --------- , S = ------ Frequency domain definition: 1 2 2 = --------- , 3 = -------- However, the format of the file specifying the wavelength dependence of the dispersion is the following: • • the second column contains the corresponding values of the first column of the file contains wavelength values Consequently, the "Frequency domain parameters" is meaningless when the dispersion is specified from a file. 700 BIDIRECTIONAL OPTICAL FIBER PMD Name and description Symbol Birefringence type Default value Units Deterministic [Deterministic, Stochastic] Determines the type of birefringence. If "Deterministic" is selected, both the strength of birefringence and principal axes are assumed constant. Therefore, the random mode coupling is disabled. If "Stochastic" is selected, the random mode coupling is enabled. Differential group delay If "Birefringence type" is set to "Deterministic", this is the value of the differential group delay. If "Birefringence type" is set to "Stochastic", the parameter is disabled. PMD coefficient d----- d 0 ps/km [-10100, 10100] DP 0, 5 ps ---------km [0, 10100] L scatt 500 m [0, 10100] scatt 100 m [0, 10100] If "Birefringence type" is set to "Stochastic", this is the value of the PMD parameter. If "Birefringence type" is set to "Deterministic", the parameter is disabled. Mean scattering section length Value range The averaged value of the fiber length at which the polarization states of the signal is randomized by applying the scattering matrix. Scattering section dispersion The dispersion of the scattering section length In the case when more than one sampled signal (separated channels) is propagating in the fiber, the PMD-induced penalties will be the same for all channels. Different penalties (and Q-factors) will be obtained if all the channels are merged (total filed approach). Birefringence and random mode coupling do not affect parameterized signals and noise bins. Nonlinearities Name and description Self-phase modulation Symbol Default value True Units Value range [True, False] Determines if the self-phase modulation (SPM) effect will be taken into account. If False, all the nonlinear effects (XPM, SRS) will be disabled. 701 BIDIRECTIONAL OPTICAL FIBER Name and description Symbol Cross-phase modulation Default value Units Value range True [True, False] Constant [Constant, From file] Determines if the XPM effects are taken into account. The parameter is active if the SPM effects are enabled. In the scalar case, XPM includes the interactions among all parameterized and sampled signals. In the vector case, only interactions between sampled signals are considered. The XPM between orthogonal polarization components is included. Effective area data type Defines if the effective area parameter value will be read from the tab or from a file. If "Constant", the value from the tab will be used. Otherwise, the parameter is treated as wavelength dependent and a separate value corresponding to the center frequency of each sampled signal. The parameterized signal and noise bin are calculated and used. Effective area A eff 80 The value of the effective area parameter. This value will be used if "Effective area data type" is set to "Constant". Otherwise the value will be ignored. m 2 [0, 1010] Effective area vs. wavelength If the "Effective area data type" is set to "From file", this tab specifies the file containing the effective area data. n2 data type Constant [Constant, From file] Defines if the n2 parameter value (nonlinear index of refraction) will be read from the tab or from a file. If "Constant", the value from the tab will be used. n2 n2 The value of the n2 parameter. If "n2 data type" is set to "Constant", this value will be used. Otherwise it will be ignored. n2 vs. wavelength If the "n2 data type" is set to "From file", this tab specifies the file containing the nonlinear index of refraction wavelength data. 702 2.6 x 10-20 m2/W [0, 10100] BIDIRECTIONAL OPTICAL FIBER Name and description Symbol Raman scattering Default value Units Value range False [True, False] 0.18 [0, 1] Raman gain [Raman gain, Raman gain efficiency, Calculate] 1e-013 [0, +INF] Interactions among all sampled signals, parameterized signals and noise bins are considered. Noise bins are treated as a weak probe with respect to the sampled signals and parameterized signals - the latter are treated as pumps. Inter-band Raman scattering [1-7] is an approximation to the full expression of the Raman polarization valid provided that the frequency separation of the interacting signals is much larger than their individual spectral bandwidths. SRS effect can be enabled only in the scalar case (fixed polarization state, "Model type" from the numerical tab should be set to "Scalar" to enable SRS) Fractional Raman contribution The fraction of the nonlinear polarization, related to the stimulated Raman scattering effect [1] Raman gain type Defines type of Raman gain. If Raman gain efficiency is selected, then its value is gr/Aeff, otherwise, it is normalized gr multiplied by Raman gain peak. There is the option to calculated the Raman gain based on fiber parameters Raman gain peak Normalized Raman gain is multiplied by Raman gain peak. Raman gain reference pump 1000 nm gr RG.dat THz - normalized Raman Gain or THz - Raman Gain T 300 K [0, +INF] Value used in the Raman gain calculation Gain X frequency File that defines the Raman gain or the Raman gain efficiency. Temperature [0, 500] Absolute temperature at which the fiber is operating. Used for noise consideration. 703 BIDIRECTIONAL OPTICAL FIBER Name and description Symbol Default value Polarization factor Keff 2 Symbol Default value Units Value range [1, 2] The value depends on the relative polarization of the fields. The value is 1 if the fields have aligned polarizations, and 2 if they have scrambled polarization. Enhanced Name and description Rayleigh scattering Units Value range False True, False Constant [Constant, From file] Defines if the Rayleigh scattering effect is enabled Rayleigh data type Defines if the Rayleigh parameter value will be read from the tab or from a file. If "Constant", the value from the tab will be used Rayleigh backscattering 5.0e-005 1/km Rayleigh.dat nm - 1/km [0, +INF] The value of the parameter. If "Rayleigh data type" is set to "Constant", this value will be used. Otherwise it will be ignored Rayleigh vs. wavelength If the "Rayleigh data type" is set to "From file", this tab specifies the file containing the Rayleigh wavelength data Include Brillouin scattering False True, False Constant [Constant, From file] Determines if the Brillouin scattering effect will be taken into account Brillouin gain data type Defines if the Brillouin gain is constant or loaded from a file Brillouin gain constant gB 4.6e-11 m/W [0, 1e10] MHz [-INF, +INF] Brillouin gain value Brillouin.dat Brillouin gain file name Specifies the Brillouin gain file name Brillouin linewidth Specifies the Brillouin linewidth 704 v 31.7 BIDIRECTIONAL OPTICAL FIBER Name and description Frequency shift Symbol vs Default value Units Value range 11 GHz [-INF, +INF] Default value Units Value range Specifies the Brillouin frequency shift Numerical Name and description Model type Symbol Scalar [Scalar, Vector] Variable [Variable, Constant] Defines the model type used for the simulation depending on the polarization state of the signal. If "Vector" is selected, the signal can have arbitrary polarization state and a system of two coupled equations, corresponding to each polarization component (x or y) of every sampled signal that is solved. If "Scalar" is selected, all the signals preserve their polarization state and a single equation (1) is solved for each sampled band. Vector simulation will be performed, regardless of the value of the model type parameter, in the following two cases 1)Two polarization components are detected at the fiber input. This will work for sampled noise because the noise is unpolarized and x- and y-polarization components are stored independently in the memory. However, sampled signals with well defined polarization state might use a different method of storage in the memory. Consequently, this parameter should be manually set to "Vector" if the polarization evolution is to be considered. 2)The PMD effect is set to Stochastic. Turning the "vector" on will disable SRS. Step size Specifies whether variable or fixed stepsize simulation will be used. If "Variable" is selected, the step size is adaptively changed depending on the value of the "Max. nonlinear phase shift" parameter and the behavior of solutions itself. Otherwise the step size is evaluated only once, at the beginning of the simulation. In some cases, the fixed step size calculation executes faster, due to the smaller number of calculations per step. However, the variable step size calculation is more flexible and can be faster in the presence of strong attenuation. 705 BIDIRECTIONAL OPTICAL FIBER Name and description Max. nonlinear phase shift Maximum phase shift (over the time window) induced by the self-phase modulation effect per step is calculated for each sampled signal. SPM-induced phase shifts are then calculated for each parameterized signal. Next, the step size is calculated in such a way that the maximum SPM-induced phase shift (over the entire set of signals) is equal to the specified value. Symbol Default value Units Value range 3 [0, 10100] Periodic [Periodic, Absorbing] 0.5 [0, 10100] 50 [1, 1000] 40 [1, 1000] 1e-3 [1e-10, 1] NL max Boundary conditions Specifies the type of boundary conditions used for the simulation Filter steepness When "Boundary conditions" option is set to "Absorbing", the "Filter steepness" parameter determines the absorption and reflection properties of the time window boundaries. The same absorbing boundary conditions are used for all sampled signals. P. A. number of iterations Maximum number of iterations executed in the Power Analysis. If convergence is not reached in this number of iterations, model returns the calculated values anyway P. A. number of steps Number of divisions (in space) of the fiber P. A. relative tolerance Used to check the convergence of the signal Discretize sampled signal False — — True, False 100 GHz Hz, GHz, THz [1e9,1e12] 0.001 — — [1e-100, 1e100] Defines whether to use a user defined discretization for sampled signals or not Frequency resolution Frequency spacing that will discretize the sampled signal P. A. step accuracy 706 BIDIRECTIONAL OPTICAL FIBER Graphs Name and description Calculate graphs Symbol Default value Units Value range False [True, False] 200 [1, 100000000] 200 [1, 100000000] True [True, False] Wavelength range [Wavelength range, One sampled signal] Defines whether to enable the 3D graphs. If disabled, no graphs will be plotted and no data is stored. Graphs are plotted for sampled signals only. Number of distance steps The number of longitudinal (or in z) snapshots (slices) that will be used to construct a 3D plot. Increasing this value will make the 3D graph look better. The number of snapshots that are stored cannot be larger than the number of steps in z taken by the simulation to obtain the solution. The latter is determined by the maximum nonlinear phase-shift parameter (numerical tab). Number of wavelength/time steps The number of stored points (in t) per snapshot. Increasing this value will make the 3D graph look better. Linear scale Determines the axis-type (linear or logarithmic) for the dependent variable. If True, the axis type is linear. The next six parameters in this tab determine which graphs will be plotted after the simulation is finished. Plot type Determines the type of the plot that will be created in either frequency or time domain. If the parameter is set to "Wavelength range", a copy of each sampled signal residing in the specified wavelength range will be created. These copies will be up-sampled and merged in a single frequency band. This single frequency band, containing all the signals, will be plotted in either frequency or time domain. The merging does not affect the original signals but affects their copies. Therefore, multiple sampled signals will be involved in the simulation. If the parameter is set to "Plot one sampled signal", a 3D graph presenting the sampled signal with central frequency given by "Signal center frequency" will be created. 707 BIDIRECTIONAL OPTICAL FIBER Simulation Name and description Default value Default value Enabled Units True Value range [True, False] Determines whether the component is enabled. If False, all the input signals reach the output port of the component without any change. Noise Name and description Default value Convert noise bins Default value Units False Value range [True, False] If True, each noise bin in the bandwidth of the signal will be converted to a Gaussian white noise, with the correct power spectral density, This noise will be added to the signal. Random numbers Name and description Generate random seed Default value Default value Units Value range True [True, False] 0 [0, 4999] Determines how the random number generator is initialized (seeded). If True, the seed index used for this initialization is a random number. Otherwise, a userspecified number is used for this purpose. Random seed index If "Generate random seed" is set to True, this value specifies the seed index. The generated pseudo-random sequence is the same one if the seed index is not changed. The value of "Random seed index" will be ignored if "Generate random seed" is set to True. Technical Background Numerical Solution To model the bidirectional signal propagation in a fiber, an algorithm that takes two numerical steps is used [1]. • 708 In the first step, the equations describing the signal propagation in the forward and backward direction are solved by an iterative method (Power analysis) and the power distribution along the fiber is calculated. BIDIRECTIONAL OPTICAL FIBER • In the second step, the signals are propagated using the nonlinear Schrödinger equation to describe the dynamic interactions between the co-propagating signals. Power Analysis The equations that describe the interactions between signals propagating in the forward direction and backward direction and describe the generation of optical noise due the Raman and Rayleigh scattering are defined by [2]: 709 BIDIRECTIONAL OPTICAL FIBER where v i v j are frequencies v is the fiber attenuation v is the Rayleigh backscattering coefficient g v i – v j is the Raman gain coefficient for frequency difference v i – v j P b (Z,v) is the backward propagating power. It includes sampled, parameterized, and noise bins signals. A eff is the effective core area K eff is the polarization factor v is the frequency interval h is Plank's constant k is the Boltzmann’s constant T is the absolute temperature. In these equations, the following physical effects were taken into account: a) pump-to-pump, signal-to-signal and pump-to-signal Raman interactions b) spontaneous Raman emission and its temperature dependency c) stimulated Raman scattering d) pump depletions due to Raman energy transfer e) high-order stokes generation f) multiple Rayleigh backscattering g) fiber loss h) spontaneous emission noise In the first solution step in this component, the equations (1) (forward and backward) are solved through direct integration. In direct integration, the signal launch configuration defines the boundary conditions in both ends of the fiber. The convergence of the model is checked in two directions: forward and backward. An iterative forward and backward integration of propagation equations must be used due to the backward propagating ASE powers and counter-directional pumping scheme that may be defined, as well as the possibility of counter directional signal propagation [2]. The forward direction is from input port 1 to output port 1. The backward direction is from input port 2 to output port 2. The convergence is checked after the integration in both directions is performed. If the variance in the gain is lesser than the tolerance desired ("Numerical" tab page), the simulation is considered finished. Otherwise, the component runs for the maximum number of iterations set by the user. 710 BIDIRECTIONAL OPTICAL FIBER When a file with the normalized Raman gain is entered, it must be given values for the Raman gain peak and Raman gain reference pump. These values are used to calculate the Raman gain used in the simulation according the following formula: where gR is the Raman gain pR is the Raman gain peak P is the gain reference pump gN is the normalized Raman Gain. The unit of Raman Gain is given in mW . If the user chooses the option to let the component calculate the Raman gain, the component will calculate the coefficients using the following equation: where is the nonlinear coefficient (6) is the fractional Raman contribution R X 1111 P – S is the Raman susceptibility for fused silica Stimulated Brillouin scattering When the stimulated Brillouin scattering (SBS) effect is included in the simulation. New terms and equations are added to the set of coupled equations, and they are related to the stokes signals introduced in the system. The modeling of SBS used here is based on reference [7] and it can not be used together with Raman amplification. After the calculation of the power distribution along the fiber for the signals, spontaneous emission and Rayleigh scattering, the dynamic interaction between the co-propagating signals are analyzed using the nonlinear Schrödinger equations 711 BIDIRECTIONAL OPTICAL FIBER Nonlinear Schrödinger Equation In this step, the coupled nonlinear Schrödinger equations are solved by using the symmetrized non-iterative split-step Fourier method. See the Optical Fiber WDM Technical Background. Scalar approach Signal propagation equations with Raman scattering In the scalar approach, the optical field maintains its polarization along the fiber length. The Model type parameter from the "Numerical" tab is set to Scalar. In this case, the following set (4) of equations governs the evolution of the slowly varying electric field envelopes (Ei). These envelopes are a set of sampled signals (SS), powers (Pl) of another set of parameterized signals (PS), and powers (Nm) of a third set of noise bins (NB). The subsystem (4a) consists of • Number of SS, the total count of sampled signals • coupled nonlinear Schrödinger (NLS) [3, 4], The subsystem (4b) contains • 712 Number of PS equations (the total count of PS) BIDIRECTIONAL OPTICAL FIBER The subsystem (4c) contains • Number of NB (the total count of NB) equations. The Raman matrices are defined according to: 713 BIDIRECTIONAL OPTICAL FIBER Raman susceptibility for fused quartz is shown in Figure 1. It should be noted that "*" means complex conjugation. Figure 1 Raman susceptibilities for fused silica [5, 6] In Equation (4a), signal. E i = E i (z,T) is the electric field envelope of the i-th sampled A frame moving at the group velocity T = the reference frequency 0 is assumed. t – z v g t – 1 0 z corresponding to The reference frequency is related to the parameter Reference wavelength through 0 = 2c 0 , with c being the light speed in vacuum. The parameter Reference wavelength is in the "Main" category of the component tool-box. The derivatives of the propagation constant of the fiber mode , with respect to n n frequency n = n = 1 2 are the first order 2 and second order 3 group velocity dispersion (GVD) parameters and are evaluated at the center frequencies i of the sampled signals. 714 BIDIRECTIONAL OPTICAL FIBER The nonlinear coefficients for every SS, NB or PS in (4) are defined according to The meaning of the terms in the left-hand side of the subsystem (4a) is the same as in the total field approach fiber model (see the technical description of this component). The first two terms in the right side of (4a) give the SPM and XPM contributions of the remaining sampled signals. The third term is the XPM contribution of the PS. The fourth and the fifth terms describe the SRS-induced interactions between the i-th sampled signal and rest of the sampled signals and with the parameterized signals, respectively. Subsystems (4b) and (4c) describe the power balance of the set of PS and NB, respectively. These are obtained by replacing the NLS equations for NB and PS with the time-averaged versions of their power conservation laws. In the absence of attenuation, the total number of photons is conserved as (4) shows. The first terms in the right sides of (4b) and (4c) take into account the attenuation effects. The second and the third terms in the right side of (4b) describe the SRS induced power transfer between the l-th PS and the rest of the PS and between the lth PS and the SS, respectively. The second and the third terms in the right side of (4c) are responsible for the SRSinduced interactions between noise bins and PS and noise bins and SS. With multiple SS present in the fiber, the SRS effect is represented through inter-band Raman scattering. This is an approximation of the full expression for the Raman polarization [3,4] that is valid if the frequency separation between the interacting signals is large enough compared to their individual bandwidths. When the frequency separation between the signals is comparable with their individual spectral bandwidth, the total field approach can be implemented by turning on the option "Merge sampled bands". In this case, the system (4a) is replaced by the following single NLS equation (7) and (4b) and (4c) remain unchanged. In equation (7), the Raman response function the Raman susceptibilities shown in Figure 1. h 1111 t is the Fourier transform of Total field approach however should be used with some care. At first in this case (single sampled band), XPM and four wave mixing effects are included automatically 715 BIDIRECTIONAL OPTICAL FIBER in the simulation and turning on or off the XPM parameter in the "Nonlinearities" tab will have no effect on the results. Keep in mind that in the total field approach, all the parameters (such as dispersion and attenuation) are evaluated just once - at the reference frequency. In this case, when multiple SS are considered, a set of parameters is evaluated for each sampled signal - at the center frequency of the corresponding signal. The meaning of the reference frequency (and reference wavelength) is the following: The subsystem (4a) is written in a frame moving with group velocity corresponding to the reference wavelength. That is, no other signal parameters are evaluated at this frequency. The reference wavelength can be either user specified or automatic, which corresponds to the averaged frequency of the center frequencies of all SS and PS. If "Dispersion data type" is set to "Constant", the dispersion parameters specified in the tabs (D and S) or, respectively, 2 and 3 , are assumed to correspond to the reference wavelength. Hence, Taylor expansion is used in this case Evaluating (8) and its first and second derivatives with respect to at the signal frequencies i gives the sets of parameters 1 i – 1 0 , 2 i and 3 i . It should be kept in mind, however, that with multiple sampled signals present, specifying nonzero 2 and 3 (or D and S) and at the same time disabling the "Group velocity dispersion" and "Third order dispersion", will result in 2 i = 0 ,i , 3 i = 0 ,i but 1 i 1 j ifi j . This means that no GVD-induced pulse broadening will be observed but pulses with different center frequencies will propagate with different group velocities. To the contrary, if all the sampled signals are merged to form a single frequency band, disabling the GVD effects will not only disable pulse broadening, but it also will set the group velocity constant for the entire sampled band considered. If "Dispersion data type" is set to "From file", the data set specified by the file is Sellmeier fitted. The dispersion parameters are calculated by analytically differentiating the fit. 716 BIDIRECTIONAL OPTICAL FIBER The file specifying the dispersion data must provide the dependence of group delay [ps/km] on the wavelength [nm]. For this reason, "Frequency domain parameters" is disabled when "Dispersion data type" is set to "From file". Vector approach When the polarization state of the incident sampled signals is not preserved during its propagation inside the optical fiber, the scalar approach is no longer applicable. A vector model is then selected and solved. The vector model is similar to the model presented in the Optical Fiber WDM (see Optical Fiber WDM Technical Background). In the same way, Raman scattering is not applied. References [1] J. Ko; S. Kim; J. Lee; S. Won; Y. S. Kim; J. Jeong, "Estimation of performance degradation of bidirectional WDM transmission systems due to Rayleigh backscattering and ASE noises using numerical and analytical models", IEEE J. of Lightwave Technology, Vol.: 21 , Issue: 4 , April 2003, Pag.:938 - 946 [2] M. Karasek, M. Menif, "Protection of surviving channels in pump-controlled gain-locked Raman fibre amplifier", Optics Communications 210 (2002) 57-65. [3] G. P. Agrawal, "Applications of nonlinear fiber optics", Academic press, 3rd edition, 2001. [4] G. P. Agrawal, "Nonlinear fiber optics", Academic press, 3rd edition, 2001. [5] R. W. Hellwarth, Prog. Quant. Electr. 5, 1 (1977). [6] P. Tchofo Dinda, G. Millot, and S. Wabnitz, JOSA B, 15, 1433, (1998). [7] A. backa, G. Jacobsen, and B. Tromborg, "Dynamic Stimulated Brillouin Scattering Analysis," J. Lightwave Technol. 18, 416- (2000) 717 BIDIRECTIONAL OPTICAL FIBER Notes: 718 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Nonlinear Dispersive Fiber (Obsolete) This component is an obsolete version that is included with OptiSystem for backwards compatibility purposes - It was replaced by the Optical Fiber component. Ports Name and description Port type Signal type Input Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Value range Length 50 km [0, INF] Constant — Constant, Wavelength Dependent/ From File 0.25 dB/km [0, INF] AtnVsLambda.dat — [0, INF] -1 dB [-INF,0] -0.022 dB [-INF,0] Fiber length Attenuation data type Defines the attenuation as a fixed constant value or as a wavelength dependent curve taken from a file Attenuation – constant Defines the attenuation as a fixed constant value, the same for all channels Attenuation vs. wavelength Defines the attenuation as a wavelength dependent curve in a file Input coupling loss Overall input coupling loss resulting from mode mismatch, Fresnel reflections, etc. Output coupling loss Overall output coupling loss resulting from mode mismatch, Fresnel reflections, etc. 719 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Dispersion Name and description Default value Default unit Value range Group delay data type Constant — Constant, Wavelength Dependent/ From File 4.9e+006 ps/km [-INF,INF] GroupVs Lambda.dat — [-INF,INF] Constant — Constant, Wavelength Dependent/ From File 4.5 ps/nm/km [-INF,INF] GVDvsLambda.dat — [-INF,INF] Constant — Constant, Wavelength Dependent/ From File 0.11 ps/nm2/km [-INF,INF] DispSlope vs. Lambda.dat — [-INF,INF] EffRIVsLambda.dat — [0,INF] Defines the group delay as a fixed constant value, or as a wavelength dependent curve taken from a file Group delay – constant Defines the group delay as a fixed constant value, the same for all channels Group delay vs. wavelength Defines the group delay as a wavelength dependent curve in a file GVD data type Defines the group-velocity dispersion as a fixed constant value, or as a wavelength dependent curve taken from a file GVD – constant Defines the group-velocity dispersion as a fixed constant value, the same for all channels GVD vs. wavelength Defines the group-velocity dispersion as a wavelength dependent curve in a file Dispersion slope data type Defines the dispersion slope as a fixed constant value, or as a wavelength dependent curve taken from a file Dispersion slope – constant Defines the dispersion slope as a fixed constant value, the same for all channels Dispersion slope vs. wavelength Defines the dispersion slope as a wavelength dependent curve in a file Effective refractive index vs. wavelength Defines the effective refractive index as a dispersive curve vs. the wavelength in a file 720 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Birefringence Name and description Default value Default unit Value range Birefringence data type Constant — Constant, Wavelength Dependent/ From File 6.2832e-005 rad/m [-1,1] BirefringenceVs Lambda.dat — [-1,1] 0.1 km [0,INF] 0.07 ps/km1/2 [0,INF] Constant — Constant, Wavelength Dependent/ From File 3 ps/km [-INF,INF] DGDVsLambda.dat — [-INF,INF] Defines the birefringence (the mismatch between the propagation constants of the two orthogonal polarization modes) as a fixed constant value, or as a wavelength dependent curve taken from a file Birefringence – constant Defines the birefringence as a fixed constant value, the same for all channels Birefringence vs. wavelength Defines the birefringence as a wavelength dependent curve in a file Coupling length of polarization mixing Coupling length of polarization scrambling PMD coefficient Polarization mode dispersion coefficient DGD data type Defines the differential group delay between the two orthogonal polarization modes as a fixed constant value, or as a wavelength dependent curve taken from a file DGD – constant Defines the differential group delay as a fixed constant value, the same for all channels DGD vs. wavelength Defines the differential group delay as a wavelength dependent curve in a file 721 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Nonlinearities Name and description Default value Default unit Value range Effective area data type Constant — Constant, Wavelength Dependent/ From File 72 2 [0,INF] EffAreaVsLambda.dat — [0,INF] Constant — Constant, Wavelength Dependent/ From File 2.6e-020 m2/W [-INF,INF] N2VsLambda.dat — [-INF,INF] RamanResN2Vs Freq.dat — [-INF,INF] 9.9e-014 m/W [0,INF] 1000 nm [0,INF] RamanGainVsFreq.dat — [0,INF] 5 fsec [0,INF] Defines the effective area of the fiber as a fixed constant value, or as a wavelength dependent curve taken from a file. Effective area – constant Defines the effective area as a fixed constant value, the same for all channels. Effective area vs. wavelength Defines the effective area as a wavelength dependent curve in a file. n2 data type Defines the nonlinear refractive index as a fixed constant value, or as a wavelength dependent curve taken from a file. n2 – constant Define the nonlinear refractive index as a fixed constant value, the same for all channels. n2 vs. wavelength Defines the nonlinear refractive index as a fixed constant value, or as a wavelength dependent curve taken from a file. Raman-resonant n2 dispersion Defines the Raman-resonant dispersion of the thirdorder nonlinear susceptibility as a frequency dependent curve in a file Peak Raman gain coeff The peak Raman gain coefficient at certain pump wavelength Pump Wavelength of Peak Raman gain coeff The pump wavelength corresponding to the above peak Raman gain coefficient Raman Gain Spectrum Defines the Raman gain spectrum vs. frequency in a file Raman self-shift Time The characteristic Raman self-frequency shifting time 722 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Effects On/Off; Model Details Name and description Default value Default unit Value range Attenuation ON — [ON, OFF] ON — [ON, OFF] ON — [ON, OFF] ON — [ON, OFF] Hi-Bi PM fiber, no PMD, fixed DGD — Hi-Bi PM fiber, no PMD, fixed DGD, Non-PM fiber, PMD, stochastic DGD, Averaged polarizations Switch On/Off the attenuation Group velocities mismatch Switch On/Off the group velocities mismatch GVD (Group velocity dispersion) Switch On/Off the group velocity dispersion GVD Slope (third-order dispersion) Switch On/Off the dispersion slope (the third-order dispersion) Polarization evolution Specify the polarization maintaining capabilities of the fiber and the polarization evolution models to use Independent pol. mode mixing of WDM channels OFF [ON, OFF] In the case of non-PM fiber, determines whether the polarization scrambling follows the same pattern for all the channels or is completely independent n2 polarization factor 1 dimensionless [0.5, 1] Raman Gain polarization factor 1 dimensionless [0.5, 1] Birefringence ON — [ON, OFF] ON — [ON, OFF] ON — [ON, OFF] ON — [ON, OFF] OFF — [ON, OFF] OFF — [ON, OFF] 100 radian [-1e+100, 1e+100] Switch On/Off the birefringence SPM (Self-phase modulation) Switch On/Off the SPM (Self-phase modulation) XPM (Cross-phase modulation) Switch On/Off the XPM (Cross-phase modulation) XPM of orthogonally polarized modes Switch On/Off the XPM of orthogonally polarized modes FWM (four-wave mixing) Switch On/Off the FWM (four-wave mixing) FWM of orthogonally polarized modes Switch On/Off the XPM of orthogonally polarized modes Maximal phase-mismatch FWM generated waves with phase-mismatches larger than this value are neglected 723 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Name and description Default value Default unit Value range SRS (stimulated Raman scattering) ON — [ON, OFF] SRS with pump wave depletion ON — [ON, OFF] OFF — [ON, OFF] Name and description Default value Default unit Value range Enabled ON — [ON, OFF] 25 — [0,INF] Fixed = Main Channel Initial Nonlinear length/Number of Steps — Fixed = Full length/Number of Steps Switch On/Off the effect of pump wave depletion in SRS RSFS (Raman self-frequency shifting) Switch On/Off the RSFS (Raman self-frequency shifting) Simulation Enable the calculations Number of steps Number of longitudinal steps Step defined as: Choose one of the three alternative ways of defining the step size Fixed = Main Channel Initial Nonlinear length/Number of Steps Variable = Main Channel Current Nonlinear length/Number of Steps Time-window boundaries Absorbing — Periodic, Absorbing OFF — [ON,OFF] 1 — [0, 65535] Choose the type of the time-window boundary conditions Random Phases Randomize the phase offsets of the channels at input Random Phases Seed The seed of the random phases 724 NONLINEAR DISPERSIVE FIBER (OBSOLETE) 3D graphics selection Name and description Default value Default unit Value range Power spectrum of channels OFF — [ON,OFF] dBm — mW, dBm OFF — [ON,OFF] ON — [ON,OFF] 0 nm [0,INF] ON — [ON,OFF] OFF — [ON,OFF] OFF — [ON,OFF] OFF — [ON,OFF] 50 — [2, 1000] Displays the average power spectrum of the channels Unit of power spectra Displays the average power spectrum of channels or the PSD of a selected channel in [mW] or [dBm] Bandwidth spectrum of channels Displays the rms bandwidths of the channels Monitor central sampled channel Monitors the center most channel if described as a sampled waveform Wavelength of sampled channel to monitor Monitors an arbitrary sampled channel, defined by its central wavelength Waveform Displays the waveform of the selected sampled channel Chirp Displays the chirp of the selected sampled channel PSD Displays the PSD of the selected sampled channel Spectral Delay Displays the spectral delay of the selected sampled channel Number of 2D snapshots in the 3D graphics Defines the number of 2D snapshots forming the selected 3D graphics Graphs Name and description X Title Y Title Fiber 3D Graph EmptyX EmptyY 725 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Parameters—Detailed descriptions In the following section, the parameters descriptions are further elaborated. There are descriptions of features pertaining to multiple parameters, and also extended descriptions of individual parameters. Note: Many parameters pertaining to the NDF can be defined as either constant or wavelength dependent/from file values. The first option is used usually for rapid development of simple designs. If a parameter is wavelength dependent (arb. curve ) you have to prepare a text file with (Wavelength ParameterValue) data pairs, and create the parameter in the appropriate Component properties dialog box. This option is recommended for detailed, quantitatively precise designs. Many parameters of the NDF, such as losses, dispersion, and effective fiber area, can be defined in both ways - as constants or curves loaded from a file. When a parameter is defined as a curve, the format of the text file is as follows: Wavelength_1 ParameterValue_1 Wavelength_2 ParameterValue_2 Wavelength_3 ParameterValue_3 ...... Wavelength_N ParameterValue_N The units of wavelength are nanometers ( nm ). The units and the value ranges of the parameter values are the same as those of the respective 'constant' parameters. For example, when a loss spectrum is loaded from file it might look like: 1500 1.99E-01 1525 1.92E-01 1550 1.89E-01 1575 1.93E-01 1600 2.05E-01 1500 0.199 1525 0.192 1550 0.189 1575 0.193 1600 0.205 or: 726 NONLINEAR DISPERSIVE FIBER (OBSOLETE) An arbitrary number of points (file lines) are permitted, except 0 (empty file). The column separator can be an arbitrary number (except 0) of either spaces or tabs. The files are opened using the standard Windows "File Open" dialog box. Technical background Origin of the nonlinearity At high optical intensities for intense electromagnetic fields, the dielectric medium behaves as a nonlinear medium. This is also the case for the fiber material. Under the influence of intense electromagnetic fields, the motion of bound electrons becomes an harmonic and, as a result, the induced polarization P from the electric dipoles becomes nonlinear function of the electric field E: P = 0 x 1 .E+x 2 :EE+x 3 :EEE+... where (j) (j =1,2,3, …) denotes the jth order of susceptibility. The lowest order nonlinearity in optical fibers originates from the third order susceptibility (3). Nonlinear effects in optical fibers The following nonlinear effects in optical fibers are caused by the third-order nonlinear susceptibility and are included in the numerical engine of the component: • Self-phase modulation (SPM) • Cross-phase modulation (XPM) • Cross-phase modulation between the orthogonal modes of a birefringent fiber (PXPM) • Four-wave mixing (FWM) • Four-wave mixing between the orthogonal modes of a birefringent fiber (PFWM) • Interchannel Stimulated Raman scattering (SRS) and intrachannel Raman selfshifting (RSS) OptiSystem currently supports several different models specialized for different signal representations and/or combinations of parameters. Model Ia This model has been derived for the separated channels signal representation. It also accounts explicitly for the nonlinear interactions and mixing of the orthogonal polarization modes in an SM fiber. It is a system of 2N coupled modified nonlinear Schrödinger equations (NLSE). This model accounts for: • background loss and linear dispersion up to third order • birefringence and PMD • nonlinearities — SPM, XPM, FWM, SRS, RSS, PXPM, and PFWM 727 NONLINEAR DISPERSIVE FIBER (OBSOLETE) For Sampled signals, the following effects are accounted for: XPM, XPM of orthogonally polarized modes, Raman, FWM, and SSFS. Whereas, for Parameterized signals and ASE noise bins, we account for Raman and FWM. There are 3 types of polarization evolution that could be taken into account: Hi-Bi PM fiber, no PMD, fixed DGD In the case of polarization maintaining fiber, we have to specify the birefringence and DGD of the fiber. Non PM fiber, PMD, stochastic DGD In this case the correlation length Lcorr and PMD coefficient have to be specified. The component allows the calculation for PMD of any order. To see the effect of PMD, the following effects must also be selected under the Effects tab: Birefringence and Group velocity mismatch Averaged polarizations In this case, the effect of the Kerr nonlinearity is averaged over the Poincaré sphere, and is taken into account with a coefficient value of 8/9. The effect of nonlinear PMD [2] is not taken into account. The intrapulse Raman scattering (or Raman Self Shifting) effect, which leads to soliton self frequency shift, has to be considered for very short optical pulses with duration ~ picosecond or smaller. 728 NONLINEAR DISPERSIVE FIBER (OBSOLETE) The model has the following form: 2 3 A ix A i A ix 1 A ix 1 ---------- 1 ---------ix- + --- 2 ------------ – --- 3 ------------- + --- i A ix = ix t z 2 i t 2 6 i t 3 2 N i j, k, l = 1 j, k, l f ijkl M x v k + l – j – i -------- A j A kv A l exp iz + f ii i = x v, = x, y 1--2 iA iy A ix exp – 2i xy z – 3 N 2 i A ix A ix + 21 f ij 2 ---fii- Ajx Aix + j = 1 j N i j n gR gR j j = 1 j j 1 f ij 2 i – i ---- A jx A ix – ig R f ii 1 N j = 1 j i j 1 2 --- i A iy 2 A ix + --- i 3 3 N f ij ---fii- Ajy 2 f ij n 2 g R i – j ---- A jx A ix f ii 1 i A ix + j = 1 j 1 2 A ix iT R ---------------- A ix t where Aix, Aiy are the slowly varying complex electric field amplitudes of the radiation in the respective x/y polarization mode of the i’th WDM channel, 1 = 1 v g ix and 1 = 1 v g iy are the inverses of the group velocities of the pol. ix modes, iy evaluated at the respective carrier frequency of the channels. coefficient, related to the dispersion parameter as: 2i is the GVD 729 NONLINEAR DISPERSIVE FIBER (OBSOLETE) 2c 2i D = – ---------------2 3i is the third-order dispersion coefficient, related to the dispersion slope as: 4c 2c- 2 S = ------- + --------- 2 3i 3 2i (8) i is the loss coefficient for the respective carrier frequency of the channel n g R is the normalized Raman gain function taken from reference [1], Figure 8.1 on page 300. = i n2 / c Aeff is the nonlinear coefficient ( 1-10 W-1km-1 ) n2 is the nonlinear refractive index equal to 3 xxxx / 8 neff ( 3.10-16 cm2/ W ) x = i (3 x /8 neff )/ (c Aeff ) is the nonlinear coefficient of the four-wave interactions and is proportional to the relevant component of the tensor. Aeff is the effective area: 2 F x ,y dx dy – – Aeff = ------------------------------------------------------ 4 F x ,y dx dy – – (9) where F(x,y) is the modal field distribution of the fiber mode. 730 NONLINEAR DISPERSIVE FIBER (OBSOLETE) The overlap integrals fij are defined by: fii = 2 2 F i x ,y F j x ,y dx dy – – -------------------------------------------------------------------------------------------------- – – 2 F i x ,y dx dy 2 F j x ,y dx dy – – (10) M is the multiplicity factor. Its value is 2 if all three waves are different — otherwise, its value is 1. The overlap integral fijkl is: F i F j F k F l -----------------------------------------------------------------------------2 2 2 2 12 Fi Fj Fk Fl fijkl= (11) where the angle brackets denote integration over the transverse coordinates x and y. Also = k n k + l n l – j n j – i n i c (12) where xy = y – x (13) are the propagation constant mismatches of the processes of FWM and (PFWM) and TR ~ 5 fsec is the slope of the Raman gain curve. Model Ib Similar to Model Ia, but disregards the polarization evolution of the signal and uses the average power of the two polarization modes. It consists of a system of only N coupled modified nonlinear Schrödinger equations (NLSE) with correspondingly adjusted nonlinear coefficients. 731 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Model I Derived for the case of the total field signal representation. All sampled signals are in a single frequency band. This is the basic method used for modeling WDM systems. It also accounts explicitly for the mixing of the orthogonal polarization modes in an SM fiber. It is a system of two coupled modified nonlinear Schrödinger equations (NLSE). This model accounts for: • background loss and linear dispersion up to third order • birefringence and PMD • nonlinearities - SPM, XPM, FWM, SRS, RSS, PXPM It works with all types of signals: Sampled, Parameterized and ASE noise bins. For parameterized and ASE noise bins, only linear losses are taken into account. 'Total field approach' automatically accounts the XPM and FWM effects. There is no possibility to switch off these effects. 'Total field approach for both polarizations' will additionally account for PXPM of orthogonally polarized signals' and PFWM of orthogonally polarized signals'. The model for the case of one polarization has the following form: 2 3 2 A A- 1--- -------A- 1--A 2 ------ 1 A ------ + --i- 2 -------– + A = i A A – iT R ------------ A z t 2 t 2 6 3 t 3 2 x t (14) All the parameters in the above equation have been explained, along with the Model Ia. Numerical Methods The three models (Model la, Model lb, and Model l) are solved by a scalar or vectorial version of the split-step Fourier transform method: A ------ = D + N A z (15) with symmetrized step size [1]. In addition, the step size can be controlled along the propagation. Step size selection rules The user can choose one of the following three ways to calculate the step size: 732 • Fixed • Initial Nonlinear Length / Number of Steps • Current Nonlinear Length / Number of Steps NONLINEAR DISPERSIVE FIBER (OBSOLETE) Fixed In this case the step size is simply z = L and N is the user defined number of steps. N , where L is the length of the fiber Initial Nonlinear Length / Number of Steps One of the well known strategies for guaranteeing accurate split-step calculations is to limit the value of the accumulated nonlinear phase-shift per step. This is equivalent to set z = L NL N LNL where L NL = 1 P 0 is the nonlinear length at the input of the fiber (a measure of the distance needed for considerable nonlinear distortions to occur), and N LNL is the user specified number of steps per L NL . Another limitation imposed is that the maximum temporal displacement of the channels due to group-velocity mismatch per step is less than 1% of the bit period. 733 NONLINEAR DISPERSIVE FIBER (OBSOLETE) Current Nonlinear Length / Number of Steps In this case, the nonlinear length is periodically recalculated along the fiber: L NL z = 1 P z . In this way, the possible changes in account. L NL z due to loss or gain are taken into The term indicates the channel used in the calculations above. When the separate channels signal representation is used, it is either the channel with the highest power or the central channel. If we use only one continuous spectral band, as in the total field signal representation, there can be only one main channel. References [1] Agrawal, G.P., “Nonlinear Fiber Optics, 3rd Edition”, Academic Press, 2001. [2] Marcuse, D., Menyuk, C.R., and Wai, P.K.H., "Application of the Manakov - PMD Equation to Studies of Signal Propagation in Optical Fibers with Randomly Varying Birefringence", Journ. Light. Technol.,15, 1735-1746 (1997). [3] Tchofo Dinda, P., Milot, G., and Wabnitz, S. "Polarization Switching and Suppression of Stimulated Raman Scattering in Birefringent Optical Fibers", JOSA B, 15, 1433-1441 (1998). 734 NONLINEAR DISPERSIVE FIBER (OBSOLETE) 735 NONLINEAR DISPERSIVE FIBER (OBSOLETE) 736 Receivers Library Regenerators • Clock Recovery • Data Recovery • 3R Regenerator • Electronic Equalizer • MLSE Equalizer • Integrate And Dump • Voltage-Controlled Oscillator 737 738 CLOCK RECOVERY Clock Recovery Compensates the time delay between the original signal at the reference port and the signal that is received at the input port. Ports Name and description Port type Signal type Reference Input Electrical Input Input Electrical Output Output Electrical Parameters Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled Results Name and description Units Signal delay s Signal delay samples Technical background The time delay is calculated from cross-correlation of the reference signal and the received signal. The signal is then shifted in time. 739 CLOCK RECOVERY 740 DATA RECOVERY Data Recovery This component recovers the binary data from the electrical signal. It can be used in 3R generators for the data recovery stage. Ports Name and description Port type Signal type Input Input Electrical Bit sequence Output Binary Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate Bits/s Bits/s [0,+INF[ Reference bit rate to use for the decision instant calculation User defined delay MBits/s GBits/s TRUE — — True, false 0 s s, ms, us, ns, ps, fs ]-INF,+INF[ FALSE — — True, false 0.5 Bit — [0,1] Defines whether the user can define the delay compensation or not Delay compensation Delay to apply to the signal input User defined decision Defines whether the component will automatically calculate the decision instant or it will be defined by the user Decision instant Value for the decision instant to use when recovering the bit sequence 741 DATA RECOVERY Name and description Default value Default unit Units Value range User defined threshold FALSE — — True, false 0.5 a.u. — ]-INF,+INF[ Defines whether the component will be automatically calculated or will be userdefined Absolute threshold Value for the threshold to use when recovering the bit sequence Export Name and description Default value Units Value range Export mode None — None, All, Marks, Spaces Export.dat — — Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines the type and if the values at decision instant will be exported or not Filename The destination file name for the data exported Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background This component allows the user to recover a bit sequence from an electrical signal. In order to recover the bit sequence, the user should provide the signal bit rate, given by the parameter Reference bit rate. The decision instant and the threshold level can be defined by the user or automatically calculated by this component. If the parameter User defined decision is disabled, the model automatically estimates the decision instant by generating internally an eye diagram and searching for the maximum opening for the eye amplitude. The time instant with the maximum opening is the decision instant, this method is valid for RZ and NRZ modulation types. The user can disable the searching and enter directly the value of the decision instant by disabling User defined decision and entering the instant using the parameter Decision instant. If the parameter User defined threshold is disabled, the threshold is calculated at the decision instant, by searching for the maximum eye opening. The threshold value will be at the center of the maximum eye opening. The user can disable the searching and 742 DATA RECOVERY enter directly the value of the threshold by disabling User defined threshold and entering the threshold using the parameter Absolute threshold. The parameter Delay compensation allows the user to compensate the propagation delays of the input signal by enabling the parameter User defined delay. If the parameter User defined delay is disable, the delay will be estimated by comparing the input signal with a signal generated by the internal clock. If parameter Export mode is different from None the value at each decision instant is exported to a file. The user can select to save all values (All), Marks or only Spaces. 743 DATA RECOVERY 744 3R REGENERATOR 3R Regenerator This component regenerates an electrical signal. Ports Name and description Port type Signal type Input Input Electrical Bit sequence Output Binary Reference signal Output Electrical Output Output Electrical Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate Bits/s Bits/s [0,+INF[ Reference bit rate to use for the decision instant calculation User defined delay MBits/s GBits/s False — — True, false 0 s s, ms, us, ns, ps, fs ]-INF,+INF[ False — — True, false 0.5 Bit — [0,1] Defines whether the user can define the delay compensation or not Delay compensation Delay to apply to the signal input User defined decision Defines whether the component will automatically calculate the decision instant or it will be defined by the user Decision instant Value for the decision instant to use when recovering the bit sequence 745 3R REGENERATOR Name and description Default value Default unit Units Value range User defined threshold False — — True, false 0.5 a.u. — ]-INF,+INF[ Defines whether the component will be automatically calculated or will be userdefined Absolute threshold Value for the threshold to use when recovering the bit sequence Technical background This component regenerates an electrical signal. It generates the original bit sequence, and a modulated electrical signal to be used for BER analysis. It is a subsystem based on the Data Recovery component and a NRZ Pulse Generator. This first output port is the bit sequence, the second one is a modulated NRZ signal and the last output is a copy of the input signal. These three signals can be connected directly to the BER Analyzer, avoiding additional connections between transmitter and the receiver stage. The following system shows a conventional connection between the BER Analyzer in the receiver stage with the transmitter stage, 2 additional connections are required between the transmitter and the BER Analyzer. 746 3R REGENERATOR By using the 3R Regenerator, there is no need for connections between the transmitter and the BER Analyzer. This is especially important for WDM systems, where you have with multiple transmitters, receivers and BER Analyzers. For more information, see “Spatial CW Laser”. 747 3R REGENERATOR Notes: 748 ELECTRONIC EQUALIZER Electronic Equalizer This component is an electronic equalizer. It can work as a fractionally or spaced feedforward equalizer (FFE), decision-feedback equalizer (DFE) or the combination of both. A least mean square (LMS) algorithm is used to update the filter tap coefficients Ports Name and description Port type Signal type Supported Modes Input Input Electrical Sampled signals Training Input Electrical Sampled signals Output Output Electrical Sampled signals Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate Bits/s Bits/s [0,+INF[ Reference bit rate to use for the decision instant calculation and tap delays Update taps coefficients MBits/s GBits/s False True, False True True, False False True, False Define whether update the tap coefficients using the LMS algorithm Linear feedback Define whether use the decision or linear output as the DFE input Decision output Define whether use the decision or linear output as the equalizer output 749 ELECTRONIC EQUALIZER LMS Name and description Default value Default unit Units Value range Limit training sequence length False [True, False 100 [0, 1e+100] 0.03 [0, 1e+100] 1 [0, 1e+100] Define whether calculate the sequence length from the training input signal of limit to a user defined value Training sequence length User defined sequence length Step size Step size for the LMS algorithm Leakage factor Leakage factor for the LMS algorithm Report The summary of filter tap coefficients before and after training and calculation Decision stage Name and description Default value Default unit Units Value range High level input 1 (a.u) [-1e+100,1e+100] 0 (a.u) [-1e+100,1e+100] 0.5 (a.u) [-1e+100,1e+100] 0.5 Bit [0,1] Name and description Default value Default unit Forward taps space 1 (HLI) Value for the high level input in the decision stage Low level input (LVI) Value for the low level input in the decision stage Absolute threshold Value for the threshold to use when recovering the bit sequence. Typically (HLI + LVI) / 2 Decision instant Value for the decision instant to use when recovering the bit sequence Forward taps The inverse of the tap delay ratio. It is a spaced equalizer if value is equal to one or a fractionally spaced otherwise 750 Units Value range [1, 100] ELECTRONIC EQUALIZER Name and description Default value Default unit Units Value range Forward taps coefficients 3 [0, 10000] 1 [-1e+100,1e+100] 0 [-1e+100,1e+100] Number of forward taps coefficients Forward[0].real Real part of the first tap coefficient Forward[0].imag Imaginary part of the first tap coefficient ... [-1e+100,1e+100] Feedback taps Name and description Default value Default unit Units Value range Feedback taps coefficients 3 [0, 10000] 1 [-1e+100,1e+100] 0 [-1e+100,1e+100] Number of feedback taps coefficients Feedback[0].real Real part of the first tap coefficient Feedback[0].imag Imaginary part of the first tap coefficient ... [-1e+100,1e+100] Graphs Name and description Default value Calculate graphs YES Default unit Units Value range [YES, NO] Determines whether calculate the error level graphs for the output and training signal Simulation Name and description Default value Enable YES Default unit Units Value range [YES, NO] Determines whether or not the component is enabled 751 ELECTRONIC EQUALIZER Graphs Name and description X Title Y Title Training error Bits Error level (a.u.) Calculation error Bits Error level (a.u.) Technical background An electronic equalizer attempts to mitigate intersymbol interference (ISI) caused by time-dispersive channels, such as chromatic dispersion and polarization mode dispersion (PMD) in single mode fibers [1], or differential mode delay (DMD) in multimode fibers [2]. This component can work as a fractionally or spaced feed-forward equalizer (FFE), decision-feedback equalizer (DFE) or the combination of both. A least mean square (LMS) algorithm is used to update the filter tap coefficients. The signal input x(t) is filtered by a forward filter, or a linear equalizer. Parameter Forward taps coefficients define the number of forward tap coefficients for the filter. Forward taps space defines the tap spaces, or the K parameter in the schematic bellow. If K is greater than one the filter is fractionally spaced. Figure 1 Equalizer schematic 752 ELECTRONIC EQUALIZER At the output of the forward filter, the output signal y'(t) goes to a decision stage where the signal is detected based on the parameters Threshold and Decision instant. The detected signal will have values of high and low level depending on parameters High level and Low level. Parameter Decision output defines if the output signal y(t) is y'(t) or the detected signal yd(t). The user can also select whether the input to the feedback filter stage is the detected signal yd(t) or the linear signal y'(t) (parameter Linear feedback). The training input signal is used to calculate the filter coefficients, based on the LMS algorithm, where the error is calculated according to: e k = y' k – d k (1) The filter taps (w) coefficients are updated according to w k + 1 = w k l + u k e k (2) Where l is the parameter Leakage factor and is the parameter Step size. The user can disable the filter updates by setting parameter Update taps coefficients to false. By default, the equalizer will estimate the filter coefficients using the training sequence. The user can limit the training sequence to a value defined by the parameter Training sequence length. If the user wants to disable the training simply set this parameter to zero or connect the training input to a electrical null component. The values for the error level ek are available in two graphs. The first graphs plots the error values versus for the training sequence, the second graph plots the error values for the detected signal. The user can provide the tap coefficients as an initial value for the equalizer, or the component can also be used as a linear FIR filter by disabling Update tap coefficients and limiting the training sequence length to zero. Alternatively, setting the Step size to zero also disables the updating of the tap coefficients and the initial values will not change during the calculation. Parameter Report presents the values of the filter coefficients before and after the training, and at the end of the calculation. References [1] J. Wang and J. M. Kahn, 'Performance of electrical equalizers in optically amplified OOK and DPSK systems', IEEE Photon. Technol. Lett. 16, 5, pp. 1397-1399, May 2004 [2] H. Wu et al, "Integrated transversal equalizers in high-speed fiber-optic systems," IEEE J. SolidState Circuits, vol. 38, no. 12, pp. 2131-2137, Dec. 2002. 753 ELECTRONIC EQUALIZER Notes: 754 MLSE EQUALIZER MLSE Equalizer This component is a MLSE (maximum likelihood sequence estimate) electronic equalizer. The component uses the Viterbi algorithm to equalize the input signal through a dispersive channel. The channel estimation is implemented as a FIR filter, with the initial tap coefficients provided by the user. Ports Name and description Port type Signal type Supported Modes Input Input Electrical Sampled signals Output Output Electrical Sampled signals Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate Bits/s Bits/s [0, 1e100] Reference bit rate to use for the decision instant calculation and tap delays Samples per bit MBits/s GBits/s 8 — — [1, 1e100] True — — [1, 1000000] 1 a.u. — [-1e100, 1e100] 0 a.u. — [-1e100, 1e100] The number of samples per bit used by the equalizer Traceback length The number of bits, or trellis branches used in the Viterbi algorithm High level input (HLI) Value for the high level input modulation Low level input (LVI) Value for the low level input modulation 755 MLSE EQUALIZER FIR channel estimates Name and description Default value Default unit Units Value range Number of coefficients 8 — — [0, 10000] 1x2 — — [-1e+100,1e+100] FIR.dat — — — Default value Default unit Units Value range — — — — — — Default unit Units Value range Number of FIR coefficients that will be used in the calculation Coefficients real imag Table with real and imaginary part of complex coefficients Filename Filename with list of coefficients Preample Name and description Preamble vector Specifies the preamble that is expect to precede the data in the input signal Postamble vector Specifies the postamble that is expect to follow the data in the input signal Simulation Name and description Default value Enable True True, False Determines whether or not the component is enabled Technical background An electronic equalizer attempts to mitigate intersymbol interference (ISI) caused by time-dispersive channels, such as chromatic dispersion and polarization mode dispersion (PMD) in single mode fibers [1]. This component is a MLSE (maximum likelihood sequence estimate) electronic equalizer [2]. The component uses the Viterbi algorithm to equalize the input signal through a dispersive channel. The channel estimation is implemented as a FIR filter, with the initial tap coefficients provided by the user The signal input x(t) is resampled based on the parameters Reference bit rate and Samples per bit. The resampled signal is then filtered by the FIR filter using the channel coefficients. The number of coefficients must be a multiple of the number of samples per bit. If the number of coefficients is not a multiple the component will add 756 MLSE EQUALIZER zero value coefficients to the FIR filter until the number of coefficients is a multiple of the number of samples per bit. Figure 1 Equalizer schematic Parameters Low and High level input defines the constellation of the signal modulation. The user can provide the filter coefficients directly by using the parameter Coefficients real imag; alternatively the measurements can be loaded from a file using the parameter Filename. The real and imaginary part of the complex coefficients, or only the real part, must be provided in the file containing one column (real part only), or two columns, where the first one refers to the real part and the second one to the imaginary part of the complex coefficient. References [1] F. Buchali, G. Thielecke, and H. Bulow, "Viterbi equalizer for mitigation of distortions from chromatic dispersion and PMD at 10 Gb/s," OFC'2004, vol.1, Paper MF-85, Feb. 2004. [2] J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw-Hill, 1995. 757 MLSE EQUALIZER 758 INTEGRATE AND DUMP Integrate And Dump This component creates a cumulative sum of the discrete-time input signal. It also resets the sum to zero according to a user defined time period. Ports Name and description Port type Signal type Input Input Electrical Reset Input Electrical Output Output Electrical Parameters Main Name and description Default value Default unit Units Value range Reset threshold 0 a.u. — [-1e100, 1e100] 1 — — [-1e100, 1e100] 0 — — [-1e100, 1e100] False — — True, False True — — True, False 0 a.u. — [-1e100, 1e100] The reset signal amplitude that resets the integrator Feedback gain Gain of the feedback loop Initial state The initial value of the integrator before the calculation begins Limiter Determines whether or not the internal limiter is enabled Saturate Determines whether or not to saturate the signal Minimum amplitude Limiter’s minimum value 759 INTEGRATE AND DUMP Name and description Default value Default unit Units Value range Maximum amplitude 1 a.u. — [-1e100, 1e100] Name and description Default value Default unit Units Value range Enable True Limiter’s maximum value Simulation True, False Determines whether or not the component is enabled Technical background The Integrate and Dump component integrates the input signal in the specified time window. The following equation describes the integration process: S Out i = K SOut i – 1 + S In i (1) Where Sout is the output signal, Sin is the input signal, K is the Feedback gain parameter. The initial state of the integrator is defined by the Initial state parameter. The integration can be reset by the control signal, where the reset threshold parameter defines in which control signal value the integration will be reset. At each reset time, the component sends the result to the output port, and then clears the internal state for the next step of integration. There is the option to introduce limits to the output signal, which are defined by the parameters Minimum amplitude and Maximum amplitude. To introduce these limits the Limiter parameter has to be set to TRUE. In this case the output signal can be saturated or not when it reaches the limits. When the Saturation parameter is FALSE the component is reset every time the limit is reached. 760 VOLTAGE-CONTROLLED OSCILLATOR Voltage-Controlled Oscillator The component simulates an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. Ports Name and description Port type Signal type Control Input Electrical Output Output Electrical Parameters Main Name and description Default value Default unit Units Value range Amplitude 2 V. V [1e-12, +INF] 100 MHz/V MHz/V [1e-12, +INF] 500 MHz Hz,MHz,GHz,THz [1e-12, 1e6] 1000 MHz Hz,MHz,GHz,THz [1e-12, 1e6] 750 MHz Hz,MHz,GHz,THz [1e-12, 10e6] Amplitude of the signal at the VCO output VCO sensitivity Defines the VCO average tuning sensitivity Minimum frequency Defines the oscillator minimum frequency Maximum Frequency Defines the oscillator maximum frequency VCO Frequency Defines the carrier frequency 761 VOLTAGE-CONTROLLED OSCILLATOR Simulation Name and description Default value Enable True Default unit Units Value range True, False Determines whether or not the component is enabled Sample rate Sample rate Hz Hz, GHz, THz [0,+INF[ Frequency simulation window Technical background The VCO component creates a signal that oscillates at a frequency determined by the input voltage. The instantaneous frequency is defined by: F(t) = S x V(t) + FC Where V(t) is the input signal, F(t) is the frequency of the output signal, S is the VCO sensitivity parameter and FC is the carrier frequency. Fmin and Fmax are the parameters Minimum and Maximum frequency respectively. 762 VOLTAGE-CONTROLLED OSCILLATOR Receivers Library Photodetectors and detectors • Photodiode PIN • APD • Optical Chirp Detector • Optical Phase Detector • Optical Power Detector 763 VOLTAGE-CONTROLLED OSCILLATOR 764 PHOTODIODE PIN Photodiode PIN PIN photodiode. Ports Name and description Port type Signal type Input Input Optical Output Output Electrical Parameters Main Name and description Default value Responsivity type Constant Responsivity 1 Responsivity vs. wavelength Responsivity.dat Units Value range [Constant, Si, Ge, InGaAs, User defined] A/W [0,100] 765 PHOTODIODE PIN Noise Name and description Default value Default unit Units Value range Dark current 10 nA nA [0,+INF[ Noise calculation type Numerical — — Analytical, Numerical, Numerical Convert noise bins Noise bandwidth source Use sample rate When “Use sample rate” is selected (default) the Sample rate parameter setting (under Downsampling) will be used to calculate both the Thermal noise and Shot noise Use sample rate, Use bandwidth settings When “Use bandwidth settings” is selected, Bandwidth (Thermal) and Bandwidth (Shot) parameters will be used to calculate the Thermal and Shot noises, respectively Add signal-ASE noise True — — True, False Add ASE-ASE noise True — — True, False Add thermal noise True — — True, False Bandwidth (Thermal) Bit rate Hz Hz, GHz, THz [1e-3,+INF[ Thermal noise calculation Defined Thermal power density 100e-024 W/Hz W/Hz, A/(Hz)0.5 Absolute temperature 298 K K Load resistance 50 Ohm Ohm True — — True, False Bandwidth (Shot) Bit rate Hz Hz, GHz, THz [1e-3,+INF[ Shot noise distribution Gaussian — — Poisson, Gaussian Thermal noise Defined, Calculated [0,+INF[ Shot noise Add shot noise Determines if shot noise is added to the signal Determines the distribution used to generate the shot noise 766 PHOTODIODE PIN Name and description Default value Time interval points 1 Default unit Units Value range 1, 2, 4, 8, 16 Used only when calculating shot noise. When set to 1, the Poisson photon count is calculated over the entire bit period. For 2, 4, 8 and 16, the time intervals for calculating the photon count will be divided accordingly (as a fraction of the bit period) Frequency response Name and description Default value Default unit Units Value range Transfer function model Ideal Junction capacitance 3 pF pF [0,+INF[ Modulation bandwidth 2 GHz GHz [0,+INF[ Ideal, RC limited, Defined Down-sampling Name and description Default value Default unit Units Value range Centered at max power True — — True, False 193.1 THz Hz, THz, nm [30,3e5] Sample rate Hz Hz, GHz, THz, nm [1e-3,+INF[ Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined Center frequency User-defined center frequency for the internal filter Sample rate Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 767 PHOTODIODE PIN Results Name and description Units Average photocurrent mA Modulation bandwidth GHz Noise bandwidth (Thermal) GHz Noise bandwidth (Shot) GHz Noise equivalent power W/sqrt(Hz) Shot noise current nA Thermal noise current nA Transit time ps 768 PHOTODIODE PIN Technical background The PIN photodiode component is used to convert an optical signal into an electrical current based on the device‘s Responsivity. The model includes: • Responsivity (constant, based on a predefined material, or user-defined) • Noise source modeling (dark current, thermal noise, shot noise) • Frequency response models (ideal, RC-limited, defined) The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channel with maximum power. If the noise calculation type in Numerical Optical noise bins are converted to Gaussian noise inside of the signal bandwidth. The combined optical field is then converted to optical power. If the option Numerical — Convert Noise Bins is selected, the output noise and signal are combined. This means that you cannot see the separate contributions of the noise. However, if you select Numerical only, the signal and noise are separated and you can select the different contributions of the noise. Figure 1 Convert noise bins enabled The PIN resamples the signal and converts the noise bins when Convert Noise Bins is enabled. Thermal noise modeling When the Thermal noise calculation = “Defined”, the PIN thermal noise current is defined based on the Thermal power density: 2 i T = (1) PwrDensity ThermalNoiseBandwidth 769 PHOTODIODE PIN When the Thermal noise calculation = “Calculated”, the PIN thermal noise current is based on the Load resistance (RL), Absolute temperature (T) and the Noise bandwidth[3]: 2 i T = 4 kB T -------------------- ThermalNoiseBandwidth RL (2) where kB is the Boltzmann Constant. The ThermalNoiseBandwidth is either set equal to the PIN photodiode Sample rate or the Bandwidth (Thermal) Shot noise modeling (Gaussian) If the parameter Add shot noise is enabled and the Shot noise distribution parameter is Gaussian, the optical power is converted to electrical current by i t = i s t + i d + i sh t (3) where is(t) is the optical signal calculated from the responsivity r: i s t = rP s t (4) and id is the dark current. When Thermal noise is enabled the Thermal noise current is also added to is(t) The mean square of the shot noise current is calculated as follows: 2 i d + sh = 2 q i s + i d B eff (5) Shot noise modeling (Poisson) If the parameter Add shot noise is enabled and Shot noise distribution parameter is Poisson, the electrical current is calculated according to [2]: 2qn e i t = ----------- + i th t t 770 (6) PHOTODIODE PIN where ne denotes the number of electrons generated in the time instant t. The n e (equal to the average number of detected photons) within the time interval t is given by: average number of generated electrons is t id n e = ---------- t + ---- t . q q (7) The number of generated electrons n e is the Poisson random variable with mean and variance equal n e . If the noise calculation type is Analytical In this case, the signal and the noise components are calculated independently. The noise components are the variance and the noise PSD. Figure 2 Convert noise bins disabled In Figure 2, the PIN resamples the signal and does not convert the noise bins if Convert Noise Bins is disabled. The output electrical signal is: (8) i t = rP t + i d Note: This signal does not include the noise components. The noise components are calculated by the noise variance and by the power spectral density. For the noise variances: 2 2 (9) 2 t = sh t + s – ASE t 771 PHOTODIODE PIN 2 where sh t is the signal shot noise: 2 sh t = 2qi s t B e where and (10) B e is the electrical bandwidth. 2 s – ASE t is the signal ASE beating: 2 2 s – ASE t = 4r P ASE t P s t (11) For the noise PSD components: P f = P TH f + P ASE – ASE f + P ASEsh f (12) where PTH(f) is the thermal noise and PASE-ASE(f) is the beating of ASE-ASE: 2 P ASE – ASE f = r P ASE f P ASE f (13) and the ASE shot noise is: P ASEsh f = qrP ASE f B e (14) Frequency response modeling When the Transfer function model is set to “RC-limited”, the frequency response of the PIN photodiode is modeled as follows [3]: I out 1 -------- = ----------------------1 + RC s i in where R is the Load resistance and C the Junction capacitance When the Transfer function model is set to “Defined” the Modulation bandwidth parameter is used in lieu of the RC time constant in Eq 15. 772 (15) PHOTODIODE PIN Noise equivalent power The sensitivity of a PIN photodiode can be defined in terms of its Noise Equivalent power (NEP) which defines the point where the received power results in an SNR = 1. The NEP is calculated as follows: 2 2 i d + sh + i T 1 NEP = ----------------------------------------- -------------------------------------------Responsivity NoiseBandwidth (16) Note: Sample rate or Bandwidth (Thermal) is used to calculate the NEP. Responsivity model The responsivity can be constant, based on a predefined material, or user-defined. The responsivity of Si, Ge, and InGaAs is calculated based on the following graph[1] Figure 1 Responsivity curves for detector materials 773 PHOTODIODE PIN For the case of an user-defined responsivity, a text file with the following format can be used: Wavelength (um) Responsivity (A/W) 0.4 0.08 0.5 0.225 0.6 0.38 0.7 0.484 0.8 0.572 Calculation results The following calculation results are provided with the PIN photodiode model: • Sampling bandwidth (GHz) • Noise bandwidth (GHz) • Average photocurrent (mA - based on the received optical sampled signal x Responsivity) • Thermal noise current (nA - calculated by taking the square root of the mean square thermal noise current) • Shot noise current (nA - calculated by taking the square root of the mean square shot noise current) • Noise equivalent power (W/sqrt(Hz)) • Modulation bandwidth (GHz - either based on the Modulation bandwidth or calculated from 1/(2RC)\ • Transit time (ps - based on the time constant of RC) References [1] Agrawal, G.P., Fiber-Optic Communication Systems. John Wiley & Sons, New York, (1997). [2] Jeruchim, M.C., Balaban, P., Shanmugan, K., Simulation of Communication Systems: Modeling, Methodology, and Techniques. Plenum Press, New York, (1997). [3] Keiser, Gerd; “Optical Fiber Communications”, 4th Ed., Tata McGraw Hill, 2008. 774 APD APD Avalanche photodiode model. Ports Name and description Port type Signal type Input Input Optical Output Output Electrical Parameters Main Name and description Default value Default unit Units Value range Responsivity type Constant Gain 3 — — [0,+INF[ Responsivity 1 A/W — [0,100] Responsivity vs. wavelength Responsivity.dat Ionization ratio 0.9 — — ]0,1] [Constant, User defined Avalanche multiplication factor Ionization factor Noise Name and description Default value Default unit Units Value range Dark current 10 nA — [0,+INF[ Dark current amplified by the avalanche effect 775 APD Name and description Default value Default unit Units Value range Noise calculation type Numerical — — Analytical, Numerical, Numerical Convert noise bins Noise bandwidth source Use sample rate When “Use sample rate” is selected (default) the Sample rate parameter setting (under Downsampling) will be used to calculate both the Thermal noise and Shot noise Use sample rate, Use bandwidth settings When “Use bandwidth settings” is selected, Bandwidth (Thermal) and Bandwidth (Shot) parameters will be used to calculate the Thermal and Shot noises, respectively Effective noise bandwidth Bit rate Hz Hz, GHz, THz [1e-3,+INF[ Add signal-ASE noise True — — True, False Add ASE-ASE noise True — — True, False Add thermal noise True — — True, False Thermal noise calculation Defined Thermal power density 100e-024 W/Hz W/Hz, A/(Hz)0.5 Absolute temperature 298 K K Load resistance 50 Ohm Ohm Add shot noise True — — True, False Gaussian — — [WMC, Gaussian] Defined, Calculated [0,+INF[ Determines if shot noise is added to the signal Shot noise distribution Determines the distribution used to generate the shot noise Downsampling Name and description Default value Default unit Units Value range Centered at max power True — — True, False 193.1 THz Hz, THz, nm [30,3e5] Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined Center frequency User-defined center frequency for the internal filter 776 APD Name and description Default value Default unit Units Value range Sample rate 5*(Sample rate) Hz Hz, GHz, THz, nm [1e-3,+INF[ Random numbers Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Results Name and description Units Average photocurrent mA Excess noise factor Noise equivalent power W/sqrt(Hz) Shot noise current nA Shot noise spectral density A^2/Hz Thermal noise current nA Thermal noise spectral density A^2/Hz Technical background The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channel with maximum power. If the noise calculation type is Numerical: Optical noise bins are converted to Gaussian noise inside of the signal bandwidth. The combined optical field is then converted to optical power. If the option Numerical — Convert Noise Bins is selected, the output noise and signal are combined. This 777 APD means that you cannot see the separate contributions of the noise. However, if you select Numerical only, the signal and noise are separated and you can select the different contributions of the noise. Figure 1 Convert noise bins enabled The APD resamples the signal and converts the noise bins when Convert Noise Bins is enabled. Thermal noise modeling When the Thermal noise calculation = “Defined”, the APD thermal noise current is defined based on the Thermal power density: 2 i T = PwrDensity NoiseBandwidth (1) When the Thermal noise calculation = “Calculated”, the APD thermal noise current is based on the Load resistance (RL), Absolute temperature (T) and the Noise bandwidth[2]: 2 i T = 4 kB T -------------------- NoiseBandwidth RL (2) where kB is the Boltzmann Constant. The NoiseBandwidth is either set equal to the APD Sample rate or the Effective noise bandwidth Shot noise modeling If the parameter Add shot noise is enabled and Shot noise distribution parameter is Gaussian, the optical power is converted to electrical current: i t = i s t + i th t + i d + i sh t 778 (1) APD where is(t) is the optical signal calculated from the responsivity r and the gain M as: (2) i s t = MrP s t and ith(t) is the thermal noise and id is the additive dark current. For the Gaussian noise model the shot noise current ish(t) is calculated according to the power spectral density: 2 (3) N sh t = 2 qM F rP s t + i dm where idm is the dark current and F depends on M: (4) F M = kM + 2 – 1 M 1 – k where k is the Ionization ratio. If the noise calculation type is Analytical: In this case, the signal and the noise components are calculated independently. The noise components are the variance in time and the noise PSD. Figure 2 Convert noise bins disabled The PIN resamples the signal and does not convert the noise bins if Convert Noise Bins is disabled. The output electrical signal is: (5) i t = rP t + i d 779 APD The noise variances are: 2 2 2 t = sh t + s – ASE t (6) 2 where sh t is the signal shot noise: 2 2 (7) 2 (8) sh t = 2qM Fi s t B e where B e is the electrical bandwidth. 2 and s – ASE t is the signal ASE beating: 2 2 s – ASE t = 4r M P ASE t P s t The noise PSD components are: P f = P TH f + P ASE – ASE f + P ASEsh f (9) where PTH(f) is the thermal noise and PASE-ASE(f) is the beating of ASE-ASE: 2 2 P ASE – ASE f = r M P ASE f P ASE f (10) and the ASE shot noise is: 2 P ASEsh f = qM FrP ASE f B e (11) Defining responsivity The responsivity can be constant, or user-defined. In the case of user-defined, a text file with the following format is required: 780 Wavelength (um) Responsivity (A/W) 0.4 0.08 0.5 0.225 0.6 0.38 0.7 0.484 0.8 0.572 APD References [1] Agrawal, G.P., Fiber-Optic Communication Systems. John Wiley & Sons, New York, (1997). [2] Keiser, Gerd; “Optical Fiber Communications”, 4th Ed., Tata McGraw Hill, 2008. 781 APD 782 OPTICAL CHIRP DETECTOR Optical Chirp Detector Converts the received optical signal chirp into electrical signal amplitude. Ports Name and description Port type Signal type Input Input Optical Output Output Electrical Parameters Main Name and description Default value Units Value range Rescale True - True, False 0 a.u. ]-INF,+INF[ 1 a.u. ]-INF,+INF[ Determines whether the output signal will be scaled or not Min. amplitude Minimum electrical signal amplitude at the output port Max. amplitude Maximum electrical signal amplitude at the output port Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 3e5] Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined Center frequency User-defined center frequency for the internal filter 783 OPTICAL CHIRP DETECTOR Name and description Default value Default unit Units Value range Sample rate 5*(Sample rate) Hz Hz, GHz, THz, nm [0,+INF[ Name and description Default value Units Value range Polarization X - X, Y Name and description Default value Units Value range Generate random seed True - True, False 0 - [0,4999] Internal filter bandwidth Polarization Determines if the chirp from the polarization X or Y of the optical signal will be converted to amplitude Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channels with maximum power. Optical noise bins are converted to gaussian noise inside the signal bandwidth. You must supply the polarization for the chirp extraction. The signal frequency (chirp) is then normalized in the range between the parameters Min. and Max. amplitude if parameter Rescale is enabled. 784 OPTICAL CHIRP DETECTOR Figure 1 Filtered signal The converter resamples the signal and converts the noise bins. They are added in time domain. Figure 2 shows the chirp detection of the X polarization component of the input optical signal when the Rescale parameter is not enabled. Figure 2 Optical chirp detection 785 OPTICAL CHIRP DETECTOR Notes: 786 OPTICAL PHASE DETECTOR Optical Phase Detector Converts the received optical signal phase into electrical signal amplitude. Ports Name and description Port type Signal type Input Input Optical Output Output Electrical Parameters Main Name and description Default value Units Value range Rescale True - True, False 0 a.u. [-1e+100, 1e+100] 1 a.u. [-1e+100, 1e+100] Determines whether the output signal will be scaled or not Min. amplitude Minimum electrical signal amplitude at the output port Max. amplitude Maximum electrical signal amplitude at the output port Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 3e5] Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined Center frequency User-defined center frequency for the internal filter 787 OPTICAL PHASE DETECTOR Name and description Default value Default unit Units Value range Sample rate 5*(Sample rate) Hz Hz, GHz, THz, nm [0,+INF[ Internal filter bandwidth Polarization Name and description Default value Units Value range Polarization X - X, Y Name and description Default value Units Value range Generate random seed True - True, False 0 - [0,4999] Determines if the phase from the polarization X or Y of the optical signal will be converted to amplitude Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channels with maximum power. Optical noise bins are converted to Gaussian noise inside the signal bandwidth. You must supply the polarization for the phase extraction. The signal phase is then normalized in the range between the parameters Min. and Max. amplitude if parameter Rescale is enabled. 788 OPTICAL PHASE DETECTOR Figure 1 Converted noise bins enabled The converter resamples the signal and converts the noise bins. They are added in time domain. Figure 2 shows the phase detection of the X polarization component of the input optical signal when the Rescale parameter is not enabled. Figure 2 Optical phase detection 789 OPTICAL PHASE DETECTOR Notes: 790 OPTICAL POWER DETECTOR Optical Power Detector Converts the received optical signal power into electrical signal amplitude. Ports Name and description Port type Signal type Input Input Optical Output Output Electrical Parameters Main Name and description Default value Units Value range Rescale True - True, False 0 a.u. [-1e+100, 1e+100] 1 a.u. [-1e+100, 1e+100] Determines whether the output signal will be scaled or not Min. amplitude Minimum electrical signal amplitude at the output port Max. amplitude Maximum electrical signal amplitude at the output port Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 3e5] Determines whether the internal filter will be centered at the maximum amplitude of the signal or if it will be user-defined Center frequency User-defined center frequency for the internal filter 791 OPTICAL POWER DETECTOR Name and description Default value Default unit Units Value range Sample rate 5*(Sample rate) Hz Hz, GHz, THz, nm [0,+INF[ Internal filter bandwidth Polarization Name and description Default value Units Value range Polarization X - X, Y Name and description Default value Units Value range Generate random seed True - True, False 0 - [0,4999] Determines if the power from the polarization X or Y of the optical signal will be converted to amplitude Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background The incoming optical signal and noise bins are filtered by an ideal rectangle filter to reduce the number of samples in the electrical signal. The new sample rate is defined by the parameter Sample rate. You can define the center frequency, or it can be calculated automatically by centering the filter at the optical channels with maximum power. Optical noise bins are converted to gaussian noise inside the signal bandwidth. You must supply the polarization for the power extraction. The signal power is then normalized in the range between the parameters Min. and Max. amplitude if parameter Rescale is enabled. 792 OPTICAL POWER DETECTOR Figure 1 Converted noise bins enabled The converter resamples the signal and converts the noise bins. They are added in time domain. Figure 2 shows the power detection of the X polarization component of the input optical signal when the Rescale parameter is not enabled. Figure 2 Optical signal detection 793 OPTICAL POWER DETECTOR 794 OPTICAL POWER DETECTOR Receivers Library Digital Signal Processing • Viterbi & Viterbi Feed Forward Phase Recovery • Dual Port Viterbi & Viterbi Feed Forward Phase Recovery • DSP for QPSK • DSP for 16-QAM • Universal DSP 795 OPTICAL POWER DETECTOR 796 VITERBI & VITERBI FEED FORWARD PHASE RECOVERY Viterbi & Viterbi Feed Forward Phase Recovery This component uses the Viterbi & Viterbi Feed Forward algorithm for phase recovery with M-PSK modulation formats Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Down sampler Name and description Default value Number of symbols Sequence length/2 Sequence length Bit rate/2 Bit rate 2 [1-Samples per bit] Cubic Linear, Cubic, Step Defines the number of symbols entering the component Symbol rate Units Value range Defines the symbol rate entering the component Samples per symbol Number of samples per symbol Interpolation Defines the type of interpolation that will be used Phase estimator Name and description Default value Units Value range Enabled ML filter 51 [1-9999] Size of the meximum likelihood filter 797 VITERBI & VITERBI FEED FORWARD PHASE RECOVERY Name and description Default value Units Value range M 4 [1-512] 0 [-1:1] M-th power Rotational factor Multiplying the output by ej*pi*Rotationfactor Technical background Figure 1 demonstrates the algorithm of V&V feed forward phase recovery [1]. For the M-PSK modulation format, the data dependency of the sampled sequence can be removed by raising it to the M-th power. The maximum likelihood filter averages the input data based on the tap size of the filter. The PU(.) function is a phase unwrapper which allows the estimated phase to vary from -infinity to +infinity rather than -pi/M to pi/M. (1) Finally the original data is multiplied by the e-jx(Estimated phase). Figure 1 V&V feed forward phase recovery algorithm References [1] Hugo B. Ferreira, Valery N. Rozental, Darli A. A. Mello, "Analysis of Phase Recovery Algorithms for DP-QPSK Optical Receivers", XXIX Simposio Brasileiro de Telecommunicac, ˜OES SBrT'11, 02-05 de Outubro de 2011, Curitiba, PR. 798 DUAL PORT VITERBI & VITERBI FEED FORWARD PHASE RECOVERY Dual Port Viterbi & Viterbi Feed Forward Phase Recovery This component uses the Viterbi & Viterbi Feed Forward algorithm for phase recovery with M-PSK modulation formats. It differs from the single port V&V FF Phase Recovery component as it has the capability to be used with coherent receivers for the in-phase and quadrature parts of the received signal. Ports Name and description Port type Signal type Input 1 Input Electrical Input 2 Input Electrical Output 1 Output Electrical Output 2 Output Electrical Parameters Down sampler Name and description Default value Number of symbols Sequence length/2 Sequence length Bit rate/2 Bit rate 2 [1-Samples per bit] Cubic Linear, Cubic, Step Defines the number of symbols entering the component Symbol rate Units Value range Defines the symbol rate entering the component Samples per symbol Number of samples per symbol Interpolation Defines the type of interpolation that will be used 799 DUAL PORT VITERBI & VITERBI FEED FORWARD PHASE RECOVERY Phase estimator Name and description Default value Units Value range Enabled ML filter 51 [1-9999] 4 [1-512] 0 [-1:1] Size of the meximum likelihood filter M M-th power Rotational factor Multiplying the output by e j*pi*Rotationfactor Technical background Figure 1 demonstrates the algorithm of V&V feed forward phase recovery [1]. For the M-PSK modulation format, the data dependency of the sampled sequence can be removed by raising it to the M-th power. The maximum likelihood filter averages the input data based on the tap size of the filter. The PU(.) function is a phase unwrapper which allows the estimated phase to vary from -infinity to +infinity rather than -pi/M to pi/M. (1) Finally the original data is multiplied by the e-jx(Estimated phase). Figure 1 V&V feed forward phase recovery algorithm References [1] Hugo B. Ferreira, Valery N. Rozental, Darli A. A. Mello, "Analysis of Phase Recovery Algorithms for DP-QPSK Optical Receivers", XXIX Simposio Brasileiro de Telecommunicac, ˜OES SBrT'11, 02-05 de Outubro de 2011, Curitiba, PR. 800 DSP FOR QPSK DSP for QPSK The DSP for QPSK component performs several important functions to aid in recovering the incoming transmission channel after coherent detection. It can be used with coherent systems designs that utilize QPSK modulation with single polarization (X channel) or dual polarization (X and Y channel) multiplexing. Ports Name and description Port type Signal type Input Input I-X Electrical Input Input Q-X Electrical Input Input I-Y Electrical Input Input Q-Y Electrical Output Output I-X Electrical Output Output Q-X Electrical Output Output I-Y Electrical Output Output Q-Y Electrical 801 DSP FOR QPSK Parameters Initialize Name and description Default value Units Value range Polarization type Dual - Single, Dual Enable DC blocking True - True, False Enable Normalization True - True, False Enable Low Pass Filter True - True, False Enable Resampling True - True, False Enable QI Compensation True - True, False Enable Dispersion Compensation True - True, False Enable Nonlinear Compensation True - True, False Enable Timing Recovery True - True, False Enable Adaptive Equalizer True - True, False Enable Frequency Offset Estimation True - True, False Enable Carrier Phase Estimation True - True, False Name and description Default value Units Type of filter Bessel Cutoff frequency 0.75 * Bit rate / 8 Hz - 0 dB [1:999] 100 dB [-9999:9999] FilterRC, Raised Cosine, 3 dB cutoff frequency of the filter Insertion loss Value range Rectangular, Gaussian, Butterworth, Bessel, Chebyshev, RC, Raised Cosine, Root Raised Cosine, Cosine Roll-off, Squared Cosine Rolloff, Inverse Gaussian Insertion loss of the filter Depth Maximum attenuation value for the filter 802 DSP FOR QPSK Name and description Default value Units Value range Order 4 - [-9999:9999] 1 - [0,1] Name and description Default value Units Number of symbols Sequence length/4 Order of the filter Roll off factor Re-sampling Automatically set to Sequence length/2 and Sequence length/4 for SP-QPSK and DP-QPSK, respectively Symbol rate Value range Bit rate/4 [0:1] Cubic Linear, Cubic, Step Automatically set to Bit rate/2 and Bit rate/4 for SP-QPSK and DPQPSK, respectively Interpolation type This parameter is reserved for future use Dispersion compensation Name and description Default value Units Value range DC calculation domain Frequency domain - Time domain, frequency 1550 nm Hz, THz, nm 1550 nm Hz, THz, nm 16.75 ps/(nm*km) 0.075 ps/(nm2*km) 50 km Select if dispersion compensation algorithm will be applied in the frequency domain or time domain Channel wavelength Central frequency of optical signal DC reference wavelength Reference wavelength for calculating fiber impairments. This value should be the same as the optical fiber reference wavelength Dispersion coefficient This value should be the same as the optical fiber dispersion coefficient Residual dispersion slope This value should be the same as the optical fiber dispersion slope Propagation length This value should be the same as the optical fiber length 803 DSP FOR QPSK Name and description Default value DC number of taps 181 Units Value range Applies to the time domain DC algorithm. The typical number of taps is between 100-200. Higher tap numbers are recommended for longer propagation lengths Fiber Alpha 0.2 Fiber N2 26e-021 Fiber Aeff 80e-012 Fiber length per span 80 Nonlinear ratio 0.48 Nonlinear step size 20 Nonlinear kk 0.76 Launch power -3 dBm Name and description Default value Units Value range Samples per block 2048 - Time domain, Frequency domain Average window size 512 nm Hz, THz, nm TR interpolation method Cubic - Cubic, FFT dB km km Timing recovery 804 DSP FOR QPSK Adaptive equalizer Name and description Default value Units Value range AE number of taps 9 - 0 - 0 - 2 - 15 - 1e-006 - 1 - Name and description Default value Units Value range FOE type Same - Same, Different 4 - - Name and description Default value Units Value range CPE symbols per block 40 - - Increase the number of taps when stronger distortion is present Delay X Shift by number of samples. Recommended setting is 0. Delay Y Shift by number of samples. Recommended setting is 0. Dispersion order Recommended setting is 2 AE number of iterations Use to update the accuracy of the taps. Step CMA () See Eq 12. It is recommended to vary this step size to determine the optimum operating point (for example from 0.5e-006 to 10e-006) Initial taps index Recommended setting is 1 Frequency offset estimation When set to “Same”, the average value of the X and Y polarization channels is used. When set to “Different”, a different frequency offset estimation is used for the X and Y polarization channels Power order of symbols Use the 4th order for QPSK and 16-QAM and 8th order for 8PSK and 64-QAM Carrier phase estimation It is recommended to vary the CPE symbols per block to determine the optimum operating point in terms of SER/BER (for example from 8 to 50) 805 DSP FOR QPSK Name and description Default value Units Value range Use interpolation in CPE False - True, False Enable this setting when the phase is changing rapidly 806 DSP FOR QPSK Results Name and description Units QI Compensation: X Cross-correlation - QI Compensation: Y Cross-correlation - Timing Recovery: X Tau Sum Before - Timing Recovery: Y Tau Sum Before - Timing Recovery: X Tau Mean Before - Timing Recovery: Y Tau Mean Before - Timing Recovery: X Tau Sum After - Timing Recovery: Y Tau Sum After - Timing Recovery: X Tau Mean After - Timing Recovery: Y Tau Mean After - Adaptive Equalizer: RMS Error After CMA - Frequency Offset: X Frequency Correction (MHz) - Frequency Offset: Y Frequency Correction (MHz) - Frequency Offset: XY Frequency Correction (MHz) - Graphs Name and description X Title Y Title CPE after unwrap: Imag X CPE after unwrap: Imag Y CPE after unwrap: Real X CPE after unwrap: Real Y Constellation after AE - X Constellation after AE - Y Constellation after CPE- X Constellation after CPE - Y Constellation after DC blocking - X Constellation after DC blocking - Y Constellation after Dispersion and Nonlinear compensation - X 807 DSP FOR QPSK Name and description Constellation after Dispersion and Nonlinear compensation - Y Constellation after Filter - X Constellation after Filter - Y Constellation after Frequency offset - X Constellation after Frequency offset - Y Constellation after Normalizing- X Constellation after Normalizing- Y Constellation after QI compensation - X Constellation after QI compensation- Y Constellation after Resampling - X Constellation after Resampling - Y Constellation after Timing recovery - X Constellation after Timing recovery - Y Constellation before DSP - X Constellation before DSP - Y Dispersion compensation: Imag taps Dispersion compensation: Real taps hxx Imag after CMA hxx Imag after RD hxx Real after CMA hxx Real after RD hxy Imag after CMA hxy Imag after RD hxy Real after CMA hxy Real after RD hyx Imag after CMA hyx Imag after RD hyx Real After CMA hyx Real After RD hyy Imag After CMA 808 X Title Y Title DSP FOR QPSK Name and description X Title Y Title hyy Imag After RD hyy Real After CMA hyy Real After RD Input timing phase: X Input timing phase: Y Output timing phase: X Output timing phase: Y Technical background The DSP for QPSK component performs several important functions to aid in recovering the incoming transmission channel(s) after coherent detection. It can be used with coherent system designs that utilize QPSK modulation with single polarization (X channel) or dual polarization (X and Y channel) multiplexing. The DSP for QPSK component includes 12 functions and algorithms starting with a preprocessing stage (3 functions) followed by the signal recovery stage (8 functions and algorithms): Preprocessing stage • Add Noise to Signal (Samples/Symbol = (2 or 4) x Samples per bit) • DC Blocking (Samples/Symbol = (2 or 4) x Samples per bit) • Normalization (Samples/Symbol = (2 or 4) x Samples per bit) Main algorithms stage • Bessel Filter (Samples/Symbol = (2 or 4) x Samples per bit) • Resampling (Samples/Symbol = 2) • Quadrature Imbalance (QI) Compensation (Samples/Symbol = 2) • Chromatic Dispersion (CD) Compensation (Samples/Symbol = 2) • Nonlinear (NL) compensation (Samples/Symbol = 2) • Timing Recovery (Samples/Symbol = 2) • Adaptive Equalizer - AE (Samples/Symbol = 2) • Down-sampling (Samples/Symbol = 1) • Frequency Offset Estimation - FOE (Samples/Symbol = 1) • Carrier Phase Estimation - CPE (Samples/Symbol = 1) 809 DSP FOR QPSK Figure 1 QPSK High Level Algorithm Design Add noise to signal Any noise source (noise bin) that falls within the bandwidth of the transmission channel will be converted into a signal and added to the optical sampled signal DC Blocking DC Blocking is applied to offset any imperfectly biased voltages in the modulators. Normalization The received signal is normalized to the QPSK grid [-1 1] Low Pass Filter The low pass filter is used to remove of the out of band noise (the default filter is a Bessel filter, with an optimum bandwidth of 0.75*Symbol rate or 0.75*bit rate/4). Other filter types can be selected; including Rectangular, Gaussian, Butterworth, Bessel, Chebyshev, RC, Raised Cosine, Root Raised Cosine, Cosine Roll-off, Squared Cosine Roll-off, and Inverse Gaussian Resampling The input sampled signal is re-sampled at a rate of 2 samples/symbol. Interpolation is used to adapt the sampled signal waveform to the new sampling rate. Users can select Linear, Cubic or Step. Cubic interpolation is the recommended interpolation method.The 1st (Value = a) and N/2+1 (Value = b) sampled signals are used for resampling (where N = Samples per symbol). After the AE stage the signal stream is resampled further to 1 sample/symbol. The N/2 + 1 sampled signal is used (Value = c) 810 DSP FOR QPSK Note: Between algorithm stages, the signals are up-sampled to their original rate (for the case of SP-QPSK, 2 x Samples per bit). For 2 samples/symbol, the first half of the sampled signals are set to a and the second half to b. For 1 sample/symbol all sampled signals are set to c. QI compensation [1] QI compensation is used to mitigate amplitude and phase imbalances within the inphase (I) and quadrature (Q) signals. Imbalances can result from at several points along the transmission path and include inappropriate bias voltage settings for the modulators, photodiode responsivity mismatches, misalignment of the polarization controller, and imperfections in the optical 90-degree hybrid. The Gram-Schmidt orthogonalization procedure (GSOP) is used to correct for nonorthogonalization. Given two non-orthogonal components of the received signal, denoted by rI (t) and rQ (t), the GSOP results in a new pair of orthonormal signals, denoted by Io(t) and Qo(t), as follows: rI t I t = ---------PI rI t Q t = r Q t – -----------------PI (1) Q t Q t = ------------PQ where = E {rI (t), rQ (t)} is the correlation coefficient; PI = E {r2I (t)}; PQ = E {Q’2(t)} and E {.} is the ensemble average operator Chromatic Dispersion (CD) Compensation Chromatic dispersion is a static, polarization-independent, phenomenon. Digital filtering can be used to compensate for chromatic dispersion resulting from propagation over fiber (non-linear impairments, such self-phase modulation (SPM) must be compensated by separate types of algorithms). The dispersion compensating filter can be implemented in either the frequency domain or time domain [2]. Frequency domain implementation The transfer function for dispersion in the frequency domain can be characterized as follows: 2 D z 2 G z w = exp – j --------------------- w 4c (2) where z is the transmission distance, w is the angular frequency, j is the imaginary unit, is the channel wavelength, c is the speed of light, and D = Do + S x o is 811 DSP FOR QPSK the dispersion coefficient of the fiber for wavelength , S is the dispersion slope, and o is the reference wavelength 812 DSP FOR QPSK Time domain implementation For the time domain a finite impulse response filter (FIR) with N taps is used. The tap weights are given by: ak = 2 2 cT 2 j c T - exp – j --------------------k --------------------- 2 2 D z D z (3) – N ---- k N ---2 2 where T = /wn, wn is the Nyquist frequency, and [x] is the integer part of x rounded towards minus infinity. Nonlinear compensation Nonlinear compensation is performed using a digital back propagation (BP) method [7]. In the receiver of a coherent optical communications system, the received photocurrents are linearly mapped to the optical field, so that both the optical amplitude and phase become available to the receiver's digital processors. The received signal can be digitally propagated through an inverse fiber model to compensate for CD and fiber nonlinearity. Back propagation requires the inverse nonlinear Schrödinger equation (NLSE) to be solved for the parameters of the optical link. For a single polarization and with spatial domain negated, the NLSE is given by: E = D + N E –z (4) where E is the complex field complex field of the received signal, D is the differential operator accounting for linear effects (CD and attenuation) and N is the nonlinear operator, which are given by:: 2 j D = --- 2 – --2 2 2 t (5) N = j E 2 Where is the attenuation factor, 2 is the group velocity dispersion parameter and is the nonlinearity parameter. Negated spatial domain means the optical link is modeled on a first-in-last-out principle. The first fiber span is the last modeled span and the beginning of each fiber span is the end of each modeled span. Figure 2 shows the power in a two-span optical system and the corresponding inverse link modeled span. The span refers to fiber span in the optical link 813 DSP FOR QPSK Figure 2 Power vs. propagation distance of a 2-span optical link (left) and the corresponding back propagation link (right) when using inverse NLSE To calculate numerical solution to Eq. (4), the split-step Fourier method (SSFM) is used [8, 9]. The fiber is treated as a series of linear sections (where only D is considered) and dispersion-less nonlinear sections (where only N is considered). Larger number of steps lead to more accurate result but increase the computation time. The linear section in BP is the same as that used for CD compensation. The nonlinear section of BP is identical to the nonlinear section used in a single-step nonlinearity compensator. The phase shifts for each sample are: NL t = kL eff E 2 (6) Where k is a compensation factor which is optimized and Leff is the effective length of each step. If each BP step compensates for one or more fiber spans, Leff is 1 – exp – L span L eff = s ------------------------------------------- (7) where Lspan is the length of each span and s is the number of fiber spans compensated for by each BP step. If each BP step only compensates for a fraction of a span, then Leff is 1 – exp – L step L eff = ------------------------------------------ (8) Timing Recovery Timing recovery is used to synchronize the symbols. Two quantities must be determined: the sampling frequency and sampling phase. For the sampling frequency the samples should be taken at the correct rate. For example oscillator drift will introduce deviations from the stated symbol rate. For the sampling phase the samples sample should be taken at the correct time within respect to the symbol period. For 814 DSP FOR QPSK example filters in the system will introduce a time delay. The timing recovery algorithm adaptively determines the correct time to sample the symbol. TA digital square and filter algorithm is used [3] - see Figure 3. Figure 3 Digital square and filter algorithm The received signal can be written as: rt = am gT t –m T – t T + n t (9) m = – where ak are the complex-valued transmitted symbols, gT(t) is the transmission signal pulse, T is the symbol duration, n(t) is the channel noise (which is assumed to be white and Gaussian), and is an unknown slowly varying time delay. Since varies very slowly, we can process the received signal block by block assuming to be constant in each block. After a receiving filter [impulse response gR(t)] the signal is sampled at a rate of 4/T, resulting in the following samples: r̃ t = r t g R t (10) KT r˜k = r̃ ------4 The sequence: xk = m = – KT KT a m g ------- – m T – T + n̂ ------- 4 4 2 (11) g t = gT T gR T represents the samples of the filtered and squared input signal and contains a spectral component at 1/T. This spectral component is determined for every section of the length LT (i.e. from 4L samples) by computing the complex Fourier coefficient at the symbol rate: 4 n + 1 LN – 1 Xn = x k e – j2k 4 (12) k – 4nL 815 DSP FOR QPSK The normalized phase: 1 ̂ = – ---------- arg X n 2 (13) is an unbiased estimate for Adaptive Equalizer (AE) The adaptive equalizer is used to compensate for residual chromatic dispersion, polarization mode dispersion (PMD) and to reduce inter-symbol interference. For dual-polarization system, butterfly structure is used for polarization demultiplex. The constant modulus algorithm (CMA) algorithm is used [4]. The cost function of the CMA is of the form J k = E y k 2 – Rp 2 (14) Where E[...] indicates the statistical expectation and y(k) the equalizer output. Rp is the constant depending only on the input data symbol, a(k), with dispersion order, p, set to 2 by default. It is defined as E a k 2p R p = --------------------------E ak p (15) The equalizer output y(k) is obtained from y k = WH X k W = w 0 k ,w 1 k ,... ,w N – 1 k T X k = x 0 k ,x 1 k – 1 ,... ,x N – 1 k – N + 1 (16) T where W is the equalizer tap weights vector, and X(k) is the equalizer input data vector. N is the length of the equalizer tap weights, T stands for the transpose of a vector and H is the complex conjugate transpose. The tap weights vector is adapted using the stochastic gradient algorithm W k + 1 = W k + X k e k 2 e k = y k Rp – y k (17) where is the step size parameter and e(k) is the error signal. The CMA algorithm minimizes the error power between the equalizer output and a constant. For an PSK signal, to obtain perfect equalization the error e(k)=0, as the symbols all lie on a ring. For dual polarization signals, there are four choices for the initial tap weights (initial value index 1 is set as the default): 816 DSP FOR QPSK Initial value index 1: hxx = [0, 0,…,0, 1, 0,…,0, 0] hxy = [0, 0,…,0, 0, 0,…,0, 0] hyx = [0, 0,…,0, 0, 0,…,0, 0] hyy = [0, 0,…,0, 1, 0,…,0, 0] Initial value index 2: hxx = [0, 0,…,0, 0, 0,…,0, 0] hxy = [0, 0,…,0, 1, 0,…,0, 0] hyx = [0, 0,…,0, 1, 0,…,0, 0] hyy = [0, 0,…,0, 0, 0,…,0, 0] Initial value index 3: hxx = [0, 0,…,0, 1, 0,…,0, 0] hxy = [0, 0,…,0, 0, 0,…,0, 0] hyx = [0, 0,…,0, 1, 0,…,0, 0] hyy = [0, 0,…,0, 0, 0,…,0, 0] Initial value index 4: hxx = [0, 0,…,0, 0, 0,…,0, 0] hxy = [0, 0,…,0, 1, 0,…,0, 0] hyx = [0, 0,…,0, 0, 0,…,0, 0] hyy = [0, 0,…,0, 1, 0,…,0, 0] It should be noted that large data sample is required to get a good result. Therefore we use multiple iterations to adapt the tap weights. If the bit length is short, then the parameter “Iterations” should be increased. Frequency Offset Estimation (FOE) The mixing with the local oscillator introduces a frequency and phase offset, leading to a rotating constellation diagram. The received signals are given by: Sk = C k e j 2fkT + k + nk (18) where {Ck} are data symbols, f is the carrier frequency offset we want to estimate, k is the carrier phase (which varies much slower compared to phase varying due to the frequency offset therefore at this step we can assume carrier phase is a constant value), T is the symbol period, and {n(k)} are zero-mean Gaussian random variables. 817 DSP FOR QPSK The 4th power is used to remove the modulation information for QPSK signals. We can then deduce the frequency offset estimate based on the maximization of the periodogram of the S4(k) as shown below [5]: 1 f est = --- arg max Z f 4 1 Z f = ---N N–1 4 S k e – j 2fkT (19) k=0 Similarly, the 8th and 16th powers are used for 8PSK and 16PSK signal formats; respectively Carrier Phase Estimation (CPE) The 4th power algorithm [6] is used to recover and subsequently remove the remaining phase mismatch between the local oscillator and the signal. Since the frequency offset is compensated, then the signals are given by: S k = Ck e j b + nk (20) Then 4th power is used to remove the modulation information. Since Ck(4th power) is a constant value, and phase noise varies slowly, we can deduce the phase noise k by block averaging est N 1--4 = arg S k 4 k = 1 (21) Where N is the block length which should be optimized based on the laser line-width and symbol rate. Unwrapping is used after calculating the phase noise to remove 4-fold ambiguity in the QPSK constellation. “Linear interpolation” could be further chosen to improve the performance especially when the phase noise varies rapidly. References [1] I. Fatadin, S. J. Savory, and D. Ives, “Compensation of Quadrature Imbalance in an Optical QPSK Coherent Receiver”, IEEE Photonics Technology Letters, Vol. 20, No. 20, pp. 17331735, Oct 15, 2008. 818 DSP FOR QPSK [2] S. J. Savory, “Digital filters for coherent optical receivers”, Optics Express, Vol. 16, No. 2, Jan 21 2008. [3] M. Oerder and H. Meyr, “Digital Filter and Square Timing Recovery", IEEE transactions on communications, Vol. 36, No. 5, pp. 605-612, May 1988. [4] D. N. Godard, “Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems”, IEEE Transactions on Communications, Vol. COM-28, No. 11, pp. 1867-1875, Nov 1980. [5] M. Morelli and U. Mengali, “Feed forward Frequency Estimation for PSK: a Tutorial Review,” IEEE Transactions on Communications, Vol. 9, No. 2, pp. 103-116, 1988. [6] A. J. Viterbi, and A. M. Viterbi, “Nonlinear Estimation of PSK-Modulated Carrier Phase with Application to Burst Digital Transmission”, IEEE Transactions on Communications, Vol. IT-29, No. 4, pp. 543-551, Nov 1983. [7] Liang B. Du and Arthur J. Lowery , “Improved single channel back propagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems”, Optics Express, vol. 18, no. 16, pp. 17075-17088, 2010. [8] K. Kikuchi, M. Fukase, and S.-Y. Kim, “Electronic post-compensation for nonlinear phase noise in a 1000-km20-Gbit/s optical QPSK transmission system using the homodyne receiver with digital signal processing,” in Optical Fiber Communication Conference (Optical Society of America, Anaheim, California, 2007), p. OTuA2. [9] A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett. 19(19), 1556-1558 (2007). 819 DSP FOR QPSK 820 DSP FOR 16-QAM DSP for 16-QAM The DSP for 16-QAM component performs digital domain impairment compensation to aid in recovering the incoming transmission signal after coherent detection. It should be used with coherent systems designs that utilize 16-QAM modulation with single polarization (X channel) or dual polarization (X and Y channel) multiplexing. Ports Name and description Port type Signal type Input Input I-X Electrical Input Input Q-X Electrical Input Input I-Y Electrical Input Input Q-Y Electrical Output Output I-X Electrical Output Output Q-X Electrical Output Output I-Y Electrical Output Output Q-Y Electrical 821 DSP FOR 16-QAM Parameters Initialize Name and description Default value Units Value range Polarization type Dual - Single, Dual Enable DC blocking True - True, False Enable Normalization True - True, False Enable Low Pass Filter True - True, False Enable Resampling True - True, False Enable QI Compensation True - True, False Enable Dispersion Compensation True - True, False Enable Nonlinear Compensation False - True, False Enable Timing Recovery True - True, False Enable Adaptive Equalizer True - True, False Enable Frequency Offset Estimation True - True, False Enable Carrier Phase Estimation True - True, False Filter Name and description Default value Units Value range Cutoff frequency 0.75 * Bit rate / 8 Hz - 0 dB [1:999] 100 dB [-9999:9999] 4 - [-9999:9999] 1 - [0,1] 3 dB cutoff frequency of the filter Insertion loss Insertion loss of the filter Depth Maximum attenuation value for the filter Order Order of the filter Roll off factor Order of the filter 822 DSP FOR 16-QAM Re-sampling Name and description Default value Number of symbols Sequence length/8 Automatically set to Sequence length/4 and Sequence length/8 for SP-16-QAM and DP-16-QAM, respectively Symbol rate Units Value range Bit rate/8 [0:1] Cubic Linear, Cubic, Step Automatically set to Bit rate/4 and Bit rate/8 for SP-16-QAM and DP16-QAM, respectively Interpolation type This parameter is reserved for future use Dispersion compensation Name and description Default value Units Value range Frequency domain - Time domain, frequency 1550 nm Hz, THz, nm 1550 nm Hz, THz, nm 16.75 ps/(nm*km) 0.075 ps/(nm2*km) 50 km Dispersion compensation parameters DC calculation domain Select if dispersion compensation algorithm will be applied in the frequency domain or time domain Channel wavelength Central frequency of optical signal DC reference wavelength Reference wavelength for calculating fiber impairments. This value should be the same as the optical fiber reference wavelength Dispersion coefficient This value should be the same as the optical fiber dispersion coefficient Residual dispersion slope This value should be the same as the optical fiber dispersion slope Propagation length This value should be the same as the optical fiber length DC number of taps 181 Applies to the time domain DC algorithm. The typical number of taps is between 100-200. Higher tap numbers are recommended for longer propagation lengths Nonlinear compensation parameters Fiber Alpha 0.2 dB 823 DSP FOR 16-QAM Name and description Default value Units Value range Fiber N2 26e-021 Fiber Aeff 80e-012 Fiber length per span 80 Nonlinear ratio 0.48 Nonlinear step size 20 Nonlinear kk 0.76 Launch power -3 dBm Name and description Default value Units Value range Samples per block 2048 - - Average window size 512 - - TR interpolation method Cubic - Cubic, FFT Name and description Default value Units Value range AE number of taps 9 - 0 - 0 - 2 - 15 - 1e-006 - km km Timing recovery Adaptive equalizer Increase the number of taps when stronger distortion is present Delay Y Shift by number of samples. Recommended setting is 0 Delay Y Shift by number of samples. Recommended setting is 0 Dispersion order Recommended setting is 2 AE number of iterations Used to update the accuracy of the taps Step CMA () See Eq 12. It is recommended to vary this step size to determine the optimum operating point (for example from 0.5e-006 to 10e-006) 824 DSP FOR 16-QAM Name and description Default value Units Value range Step RD () 6e-006 - 1 - [1-4] Name and description Default value Units Value range FOE type Same - Same, Different 4 - - Name and description Default value Units Value range Number of test phases (B) 32 - - 40 - - False - True, False See Eq 14. It is recommended to vary this step size to determine the optimum operating point (for example from 0.5e-006 to 10e-006) Initial taps index Recommended setting is 1 Frequency offset estimation When set to “Same”, the average value of the X and Y polarization channels is used. When set to “Different”, a different frequency offset estimation is used for the X and Y polarization channels Power order of symbols Use the 4th order for QPSK and 16-QAM and 8th order for 8PSK and 64-QAM Carrier phase estimation See Eq 18. CPE symbols per block It is recommended to vary the CPE symbols per block to determine the optimum operating point (for example from 8 to 50) Use interpolation in CPE Enable this setting when the phase is changing rapidly 825 DSP FOR 16-QAM Results Name and description Units QI Compensation: X Cross-correlation - QI Compensation: Y Cross-correlation - Timing Recovery: X Tau Sum Before - Timing Recovery: Y Tau Sum Before - Timing Recovery: X Tau Mean Before - Timing Recovery: Y Tau Mean Before - Timing Recovery: X Tau Sum After - Timing Recovery: Y Tau Sum After - Timing Recovery: X Tau Mean After - Timing Recovery: Y Tau Mean After - Adaptive Equalizer: RMS Error After CMA - Adaptive Equalizer: RMS Error After RD - Frequency Offset: X Frequency Correction (MHz) - Frequency Offset: Y Frequency Correction (MHz) - Frequency Offset: XY Frequency Correction (MHz) - Graphs Name and description CPE after unwrap: Imag X CPE after unwrap: Imag Y CPE after unwrap: Real X CPE after unwrap: Real Y Constellation after AE - X Constellation after AE - Y Constellation after CPE- X Constellation after CPE - Y Constellation after DC blocking - X Constellation after DC blocking - Y Constellation after Dispersion and Nonlinear compensation - X 826 X Title Y Title DSP FOR 16-QAM Name and description X Title Y Title Constellation after Dispersion and Nonlinear compensation - Y Constellation after Filter - X Constellation after Filter - Y Constellation after Frequency offset - X Constellation after Frequency offset - Y Constellation after Normalizing- X Constellation after Normalizing- Y Constellation after QI compensation - X Constellation after QI compensation- Y Constellation after Resampling - X Constellation after Resampling - Y Constellation after Timing recovery - X Constellation after Timing recovery - Y Constellation before DSP - X Constellation before DSP - Y Dispersion compensation: Imag taps Dispersion compensation: Real taps hxx Imag after CMA hxx Imag after RD hxx Real after CMA hxx Real after RD hxy Imag after CMA hxy Imag after RD hxy Real after CMA hxy Real after RD hyx Imag after CMA hyx Imag after RD hyx Real After CMA hyx Real After RD hyy Imag After CMA 827 DSP FOR 16-QAM Name and description X Title Y Title hyy Imag After RD hyy Real After CMA hyy Real After RD Input timing phase: X Input timing phase: Y Output timing phase: X Output timing phase: Y Technical background The DSP for 16-QAM component performs several important functions to aid in recovering the incoming transmission channel(s) after coherent detection. It can be used with coherent system designs that utilize 16-QAM modulation with single polarization (X channel) or dual polarization (X and Y channel) multiplexing. The DSP for 16-QAM component includes 12 functions and algorithms starting with a preprocessing stage (3 functions) followed by the signal recovery stage (8 functions and algorithms) - see Figure 1: Preprocessing stage • Add Noise to Signal (Samples/Symbol = (4 or 8) x Samples per bit) • DC Blocking (Samples/Symbol = (4 or 8) x Samples per bit) • Normalization (Samples/Symbol = (4 or 8) x Samples per bit) Main algorithms stage 828 • Bessel Filter (Samples/Symbol = (4 or 8) x Samples per bit) • Resampling (Samples/Symbol = 2) • Quadrature Imbalance (QI) Compensation (Samples/Symbol = 2) • Chromatic Dispersion (CD) Compensation (Samples/Symbol = 2) • Nonlinear (NL) Compensation (Samples/Symbol = 2) • Timing Recovery (Samples/Symbol = 2) • Adaptive Equalizer - AE (Samples/Symbol = 2) • Down-sampling (Samples/Symbol = 1) • Frequency Offset Estimation - FOE (Samples/Symbol = 1) • Carrier Phase Estimation - CPE (Samples/Symbol = 1) DSP FOR 16-QAM Figure 1 DSP 16-QAM High Level Algorithm Design Add noise to signal Any noise source (noise bin) that falls within the bandwidth of the transmission channel will be converted into a signal and added to the optical sampled signal. DC Blocking DC Blocking is applied to offset any imperfectly biased voltages in the modulators. Normalization The received signal is normalized to the 16-QAM grid [-3 -1 1 3] Bessel Filter A 4th order (as a default order) Bessel filter is used to remove of the out of noise (the optimum bandwidth of the Bessel filter is 0.75*symbol rate or 0.75*bit rate/8). Resampling The input sampled signal is re-sampled at a rate of 2 samples/symbol. Interpolation is used to adapt the sampled signal waveform to the new sampling rate. Users can select Linear, Cubic or Step. Cubic interpolation is the recommended interpolation method.The 1st (Value = a) and N/2+1 (Value = b) sampled signals are used for resampling (where N = Samples per symbol). After the AE stage the signal stream is resampled further to 1 sample/symbol. The N/2 + 1 sampled signal is used (Value = c) Note: Between algorithm stages, the signals are up-sampled to their original rate (for the case of 16-QAM, 8 x Samples per bit). For 2 samples/symbol, the first half of the sampled signals are set to a and the second half to b. For 1 sample/symbol all sampled signals are set to c. 829 DSP FOR 16-QAM QI compensation [1] QI compensation is used to mitigate amplitude and phase imbalances within the inphase (I) and quadrature (Q) signals. Imbalances can result from at several points along the transmission path and include inappropriate bias voltage settings for the modulators, photodiode responsivity mismatches, misalignment of the polarization controller, and imperfections in the optical 90-degree hybrid. The Gram-Schmidt orthogonalization procedure (GSOP) is used to correct for nonorthogonalization. Given two non-orthogonal components of the received signal, denoted by rI (t) and rQ (t), the GSOP results in a new pair of orthonormal signals, denoted by Io(t) and Qo(t), as follows: rI t I t = ---------PI rI t Q t = r Q t – -----------------PI (1) Q t Q t = ------------PQ where = E {rI (t), rQ (t)} is the correlation coefficient; PI = E {r2I (t)}; PQ = E {Q’2(t)} and E {.} is the ensemble average operator Chromatic Dispersion (CD) Compensation Chromatic dispersion is a static, polarization-independent, phenomenon. Digital filtering can be used to compensate for chromatic dispersion resulting from propagation over fiber (non-linear impairments, such self-phase modulation (SPM) must be compensated by separate types of algorithms). The dispersion compensating filter can be implemented in either the frequency domain or time domain [2]. Frequency domain implementation The transfer function for dispersion in the frequency domain can be characterized as follows: 2 D z 2 G z w = exp – j --------------------- w 4c (2) where z is the transmission distance, w is the angular frequency, j is the imaginary unit, is the channel wavelength, c is the speed of light, and D = Do + S x o is the dispersion coefficient of the fiber for wavelength , S is the dispersion slope, and o is the reference wavelength 830 DSP FOR 16-QAM Time domain implementation For the time domain a finite impulse response filter (FIR) with N taps is used. The tap weights are given by: ak = 2 2 cT 2 j c T - exp – j --------------------k --------------------- 2 2 D z D z (3) – N ---- k N ---2 2 where T = /wn, wn is the Nyquist frequency, and [x] is the integer part of x rounded towards minus infinity. Nonlinear compensation Nonlinear compensation is performed using a digital back propagation (BP) method [9]. In the receiver of a coherent optical communications system, the received photocurrents are linearly mapped to the optical field, so that both the optical amplitude and phase become available to the receiver's digital processors. The received signal can be digitally propagated through an inverse fiber model to compensate for CD and fiber nonlinearity. Back propagation requires the inverse nonlinear Schrödinger equation (NLSE) to be solved for the parameters of the optical link. For a single polarization and with spatial domain negated, the NLSE is given by: E = D + N E –z (4) where E is the complex field complex field of the received signal, D is the differential operator accounting for linear effects (CD and attenuation) and N is the nonlinear operator, which are given by:: 2 j D = --- 2 – --2 2 2 t (5) N = j E 2 Where is the attenuation factor, 2 is the group velocity dispersion parameter and is the nonlinearity parameter. Negated spatial domain means the optical link is modeled on a first-in-last-out principle. The first fiber span is the last modeled span and the beginning of each fiber span is the end of each modeled span. Figure 2 shows the power in a two-span optical system and the corresponding inverse link modeled span. The span refers to fiber span in the optical link 831 DSP FOR 16-QAM Figure 2 Power vs. propagation distance of a 2-span optical link (left) and the corresponding back propagation link (right) when using inverse NLSE To calculate numerical solution to Eq. (4), the split-step Fourier method (SSFM) is used [10, 11]. The fiber is treated as a series of linear sections (where only D is considered) and dispersion-less nonlinear sections (where only N is considered). Larger number of steps lead to more accurate result but increase the computation time. The linear section in BP is the same as that used for CD compensation. The nonlinear section of BP is identical to the nonlinear section used in a single-step nonlinearity compensator. The phase shifts for each sample are: NL t = kL eff E 2 (6) Where k is a compensation factor which is optimized and Leff is the effective length of each step. If each BP step compensates for one or more fiber spans, Leff is 1 – exp – L span L eff = s ------------------------------------------- (7) where Lspan is the length of each span and s is the number of fiber spans compensated for by each BP step. If each BP step only compensates for a fraction of a span, then Leff is 1 – exp – L step L eff = ------------------------------------------ (8) Timing Recovery Timing recovery is used to synchronize the symbols. Two quantities must be determined: the sampling frequency and sampling phase. For the sampling frequency the samples should be taken at the correct rate. For example oscillator drift will introduce deviations from the stated symbol rate. For the sampling phase the samples sample should be taken at the correct time within respect to the symbol period. For 832 DSP FOR 16-QAM example filters in the system will introduce a time delay. The timing recovery algorithm adaptively determines the correct time to sample the symbol. The digital square and filter algorithm is used [3] - see Figure 3. Figure 3 Digital square and filter algorithm The received signal can be written as: rt = am gT t –m T – t T + n t (9) m = – where ak are the complex-valued transmitted symbols, gT(t) is the transmission signal pulse, T is the symbol duration, n(t) is the channel noise (which is assumed to be white and Gaussian), and is an unknown slowly varying time delay. Since varies very slowly, we can process the received signal block by block assuming to be constant in each block. After a receiving filter [impulse response gR(t)] the signal is sampled at a rate of 4/T, resulting in the following samples: r̃ t = r t g R t (10) KT r˜k = r̃ ------4 The sequence: xk = m = – KT KT a m g ------- – m T – T + n̂ ------- 4 4 2 (11) g t = gT T gR T represents the samples of the filtered and squared input signal and contains a spectral component at 1/T. This spectral component is determined for every section of the length LT (i.e. from 4L samples) by computing the complex Fourier coefficient at the symbol rate: 4 n + 1 LN – 1 Xn = x k e – j2k 4 (12) k – 4nL 833 DSP FOR 16-QAM The normalized phase: 1 ̂ = – ---------- arg X n 2 (13) is an unbiased estimate for Adaptive Equalizer (AE) The adaptive equalizer is used to compensate for residual chromatic dispersion, polarization mode dispersion (PMD) and to reduce inter-symbol interference. For dual-polarization system, the butterfly structure is used for polarization demultiplex. Two-stage Constant modulus algorithm- radius directed (CMA-RD) algorithm is used [4,5]. CMA implementation The cost function of the CMA is of the form J k = E y k 2 – Rp 2 (14) Where E[...] indicates the statistical expectation and y(k) the equalizer output. Rp is the constant depending only on the input data symbol, a(k), with dispersion order, p, set to 2 by default. It is defined as E a k 2p R p = --------------------------E ak p (15) The equalizer output y(k) is obtained from y k = WH X k W = w 0 k ,w 1 k ,... ,w N – 1 k T X k = x 0 k ,x 1 k – 1 ,... ,x N – 1 k – N + 1 (16) T where W is the equalizer tap weights vector, and X(k) is the equalizer input data vector. N is the length of the equalizer tap weights, T stands for the transpose of a vector and H is the complex conjugate transpose. The tap weights vector is adapted using the stochastic gradient algorithm W k + 1 = W k + X k e k 2 e k = y k Rp – y k (17) where is the step size parameter and e(k) is the error signal. The CMA algorithm minimizes the error power between the equalizer output and a constant. For an PSK signal, to obtain perfect equalization the error e(k)=0, as the symbols all lie on a ring. While for an 16 QAM signal, the error e(k) cannot reach zero 834 DSP FOR 16-QAM and thus we use CMA for first order convergence and the RD algorithm as the second stage to fine tune the equalization. RD implementation The RD optimization is based on the equalizer output and the nearest constellation radius. The error criterion for RD is defined as: p p e k = y k R̂ k – y k (18) where Rk is the radius of the nearest constellation symbol for each equalizer output (p= 2 by default). The tap weights for the RD are then updated as follows: W k + 1 = W k + X k e k p e k = R̂ k – y k (19) p 835 DSP FOR 16-QAM For dual polarization signals, there are four choices for the initial tap weights (initial value index 1 is set as the default): Initial value index 1: hxx = [0, 0,…,0, 1, 0,…,0, 0] hxy = [0, 0,…,0, 0, 0,…,0, 0] hyx = [0, 0,…,0, 0, 0,…,0, 0] hyy = [0, 0,…,0, 1, 0,…,0, 0] Initial value index 2: hxx = [0, 0,…,0, 0, 0,…,0, 0] hxy = [0, 0,…,0, 1, 0,…,0, 0] hyx = [0, 0,…,0, 1, 0,…,0, 0] hyy = [0, 0,…,0, 0, 0,…,0, 0] Initial value index 3: hxx = [0, 0,…,0, 1, 0,…,0, 0] hxy = [0, 0,…,0, 0, 0,…,0, 0] hyx = [0, 0,…,0, 1, 0,…,0, 0] hyy = [0, 0,…,0, 0, 0,…,0, 0] Initial value index 4: hxx = [0, 0,…,0, 0, 0,…,0, 0] hxy = [0, 0,…,0, 1, 0,…,0, 0] hyx = [0, 0,…,0, 0, 0,…,0, 0] hyy = [0, 0,…,0, 1, 0,…,0, 0] It should be noted that a large data sample is required to get a good result. Therefore we use multiple iterations to adapt the tap weights. If the bit length is short, then the parameter “Iterations” needs to be increased. Frequency Offset Estimation (FOE) The mixing with the local oscillator introduces a frequency and phase offset, leading to a rotating constellation diagram. The received signals are given by: Sk = C k e j 2fkT + k + nk (20) where {Ck} are data symbols, f is the carrier frequency offset we want to estimate, k is the carrier phase (which varies much slower compared to phase varying due to 836 DSP FOR 16-QAM the frequency offset therefore at this step we can assume carrier phase is a constant value), T is the symbol period, and {n(k)} are zero-mean Gaussian random variables. For 16QAM the modulation information cannot be removed by 4th power. However, by following the approach described in [6], S4(k) can be decomposed as: 4 S k = A e j 4 2fkT + k A = 4 EC k + e k (21) where A is a constant amplitude and e(k) is a zero mean process that can be viewed as a noise process. We can then deduce the frequency offset estimate based on the maximization of the periodogram (estimate of spectral density of a signal) of the S4(k) as shown below [7]: 4 1 S k = --- arg max Z f 4 1 Z f = ---N N–1 4 S k e (22) – j 2fkT k=0 Carrier Phase Estimation (CPE) The blind phase search (BPS) algorithm [8] is used to recover and subsequently remove the remaining phase mismatch between the local oscillator and the signal. Figure 4 BPS algorithm 837 DSP FOR 16-QAM The idea of the BPS algorithm is to try different test phases and find the optimum one. The received signal Zk is rotated by B test carrier phase angles b with: b b = --- --B 2 with b 0 ,1 ,... B – 1 (23) All rotated symbols are fed into a decision circuit and the squared distance |dk,b|2 to the closest constellation point is calculated in the complex plane: d k b 2 = Zk e j b – X̂ k b 2 (24) where Xk,b is the decision of Zkejb The block averaging is used to mitigate the effect of ASE noise, that is, assuming a block of N symbols have the same phase noise. This assumption is reasonable since phase noise is a slowing varying variable. The distance of N consecutive test symbols rotated by the same carrier phase angle b are summed up as follows N S k b = dk – n b 2 (25) n=1 The optimum vale of N depends on the laser line-width symbol duration product. The decoded output symbol Xk can be selected from Xk,b by a switch controlled by the index mk,min of the minimum distance sum. Unwrapping is used after calculating the phase noise to remove the 4-fold ambiguity in the squared 16QAM constellation. “Linear interpolation” can also be used to improve the performance especially when the phase noise varies rapidly. Inserting your own MATLAB algorithm The algorithms contained in the DSP for 16-QAM component are modular in design so that users can replace one or more existing algorithms with their own designs. For example, if a user wishes to use their own Frequency Offset Estimation (FOE) algorithm in lieu of the algorithm included within the OptiSystem DSP, the MATLAB component can be used as shown in Figure 3. For the first DSP component, the algorithms before the FOE should be enabled and all remaining algorithms (including FOE) should be disabled. For the second DSP component, all the algorithms before the FOE (and including the FOE) should be disabled and all remaining algorithms should be enabled. 838 DSP FOR 16-QAM Figure 5 MATLAB algorithm being used to replace the FOE algorithm of the OptiSystem DSP 16-QAM When setting up the MATLAB m-file the input and output sampled data sets of the MATLAB component must be equal to the global parameter Number of samples. For FOE one sample/symbol is used. Therefore, “down-sampling” should be used for the input signal and “up-sampling” should be used for the output signal. The MATLAB mfile code is as follows: 839 DSP FOR 16-QAM Example MATLAB m-file for replacing a DSP algorithm module 840 DSP FOR 16-QAM References [1] I. Fatadin, S. J. Savory, and D. Ives, “Compensation of Quadrature Imbalance in an Optical QPSK Coherent Receiver”, IEEE Photonics Technology Letters, Vol. 20, No. 20, pp. 17331735, Oct 15, 2008. [2] S. J. Savory, “Digital filters for coherent optical receivers”, Optics Express, Vol. 16, No. 2, Jan 21 2008. [3] M. Oerder and H. Meyr, “Digital Filter and Square Timing Recovery”, IEEE transactions on communications, Vol. 36, No. 5, pp. 605-612, May 1988. [4] D. N. Godard, “Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems”, IEEE Transactions on Communications, Vol. COM-28, No. 11, pp. 1867-1875, Nov 1980. [5] W. A. Sethares, G. A. Rey, C. R. Johnson, “Approaches to blind equalization of signals with multiple modulus,” in Proc. Int. Conf. Acoust., Speech, Signal Process., Vol. 2, pp. 972-975, May 1989(ICASSP). [6] P. Ciblat and L. Vandendorpe, “Blind carrier frequency offset estimation for non-circular constellation based transmission”, IEEE Transactions on Signal Processing, vol. 51, no. 5, pp. 1378-1389, May 2003. [7] M. Morelli and U. Mengali, “Feedforward Frequency Estimation for PSK: a Tutorial Review,” IEEE Transactions on Communications, Vol. 9, No. 2, pp. 103-116, 1988. [8] T. Pfau, S. Hoffmann, and R. Noe, “Hardware-Efficient Coherent Digital Receiver Concept With Feed-forward Carrier Recovery for M-QAM Constellations”, Journal of Lightwave Technology, Vol. 27, No. 8, pp. 989-999, Apr 15, 2009. [9] Liang B. Du and Arthur J. Lowery , “Improved single channel back propagation for intra-channel fiber nonlinearity compensation in long-haul optical communication systems”, Optics Express, vol. 18, no. 16, pp. 17075-17088, 2010. [10] K. Kikuchi, M. Fukase, and S.-Y. Kim, “Electronic post-compensation for nonlinear phase noise in a 1000-km20-Gbit/s optical QPSK transmission system using the homodyne receiver with digital signal processing,” in Optical Fiber Communication Conference (Optical Society of America, Anaheim, California, 2007), p. OTuA2. [11] A. J. Lowery, “Fiber nonlinearity mitigation in optical links that use OFDM for dispersion compensation,” IEEE Photon. Technol. Lett. 19(19), 1556-1558 (2007). 841 DSP FOR 16-QAM 842 UNIVERSAL DSP Universal DSP The Universal DSP component performs digital domain impairment compensation to aid in recovering the incoming transmission signal after coherent detection. The Universal DSP component combines the capabilities of the DSP for 16-QAM and DSP for QPSK components and provides support for a broader set of higher order modulation formats; including: • BPSK, QPSK, 8PSK, 16PSK • 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, 256QAM In addition, for QAM modulation formats; square, star, and circular constellation formats are supported. Ports Name and description Port type Signal type Input Input I-X Electrical Input Input Q-X Electrical Input Input I-Y Electrical Input Input Q-Y Electrical Output Output I-X Electrical Output Output Q-X Electrical Output Output I-Y Electrical Output Output Q-Y Electrical 843 UNIVERSAL DSP Parameters Initialize Name and description Default value Units Value range Polarization type Dual - Single, Dual Modulation type 16QAM BPSK, QPSK, 8PSK, 16PSK, 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, 256QAM Constellation type (if QAM) Square Square, Star, Circular Defines the type of QAM constellation map to be processed (must match the setting of the associated QAM transmitter) Star and circular level radii 16QAM Defines the amplitude of the radius for each concentric circle (must match the setting of the associated QAM transmitter). The format is r1 r2 ...rN (space delimited). For example if set to “1”, all symbols will be placed along a concentic circle of radius = 1. If set to “1 2”, symbols will be allocated evenly onto two concentric circles of radii 1 and 2. Use Default Values True - True, False Enable DC blocking True - True, False Enable Normalization True - True, False Enable Low Pass Filter True - True, False Enable Resampling True - True, False Enable QI Compensation True - True, False Enable Dispersion Compensation True - True, False Enable Nonlinear Compensation False - True, False Enable Timing Recovery True - True, False Enable Adaptive Equalizer True - True, False Enable Frequency Offset Estimation True - True, False Enable Carrier Phase Estimation True - True, False 844 UNIVERSAL DSP Filter Name and description Default value Type of filter Bessel Cutoff frequency 0.75 * Bit rate /8 Hz - 0 dB [1:999] 100 dB [-9999:9999] 4 - [-9999:9999] 1 - [0,1] 3 dB cutoff frequency of the filter Insertion loss Units Value range Rectangular, Gaussian, Butterworth, Bessel, Chebyshev, RC, Raised Cosine, Root Raised Cosine, Cosine Roll-off, Squared Cosine Rolloff, Inverse Gaussian Insertion loss of the filter Depth Maximum attenuation value for the filter Order Order of the filter Roll off factor Order of the filter Re-sampling Name and description Default value Number of symbols Sequence length/8 Automatically set to Sequence length/4 and Sequence length/8 for SP-16-QAM and DP-16-QAM, respectively Symbol rate Units Value range Bit rate/8 [0:1] Cubic Linear, Cubic, Step Automatically set to Bit rate/4 and Bit rate/8 for SP-16-QAM and DP16-QAM, respectively Interpolation type This parameter is reserved for future use Dispersion compensation Name and description Default value Units Value range Dispersion compensation parameters 845 UNIVERSAL DSP Name and description Default value Units Value range DC calculation domain Frequency domain - Time domain, frequency 1550 nm Hz, THz, nm 1550 nm Hz, THz, nm 16.75 ps/(nm*km) 0.075 ps/(nm2*km) 50 km Select if dispersion compensation algorithm will be applied in the frequency domain or time domain Channel wavelength Central frequency of optical signal DC reference wavelength Reference wavelength for calculating fiber impairments. This value should be the same as the optical fiber reference wavelength Dispersion coefficient This value should be the same as the optical fiber dispersion coefficient Residual dispersion slope This value should be the same as the optical fiber dispersion slope Propagation length This value should be the same as the optical fiber length DC number of taps 181 Applies to the time domain DC algorithm. The typical number of taps is between 100-200. Higher tap numbers are recommended for longer propagation lengths Nonlinear compensation parameters Fiber Alpha 0.2 Fiber N2 26e-021 Fiber Aeff 80e-012 Fiber length per span 80 Nonlinear ratio 0.48 Nonlinear step size 20 Nonlinear kk 0.76 Launch power -3 dBm Name and description Default value Units Value range Samples per block 2048 - - Average window size 512 - - dB km km Timing recovery 846 UNIVERSAL DSP Name and description Default value Units Value range TR interpolation method Cubic - Cubic, FFT Name and description Default value Units Value range AE number of taps 9 - 0 - 0 - 2 - 15 - 1e-006 - 6e-006 - 1 - [1-4] Name and description Default value Units Value range FOE type Same - Same, Different 4 - - Adaptive equalizer Increase the number of taps when stronger distortion is present Delay Y Shift by number of samples. Recommended setting is 0 Delay Y Shift by number of samples. Recommended setting is 0 Dispersion order Recommended setting is 2 AE number of iterations Used to update the accuracy of the taps Step CMA () See Eq 12. It is recommended to vary this step size to determine the optimum operating point (for example from 0.5e-006 to 10e-006) Step RD () See Eq 14. It is recommended to vary this step size to determine the optimum operating point (for example from 0.5e-006 to 10e-006) Initial taps index Recommended setting is 1 Frequency offset estimation When set to “Same”, the average value of the X and Y polarization channels is used. When set to “Different”, a different frequency offset estimation is used for the X and Y polarization channels Power order of symbols Use the 4th order for QPSK and 16-QAM and 8th order for 8PSK and 64-QAM 847 UNIVERSAL DSP Carrier phase estimation Name and description Default value Units Value range Number of test phases (B) 32 - - 40 - - False - True, False See Eq 18. CPE symbols per block It is recommended to vary the CPE symbols per block to determine the optimum operating point (for example from 8 to 50) Use interpolation in CPE Enable this setting when the phase is changing rapidly Power order 848 4 UNIVERSAL DSP Results Name and description Units QI Compensation: X Cross-correlation - QI Compensation: Y Cross-correlation - Timing Recovery: X Tau Sum Before - Timing Recovery: Y Tau Sum Before - Timing Recovery: X Tau Mean Before - Timing Recovery: Y Tau Mean Before - Timing Recovery: X Tau Sum After - Timing Recovery: Y Tau Sum After - Timing Recovery: X Tau Mean After - Timing Recovery: Y Tau Mean After - Adaptive Equalizer: RMS Error After CMA - Adaptive Equalizer: RMS Error After RD - Frequency Offset: X Frequency Correction (MHz) - Frequency Offset: Y Frequency Correction (MHz) - Frequency Offset: XY Frequency Correction (MHz) - Graphs Name and description X Title Y Title CPE after unwrap: Imag X CPE after unwrap: Imag Y CPE after unwrap: Real X CPE after unwrap: Real Y Constellation after AE - X Constellation after AE - Y Constellation after CPE- X Constellation after CPE - Y Constellation after DC blocking - X Constellation after DC blocking - Y Constellation after Dispersion and Nonlinear compensation - X 849 UNIVERSAL DSP Name and description Constellation after Dispersion and Nonlinear compensation - Y Constellation after Filter - X Constellation after Filter - Y Constellation after Frequency offset - X Constellation after Frequency offset - Y Constellation after Normalizing- X Constellation after Normalizing- Y Constellation after QI compensation - X Constellation after QI compensation- Y Constellation after Resampling - X Constellation after Resampling - Y Constellation after Timing recovery - X Constellation after Timing recovery - Y Constellation before DSP - X Constellation before DSP - Y Dispersion compensation: Imag taps Dispersion compensation: Real taps hxx Imag after CMA hxx Imag after RD hxx Real after CMA hxx Real after RD hxy Imag after CMA hxy Imag after RD hxy Real after CMA hxy Real after RD hyx Imag after CMA hyx Imag after RD hyx Real After CMA hyx Real After RD hyy Imag After CMA 850 X Title Y Title UNIVERSAL DSP Name and description X Title Y Title hyy Imag After RD hyy Real After CMA hyy Real After RD Input timing phase: X Input timing phase: Y Output timing phase: X Output timing phase: Y Technical background The Universal DSP component combines the capabilities of the DSP for 16-QAM and DSP for QPSK components and provides support for a broader set of higher order modulation formats; including: • BPSK, QPSK, 8PSK, 16PSK • 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, 256QAM In addition, for QAM modulation formats; square, star, and circular constellation formats are supported. For further information on the DSP algorithms please refer to the technical background descriptions of the DSP for QPSK or DSP for 16-QAM components. 851 UNIVERSAL DSP 852 UNIVERSAL DSP Receivers Library Demodulators • Electrical Amplitude Demodulator • Electrical Phase Demodulator • Electrical Frequency Demodulator • Quadrature Demodulator • OFDM Demodulation (OS12) • OFDM Demodulator Measured • OFDM Demodulation • OFDM Demodulation Dual Polarization • Burst Demodulator • M-ary Threshold Detector • Decision • PAM Decision 853 UNIVERSAL DSP Notes: 854 ELECTRICAL AMPLITUDE DEMODULATOR Electrical Amplitude Demodulator A coherent amplitude demodulator. Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Main Name and description Default value Units Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 deg, rad ]-INF,+INF[ Frequency of the input signal carriert Phase Phase of the input signal carrier Gain 1 ]-INF,+INF[ Linear gain to be applied to the signal input Low Pass Filter Name and description Default value Units Value range Cut off frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 3 dB cut off frequency of the filter Filter type Internal filter type Roll Off factor Cosine Roll Off Rectangular, Cosine Roll Off, Squared Cosine Roll Off 0.2 [0.1] 855 ELECTRICAL AMPLITUDE DEMODULATOR Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled Technical background The component implements an analog demodulator for amplitude-modulated signals. The output signal is demodulated according to: v out t = Gv in t cos 2f c t + c h low t where v in is the input electrical signal, frequency, , G is the parameter gain, f c is the carrier c is the phase of the carrier, and h low is the time response of the low pass filter. The filter type is described according to filter components in the Electrical Filters library: • rectangle • cosine roll off • squared cosine roll off Figure 1 shows a block diagram of this component. Figure 1 856 Electrical amplitude demodulator block diagram ELECTRICAL PHASE DEMODULATOR Electrical Phase Demodulator A coherent phase demodulator. Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Main Name and description Default value Units Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 deg, rad ]-INF,+INF[ Frequency of the input signal carriert Phase Phase of the input signal carrier Peak to peak amplitude 1 ]-INF,+INF[ Peak to peak output signal Low Pass Filter Name and description Default value Units Value range Cut off frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 3 dB cut off frequency of the filter Filter type Internal filter type Roll Off factor Cosine Roll Off Rectangular, Cosine Roll Off, Squared Cosine Roll Off 0.2 [0.1] 857 ELECTRICAL PHASE DEMODULATOR Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled Technical background This component implements an analog demodulator for phase-modulated signals. The output signal is demodulated using a frequency discriminator followed by an integrator according to: d v d t = ----- v in t dt v t = v d t dt v out t = v t cos 2f c t + c h low t where v in is the input electrical signal, f c is the carrier frequency, c is the phase of the carrier, and h low is the time response of the low pass filter. The signal is then scaled to the user-defined peak-to-peak amplitude. The filter type is described according to filter components in the Electrical Filters library: • rectangle • cosine roll off • squared cosine roll off Figure 1 shows a block diagram of this component. 858 ELECTRICAL PHASE DEMODULATOR Figure 1 Electrical phase demodulator block diagram 859 ELECTRICAL PHASE DEMODULATOR 860 ELECTRICAL FREQUENCY DEMODULATOR Electrical Frequency Demodulator Frequency demodulator based on a frequency discriminator. Ports Name and description Port type Signal type Input Input Electrical Output Output Electrical Parameters Main Name and description Default value Units Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 deg, rad ]-INF,+INF[ Frequency of the input signal carriert Phase Phase of the input signal carrier Peak to peak amplitude 1 ]-INF,+INF[ Peak to peak output signal Low Pass Filter Name and description Default value Units Value range Cut off frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 3 dB cut off frequency of the filter Filter type Internal filter type Roll Off factor Cosine Roll Off Rectangular, Cosine Roll Off, Squared Cosine Roll Off 0.2 [0.1] 861 ELECTRICAL FREQUENCY DEMODULATOR Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled Technical background This component implements an analog demodulator for frequency-modulated signals. The output signal is demodulated using a frequency discriminator according to: d v d t = ----- v in t dt v out t = v d t cos 2f c t + c h low t where of the . v in is the input electrical signal, f c is the carrier frequency, c is the phase carrier, and h low is the time response of the low pass filter. The signal is then scaled to the user-defined peak-to-peak amplitude. The filter type is described according to filter components in the Electric Filters library: • rectangle • cosine roll off • squared cosine roll off Figure 1 shows a block diagram of this component. 862 ELECTRICAL FREQUENCY DEMODULATOR Figure 1 Electrical frequency demodulator block diagram 863 ELECTRICAL FREQUENCY DEMODULATOR 864 QUADRATURE DEMODULATOR Quadrature Demodulator A coherent amplitude demodulator for quadrature components (I and Q). Ports Name and description Port type Signal type Input Input Electrical Output-I Output Electrical Output-Q Output Electrical Parameters Main Name and description Default value Units Value range Frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 0 deg, rad ]-INF,+INF[ Frequency of the input signal carrier Phase Phase of the input signal carrier Gain 1 ]-INF,+INF[ Linear gain to be applied to the signal input Low Pass Filter Name and description Default value Units Value range Cut off frequency 50 MHz, Hz, GHz, Thz [0,+INF[ 3 dB cut off frequency of the filter Filter type Internal filter type Roll Off factor Cosine Roll Off Rectangular, Cosine Roll Off, Squared Cosine Roll Off 0.2 [0.1] 865 QUADRATURE DEMODULATOR Simulation Name and description Default value Units Value range Enabled True — True, False Determines whether or not the component is enabled Technical background This component implements an analog demodulator using a carrier generator for Q and I quadrature components. The output signal is demodulated according to: v I t = Gv in t cos 2f c t + c h low t v Q t = – G v in t sin 2f c t + c h low t where v in is the input electrical signal, frequency, G is the parameter gain, f c is the carrier c is the phase of the carrier, and h low is the time response of the low pass filter. The filter type is described according to filter components in the Electric Filters library: • rectangle • cosine roll off • squared cosine roll off Figure 1 shows a block diagram of this component. Figure 1 866 Quadrature demodulator block diagram OFDM DEMODULATION (OS12) OFDM Demodulation (OS12) This component demodulates the OFDM signal into a digital signal. Ports Name and description Port type Signal type Input - I Input Electrical Input - Q Input Electrical Output - I 1 Output M-ary Output - Q 1 Output M-ary Parameters Main Name and description Default value Default unit Value range Reference bit rate Bit rate Bits/s, MBits/s, GBits/s [1,1e12] 0 ns, ms, s ]-INF,+INF[ 1 - [1,1000] 4 - [1,100e6] False - True, False 30 - [0,100e6] Bit rate of the transmitted signal Delay compensation Delay to apply to the input signal Number of output ports Define the number of Users for the OFDM demodulator Number of subcarriers Number of subcarriers used in the transmission by each user User defined position If True each user can define the position of its initial subcarrier Position array Array containing the initial subcarrier positions for each user 867 OFDM DEMODULATION (OS12) Name and description Default value Default unit Value range Number of FFT points 64 - [1,100e6] False - True, False 0 - [0,100e6] Number of points used in the FFT Symmetric spectrum Defines if the input vector to the IFFT is constrained to have Hermetian symmetry Number of prefix points Defines the number of points used in the guard period Simulation Name and description Default value Default units Unit Value range Enabled True - - True, False Determines whether or not the component is enabled Random numbers Name and description Default value Units Value range Generate random seed True - True, False 0 - [0,4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Graphs Name and description X Title Y Title OFDM FFT Frequency (Hz) Amplitude (a.u.) Technical background The OFDM [1] Demodulator basically does the reverse operation of the OFDM Modulator, the guard period is removed. The FFT of each OFDM symbol is then taken to find the original transmitted spectrum. The phase angle of each transmission carrier is then evaluated and converted back to the data word by demodulating the received phase. 868 OFDM DEMODULATION (OS12) The reference bit rate parameter refers to the original bit rate of the digital signal transmitted, while the delay compensation parameter is used to synchronize the received signal. References [1] Armstrong, J. , “OFDM for Optical Communications”, J. Lightwave Technology, vol. 27, pp. 189204, Feb 2009. 869 OFDM DEMODULATION (OS12) Notes: 870 OFDM DEMODULATOR MEASURED OFDM Demodulator Measured This component demodulates the OFDM signal into a digital signal. Ports Name and description Port type Signal type Supported Modes Input - I Input Electrical - Input - Q Input Electrical - Output - I 1 Output M-Ary - Output - Q 1 Output M-Ary - Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [ 0, 1e+012 ] 0 s s, ms, ns [ -1e+100, 1e+100 ] 64 x 1 - - - Subcarriers.dat - - - False - - [True, False] Bit rate of the transmitted signal Delay compensation Delay to apply to the input signal Subcarrier index Table of the subcarrier index data Subcarrier index file name File name of the subcarrier index data Symmetric spectrum Defines if the input vector to the IFFT is constrained to have Hermetian symmetry 871 OFDM DEMODULATOR MEASURED Name and description Default value Default unit Units Value range Number of prefix points 0 - - [ 0, 1e+008 ] Name and description Default value Default unit Units Value range Equalizer False - - [True, False] 64 x 2 - - - Equalizer.dat - - - Name and description Default value Default unit Units Value range Enabled True - - [True, False] Name and description Default value Default unit Units Value range Generate random seed True - - [True, False] 0 - - [ 0, 4999 ] Defines the number of points used in the guard period Equalizer Defines whether or not the equalizer is enabled Equalizer coefficients Table of the equalizer coefficients data Equalizer coefficients file name File name of the equalizer coefficients data Simulation Determines whether or not the component is enabled Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined random seed index 872 OFDM DEMODULATOR MEASURED Graphs Name and description X Title Y Title OFDM FFT Frequency (Hz) Amplitude (a.u.) Results Name and description Unit Number of FFT points - Number of subcarriers - Technical Background The OFDM Demodulator Measured [1] basically does the reverse operation of the OFDM Modulator Measured. Figure 1 OFDM DeModulator Measured diagram The reference bit rate parameter refers to the original bit rate of the digital signal transmitted, while the delay compensation parameter is used to synchronize the received signal. The format of the file for loaded subcarrier index data is the same as defined in OFDM Modulator Measured. After the FFT, a single tap equalizer (defined by the parameter “Equalizer coefficients”) can be applied to the subcarriers data to compensate for channel distortions. If the Equalizer coefficients data is defined by uploading a file, the format of the file must be similar to the following (the first column stands for the real part and the second column stands for the imaginary part): 873 OFDM DEMODULATOR MEASURED Figure 2 Example of a file loaded for the equalizer data References [1] Armstrong, J. , “OFDM for Optical Communications”, J. Lightwave Technology, vol. 27, pp. 189204, Feb 2009. 874 OFDM DEMODULATION OFDM Demodulation This component modulates a digital signal into multiple orthogonal sub-carriers. Ports Name and description Port type Signal type Input - I Input M-ary Input - Q Input M-ary Input - Training Input Electrical Output - I Output Electrical Output - Q Output Electrical Parameters Main Name and description Default value Default unit Value range Bit rate Bit rate bits/s - Symbol rate Symbol rate symbols/s - Maximum possible sub-carriers 64 - - False - - 0 - - Enable dispersion compensation False - True, False Number of training symbols 0 - - Location of pilot symbols none Table with the sub-carrier index data Symmetric spectrum Defines if the input vector to the IFFT is constrained to have Hermitian symmetry Number of prefix points Defines the number of points used in the guard period 875 OFDM DEMODULATION Name and description Default value Default unit Value range Output port parameters Number of output ports (users) 1 Number of sub-carriers per port 1 Sub-carrier locations 1 Modulation type per port QPSK Dispersion and nonlinear compensation Name and description Default value Default units Unit Value range Channel wavelength 1550 nm Hz, THz, nm DC Reference wavelength 1550 nm Hz, THz, nm Dispersion coefficient 16.75 ps/(nm*km) Residual dispersion slope 0.075 ps/(nm^2*km) Propagation length 50 km Name and description Default value Default units Unit Value range Enabled True - - True, False Name and description Default value Default units Unit Value range Generate random seed True - - True, False Random seed index 0 - - - Simulation Determines whether or not the component is enabled Random numbers 876 OFDM DEMODULATION Graphs Name and description X Title Y Title EVM per subcarrier Frequency (Hz) Amplitude (a.u.) OFDM FFT Frequency (Hz) Amplitude (a.u.) SER per subcarrier Subcarrier (a.u.) SER (a.u.) Technical background Orthogonal frequency division multiplexing (OFDM) is a multi-carrier transmission technique[1], which divides the available spectrum into many orthogonal subcarriers, each one being modulated by a lower rate data stream. The purpose of this format is to significantly reduce inter-carrier and inter-symbol interference (ICI and ISI). Figure 1 shows a schematic of the OptiSystem OFDM Demodulation component. Figure 1 Schematic representation of the OFDM demodulation component Electrical in These represent the electrical signals from the optical detectors (for the I and Q streams). A/D Downsampling Analog to digital conversion is accomplished by downsampling to the global symbol rate 877 OFDM DEMODULATION Dispersion compensation Digital filtering can be used to compensate for the chromatic dispersion which results from propagation over a fiber. It is implemented in the frequency domain using the following transfer function [2]: 2 D z 2 G z w = exp – j --------------------- w 4c (1) where z is the transmission distance, w is the angular frequency, j is the imaginary unit,is the channel wavelength, c is the speed of light, and D = Do + S x o is the dispersion coefficient of the fiber for wavelength , S is the dispersion slope, and o is the reference wavelength. These parameters are identical to those used in the single mode optical fiber components. Remove cyclical prefix When a guard extension or cyclic prefix is added in the modulator, to reduce the ISI and ICI, it must be removed at this stage. Figure 2 represents the ideal case where the received signal is undistorted in the prefix range Figure 2 Relation between and OFDM symbol with and without a prefix Figures 2a) and 2b) are two possible signals over one OFDM period and Figure 2c) is the OFDM signal period with the prefix removed. These signals have been idealized for illustrative purposes. FFT Each time domain OFDM subcarrier is converted back to a symbol stream by performing a Fourier transform (see Figure 3). The white squares are useful symbols. blue squares are the known pilot symbols and red squares are the known training symbols 878 OFDM DEMODULATION Figure 3 A representation of the OFDM symbols and the location of the pilot and training symbols Training symbols, channel estimation By comparing the received symbols (at the training symbols locations) to the original symbols we can construct a transfer function to compensate for chromatic dispersion, fiber non-linearities, polarization mode dispersion and polarization dependent loss. Note that there already exists a routine to compensate for chromatic dispersion (see Dispersion compensation stage). Using both improves the symbol error rate (SER) results. The transfer function for dispersion in the frequency domain can be characterized as follows: t k training ----------------------t k Rx t k training i H k = ----------------------- = ------------------------------t k Rx N training (2) where k is the sub-carrier index, i is the training symbol index (which is averaged over), NT is the number of training symbols, tk, Rx are the received symbols in the training symbol locations and tk, training are the original symbols. Pilot symbols, carrier phase estimation In a physical system, especially for a heterodyne receiver configuration, the phase will drift over time. It is usually small enough that we can assume the drift remains relatively constant over each OFDM symbol but changes from one OFDM symbol to the next. This is compensated by modifying the transfer function above to one that varies between OFDM symbols [4] 2 H' · k l Hk = exp – j l -----------H k* (3) 879 OFDM DEMODULATION where l is the OFDM symbol index and lis the estimated phase over each OFDM symbol: 1 l = -----Np Np arg yln – arg xln (4) n=1 where the index n goes over the Np pilot symbols used within each OFDM symbol, yln is the received pilot symbol and xln is the original transmitted pilot symbol. Since it is assumed that the phase drift is approximately constant over each OFDM symbol, an average over the pilots is taken. Decision, EVM and SER computation Decision The Decision block processes the I and Q channels by normalizing each channel to their respective m-PSK or m-QAM grid and performs a decision on each symbol based on normalized threshold settings. EVM Once the decision is made, the EVM is calculated as follows: 2 S– S D EVM = ------------------------------- 100 % 2 S D (5) S D is where S is the symbol sequence, indicates the mean value, and the decision of S. The average EVM and EVM per subcarrier are shown in the results as well as graphed. SER The received signals (after decision) are compared with the originally transmitted symbols to count the symbol errors and calculate the SER Errors SER = ------------------------------------------------------------------------------------------------------------------------------------------------------------SymbolSequenceLength – PilotSymbols – TrainingSymbols (6) Sub-carrier locations The OFDM component allows the user a number of options to specify the locations of the sub-carriers being used. See below for examples of the notation used. 880 Notation Sub-carrier allocation 1, 5, 10 Sub-carriers placed at positions 1, 5, and 10 1,5,10,21-30 Sub-carriers placed at positions 1, 5, 10 and 21 to 30 OFDM DEMODULATION 1,5,10,21-30x2 Sub-carriers placed at positions 1, 5, 10, 21, 23, 25, 27, 29 “x2” means that positions are skipped by two locations 1#4x3 Sub-carriers placed at positions 1, 4, 7, and 10 “#” represents the number of sub-carriers to be positioned 1,5,10;31,35,40 Port 1 has positions 1, 5, and 10 Port 2 has positions 31, 35 and 40 Semi-colons are used to separate the sub-carriers by port number Examples The following examples show how to set up the OFDM Demodulation component. They could be used as the demodulators for Examples #1 and Examples #2 in the Help documentation of the OFDM Modulation component. For OFDM system examples, please refer to the example projects in “OptiSystem 13 Samples\ Advanced modulation systems\ OFDM systems” Example 1: Single polarization one port In this example, a QPSK sequence is sent to the OFDM modulation component. There are 128 possible subcarriers available. Of these, 80 are used and placed at locations 1 to 40 and 89 to 128. Figure 4 Example of single polarization QPSK system (OFDM Modulator) 881 OFDM DEMODULATION Figure 5 Example of single polarization QPSK system (OFDM Demodulation) In this example, pilot carriers have been placed at carriers 25,44,64,84 and 104. They must fall on the used sub-carrier locations (here from 25 to 104). The number of pilot carriers used is generally a matter of experimentation. It is desirable to use the minimum possible for the required SER to get maximum spectral efficiency. In this case dispersion compensation was chosen, which requires appropriate parameters. You can simply copy and paste the parameters used for the optical fiber. If using a dispersion compensating fiber, disable this option. Of particular note: the Modulation per port gives the modulation formats used in this system. The formats available are: BPSK, QPSK, 8PSK, 16PSK, 4QAM, 16QAM and 64QAM. Typical results are shown below: Figure 6 Typical results for single polarization single user system 882 OFDM DEMODULATION Example #2: Single polarization, two ports. In this example the total number of subcarriers available is again 128. The subcarriers for the first port are located at 25 to 64 (could use 25#40). The sub-carriers for the second port are located at 65 to 104 (could use 65#40). This creates a total of 80 sub-carriers. An example setup is shown in Figures 7/8. Figure 7 An example of a mixed modulation single polarization OFDM modulation system and a representation of the sub-carrier locations Figure 8 An example of a mixed modulation single polarization OFDM Demodulation system and a representation of the sub-carrier locations 883 OFDM DEMODULATION References [1] X. Liu, F. Buchali, and R. W. Tkach, “Improving the nonlinear tolerance of polarization-DivisionMultiplexed CO-OFDM in long-haul fiber transmission,” J. Lightw. Tech., vol. 27, no. 16, pp. 36223640, 2009. [2] S.J. Savory, “Digital filters for coherent optical receivers”, Optics Express, vol 16, no. 2, Jan 21 2008. [3] X. Liu and F. Buchali, “A novel channel estimation method for PDM-OFDM enabling improved tolerance to WDM nonlinearity,” presented at the OFC'09, paper OWW5. [4] X. Yi, W. Shieh and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Phot. Tech. Lett., vol 19, pp. 919-921, 2007 884 OFDM DEMODULATION DUAL POLARIZATION OFDM Demodulation Dual Polarization This component demodulates the OFDM signal into a a digital M-ary signal. It is specifically designed to be used for OFDM systems with dual polarization multiplexing. Ports Name and description Port type Signal type Input - IX Input Electrical Input - QX Input Electrical Input - Training X Input Electrical Input - IY Input Electrical Input - QY Input Electrical Input - Training Y Input Electrical Output - IX Output M-ary Output - QX Output M-ary Output - IY Output M-ary Output - QY Output M-ary Parameters Main Name and description Default value Default unit Value range Bit rate Bit rate bits/s - Symbol rate Symbol rate symbols/s - Maximum possible sub-carriers 64 - - Table with the sub-carrier index data 885 OFDM DEMODULATION DUAL POLARIZATION Name and description Default value Default unit Value range Symmetric spectrum False - - 0 - - Enable dispersion compensation False - True, False Number of training symbols 0 - - Location of pilot symbols: X none Location of pilot symbols: Y none Defines if the input vector to the IFFT is constrained to have Hermitian symmetry Number of prefix points Defines the number of points used in the guard period Output port parameters: X polarization Number of output ports (users): X 1 Number of sub-carriers per port: X 1 Sub-carrier locations: X 1 Modulation type per port: X QPSK Output port parameters: Y polarization Number of output ports (users): Y 1 Number of sub-carriers per port: Y 1 Sub-carrier locations: Y 1 Modulation type per port: Y QPSK Dispersion and nonlinear compensation Name and description Default value Default units Unit Channel wavelength 1550 nm Hz, THz, nm DC Reference wavelength 1550 nm Hz, THz, nm Dispersion coefficient 16.75 ps/(nm*km) Residual dispersion slope 0.075 ps/(nm^2*km) Propagation length 50 km 886 Value range OFDM DEMODULATION DUAL POLARIZATION Simulation Name and description Default value Default units Unit Value range Enabled True - - True, False Name and description Default value Default units Unit Value range Generate random seed True - - True, False Random seed index 0 - - - Determines whether or not the component is enabled Random numbers Graphs Name and description X Title Y Title EVM per subcarrier, X polarization Frequency (Hz) Amplitude (a.u.) EVM per subcarrier, Y polarization Frequency (Hz) Amplitude (a.u.) OFDM FFT, X polarization Frequency (Hz) Amplitude (a.u.) OFDM FFT, Y polarization Frequency (Hz) Amplitude (a.u.) SER per subcarrier, X polarization Subcarrier (a.u.) SER (a.u.) SER per subcarrier, Y polarization Subcarrier (a.u.) SER (a.u.) Technical background Orthogonal frequency division multiplexing (OFDM) is a multi-carrier transmission technique[1], which divides the available spectrum into many orthogonal subcarriers, each one being modulated by a lower rate data stream. The purpose of this format is to significantly reduce inter-carrier and inter-symbol interference (ICI and ISI). Figure 1 shows a schematic of the OptiSystem OFDM Demodulation Dual Poloarization component. 887 OFDM DEMODULATION DUAL POLARIZATION Figure 1 Schematic representation of the OFDM Demodulation (DP) component Electrical in These represent the electrical signals from the optical detectors (for the I and Q streams) for both X and Y polarization channels. A/D Downsampling Analog to digital conversion is accomplished by downsampling to the global symbol rate Dispersion compensation Digital filtering can be used to compensate for the chromatic dispersion which results from propagation over a fiber. It is implemented in the frequency domain using the following transfer function [2]: 2 D z 2 G z w = exp – j --------------------- w 4c (1) where z is the transmission distance, w is the angular frequency, j is the imaginary unit,is the channel wavelength, c is the speed of light, and D = Do + S x o is the dispersion coefficient of the fiber for wavelength , S is the dispersion slope, and o is the reference wavelength. These parameters are identical to those used in the single mode optical fiber components. Remove cyclical prefix When a guard extension or cyclic prefix is added in the modulator, to reduce the ISI and ICI, it must be removed at this stage. Figure 2 represents the ideal case where the received signal is undistorted in the prefix range 888 OFDM DEMODULATION DUAL POLARIZATION Figure 2 Relation between and OFDM symbol with and without a prefix Figures 2a) and 2b) are two possible signals over one OFDM period and Figure 2c) is the OFDM signal period with the prefix removed. These signals have been idealized for illustrative purposes. FFT Each time domain OFDM subcarrier is converted back to a symbol stream by performing a Fourier transform (see Figure 3). The white squares are useful symbols. Blue squares are the known pilot symbols and red squares are the known training symbols Figure 3 A representation of the OFDM symbols and the location of the pilot and training symbols Training symbols, channel estimation By comparing the received symbols (at the training symbols locations) to the original symbols we can construct a transfer function to compensate for chromatic dispersion, fiber non-linearities, polarization mode dispersion and polarization dependent loss. Note that there already exists a routine to compensate for chromatic dispersion (see Dispersion compensation stage). Using both improves the symbol error rate (SER) results. 889 OFDM DEMODULATION DUAL POLARIZATION In the OFDM Demodulation Dual Polarization component, the training symbols must be of the format: tk i = t x k i t y k i = t 1x k i t x k i t 2x k i NT NT = t k i + ------ = i = 1 ----- 2 2 t 1y k i – t y k i t 2y k i (2) where k is the sub-carrier index, i is the training symbol index (which is averaged over), NT is the number of training symbols When the pilot symbols in the X polarization and the Y polarization overlap, the transfer function is given by [3,4]: Hk = t 1x k i + t 2x k i t 1x k i – t 2x k i --------------------------------------------------------------------------------------2t x k i 2t y k i t 1y k i + t 2y k i t 1y k i – t 2y k i --------------------------------------------------------------------------------------2t x k i 2t y k i (3) i If there is no overlap of the X and Y polarization at subcarrier index k, the transfer function is [3,4]: tk i H k = ------------ t k i i (4) where t’k(i) are the received symbols in the training symbol locations, tk(i) are the original symbols and <...>i denotes the average over the training symbols. Pilot symbols, carrier phase estimation In a physical system, especially for a heterodyne receiver configuration, the phase will drift over time. It is usually small enough that we can assume the drift remains relatively constant over each OFDM symbol but changes from one OFDM symbol to the next. This is compensated by modifying the transfer function above to one that varies between OFDM symbols [4] 2 H' · k l Hk = exp – j l -----------H* (5) k where l is the OFDM symbol index and lis the estimated phase over each OFDM symbol: 1 l = -----Np Np arg yln – arg xln (6) n=1 where the index n goes over the Np pilot symbols used within each OFDM symbol, yln is the received pilot symbol and xln is the original transmitted pilot symbol. Since it is 890 OFDM DEMODULATION DUAL POLARIZATION assumed that the phase drift is approximately constant over each OFDM symbol, an average over the pilots is taken. Decision, EVM and SER computation Decision The Decision block processes the I and Q channels by normalizing each channel to their respective m-PSK or m-QAM grid and performs a decision on each symbol based on normalized threshold settings. EVM Once the decision is made, the EVM is calculated as follows: 2 S– S D EVM = ------------------------------- 100 % 2 S D (7) S D is where S is the symbol sequence, indicates the mean value, and the decision of S. The average EVM and EVM per subcarrier are shown in the results as well as graphed. SER The received signals (after decision) are compared with the originally transmitted symbols to count the symbol errors and calculate the SER Errors SER = ------------------------------------------------------------------------------------------------------------------------------------------------------------SymbolSequenceLength – PilotSymbols – TrainingSymbols (8) Sub-carrier locations The OFDM component allows the user a number of options to specify the locations of the sub-carriers being used. See below for examples of the notation used. Notation Sub-carrier allocation 1, 5, 10 Sub-carriers placed at positions 1, 5, and 10 1,5,10,21-30 Sub-carriers placed at positions 1, 5, 10 and 21 to 30 1,5,10,21-30x2 Sub-carriers placed at positions 1, 5, 10, 21, 23, 25, 27, 29 “x2” means that positions are skipped by two locations 1#4x3 Sub-carriers placed at positions 1, 4, 7, and 10 “#” represents the number of sub-carriers to be positioned 1,5,10;31,35,40 Port 1 has positions 1, 5, and 10 Port 2 has positions 31, 35 and 40 Semi-colons are used to separate the sub-carriers by port number 891 OFDM DEMODULATION DUAL POLARIZATION Example The operation of the OFDM Demodulation Dual Polarization component is similar to that of the OFDM Demodulation component except that both the X and Y polarization components need to be specified. In this example (Fig 4) both polarizations use the same subcarrier locations. The tophalf of the component represents the inputs and outputs for the X polarization and the bottom half the inputs and outputs for the Y polarization. Figure 4 Example of dual polarization QPSK system (OFDM Modulator) Pilot carriers have been placed at carriers 25,44,64,84 and 104. They must fall on the used subcarrier locations (here from 25 to 104). The number of pilot carriers used is generally a matter of experimentation. It is desirable to use the minimum possible for the required SER to get maximum spectral efficiency. In this case dispersion compensation was chosen, which requires appropriate parameters (for example by copying the parameters used for the optical fiber). When using a dispersion compensating fiber, make sure to disable this option. The corresponding OFDM Demodulator is shown in Figure 5. Figure 5 Example of OFDM Demodulation setup for QPSK symbols 892 OFDM DEMODULATION DUAL POLARIZATION References [1] X. Liu, F. Buchali, and R. W. Tkach, “Improving the nonlinear tolerance of polarization-DivisionMultiplexed CO-OFDM in long-haul fiber transmission,” J. Lightw. Tech., vol. 27, no. 16, pp. 36223640, 2009. [2] S.J. Savory, “Digital filters for coherent optical receivers”, Optics Express, vol 16, no. 2, Jan 21 2008. [3] X. Liu and F. Buchali, “A novel channel estimation method for PDM-OFDM enabling improved tolerance to WDM nonlinearity,” presented at the OFC'09, paper OWW5. [4] X. Yi, W. Shieh and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Phot. Tech. Lett., vol 19, pp. 919-921, 2007 893 OFDM DEMODULATION DUAL POLARIZATION 894 BURST DEMODULATOR Burst Demodulator This component demodulates bursts from an input signal according to a control signal. Ports Name and description Port type Signal type Input Input Electrical Control Input Electrical Output Output Electrical Parameters Main Name and description Default value Threshold 0.5 Units Value range ]-INF, +INF[ Control signal threshold value Simulation Name and description Default value Enabled True Units Value range True, False Determines whether or not the component is enabled Technical background This component demodulates bursts from an input signal, and the locations of the bursts are defined by the control signal. Figure 1 is an example showing how to connect the Burst Demodulator. 895 BURST DEMODULATOR Figure 1 Burst demodulator - Layout Figure 2 Burst demodulator - Principle Signal to Burst Modulator Control Signal After Burst Modulator After Burst Demodulator The basic principle of the Burst demodulator is illustrated in Figure 2. As we can see, whenever the control signal is above the threshold level, the Burst demodulator will demodulate the burst into output signal. 896 M-ARY THRESHOLD DETECTOR M-ary Threshold Detector Decodes multilevel pulses to a M-ary signal output. Ports Name and description Port type Signal type Input Input Electrical Output Output M-ary Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate Bits/s Bits/s [0,+INF[ Reference bit rate to use for the decision instant calculation Delay compensation MBits/s GBits/s 0 s Threshold amplitudes -5, -3.5, -1.5, 0 a.u. List of threshold levels for decision 1.5, 3.5, 5 Decision instant 0.5 Delay to apply to the signal input s, ms, us, ns, ps, fs ]-INF,+INF[ ]-INF,+INF[ — [0,1] Position (as ratio of symbol period) where decision instant is taken when recovering the bit sequence Output amplitudes List of multilevel symbols for the output M-ary sequence -7, -5, -3, -1, 1, 3, 5, 7 a.u. ]-INF,+INF[ 897 M-ARY THRESHOLD DETECTOR Simulation Name and description Default value Units Value range Enabled True — True, False Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines whether or not the component is enabled Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background This model compares the electrical signal at a user-defined decision instant with a list of threshold levels. The comparison generates an index used to generate the output amplitude. For example, if the signal input has a value of -3.3, the output level will be -3, since 3.3 is between -3.5 and -1.5. The delay compensation parameter allows the user to compensate delay occurred during the signal propagation. The number of output levels must be greater than the number of threshold levels. By selecting ‘parameter enable’ to false, the module will generate the levels at the decision instant without comparison and decision based on the output levels. This means the user can access the values at decision instant before the quantization. 898 DECISION Decision The Decision component processes the I and Q electrical signal channels received from the DSP stage, normalizes the electrical amplitudes of each I and Q channel to the respective m-PSK or m-QAM grid and performs a decision on each received symbol based on normalized threshold settings. It supports the following modulation formats: • BPSK, QPSK, 8PSK, 16PSK • 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, 256QAM In addition, for QAM modulation formats; square, star, and circular constellation formats are supported The Decision component supports single or dual polarization (SP/DP) multiplexing schemes Ports Name and description Port type Signal type Input 1 Reference binary signal Binary Input 2 Input I-X Electrical Input 3 Input Q-X Electrical Input 4 Input I-Y Electrical Input 5 Input Q-Y Electrical Output 1 Output I-X M-ary Output 2 Output Q-X M-ary Output 3 Output I-Y M-ary Output 4 Output Q-Y M-ary 899 DECISION Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate bits/s Bits/s, MBits/s, GBits/s [0,+INF[ Polarization type Dual - - Single, Dual Modulation format QPSK - - BPSK, QPSK, 8PSK, 16PSK, 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, 256QAM Constellation type (if QAM) Square - - Square, Star, Circular - - - - False - - True, False Bit rate/4 - - - False - - True, False False - - True, False Reference bit rate to use for the decision instant calculation Defines the type of QAM constellation map to be normalized and decoded (must match the setting of the associated QAM transmitter) Star and circular level radii Defines the amplitude of the radius for each concentric circle (must match the setting of the associated QAM transmitter). The format is r1 r2 ...rN (space delimited). For example if set to “1”, all symbols will be placed along a concentic circle of radius = 1. If set to “1 2”, symbols will be allocated evenly onto two concentric circles of radii 1 and 2. Use default symbol rate When selected, and upon clicking the OK button, the Symbol rate field will be updated based on the Polarization type and Modulation format Symbol rate When Use default symbol rate is selected, this value (if changed) may be overwritten upon selecting the OK buttoon DC blocking When selected enables DC blocking Normalization When selected enables Normalization 900 DECISION Name and description Default value Default unit Units Value range Optimize decision True - - True, False False - - True, False False - - True, False When selected, additional procedures are performed to correct any residual mis-alignment or rotations in the constellation prior to applying the soft decisions. Gray code When selected enables Gray encoding Differential coding When selected enables Differential encoding 901 DECISION Results Name and description Unit SER - Symbol error rate EVM (%) - Error vector magnitude (%) Number of Symbol Errors - Total number of counted Symbol errors for Symbol sequence Number of X Symbol Errors Number of counted Symbol errors for Symbol sequence (Xpolarization channel) Number of Y Symbol Errors Number of counted Symbol errors for Symbol sequence (Ypolarization channel) EVM_X (%) - Error vector magnitude (X-polarization channel) EVM_Y (%) - Error vector magnitude (Y-polarization channel) Total Number of symbols - Total number of symbols processed by the Decision component Number of symbols used in SER and EVM Number of symbols used for calculating the SER and EVM (this is dependent on the number of Guard bits used Technical background The Decision component processes the I and Q electrical signal channels received from the DSP stage, normalizes the electrical amplitudes of each I and Q channel to the respective m-PSK or m-QAM grid and performs a decision on each received symbol based on normalized threshold settings. It supports the following modulation formats: • BPSK, QPSK, 8PSK, 16PSK • 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, 256QAM In addition, for QAM modulation formats; square, star, and circular constellation formats are supported The Decision component supports single or dual polarization (SP/DP) multiplexing schemes 902 DECISION Prior to processing the input data, the electrical signals are first re-sampled to 2 Samples per symbol (1st and N/2+1 sampled signals are used for the re-sampling (where N = Samples per symbol). The second data point (N/2+1) is then selected - to bring the sampling rate to 1 Sample/symbol. The Decision component performs the following functions (in order): • DC blocking • Normalization • Error Vector Magnitude (EVM) calculation • Decision • Calculate Symbol Error Rate (SER) DC Blocking DC Blocking is applied to offset any imperfectly biased voltages in the modulators. Note: If the DSP for QPSK or DSP for 16-QAM component is used before the Decision component and DC blocking is enabled for the DSP component, the parameter DC blocking can be disabled for the Decision component. Normalization The received signal is normalized to the QPSK grid [-1 1] or 16-QAM grid [-3 -1 1 3]. EVM calculation The EVM of the received signals is calculated as follows: 2 S– S D EVM = ------------------------------- 100 % 2 S D where S is the symbol sequence, the decision of S. indicates the mean value, and (1) S D is Decision The decision algorithm performs a soft decision on all the received symbols based on the threshold boundaries. For example for QPSK the boundaries (x = 0; y = 0) are used. Similarly, for 16-QAM the boundaries (x = -1, 0, 2; y = -2, 0, +2) are used. (See Figure 1) 903 DECISION Figure 1 Examples decision boundaries for QPSK and 16-QAM When “Optimize decision” is selected, three additional procedures are performed to correct any residual mis-alignment or rotations in the constellation prior to applying the soft decisions. Constellation rotation The dispersion in the fiber, laser line-width and frequency offset may cause the constellations to rotate. Due to the 4-fold ambiguity of the constellation, the recovered signals may be rotated by m x /2 radians compared to the original transmitted signals. Through correlation, the signals are returned back to the same position as the transmitted signals. Alignment The presence of fiber and filters in the line may cause a time delay in the transmitted signals and may lead to a timing misalignment between the received signals with the original transmitted signals. We also use correlation to align the received signals to the original transmitted signals. Polarization rotation For dual-polarization, because the polarization states may rotate along the fiber, the received X and Y channels may switch between polarization states (the transmitted X channel becomes the Y channel and the transmitted Y channel becomes the X channel). This procedure checks for this polarization rotation and rotates it back to its original position at transmission. Calculate SER After completing optimization (when enabled), the received symbols are compared with the original transmitted symbols to count the symbol errors and calculate the symbol error rate (SER). Guard symbols are taken into account when calculating the SER. 904 DECISION For the case of a single polarization system the SER is: Errors SER = ---------------------------------------------------------------------------------------------------------------------SymbolSequenceLength – 2 GuardSymbols (2) For the case of a dual polarization system the SER is: XErrors + YErrors SER = ----------------------------------------------------------------------------------------------------------------------------------2 SymbolSequenceLength – 2 GuardSymbols (3) where the Errors are counted only for the portion of the Symbol sequence outside of the Guard symbols The relationship between Guard symbols and the global parameter Guard bits, and Symbol length and the global parameter Sequence length, are shown in the following table (Ceiling represents the smallest following mapped integer of the real number): Modulation format Guard symbols Symbol length DP-16-QAM Ceiling(GuardBits/8) Ceiling(SequenceLength/8) 16-QAM Ceiling(GuardBits/4) Ceiling(SequenceLength/4) DP-QPSK Ceiling(GuardBits/4) Ceiling(SequenceLength/4) QPSK Ceiling(GuardBits/2) Ceiling(SequenceLength/2) Differential coding [1, 2] Differential encoding/decoding is used to resolve phase ambiguity problems with mQAM and mPSK modulation formats. For 32-QAM and 128-QAM square constellations a look up table based on Ref 3 is used. For all other constellations the technique defined in Ref 2 is used For 16-QAM differential encoding, a group of 4 bits is mapped into one of the 24 possible transitions between two consecutive complex symbols S(i-1) and S(i). The transition can be expressed in terms of two differential angles { }, where is determined by the first dibit (one of four patterns from two consecutive bits: 00, 01, 10, 11) of the QAM symbol and is determined by the second dibit. The dibit to the differential angle mapping is as follows: Dibit Differential angle 00 0 01 /2 11 01 3/2 905 DECISION The complex symbol S(i) represents the summation of the quadrant center C(i) and a displacement D(i): Si = Ci + Di (4) The differential 16-QAM encoding rule can be described as two recursive updating formulas:: Si = Ci – 1 e j 1 i Di = Di – 1 e j 2 i (5) The initial symbol S(0) is set be letting C(0) = Re j/4 and D(0) = re j/4, with: R = 2 2 r = (6) 2 where R denotes the distance between the origin and the quadrant center, and r denotes the distance between the quadrant center and the constellation point. All the symbols can be expressed as: S i = a i + jb i where a b { 1, 3} (7) For QPSK differential encoding, a group of 4 bits is mapped into one of the 22 possible transitions between two consecutive complex symbols S(i-1) and S(i). The transition can be expressed in terms of the differential angle . The dibit to the differential angle mapping is as follows: Dibit Differential angle 00 0 01 /2 11 01 3/2 The differential QPSK encoding rule can be described as an updating formula: Si = Si – 1 e j i (8) The initial symbol S(0) is set be letting S(0) = re j/4, with: r = 906 2 (9) DECISION where r denotes the distance between the origin center and the constellation point. All the symbols can be expressed as: S i = a i + jb i where a b 1 (10) References [1] J.-K. Hwang, Y.-L. Chiu, and C.-S. Liao, "Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system," Int. J. Commun. Syst., vol. 21, no. 6, pp. 631-641, 2008. [2] Wei, Ruey Y, “Differential encoding by a look-up table for quadrature-amplitude modulation”, IEEE Transactions on Communications, V59 2011, pp 84-94 907 DECISION 908 PAM DECISION PAM Decision This PAM Decision component processes PAM electrical signal channels, normalizes the electrical amplitudes of each PAM channel and performs a decision on each received symbol based on normalized threshold settings. The PAM Decision component supports all m-PAM settings (PAM-4, PAM-8, PAM-16, etc.). Ports Name and description Port type Signal type Input 1 Reference binary signal Binary Input 2 Input PAM Electrical Output 1 Output PAM M-ary Parameters Main Name and description Default value Default unit Units Value range Reference bit rate Bit rate bits/s Bits/s, MBits/s, GBits/s [0,+INF[ Bit rate/4 - - - False - - True, False False - - True, False True - - True, False Reference bit rate to use for the decision instant calculation Symbol rate Symbol to be used for demodulting the PAM signal stream DC blocking When selected enables DC blocking Normalization When selected enables Normalization Optimize decision When selected, additional procedures are performed to correct any residual mis-alignment or rotations in the constellation prior to applying the soft decisions. 909 PAM DECISION Name and description Default value Default unit Units Value range Gray code False - - True, False When selected enables Gray encoding Results Name and description Unit SER - Symbol error rate EVM (%) - Error vector magnitude (%) Number of Symbol Errors - Total number of counted Symbol errors for Symbol sequence Total Number of symbols - Total number of symbols processed by the Decision component Number of symbols used in SER and EVM Number of symbols used for calculating the SER and EVM (this is dependent on the number of Guard bits used Technical background This PAM Decision component processes PAM electrical signal channels, normalizes the electrical amplitudes of each PAM channel and performs a decision on each received symbol based on normalized threshold settings. The PAM Decision component supports all m-PAM settings (PAM-4, PAM-8, PAM-16, etc.) The Decision component performs the following functions (in order): • DC blocking • Normalization • Error Vector Magnitude (EVM) calculation • Decision • Calculate Symbol Error Rate (SER) DC Blocking DC Blocking is applied to offset any imperfectly biased voltages in the modulators Normalization The received signal is normalized to the respective m-PAM grid. For example PAM-4 (2 bits/symbol) symbols are normalized to the [-3 -1 1 3] amplitude grid 910 PAM DECISION EVM calculation The EVM of the received signals is calculated as follows: 2 S– S D EVM = ------------------------------- 100 % 2 S D where S is the symbol sequence, the decision of S. indicates the mean value, and (1) S D is Decision The decision algorithm performs a soft decision on all the received symbols based on the threshold boundaries. For example, for PAM-4, the following decision boundaries are used: y = -2, 0, +2 When “Optimize decision” is selected, two additional procedures are performed to correct any residual mis-alignment or rotations in the constellation prior to applying the soft decisions. Constellation rotation The dispersion in the fiber, laser line-width and frequency offset may cause the constellations to rotate. Due to the 2-fold ambiguity of the constellation, the recovered signals may be rotated by m x radians compared to the original transmitted signals. Through correlation, the signals are returned back to the same position as the transmitted signals. Alignment The presence of fiber and filters in the line may cause a time delay in the transmitted signals and may lead to a timing misalignment between the received signals with the original transmitted signals. We also use correlation to align the received signals to the original transmitted signals. Calculate SER After completing optimization (when enabled), the received symbols are compared with the original transmitted symbols to count the symbol errors and calculate the symbol error rate (SER). Guard symbols are taken into account when calculating the SER. The SER is: Errors SER = ---------------------------------------------------------------------------------------------------------------------SymbolSequenceLength – 2 GuardSymbols (2) where the Errors are counted only for the portion of the Symbol sequence outside of the Guard symbols 911 PAM DECISION The relationship between Guard symbols and the global parameter Guard bits, and Symbol length and the global parameter Sequence length, are shown in the following table (Ceiling represents the smallest following mapped integer of the real number): 912 Modulation format Guard symbols Symbol length PAM-4 Ceiling(GuardBits/2) Ceiling(SequenceLength/2) PAM-8 Ceiling(GuardBits/3) Ceiling(SequenceLength/3) PAM-16 Ceiling(GuardBits/4) Ceiling(SequenceLength/4) PAM DECISION Receivers Library Decoders • PAM Sequence Decoder • QAM Sequence Decoder • PSK Sequence Decoder • DPSK Sequence Decoder • PPM Sequence Decoder • DPIM Sequence Decoder • 4B5B Sequence Decoder • NRZI Sequence Decoder • AMI Sequence Decoder • Manchester Sequence Decoder • 4B3T Sequence Decoder • 8B10B Sequence Decoder 913 PAM DECISION Notes: 914 PAM SEQUENCE DECODER PAM Sequence Decoder Decodes a PAM M-ary symbol sequence to a binary signal. Ports Name and description Port type Signal type PAM sequence Input M-ary Bit sequence Output Binary Parameters Main Name and description Default value Units Value range Bits per symbol 2 [0,100] False True, False False True, False Number of bits per symbol used in the coding Gray code Defines whether or not to use Gray code User-defined PAM map Defines whether to calculate PAM values based on userdefined values PAM amplitudes (a.u.) 4x2 PAM amplitudes file name PAM_IQ.dat Name of file that contains initial I-Q values Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled 915 PAM SEQUENCE DECODER Technical background When transmitting information, we can vary the amplitude of a signal according to the source symbols. The amplitude values are taken from the set of amplitudes [1]: a i = 2i – 1 – M i = 1 2 ...M M is the number of possible sequence of binary digits, calculated according h to: M = 2 h is the number of bits per symbol. . The PAM decoder will calculate the value of i for each amplitude of the signal k : where i = a k + 1 + M 2 and convert the values of i to the equivalent binary sequence. If bits per symbol ( h ) equals 2, Bit sequence i ai 00 1 -3 01 2 -1 10 3 1 11 4 3 If bits per symbol ( h ) equals 3, 916 M equals 4, the values of a and i will be: M equals 8, the values of a and i will be: Bit sequence i ai 000 1 -7 001 2 -5 010 3 -3 011 4 -1 100 5 1 101 6 3 110 7 5 111 8 7 PAM SEQUENCE DECODER Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. In the case where bits per symbol ( h ) equals 3, M equals 8, with Gray code, the values of a will be: Bit sequence ai 000 -7 001 -5 101 -3 100 -1 110 1 111 3 011 5 010 7 When User-defined PAM map is selected, the component will determine the associated bit symbol based on the PAM amplitudes contained in the PAM amplitudes MxN parameters array. Note 1: The Gray code feature is disabled when User-defined PAM map is selected. Note 2: When re-constructing the bit sequence for an odd bits/symbol PAM system, the last bit symbol will be incomplete (as the bit sequence length in OptiSystem is always a power of 2). It is thus recommended to ignore the bits associated with the final symbol when performing BER analysis. PAM data, and associated source symbols, can be loaded initially from a data file (the default is otherwise PAM4). The required format is two tab-delimited, or spaced, columns as follows (example here is for PAM8): 000 -7 001 -5 010 -3 011 -1 100 1 101 3 110 5 111 7 References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). 917 PAM SEQUENCE DECODER 918 QAM SEQUENCE DECODER QAM Sequence Decoder Decodes two parallel QAM M-ary symbol sequences to a binary signal. Ports Name and description Port type Signal type Input - I Input M-ary Input - Q Input M-ary Bit sequence Output Binary Parameters Main Name and description Default value Bits per symbol (b/sym) 2 Units Value range [0,100] Number of bits per symbol used in the coding Constellation map Square - Square, Star, Circular - - - Defines the type of QAM constellation map to be coded. If set to Star or Circular the symbols are arranged evenly onto concentric circles with radii defined by the parameter Star and cicular level radii Star and circular level radii Defines the amplitude of the radius for each concentric circle. The format is r1 r2 ...rN (space delimited). For example if set to “1”, all symbols will be placed along a concentic circle of radius = 1. If set to “1 2”, symbols will be allocated evenly onto two concentric circles of radii 1 and 2. NOTE: The number of radii must be set to a power of 2 value (2, 4, 8, ...) to ensure an even distribution of symbols for all concentric circles. Also, no more than 16 symbols can be placed on any concentric circle. Gray code False True, False Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used 919 QAM SEQUENCE DECODER Name and description Default value Units Value range Differential coding False True, False False True, False Defines whether to use Differential encoding. If Differential encoding is selected, Graycoding cannot be used User-defined I-Q map Defines whether to calculate IQ values based on userdefined values I-Q amplitudes (a.u.) 64x3 I-Q amplitudes file name QAM_IQ.dat Name of file that contains initial I-Q values Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled Technical background In the QAM sequence decoder, the bit sequence is split into two parallel subsequences, each can be transmitted in two quadrature carriers when building a QAM modulator. This is achieved by using a serial to parallel converter. Square QAM maps When transmitting information, we can vary the amplitude of a signal according to the source symbols. For each output port, the value of the amplitude takes value from the set of amplitudes [1][ a 1 = 2i – 1 – M i = 1 2 ..., M where M is the number of possible sequence of binary digits, calculated according to: M = 2 h2 where h is the number of bits per symbol. The equivalent QAM set is given by the square of M . This means: If h = QAM. 920 2 , M = 2 , then we have a 4-QAM. If h = 4 , M = 4 , then we have a 16- QAM SEQUENCE DECODER If h = 6 , 256-QAM. M = 8 , then we have a 64-QAM. If h = 8 , M = 16 , then we have a The QAM decoder calculates the value of i for the amplitude of each signal input k : i = ak + 1 + M 2 and convert the values of i to the equivalent binary sequence. If bits per symbol ( h ) equals 4, we have a 16-QAM that requires 2 consecutive bits from the input sequence for each sub-sequence: Sequence Subsequence I/i a Subsequence Q / i a 0000 00 / 1 -3 00 / 1 -3 0001 00 / 1 -3 01 / 2 -1 0010 00 / 1 -3 10 / 3 1 0011 00 / 1 -3 11 / 4 3 0100 01 / 2 -1 00 / 1 -3 0101 01 / 2 -1 01 / 2 -1 0110 01 / 2 -1 10 / 3 1 0111 01 / 2 -1 11 / 4 3 1000 10 / 3 1 00 / 1 -3 1001 10 / 3 1 01 / 2 -1 1010 10 / 3 1 10 / 3 1 1011 10 / 3 1 11 / 4 3 1100 11 / 4 3 00 / 1 -3 1101 11 / 4 3 01 / 2 -1 1110 11 / 4 3 10 / 3 1 1111 11 / 4 3 11 / 4 3 Using Gray code, adjacent signal amplitudes that correspond to binary sequences will differ by only one digit. Star and Circular QAM maps Star and Circular constellations can also be decoded by the QAM sequence decoder. These are defined with the Constellation map and Star and circular level radii parameters. For example (Fig 1) to decode a 16-QAM star constellation with two orbital levels of radii 1 and 2, set the parameters Bits per symbol (b/sym) = 4, Constellation map = Star and Star and circular level radii = 1 2 (the format is r1 r2....rN - space delimited). 921 QAM SEQUENCE DECODER NOTE: The number of radii must be set to a power of 2 value (2, 4, 8,...) to ensure an even distribution of symbols along all the concentric circles (orbitals). Also, no more than 16 symbols can be placed on any concentric circle. Figure 1 16-QAM star with two orbital levels (2 amplitudes and 8 phases) User Defined QAM maps When User-defined I-Q map is selected, the component will determine the associated bit symbol based on the I and Q amplitudes contained in the I-Q amplitudes MxN parameters array. Note 1: The Gray code feature is disabled when User-defined I-Q map is selected. Note 2: When re-constructing the bit sequence for an odd bits/symbol QAM system, the last bit symbol will be incomplete (as the bit sequence length in OptiSystem is always a power of 2). It is thus recommended to ignore the bits associated with the final symbol when performing BER analysis. I-Q data, and associated source symbols, can be loaded initially from a data file (the default is otherwise 16-QAM). The required format is three tab-delimited, or spaced, columns as follows (example here is for 16-QAM): 922 Sequence I Q 0000 -3 -3 0001 -3 -1 0010 -3 1 0011 -3 3 0100 -1 -3 QAM SEQUENCE DECODER Sequence I Q 0101 -1 -1 0110 -1 1 0111 -1 3 1000 1 -3 1001 1 -1 1010 1 1 1011 1 3 1100 3 -3 1101 3 -1 1110 3 1 1111 3 3 Please refer to the “Advanced modulation formats/QAM systems” folder in the “Samples” directory for example data files for 4-QAM, 8-QAM, 16-QAM, 32-QAM and 64-QAM I-Q maps Differential coding [2, 3] Differential encoding/decoding is used to resolve phase ambiguity problems with mQAM and mPSK modulation formats. Note: The Differential coding feature is disabled when User-defined I-Q map is selected For 32-QAM and 128-QAM square constellations a look up table based on Ref 3 is used. For all other constellations the technique defined in Ref 2 is used For example, two-stage differential decoding is used for 16-QAM to detect the correct bit sequence. The quadrant center can be decided as: Ĉ p i = R sign real X i + jsign imag X i (1) where real[x] and imag[x] denote the real and imaginary parts of a complex number x, respectively, and sign(x) denotes the sign of the number. From Cp(i) and Cp(i-1) the first differential angle and the corresponding dibit can be detected according to the following rule: Cp(i) x (Cp(i-1))* Differential angle R2 0 jR2 /2 923 QAM SEQUENCE DECODER -R2 -jR2 3/2 Once Cp(i) and have been detected, the second displacement vector can be similarly obtained: D̂ p i = r sign real X i – Ĉ p i + jsign imag X i – Ĉ p i (2) and the second differential angle detected as follows: Dp(i) x (Dp(i-1))* Differential angle r2 0 jr2 /2 -r2 -jr2 3/2 The symbols are then decoded according to the following mapping table: Dibit Differential angle 00 0 01 /2 11 01 3/2 References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] J.-K. Hwang, Y.-L. Chiu, and C.-S. Liao, "Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system," Int. J. Commun. Syst., vol. 21, no. 6, pp. 631-641, 2008. [3] Wei, Ruey Y, “Differential encoding by a look-up table for quadrature-amplitude modulation”, IEEE Transactions on Communications, V59 2011, pp 84-94 924 PSK SEQUENCE DECODER PSK Sequence Decoder Ports Name and description Port type Signal type Input - I Input M-ary Input - Q Input M-ary Bit sequence Output Binary Parameters Main Name and description Default value Bits per symbol (b/sym) 2 Units Value range [0,100] Number of bits per symbol used in the coding Phase offset 45 deg, rad ]-INF, +INF[ Initial phase offset Gray code False True, False False True, False Defines whether to use Gray coding. If Gray coding is selected, Differential coding cannot be used Differential coding (2 b/sym only) Defines whether to use Differential encoding. This feature is disabled if bits/symbol is not equal to 4.If Differential encoding is selected, Graycoding cannot be used Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled 925 PSK SEQUENCE DECODER Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1]: 2 i = ------ i – 1 + i = 1 2 ...M M where M is the number of possible sequence of binary digits, calculated according to: M = 2 h where h is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature channel will have amplitudes according to: I i = cos i i = 1 2 ...M Q i = sin i i = 1 2 ...M The PSK decoder will calculate the value of i for the phase of each signal input k : k = arc tan Q k I k k – M i = ------------------------- + 1 2 and convert the values of i to the equivalent binary sequence. Assuming = 0 , if bits per symbol ( h ) equals 2, and I and Q will be: Bit sequence I Q 00 1 0 01 0 1 10 -1 0 11 0 -1 926 M = 4 , then the values for PSK SEQUENCE DECODER Assuming = 0 , if bits per symbol ( h ) equals 3, and I and Q will be Bit sequence I Q 000 1 0 M = 8 , then the values for 001 ------22 010 0 ------22 1 011 2 – ------2 100 -1 ------22 0 101 2 – ------2 2 – ------2 110 0 -1 111 ------22 2 – ------2 Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. Differential coding [2] The decision of the symbol is detected as:: Ŝ p i = r sign real X i + jsign imag X i (1) where real[x] and imag[x] denote the real and imaginary parts of a complex number x, respectively, and sign(x) denotes the sign of the number. From Sp(i) and Sp(i-1) the differential angle and the corresponding dibit can be detected according to the following rule: Cp(i) x (Cp(i-1))* Differential angle r2 0 jr2 /2 -r2 -jr2 3/2 927 PSK SEQUENCE DECODER The symbols are then decoded according to the following mapping table: Dibit Differential angle 00 0 01 /2 11 01 3/2 References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] J.-K. Hwang, Y.-L. Chiu, and C.-S. Liao, "Angle differential-QAM scheme for resolving phase ambiguity in continuous transmission system," Int. J. Commun. Syst., vol. 21, no. 6, pp. 631-641, 2008. 928 DPSK SEQUENCE DECODER DPSK Sequence Decoder Decodes two parallel DPSK M-ary symbol sequences to binary signals. Ports Name and description Port type Signal type Input - I Input M-ary Input - Q Input M-ary Bit sequence Output Binary Parameters Main Name and description Default value Bits per symbol 2 Units Value range [0,100] Number of bits per symbol used in the coding Phase offset 45 deg, rad ]-INF, +INF[ Initial phase offset Gray code False True, False Defines whether or not to use Gray code Simulation Name and description Default value Default unit Units Value range Enabled True — — True, False Determines whether or not the component is enabled 929 DPSK SEQUENCE DECODER Technical background When transmitting information, we can vary the phase of a signal according to the source symbols. The phase values are taken from the set of angles [1], [2]: 2 ki = k – 1 + ------ i – 1 + i = 1 2 ...M M where ki is the phase value for the current symbol, and the previous symbol. k – 1 is phase value for M is the number of possible sequence of binary digits, calculated according to: M = 2 h where h is the number of bits per symbol, and is the phase offset. The in-phase and the quadrature-channel will have amplitudes according to: I ki = cos ki i = 1 2 ...M Q ki = sin ki i = 1 2 ...M i from the phase difference between The DPSK decoder will calculate the value of consecutive signals k and k – 1 : k = arc tan Q k I k k – k – 1 – M i = ------------------------------------------- + 1 2 Assuming = 0 , if bits per symbol ( h ) equals 2, M equals 4, the values of I and Q will be: k Bit sequence I Q 0 00 1 0 1 01 0 1 2 10 -1 0 3 11 0 -1 930 DPSK SEQUENCE DECODER Assuming Q will be: = 0 , if bits per symbol ( h ) equals 3, M equals 8, the values of I and k Bit sequence I Q 0 000 1 0 1 001 ------22 2 010 3 011 0 ------22 1 2 – ------2 ------22 4 100 5 101 -1 0 2 – ------2 6 110 7 111 0 2 – ------2 -1 ------22 2 – ------2 Using Gray code, the adjacent signal amplitudes that correspond to the binary sequences will differ by only one digit. 931 DPSK SEQUENCE DECODER References [1] Benedetto, S., Biglieri, E., Castellani, V., Digital Transmission Theory. Prentice-Hall, N.Y., (1987). [2] Pawula, R.F., “On M-ary DPSK Transmission Over Terrestrial and Satellite Channels”, IEEE Trans. on Commun. COM-32, 752-761, (July 1984). 932 PPM SEQUENCE DECODER PPM Sequence Decoder Decodes a pulse position modulation (PPM) symbol sequence to a binary signal. Ports Name and description Port type Signal type PPM Sequence Input Binary Bit Sequence Output Binary Parameters Main Name and description Default value Units Value range Bits per symbol 2 - [0,100] Number of bits per symbol used in the coding Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background The decoder reads the sequence of symbols from the input port and converts them back into binary code [1]. For instance, given the symbol sequence 0000 0100 0001 0000 0000 0010 0000 0001 1000 0000, with 3 bits per symbol, the original bit sequence is Symbols Position Bit sequence 0000 0100 5 101 0001 0000 3 011 933 PPM SEQUENCE DECODER Symbols Position Bit sequence 0000 0010 6 110 0000 0001 7 111 1000 0000 0 000 References [1] Z. Ghassemlooy, A. R. Hayes, “Digital pulse interval modulation for IR communication systems-a review”, Int. J. Commun. Syst, vol 13, pp 519-536, Nov 2000. 934 DPIM SEQUENCE DECODER DPIM Sequence Decoder Decodes a digital pulse interval modulation (DPIM) symbol sequence to a binary signal. Ports Name and description Port type Signal type DPIM Sequence Input Binary Bit Sequence Output Binary Parameters Main Name and description Default value Units Value range Bits per symbol 2 - [0,100] Number of bits per symbol used in the coding Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background The decoder reads the sequence of symbols from the input port and converts them back into binary code [1]. For instance, given the symbol sequence 10 100 1000 10000, with 2 bits per symbol, the original bit sequence is Symbols Position Bit sequence 10 1 00 935 DPIM SEQUENCE DECODER Symbols Position Bit sequence 100 2 01 1000 3 10 10000 4 11 If the symbol sequence is 1000 10 100 100 100000, with 3 bits per symbol, the original bit sequence is Symbols Position Bit sequence 1000 3 010 10 1 000 100 4 001 100 2 001 100000 5 100 References [1] Z. Ghassemlooy, A. R. Hayes, “Digital pulse interval modulation for IR communication systems-a review”, Int. J. Commun. Syst, vol 13, pp 519-536, Nov 2000. 936 4B5B SEQUENCE DECODER 4B5B Sequence Decoder Decodes a 4B/5B symbol sequence to a binary signal. Ports Name and description Port type Signal type 4B5B Sequence Input Binary Bit Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background The decoder reads the sequence of 4B/5B symbols from the input port and converts them back into binary code [1]. The decoder reads the 5-Bit symbols, matches them to corresponding 4-Bit symbols, and returns the original signal. References [1] B. A. Forouzan, Data Communications and Networking, McGraw-Hill Science, 2003. 937 4B5B SEQUENCE DECODER Notes: 938 NRZI SEQUENCE DECODER NRZI Sequence Decoder Decodes a non-return to zero inverted (NRZI) symbol sequence to a binary signal. Ports Name and description Port type Signal type NRZI Sequence Input Binary Bit Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background The decoder reads the sequence of NRZI symbols from the input port and converts them back into binary code [1]. If 10111011100 is an NRZI bit sequence, then the original signal is 11100110010. References [1] B. A. Forouzan, Data Communications and Networking, McGraw-Hill Science, 2003. 939 NRZI SEQUENCE DECODER 940 AMI SEQUENCE DECODER AMI Sequence Decoder Decodes an alternate mark inversion (AMI) symbol sequence to a binary signal. Ports Name and description Port type Signal type AMI Sequence Input Binary Bit Sequence Output Binary Parameters Main Name and description Default value Units Value range Encoding type Bipolar - Bipolar, B8ZS, B6ZS, B3ZS, HDB3 Name and description Default value Units Value range Enabled True - True, False Simulation Determines whether or not the component is enabled Technical background Different decoding types are available [1] [2]: Bipolar Converts an M-ary AMI sequence of +’s, 0’s and –‘s into 1’s and 0’s, where a + or a – represent a 1, and a 0 represents 0. Bipolar AMI sequence Sequence +00-+-+0- 100111101 941 AMI SEQUENCE DECODER Bipolar AMI sequence Sequence 0+-00+-+- 011001111 B8ZS Searches for the following patters: 000-+0+- or 000+-0-+, and replaces them with 0’s. B8ZS AMI sequence Bipolar AMI sequence Sequence +0-000-+0+-+-0 +0-00000000+-0 10100000000110 +000+-0-+-+0-+ +00000000-+0-+ 10000000011011 B6ZS This mode is the exact same as the B8ZS, except it searches for 0-+0+- and 0+-0-+. B6ZS AMI sequence Bipolar AMI sequence Sequence +0-0-+0+-+-0 +0-000000+-0 101000000110 +0+-0-+-+0-+ +000000-+0-+ 100000011011 B3ZS This mode scans for the following patterns: 00-, 00+, -0-, +0+, and replaces each one with three zeros, depending on the preceding bit and on the number of non-zero bits there were since the last substitution. B3ZS AMI Sequence Sequence +0-00-+-0+00+ 1010001101000 +0-+-0-+-+0+ 101100011000 HDB3 This mode is the exact same as the B3ZS, except the patters are: 000-, 000+, +00+, -00-. HDB3 AMI Sequence Sequence +0-000-+-0+000+ 101000011010000 +0-+-00-+-+00+ 10110000110000 942 AMI SEQUENCE DECODER References [1] W. Stallings, Data and Computer Communications, Prentice Hall, 2006. [2] D. R. Smith, Digital Transmission Systems, Springer, 2003. 943 AMI SEQUENCE DECODER Notes: 944 MANCHESTER SEQUENCE DECODER Manchester Sequence Decoder Decodes a Manchester symbol sequence to a binary signal. Ports Name and description Port type Signal type Manchester sequence Input Binary Bit Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background The component decodes a sequence by generating a 1 symbol for a 1->0 transition and a 0 symbol for a 0->1 transition The bandwidth of the decoded signal is half the original bandwidth [1].. Sequence Manchester sequence 1001100110011001 10101010 1010100101011001 11100010 References [1] B. A. Forouzan, Data Communications and Networking, McGraw-Hill Science, 2003. 945 MANCHESTER SEQUENCE DECODER Notes: 946 4B3T SEQUENCE DECODER 4B3T Sequence Decoder Decodes a 4B3T symbol sequence to a binary signal. Ports Name and description Port type Signal type 4B3T sequence Input Binary Bit Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background This mapping from 4 bits to 3 ternary states is given in a table known as Modified Monitoring State 43 (MMS43) [1] [2]. Because the each block of three ternary symbols is uniquely associated with one block of four bits, the decoder can directly map the ternary symbol back to information bits by table lookup. References [1] D. J. Morris, Pulse Code Formats for Fiber Optical Data Communication, CRC, 1983. [2] D. R. Smith, Digital Transmission Systems, Springer, 2003. 947 4B3T SEQUENCE DECODER Notes: 948 8B10B SEQUENCE DECODER 8B10B Sequence Decoder Decodes a 8B10B symbol sequence to a binary signal. Ports Name and description Port type Signal type 8B10B sequence Input Binary Bit Sequence Output Binary Parameters Simulation Name and description Default value Units Value range Enabled True - True, False Determines whether or not the component is enabled Technical background Described in [1] in detail, 8B10B coding decomposes each 8-bits into two blocks of 5 bits and 3 bits, converting them to 6-bit and 4-bit equivalents, respectively. Each consecutive blocks exhibit a total average of zero (DC-balanced). References [1] A. X. Widmer, P. A. Franaszek, “A DC-Balanced, Partitioned-Block, 8B/10B Transmission Code”, IBM Journal of Research and Development, Vol 27, No 5, pp 440, 1983. 949 8B10B SEQUENCE DECODER 950 8B10B SEQUENCE DECODER Receivers Library Optical receivers • Optical Receiver • Optical DPSK Receiver • Optical Coherent PSK/QAM Receiver • Optical Coherent QAM Receiver • Optical Coherent DP PSK/QAM Receiver • Optical Coherent DP-16-QAM Receiver • 90 Degree Optical Hybrid 951 8B10B SEQUENCE DECODER 952 OPTICAL RECEIVER Optical Receiver This component is an optical receiver subsystem built using a PIN or APD photodetector, a Bessel filter and a 3R regenerator. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals, Noise bins Bit Sequence Output Binary Reference Output Electrical Output Output Electrical Default unit Units Parameters Main Name and description Default value Value range Photodetector PIN [PIN, APD] 3 [0, 1e+100] 0.9 [1e-100, 1] Select the photodetector type: PIN or APD Gain The avalanche gain for the photodetector APD Ionization ratio The ionization ratio for the photodetector APD Responsivity 1 A/W [0, 100] 10 nA [0, 1e+100] The responsivity of the photodetector Dark current The photodetector dark current 953 OPTICAL RECEIVER Name and description Default value Default unit Units Value range Responsivity type APD Constant [Constant, User defined Responsivity type PIN Constant [Constant, Si, Ge, InGaAs, User defined] Responsivity vs. wavelength Responsivity.dat Low Pass Filter Name and description Default value Default unit Units Value range Cutoff frequency 0.75* bit rate Hz Hz, MHz, GHz [0, 1e+100] 0 dB [0, 1e+100] 100 dB [0, 1e+100] 3-dB cutoff frequency of the filter Insertion loss Insertion loss of the filter Depth Maximum attenuation value for the filter Order 4 [1, 100] Order of the function 3R Regenerator Name and description Default value Default unit Units Value range Reference bit rate Bit rate Bits/s Bits/s, MBits/s, GBits/s [0, 1e+012] Reference bit rate to use for the decision instant calculation User defined delay NO [YES, NO] Defines whether the user can define the delay compensation Delay compensation 0 s Delay to apply to the signal input User defined decision NO s, ms, us, ns, ps, fs [-1e+100, 1e+100] [YES, NO] Defines whether the component will automatically calculate the decision instant or it will be defined by the user Decision instant Value for the decision instant to use when recovering the bit sequence 954 0.5 Bit [0, 1] OPTICAL RECEIVER Name and description Default value User defined threshold NO Default unit Units Value range [YES, NO] Defines whether the threshold will be automatically calculated or it will be user defined Absolute threshold 0.5 a.u Name and description Default value Default unit Centered at max power YES [-1e+100, 1e+100] Value for the threshold to use when recovering the bit sequence Down-sampling Units Value range [YES, NO] Determines whether the internal filter will be centered at the maximum amplitude of the signal or it will be user defined Center frequency 193.1 THz Hz, THz, nm [30, 300000] 5* (Sample rate) Hz Hz, GHz, THz, nm [1, 1e+100] Name and description Default value Default unit Units Value range Noise calculation type Numerical Analytical, Numerical, Numerical convert noise bins Add signal-ASE noise YES [YES, NO] Add ASE-ASE noise YES [YES, NO] Add shot noise YES [YES, NO] Add thermal noise YES [YES, NO] Estimate receiver noise NO [YES, NO] User-defined center frequency of the internal filter Sample rate Sample rate of the signal output Noise Determines if shot noise is added to the signal Determines whether the receiver should estimate the thermal noise or not Thermal noise 1e-22 W/Hz W/Hz, A/Hz^.5 [0, 1e+100] 955 OPTICAL RECEIVER Name and description Default value Default unit Units Value range Approximate sensitivity -18 dBm [-1e+100,0] 10 dB [0, 1e+100] The receiver sensitivity parameter Reference extinction ratio Reference extinction ratio used to measured the sensitivity Reference Q factor 6.4624 [0, 1000] Target Q factor for the current sensitivity Random Numbers Name and description Default value Default unit Units Value range Generate random seed YES [YES, NO] 0 [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background This component is an optical receiver subsystem. The subsystem was built using two different types of photo-detectors, one Bessel filter and the 3R Regenerator. The component properties allow the user to select the internal component parameters. Depending on the choice between PIN and APD, the Switch/Select components will redirect the signal into the proper photodetector type. 956 OPTICAL RECEIVER When Estimate receiver sensitivity is enabled, the parameters Approximate sensitivity (Psen), Reference extinction ratio (ER) and Reference Q factor (Qref) are used to calculate the associated shot and thermal noise RMS currents as follows: shot = K 12 + 20 thermal (1) i1 – i0 -------------- – shot Q ref = --------------------------------2 NEB where, 1 P 0 = 2 P sen ----------------- ER + 1 ER P 1 = 2 P sen ----------------- ER + 1 i0 = M R P0 + id i1 = M R P1 + id (2) 12 2 = NEB c M EF R P 1 + i d 2 20 = NEB c M EF R P 0 + i d K = 1 Q ref NEB = 2 f cutoff In the above equations, P0 and P1 represent the expected receive power levels for Logic 0 and Logic 1, i0 and i1 represent the resulting detection currents (based on responsivity R and the dark current id), c is the elementary electron charge, M is the APD gain factor, EF is the Excess Noise Factor, NEB is the noise equivalent bandwidth and fcutoff is the filter cut-off frequency. Note: For the case of a PIN photodetector M=1 and EF=1. 957 OPTICAL RECEIVER 958 OPTICAL DPSK RECEIVER Optical DPSK Receiver The component simulates a differential phase-shift keying receiver. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals, Noise bins Output Output Electrical - Parameters MZI Name and description Default value Default unit Units Value range Delay 1 / Bit rate s s, ms, us, ns, ps, fs [ 0, 1e100] 1550 nm Hz, THz, nm [1300, 1800] Name and description Default value Default unit Units Value range Photodetector PIN - - [PIN, APD] 3 - - [0, 1e+100] Time delay applied in one of the interferometer arms Reference Wavelength Wavelength that will be referenced for the time delay Photodetector Select the photodetectors type: PIN or APD Gain The avalanche gain for the photodetector APD 959 OPTICAL DPSK RECEIVER Name and description Default value Default unit Units Value range Ionization ratio 0.9 - - [1e-100, 1] 1 A/W - [0, 100] 10 nA - [0, 1e+100] The ionization ratio for the photodetector APD Responsivity The responsivity of the photodetector Dark current The photodetector dark current Responsivity type APD Constant [Constant, User defined Responsivity type PIN Constant [Constant, Si, Ge, InGaAs, User defined] Responsivity vs. wavelength Responsivity.dat Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 300000] 5* (Sample rate) Hz Hz, GHz, THz, nm [1, 1e+100] Name and description Default value Default unit Units Value range Noise calculation type Numerical - - Analytical, Numerical, Numerical convert noise bins Add signal-ASE noise True - - True, False Add ASE-ASE noise True - - True, False Add thermal noise True - - True, False Thermal noise 1e-22 W/Hz W/Hz, A/Hz^.5 [0, 1e+100] Determines whether the internal filter will be centered at the maximum amplitude of the signal or will it be user defined Center frequency User-defined center frequency of the internal filter Sample rate Sample rate of the signal output Noise 960 OPTICAL DPSK RECEIVER Name and description Default value Default unit Units Value range Add shot noise True - - True, False Gaussian - - Poisson, Gaussian Name and description Default value Default unit Units Value range Generate random seed True - - True, False 0 - - [0, 4999] 1 - - [0, 4999] Determines if shot noise is added to the signal Shot noise distribution Determines the distribution used to generate the shot noise Random Numbers Determines if the seed is automatically defined and unique Random seed index PD 1 User-defined seed index for noise generation for photodetector 1 Random seed index PD 2 User-defined seed index for noise generation for photodetector 2 961 OPTICAL DPSK RECEIVER Technical background The DPSK receiver consists of a Mach-Zehnder interferometer (MZI) for delay demodulation and followed by balanced detection. Figure below shows the layout representing the receiver. Figure 1 DPSK receiver layout 962 OPTICAL DPSK RECEIVER Notes: 963 OPTICAL DPSK RECEIVER 964 OPTICAL COHERENT PSK/QAM RECEIVER Optical Coherent PSK/QAM Receiver The component simulates an optical coherent receiver for m-PSK or m-QAM signals based on an homodyne design. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals, Noise bins External oscillator Input Optical Sampled signals, Noise bins Output - I Output Electrical - Output - Q Output Electrical - Parameters Local oscillatorI Name and description Default value Default unit Units Value range External oscillator False - - True, False 193.1 THz Hz,THz, nm [0,+INF[ Power 0 dBm W, mW, dBm ]-INF,+INF[ Linewidth 0.01 MHz - [0,+INF[ Initial phase 0 deg - ]-INF,+INF[ LO sample rate Sample rate Hz Hz, GHz, THz, nm [1, 1e+100] Defines if the local oscillator will have the input signal generated internally or will it be generated by an external source Frequency Emission frequency Sample rate of the local oscillator 965 OPTICAL COHERENT PSK/QAM RECEIVER Photodetector Name and description Default value Default unit Units Value range Photodetector PIN - - PIN, APD 3 - - [0, 1e+100] 0.9 - - [1e-100, 1] 1 A/W - [0, 100] 10 nA - [0, 1e+100] Select the photodetector type: PIN or APD Gain The avalanche gain for the photodetector APD Ionization ratio The ionization ratio for the photodetector APD Responsivity The responsivity of the photodetector Dark current The photodetector dark current Responsivity type APD Constant [Constant, User defined Responsivity type PIN Constant [Constant, Si, Ge, InGaAs, User defined] Responsivity vs. wavelength Responsivity.dat Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 300000] 5* (Sample rate) Hz Hz, GHz, THz, nm [1, 1e+100] Determines whether the internal filter will be centered at the maximum amplitude of the signal or will it be user defined Center frequency User-defined center frequency of the internal filter Sample rate Sample rate of the signal output 966 OPTICAL COHERENT PSK/QAM RECEIVER Noise Name and description Default value Default unit Units Value range Noise calculation type Numerical - - Analytical, Numerical, Numerical convert noise bins Add signal-ASE noise True - - True, False Add ASE-ASE noise True - - True, False Add thermal noise True - - True, False Thermal noise 1e-22 W/Hz W/Hz, A/Hz^.5 [0, 1e+100] Add shot noise True - - True, False Gaussian - - Poisson, Gaussian Determines if shot noise is added to the signal Shot noise distribution Determines the distribution used to generate the shot noise Simulation Name and description Default value Default unit Units Value range Iterations Iterations - - [1,+INF[ Number of times to repeat the calculation Random Numbers Name and description Default value Default unit Units Value range Generate random seed True - - True, False 0 - - [0, 4999] 1 - - [0, 4999] 2 - - [0, 4999] Determines if the seed is automatically defined and unique Random seed index PD 1 User-defined seed index for noise generation for photodetector 1 Random seed index PD 2 User-defined seed index for noise generation for photodetector 2 Random seed index PD 3 User-defined seed index for noise generation for photodetector 3 967 OPTICAL COHERENT PSK/QAM RECEIVER Name and description Default value Default unit Units Value range Random seed index PD 4 3 - - [0, 4999] 0 - - [0, 4999] User-defined seed index for noise generation for photodetector 4 Random seed index LO User-defined seed index for noise generation for local oscillator Technical background The optical coherent PSK receiver consists of a homodyne receiver design. The component is formed by a set of 3 dB fiber couplers, an LO laser, and a balanced detection. Figure 1 shows the layout representing the receiver. Figure 1 PSK receiver layout 968 OPTICAL COHERENT QAM RECEIVER Optical Coherent QAM Receiver The component simulates an optical coherent receiver for QAM signals based on a homodyne design. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals, Noise bins External oscillator Input Optical Sampled signals, Noise bins Output - I Output Electrical - Output - Q Output Electrical - Parameters Local oscillatorI Name and description Default value Default unit Units Value range External oscillator False - - True, False 193.1 THz Hz,THz, nm [0,+INF[ Power 0 dBm W, mW, dBm ]-INF,+INF[ Linewidth 0.01 MHz - [0,+INF[ Initial phase 0 deg - ]-INF,+INF[ LO sample rate Sample rate Hz Hz, GHz, THz, nm [1, 1e+100] Defines if the local oscillator will have the input signal generated internally or will it be generated by an external source Frequency Emission frequency Sample rate of the local oscillator 969 OPTICAL COHERENT QAM RECEIVER Photodetector Name and description Default value Default unit Units Value range Photodetector PIN - - PIN, APD 3 - - [0, 1e+100] 0.9 - - [1e-100, 1] 1 A/W - [0, 100] 10 nA - [0, 1e+100] Select the photodetectors type: PIN or APD Gain The avalanche gain for the photodetector APD Ionization ratio The ionization ratio for the photodetector APD Responsivity The responsivity of the photodetector Dark current The photodetector dark current Responsivity type APD Constant [Constant, User defined Responsivity type PIN Constant [Constant, Si, Ge, InGaAs, User defined] Responsivity vs. wavelength Responsivity.dat Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 300000] 5* (Sample rate) Hz Hz, GHz, THz, nm [1, 1e+100] Determines whether the internal filter will be centered at the maximum amplitude of the signal or will it be user defined Center frequency User-defined center frequency of the internal filter Sample rate Sample rate of the signal output 970 OPTICAL COHERENT QAM RECEIVER Noise Name and description Default value Default unit Units Value range Noise calculation type Numerical - - Analytical, Numerical, Numerical convert noise bins Add signal-ASE noise True - - True, False Add ASE-ASE noise True - - True, False Add thermal noise True - - True, False Thermal noise 1e-22 W/Hz W/Hz, A/Hz^.5 [0, 1e+100] Add shot noise True - - True, False Gaussian - - Poisson, Gaussian Determines if shot noise is added to the signal Shot noise distribution Determines the distribution used to generate the shot noise Simulation Name and description Default value Default unit Units Value range Iterations Iterations - - [1,+INF[ Number of times to repeat the calculation Random Numbers Name and description Default value Default unit Units Value range Generate random seed True - - True, False 0 - - [0, 4999] 1 - - [0, 4999] 2 - - [0, 4999] Determines if the seed is automatically defined and unique Random seed index PD 1 User-defined seed index for noise generation for photodetector 1 Random seed index PD 2 User-defined seed index for noise generation for photodetector 2 Random seed index PD 3 User-defined seed index for noise generation for photodetector 3 971 OPTICAL COHERENT QAM RECEIVER Name and description Default value Default unit Units Value range Random seed index PD 4 3 - - [0, 4999] 0 - - [0, 4999] User-defined seed index for noise generation for photodetector 4 Random seed index LO User-defined seed index for noise generation for local oscillator Technical background The optical coherent QAM receiver consists of a homodyne receiver design. The component is formed by a set of 3 dB fiber couplers, a LO laser, and balanced detection. Figure below shows the layout representing the receiver. Figure 1 QAM receiver layout 972 OPTICAL COHERENT DP PSK/QAM RECEIVER Optical Coherent DP PSK/QAM Receiver The component simulates an optical dual-polarization coherent receiver for m-PSK or m-QAM signals based on a homodyne design. Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals, Noise bins External oscillator Input Optical Sampled signals, Noise bins Output X- I Output Electrical - Output X- Q Output Electrical - Output Y- I Output Electrical - Output Y- Q Output Electrical - Parameters Local oscillator Name and description Default value Default unit Units Value range External oscillator False - - True, False 193.1 THz Hz,THz, nm [0,+INF[ Power 0 dBm W, mW, dBm ]-INF,+INF[ Linewidth 0.01 MHz - [0,+INF[ Initial phase 0 deg - ]-INF,+INF[ Defines if the local oscillator will have the input signal generated internally or will it be generated by an external source Frequency Emission frequency 973 OPTICAL COHERENT DP PSK/QAM RECEIVER Name and description Default value Default unit Units Value range LO sample rate Sample rate Hz Hz, GHz, THz, nm [1, 1e+100] Name and description Default value Default unit Units Value range Photodetector PIN - - [PIN, APD] 3 - - [0, 1e+100] 0.9 - - [1e-100, 1] 1 A/W - [0, 100] 10 nA - [0, 1e+100] Sample rate of the local oscillator Photodetector Select the photodetectors type: PIN or APD Gain The avalanche gain for the photodetector APD Ionization ratio The ionization ratio for the photodetector APD Responsivity The responsivity of the photodetector Dark current The photodetector dark current Responsivity type APD Constant [Constant, User defined Responsivity type PIN Constant [Constant, Si, Ge, InGaAs, User defined] Responsivity vs. wavelength Responsivity.dat Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 300000] 5* (Sample rate) Hz Hz, GHz, THz, nm [1, 1e+100] Determines whether the internal filter will be centered at the maximum amplitude of the signal or will it be user defined Center frequency User-defined center frequency of the internal filter Sample rate Sample rate of the signal output 974 OPTICAL COHERENT DP PSK/QAM RECEIVER Noise Name and description Default value Default unit Units Value range Noise calculation type Numerical - - Analytical, Numerical, Numerical convert noise bins Add signal-ASE noise True - - True, False Add ASE-ASE noise True - - True, False Add thermal noise True - - True, False Thermal noise 1e-22 W/Hz W/Hz, A/Hz^.5 [0, 1e+100] Add shot noise True - - True, False Gaussian - - Poisson, Gaussian Determines if shot noise is added to the signal Shot noise distribution Determines the distribution used to generate the shot noise Simulation Name and description Default value Default unit Units Value range Iterations Iterations - - [1,+INF[ Number of times to repeat the calculation Random Numbers Name and description Default value Default unit Units Value range Generate random seed True - - True, False 0 - - [0, 4999] 1 - - [0, 4999] 2 - - [0, 4999] Determines if the seed is automatically defined and unique Random seed index PD 1 User-defined seed index for noise generation for photodetector 1 Random seed index PD 2 User-defined seed index for noise generation for photodetector 2 Random seed index PD 3 User-defined seed index for noise generation for photodetector 3 975 OPTICAL COHERENT DP PSK/QAM RECEIVER Name and description Default value Default unit Units Value range Random seed index PD 4 3 - - [0, 4999] 0 - - [0, 4999] User-defined seed index for noise generation for photodetector 4 Random seed index LO User-defined seed index for noise generation for local oscillator Technical background The optical coherent dual-polarization PSK receiver consists of a homodyne receiver design. The component has a LO laser polarized at 45o relative to the polarization beam splitter, and the received signal is separately demodulated by each LO component using two single polarization PSK receivers. Figure 1 shows the layout representing the receiver. Figure 1 DP-QSK receiver layout 976 OPTICAL COHERENT DP-16-QAM RECEIVER Optical Coherent DP-16-QAM Receiver This component simulates an optical coherent receiver for dual-polarization 16-QAM signals based on a homodyne design Ports Name and description Port type Signal type Supported Modes Input Input Optical Sampled signals, Noise bins External oscillator Input Optical Sampled signals, Noise bins Output X- I Output Electrical - Output X- Q Output Electrical - Output Y- I Output Electrical - Output Y- Q Output Electrical - Parameters Local oscillator Name and description Default value Default unit Units Value range External oscillator False - - True, False 193.1 THz Hz,THz, nm [0,+INF[ Power 0 dBm W, mW, dBm ]-INF,+INF[ Linewidth 0.01 MHz - [0,+INF[ Initial phase 0 deg - ]-INF,+INF[ Defines if the local oscillator will have the input signal generated internally or will it be generated by an external source Frequency Emission frequency 977 OPTICAL COHERENT DP-16-QAM RECEIVER Name and description Default value Default unit Units Value range LO sample rate Sample rate Hz Hz, GHz, THz, nm [1, 1e+100] Name and description Default value Default unit Units Value range Photodetector PIN - - [PIN, APD] 3 - - [0, 1e+100] 0.9 - - [1e-100, 1] 1 A/W - [0, 100] 10 nA - [0, 1e+100] Sample rate of the local oscillator Photodetector Select the photodetectors type: PIN or APD Gain The avalanche gain for the photodetector APD Ionization ratio The ionization ratio for the photodetector APD Responsivity The responsivity of the photodetector Dark current The photodetector dark current Responsivity type APD Constant [Constant, User defined Responsivity type PIN Constant [Constant, Si, Ge, InGaAs, User defined] Responsivity vs. wavelength Responsivity.dat Downsampling Name and description Default value Default unit Units Value range Centered at max power True - - True, False 193.1 THz Hz, THz, nm [30, 300000] 5* (Sample rate) Hz Hz, GHz, THz, nm [1, 1e+100] Determines whether the internal filter will be centered at the maximum amplitude of the signal or will it be user defined Center frequency User-defined center frequency of the internal filter Sample rate Sample rate of the signal output 978 OPTICAL COHERENT DP-16-QAM RECEIVER Noise Name and description Default value Default unit Units Value range Noise calculation type Numerical - - Analytical, Numerical, Numerical convert noise bins Add signal-ASE noise True - - True, False Add ASE-ASE noise True - - True, False Add thermal noise True - - True, False Thermal noise 1e-22 W/Hz W/Hz, A/Hz^.5 [0, 1e+100] Add shot noise True - - True, False Gaussian - - Poisson, Gaussian Determines if shot noise is added to the signal Shot noise distribution Determines the distribution used to generate the shot noise Simulation Name and description Default value Default unit Units Value range Iterations Iterations - - [1,+INF[ Number of times to repeat the calculation Random Numbers Name and description Default value Default unit Units Value range Generate random seed True - - True, False 0 - - [0, 4999] 1 - - [0, 4999] 2 - - [0, 4999] Determines if the seed is automatically defined and unique Random seed index PD 1 User-defined seed index for noise generation for photodetector 1 Random seed index PD 2 User-defined seed index for noise generation for photodetector 2 Random seed index PD 3 User-defined seed index for noise generation for photodetector 3 979 OPTICAL COHERENT DP-16-QAM RECEIVER Name and description Default value Default unit Units Value range Random seed index PD 4 3 - - [0, 4999] 0 - - [0, 4999] User-defined seed index for noise generation for photodetector 4 Random seed index LO User-defined seed index for noise generation for local oscillator Technical background The optical coherent dual-polarization 16-QAM receiver consists of a homodyne receiver design. The component has a LO laser polarized at 45 degrees relative to the polarization beam splitter, and the received signal is separately demodulated by each LO component using two single polarization 16-QAM receivers. Figure below shows the layout representing the receiver. Figure 1 DP-16-QAM receiver layout 980 OPTICAL COHERENT DP-16-QAM RECEIVER Notes: 981 OPTICAL COHERENT DP-16-QAM RECEIVER 982 90 DEGREE OPTICAL HYBRID 90 Degree Optical Hybrid The 90º optical hybrid is used for coherent signal demodulation for either homodyne or heterodyne detection [1]. Ports Name and description Port type Signal type Supported Modes Input 1 Input Optical - Input 2 Input Optical - Output 1 Output Optical - Output 2 Output Optical - Output 3 Output Optical - Output 4 Output Optical - Technical background The 90 deg Optical Hybrid component is built according to Figures 1 and 2. The received signal is fed into input A and split evenly by DC1. The phase between the signals at the ports R and T can be tuned in phase with PS 1. The local oscillator (LO) signal is fed into input D and split evenly by DC2. If the phase between the LO signal at the ports S and U is adjusted to 90 degree by PS2, the four intermediate frequency signals at the output ports (W, X, Y and Z) show the desired phase relations of the 90 degree hybrid: 180o, 90o and 270o for X, Y, Z with respect to W. 983 90 DEGREE OPTICAL HYBRID Figure 1 90 Deg Optical Hybrid component layout Figure 2 90 Deg Optical Hybrid principal of operation (DC: 3-dB directional coupler; PS: phase shifter) Describing the function of the phase shifters by a multiplication with exp(j1) and exp(j2), respectively, and assuming equal path lengths for the waveguides interconnecting the couplers, the transfer matrix of the bridge circuit is 984 90 DEGREE OPTICAL HYBRID The optical fields of the signal carrier and local oscillator can be described by the complex amplitudes: As = P s exp j s t (1) A LO = P LO exp j LO t If the phase shifters in are set to 1=0o, and1=90o, the intensities of the superimposed optical fields at the four output ports are given by A w 2 = 1 4 P s + P LO – 2 P s P LO cos t A x 2 = 1 4 P s + P LO + 2 P s P LO cos t (2) A y 2 = 1 4 P s + P LO + 2 P s P LO sin t A z 2 = 1 4 P s + P LO – 2 P s P LO sin t where (t) = s(t) -LO(t) is the relative phase between the LO signal and the received signal carrier. References [1] http://www.optoplex.com/Optical_Hybrid.htm (accessed 6 July 2014) [2] D. Hoffmann, H. Heidrich, G. Wenke, R. Langenhorst, and E. Dietrich, “Integrated Optics Eight-Port 90 deg Hybrid on LiNbO3”, J. Lightw. Tech., vol. 7, no. 5, pp. 794-798, May 1989. 985 90 DEGREE OPTICAL HYBRID 986 Amplifiers Library Optical • EDFA Black Box • EDFA • Optical Amplifier • Optical Amplifier Measured • Optical Fiber Amplifier 987 Notes: 988 EDFA BLACK BOX EDFA Black Box Designs erbium doped fiber amplifiers (EDFAs) pumped by 980 nm or 1480 nm. Requires just the experimental characterization of a practical device such as the gain spectrum and noise figure under nonsaturated and saturated conditions. Details about erbium-doped fiber specifications and elements in the layout are not required to perform the simulations. The amplifier is specified to operate under conditions required by wavelength division multiplex (WDM) systems. Ports Name and description Port type Signal type Input Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Operation mode Saturation — — Gain control, Power control, Saturation 20 dB — [0,100] 5 dBm W, mW, dBm [-100,100] Amplifier operation mode Gain Determines the signal gain Power Determines the signal output power 989 EDFA BLACK BOX Measurements Name and description Default value Units Value range File wavelength unit m — nm, m, Hz, THz Gain1.dat — — Gain2.dat — — 0.1 nm [0.0001,10] Power dBm Power, Spectral density, Noise figure True — True, False Noise.dat — — 1540 nm [800,1700] Saturation.dat — — Name and description Default value Units Value range Relative error 0.1 dB ]0,100] Cubic — Linear, Cubic Determines the wavelength unit First gain spectrum file name Filename with the gain spectra measurements Second gain spectrum file name Filename with the gain spectra measurements OSA bandwidth Set the bandwidth of the Optical Spectrum Analyzer Noise type Select the noise type Noise Determines if ASE is included in the calculation or not Noise spectrum file name Filename concerning the noise spectra Saturation wavelength Determines the saturation wavelength Saturation file name Filename concerning the saturation spectra Numerical Determines the relative error acceptable in each calculation Interpolation algorithm Determines the interpolation algorithm for the measured data 990 EDFA BLACK BOX Polarization Name and description Default value Units Value range Polarization filter None — None, Polarization X, Polarization Y Name and description Default value Units Value range Enabled True — True, False Determines the polarization of the filter Simulation Determines whether or not the component is enabled Noise Name and description Default value Default unit Units Value range Noise bins spacing 125 GHz Hz, GHz, THz, nm [1,1000] –100 dB — ]-INF,0[ 3 dB — [0,+INF] Convert noise bins — — True, False Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Specifies the noise bins spacing Noise threshold Minimum value for adaptation of noise bins Noise dynamic Threshold ratio for adaptation of noise bins Convert noise bins Determines if the generated noise bins are incorporated into the signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation 991 EDFA BLACK BOX Graphs Name and description X Title Y Title First gain spectrum Wavelength (m) Gain (dB) Second gain spectrum Wavelength (m) Gain (dB) Noise spectrum Wavelength (m) Power (dBm) Saturation Input power (dBm) Gain (dB) Technical background Using input parameters as the characterization of the gain spectrum and noise figure under non-saturated and saturated conditions measured to a practical device is sufficient for designing the amplifier performance using this black box model. Additional information concerning fiber specifications, such as absorption and emission cross-sections, erbium doping, core radius, or details related to the amplifier layout, is not required in this case. Curves containing the amplifier characterization are available internally as a default in the software, which makes it possible for you to perform simulations. Three different control modes are available that allow you to perform the amplifier analysis under distinct points of view. Each mode control – gain, power control, and saturation – defines a different amplifier operating condition. The black box model enables passive components, such as optical isolators, equalizer filters, and several types of couplers, to be included in the amplifier design while considering an additional loss variation along the amplifier due to the active and passive components. The gain and the noise characterization measured to distinct states of operation are provided as input files that enable the complete modelling of the amplifier performance. Operation Modes Fiber amplifiers used in WDM systems usually make use of control systems as power or gain. It is useful to include the option in the EDFA Black Box to select one of three operation modes: 992 • Gain mode: Based on a control of the amplifier gain (Gain Control) relating the input and output signals (with or without the generated amplified spontaneous emission (ASE). • Power Control mode: Considers the value of the output power to control the amplifier performance (Power Control). • Saturation mode: Considers the amplifier operating in a saturated condition (Saturation). EDFA BLACK BOX Gain Control mode In this mode, you set the gain amplifier (Gain in dB units). The gain calculation is performed using Equation 1, where the total input (Pin) and the output (Pout) power spectra are considered. The specified amplifier gain (Gspeci) is given by the ratio of the total output power and input total power, with or without the generated ASE. + Pout + S ASE f df (1) – G speci = -------------------------------------------------------------------P in SASE(f) represents the spectral density of the amplified spontaneous emission integrated on the optical frequency f. Note: You can include the noise by selecting the noise type as power, spectral density, or noise figure in the EDFA Black Box Properties dialog box. Power Control mode The value that you define in the power control mode is the desired amplifier output power (Power in dBm units). The specified amplifier output power (Pspeci) that includes the spectral ASE is: + P speci = G Pin – (2) S ASE f df – where G is the amplifier gain. The option to select the noise type that will be included in the simulations is also available in this control mode. Saturation mode In the saturation mode, the gain is the specified parameter. The noise type can be selected in this mode, and two experimental gain curves are inserted as input files considering two different saturation conditions. The gain curve in a saturated condition is provided in a file format containing two columns. The first column refers to the signal output power given in [dBm] units. The second column gives the gain in [dB] units. 993 EDFA BLACK BOX An example of the saturated gain input file is: Signal output power (dBm) Gain (dB) –40 28.82 –30 28.83 –20 28.82 –10 28.81 0 28.72 ... where the signal output power is given in [dBm] units and the gain is in [dB] units. There is no limit of rows or power spacing previously defined. Basic equations The black box model considers a two-level Er3+ system assumption that is usually adopted to model erbium-doped fiber amplifiers [1]. The propagating equation written as a function of the absorption and emission coefficients, () and () respectively, is [2]: eq dP ,z -----------------= + I z – P ,z + I z P ASE dz (3) I(z) represents the fraction of active ions in the excited state, P(,z) describes the propagating power at a specific wavelength and fiber position, and PASEeq is the term that includes the amplified spontaneous emission (ASE) as an equivalent ASE power. The solution to Equation 3 is: eq P ,L = G P ,0 + P ASE (4) where L is the total Er-doped fiber length and P(,0) represents the power at the wavelength and at the fiber input. Considering the scope of this approximation, PASEeq() works as an independent source of amplified spontaneous emission. The total gain along the erbium-doped fiber is: G z = exp + I z – z (5) where I z is the updated term that represents the detailed evolution of the population inversion along the erbium-doped fiber. 994 EDFA BLACK BOX The black box model takes into account a multiple-stage amplifier, where all amplifier stages use the same type of erbium-doped fiber (the same absorption and emission coefficients are considered). Figure 1 shows a sketch of an amplifier set up in two sections, containing passive elements such as optical isolators, couplers, taps and one filter. The total Er-doped fiber length and the total gain are L and G respectively. Figure 1 Erbium doped amplifier set up in multiple stages, where the black box parameters G , IL , ILin are indicated If the insertion loss is included in the analysis, the gain G is written as: G = [GA + GB ]/ IL . Amplifier gain In order to model the gain of the amplifier, two different states of operation are considered where each state has a characteristic population inversion. The amplifier gain expression is given as a function of a reference gain value, (for example, [2]): log G = T log G ref – log G ref ref ref + log G ref (6) ref where ref and G ref specifies the wavelength and the gain at a reference amplifier operating point. The term T ref is named tilt function and is obtained by the ratio of the gain curves measured in the two states of operation. One acts as a reference curve (for example, ref G ). The tilt function is given by the analytical expression: log G 1 – log G 2 T = ------------------------------------------------------------------log G 1 ref – log G 2 ref (7) 995 EDFA BLACK BOX where G 1 and G 2 are the gain measured to the state1 and state2 respectively of the amplifier operation. The experimental gain, measured at these two states of operation, is provided as input file in the black box model. It is convenient to introduce this concept of tilt function in the model, since it considers the interdependence between the ratio of the characteristic gain and the absorption and emission coefficients. On the other side, as the internal losses IL() caused by passive elements modify both G1() and G2() in the same manner, the tilt function isn’t affected by optical circuitry variations. By choosing G2() equal to G(), the expression for the amplifier at the operation point is: log G = log G 1 – T log G 1 ref – log G ref ref ref log G = log G 2 + T log G ref (8) (9) ref where log G specifies the gain difference between log G ref – log G 2 ref or log G 1 ref – log G 2 ref . The term log G is a free parameter and may be altered to adjust the gain. Gain measurement The gain curves are critical to the black box model operation. The best way to obtain these values used as input files in the model is by measuring them in a practical amplifier. It is important to note that the precision of these measurements defines the accuracy of the simulated results. However, the model alternatively accepts curves generated by a simulated amplifier that supplies gain and ASE curves as the output files. Obtaining Gain Curve G1 The first gain profile is acquired with the amplifier operating in a constant saturated regime that assures a specific population inversion. This condition can be obtained by coupling a large signal input power to the amplifier, typically 10 dBm, at the wavelength ref (e.g., 1540 nm), which is maintained constantly. A small signal with power equal to 30 dBm (for instance) is added to the amplifier input as a probe signal. Its frequency (probe signal) is scanned through the range defined by the two-limit frequencies, which is written in terms of signal wavelength and usually varies from 1530 nm to 1570 nm. This scan over the probe signal allows you to obtain the spectral gain for one specific saturated condition. This method was checked by analyzing a series of gain curves measured at the same saturated conditions, and a nominally identical population inversion was recorded [2]. 996 EDFA BLACK BOX Obtaining Gain Curve G2 Analogous measurement procedure is repeated to obtain the second gain profile. However, in this case, the probe signal input is enlarged to –20 dBm, and the reference signal at a selected wavelength (1540 nm) can be varied. This new signal input combination results in a different population inversion condition, which characterizes the gain G 2 . The difference is that the added signal test presents larger potency, typically 20 dBm, which causes a change in the gain curve profile by saturating the amplifier. With the value obtained for the gain in each wavelength, the gain curve profile is obtained. The high signal power, with the same ref, can also be altered, since the total sum of the power is larger than the sum of the power to generate the curve G1. The experimental gain curves must be provided in files containing two columns. The first column refers to the wavelength specified in [nm], [m], [Hz] or [THz] units. The second column gives the gain in [dB] units. As an example of the gain input file is: Wavelength [nm] G [dB] 1535.58 38.17 1538.95 34.09 1542.11 33.35 1545.26 33.17 ... where the wavelength is given in [nm] units and the gain is in [dB] units. There is no limit of rows or wavelength spacing previously defined. Amplifier noise figure The noise figure is the figure of merit that usually describes the amplifier noise performance. In order to evaluate the noise figure, three different options are available. You can select the input format of noise that will be considered to perform the calculations. The first option is to select the noise input in terms of ASE power. In this case, the ASE noise spectral density is written as: P S power = -----------f (10) where P() is the ASE power measured at each wavelength range and f is the bandwidth considered in the ASE spectrum acquisition. 997 EDFA BLACK BOX Another option to evaluate the amplifier noise performance is to select the ASE spectral density. In this case, the spectral density S() is required as input file and is written as: S = hf 10 NF 10 G – 1 (11) where h is the Planck constant, f is the optical frequency, and the exponent NF() is the noise figure as a function of the signal wavelength. The model will internally calculate the noise figure considering the noise curve provided as input file. Rewriting Equation 11 in terms of noise figure produces [3]: S + hf NF = 10 log -----------------------hf G (12) The third option is to select the noise figure value given as a function of the signal wavelength. In this case, the ASE spectrum is modeled considering the provided noise figure value. It is also possible to evaluate the noise figure considering different amplifier state operation that means to consider distinct gain values. In this case, the spectral density given by Equation 11 is rewritten including the gain variation (G in linear units or logG in dB units). The new spectral noise density is dependent on the amplifier gain and is: S ,log G = hf 10 NF 10 G ,log G – 1 (13) where log G can be calculated from Equation 8 and Equation 9. Equivalent ASE noise measurement The experimental ASE noise curves complement the measured parameters required by the black box model. Obtaining equivalent ASE noise The third input to obtain (experimental) is the amplified spontaneous emission. In the ASE acquisition curve, only the saturating signal must be maintained turned-on and operating with a constant power at a specified signal wavelength (1540 nm as suggested in the previous measurement descriptions). This is sufficient to produce population inversion along the Er-doped fiber. The spectrum obtained at the fiber output registers the amplified spontaneous emission observed along the whole wavelength range considered (1530 nm to 1570 nm, typically). 998 EDFA BLACK BOX The experimental gain curves must be provided in files containing two columns. The first column refers to the wavelength specified in [nm], [m], [Hz] or [THz] units. The second column gives the ASE noise curve in [dBm] units. An example of input file: Wavelength [nm] ASE [dBm] 1543 –25.13 1544 –25.20 1546 –25.42 1551 –26.43 where the wavelength is in [nm] units and the gain is in [dB] units. There is no limit of rows or wavelength spacing previously defined. 999 EDFA BLACK BOX References [1] E. Desurvire, “Erbium-Doped Fiber Amplifiers – Principles and Applications”, John Wiley & Sons, Inc., USA, 1994. [2] J. Burgmeier, A. Cords, R. März, C. Schäffer, B. Stummer “A black box model of EDFA’s operating in WDM systems”, J. Lightwave Technol., Vol. 16, N. 7, pp. 1271-1275, 1998. [3] S. P. Bastien, H. R. D. Sunak, B. Sridhar, V. E. Kalomiris “Temporal, spatial and spectral modeling of erbium doped fiber amplifiers”, SPIE – Physic and Simulations of Optoelectronic Devices, pp. 2-11, 1992. 1000 EDFA EDFA Designs Er-doped fiber amplifiers by considering numerical solutions of the rate and the propagation equations under stationary conditions. The model includes amplified spontaneous emission (ASE) as observed in the amplifier Erbium Doped Fiber. However, this module allows you to select forward and/or backward pump, as well as the pump power values. Ports Name and description Port type Signal type Input Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Core radius 2.2 µm — [0.1,10] 2.2 µm — [0.1,10] 10 ms — [0.01,100] 0.24 — — [0.1,1] 1e+025 m–3 m–3~ppmwt~wt% [1,+INF[ 0.1 dB/cm — [0,100] 0.15 dB/cm — [0,100] Determines the Er-doped fiber core radius Er doping radius Specifies the Er-doped radius Er metastable lifetime Determines the Er metastable lifetime Numerical aperture Specifies the numerical aperture of the Er-doped fiber Er ion density Specifies the Er doping in the Er-doped fiber Loss at 1550 nm Determines the fiber loss at 1550 nm Loss at 980 nm Determines the fiber loss at 980 nm 1001 EDFA Name and description Default value Default unit Units Value range Length 5 m — [0,10000] Determines the Er-doped fiber length Pumping Name and description Default value Default unit Units Value range Forward pump power 100 mW W, mW, dBm [0,+INF[ 0 mW W, mW, dBm [0,+INF[ 980 nm — [700,1600] 980 nm — [700,1600] Name and description Default value Units Value range File frequency unit nm — nm, m, Hz, THz False — True, False Erbium.dat — — Name and description Default value Units Value range Relative error 0.0001 — ]0,1] 50 — [10,10000] Determines the co-propagating pump power Backward pump power Determines the counter-propagating pump power Forward pump wavelength Determines the co-propagating pump wavelength Backward pump wavelength Determines the counter-propagating pump wavelength Cross-sections Determines the frequency unit of the file with the measurements OptiAmplifier format Determines the format of the OptiAmplifier file cross-section file name Determines the cross-section file Numerical Determines the relative error acceptable in each calculation Max. number of iterations Specifies the maximum number of times to repeat the calculation 1002 EDFA Name and description Default value Units Value range Longitudinal steps 100 — [10,10000] Determines the number of longitudinal steps in the calculation Polarization Name and description Default value Units Value range Polarization filter None — None, Polarization X, Polarization Y Name and description Default value Units Value range Enabled Yes — [0, 0] Determines the polarization of the filter Simulation Determines whether or not the component is enabled Noise Name and description Default value Default unit Units Value range Noise center frequency 193.4 THz Hz, THz, nm [30, 30] 13 THz Hz, Thz, nm [1e-100, 1e-100] 125 GHz Hz, GHz, THz, nm [1,1] –100 dB — [-1e+100, -1e+100] 3 dB — [0, 0] Convert noise bins — — [0, 0] Determines the noise center frequency Noise bandwidth Bandwidth to increase noise bins Noise bins spacing Determines noise bins spacing Noise threshold Minimum value for adaptation of noise bins Noise dynamic Threshold ratio for adaptation of noise bins Convert noise bins Determines if the generated noise bins are incorporated into the signal 1003 EDFA Random numbers Name and description Default value Units Value range Generate random seed Yes — [0, 0] 0 — [0, 0] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Graphs Name and description X Title Y Title Absorption parameters Wavelength (m) Cross-section (m2) Emission parameters Wavelength (m) Cross-section (m2) Technical background The routines in EDFA numerically solve the rate equations coupled with propagating equations under stationary conditions. It is assumed a two-level Er system approximation and the rate equations are based on the energy level diagram. The same expressions described in the module Er Doped Fiber are adopted by this model. The main difference is related to the amplifier pump scheme selection. You can choose co-propagating, counter-propagating, or bi-directional pump schemes with the option to set wavelength and pump power. Geometrical Er-doped fiber parameters and cross-section curves are required as input files. As output files, you can access gain, output power values, and noise figure determined in the ASE bandwidth set as noise input data. Er Doped Fiber rate and propagation equations The lifetime transition from level 4I11/2 is of the order of microseconds for silicate hosts. Therefore, it is reasonable to neglect the population density N3 in the rate equations description. A two-level system approximation is used in this case. Under the assumption of the normalized population densities N1 and N2 at the ground and metastable energy level, 4I15/2 and 4I13/2 populations are calculated by numerically solving the rate and propagation equations[1]: N 2 z ,t N 2 z ,t 1 --------------------- = – ----------------- – -------t A eff N e a a n n + n N2 z ,t – n Pn + – z ,t + P n z ,t n=1 (1) 1004 EDFA N2 + N1 = 1 (2) P n z ,t e a a e ------------------------ = u n n n + n N 2 z ,t – n – P n z ,t + 2N 2 n n z (3) where the optical powers are expressed in units of number of photons per unit time, is the metastable spontaneous emission lifetime, N is the number of channels taken into account in the simulation (including signals, pumps, and ASE bins), is the number density of the active erbium ions, is the attenuation coefficient (which takes into account the background loss of the fiber), is the frequency step used in the simulation to resolve the ASE spectrum, and Aeff is the effective doped area given 2 by b , where b is the Er doping radius (it is considered a uniform distribution of erbium ions in the area given by the Er doping radius region). The nth channel of wavelength n has optical power Pn(z,t) at location z and time t, e a with emission and absorption cross-section n and n respectively, and confinement factor n . The superscript symbols + and – are used to indicate channels traveling in forward (from 0 to L) and backward (from L to 0) directions, respectively. For beams traveling in the forward direction u n = 1 and for beams in the opposite direction u n = – 1 . The overlap integrals n between the LP01 mode intensity (which is used in this program) distribution doped region area are given by: b E r , 2 r dr 0 n = ---------------------------------- E r , 2 r dr 0 (4) where E(r, ) gives the electric density field. Solving Equation 1, Equation 2, and Equation 3 under stationary conditions allows you to determine the amplifier performance features. The fiber parameters such as core and Er doping radius, Er metastable lifetime, numerical aperture, Er ion density, loss at 980 nm and 1550 nm, and the fiber length are required as input values. The absorption and emission cross-section are also required as input files. 1005 EDFA Absorption and Emission cross-sections There are two options available to you to prepare the cross-section file, which is specified in an ASCII file. The first option is to provide the cross-section input file in three columns. The first column refers to the wavelength in [m], [nm], [Hz] or [THz] units. The second column gives the absorption cross- section in [m2] units. The third column gives the emission cross-section in [m2] units. In this case, the cross-section file format is: (nm) m m 929.982 9.28e-27 0 930.172 7.05e-27 0 1029.972 2.85e-27 0 1030.072 3.59e-27 0 1450.6 2.086e-26 1.726e-27 1450.8 2.186e-26 1.823e-27 1649.8 1.540e-26 8.228e-26 1650.0 1.540e-26 8.280e-26 a 2 e 2 . . . . . . The second option is to consider the absorption and emission coefficients (or Giles parameters) as input parameters that are converted to cross-section by internal routines in the software. This is especially interesting when only Giles parameters are measured to the Er-doped fiber. The file format in this case contains three columns. The first column refers to the wavelength in [m], [nm], [Hz] or [THz] units. The second column gives the absorption coefficient in [dB/m] units. The third column gives the emission coefficient in [dB/m] units. An example of this input file is: (nm) (dB/m) g* (dB/m) 929.982 0.39168 0 930.172 0.2856 0 –0.05508 0 . . . 1029.972 1006 EDFA (nm) (dB/m) g* (dB/m) 1030.072 –0.14484 0 1450.6 1.8075 0.35599973 1450.8 1.815 0.360619883 1649.8 0.005 0.484116259 1650.0 –0.0175 0.477803876 . . . where the wavelength is given in [nm] units, absorption and emission coefficients are in [dB/m]. 1007 EDFA References [1] C.R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” Journal of Lightwave Technology, Vol. 9, N. 2, pp. 271-283, 1991. 1008 OPTICAL AMPLIFIER Optical Amplifier Enables the design of amplifiers, including EDFAs, that consider pre-defined operational conditions. This means that expected gain, noise figure, and amplifier output power can be previously specified. The amplifier presents the same facilities as a black box model, which enables you to select the operation mode with gain control, power control, or to perform simulations under saturated conditions, as well as define the expected amplifier performance. It is specially suited to perform prompt performance analysis of one or cascaded amplifiers in a long-haul system. Ports Name and description Port type Signal type Input Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Operation mode Gain control — — Gain control, Power control, Signal power control, Saturation 20 dB — [0,100] 10 dBm W, mW, dBm [-100,100] 10 dBm — [-100,100] Output — — Input, Output Amplifier operation mode Gain Determines the signal gain Power Determines the signal output power Saturation power Specifies the optical power at the gain compressed by 3 dB Saturation port Determines the amplifier saturation port 1009 OPTICAL AMPLIFIER Name and description Default value Default unit Units Value range Include noise YES — — — Noise figure 4 dB — [3,100] Name and description Default value Units Value range Polarization filter None — None, Polarization X, Polarization Y Name and description Default value Units Value range Enabled True — True, False Determines the amplifier noise figure Polarization Determines the polarization of the filter Simulation Determines whether or not the component is enabled Noise Name and description Default value Default unit Units Value range Noise center frequency 193.4 THz Hz, THz, nm [30, 3e+006] Noise bandwidth 13 THz Hz, THz, nm [1e-100, 1e+100] Noise bins spacing 125 GHz Hz, GHz, THz, nm [1,1000] Convert noise bins — — True, False Name and description Default value Units Value range Generate random seed True — True, False Specifies the noise bins spacing Convert noise bins Determines if the generated noise bins are incorporated into the signal Random numbers Determines if the seed is automatically defined and unique 1010 OPTICAL AMPLIFIER Name and description Default value Units Value range Random seed index 0 — [0,4999] User-defined seed index for noise generation Technical background The simulation of the flat gain amplifier is performed in the opposite way than that used by the previous described models. In this case, the desired amplifier performance given by the gain, the output power, the saturated output power, and the noise figure values are used as input parameters to design the amplifier. The input data are related by the propagation equation written in terms of the parameter required in each mode selected. There are three different mode controls — Gain control, Power Control, and Saturation. Large and small input signal can be considered in this amplifier model. The concept of the flat gain amplifier enabling you to define the device performance makes this model flexible to design amplifiers considering different applications in a system such as booster, in-line, and preamplifier. The amplified spontaneous emission is included in the model of the Flat Gain EDFA and it is built from the noise figure input value. Operation Modes The Flat Gain EDFA subsystem enables three operation modes, which you can select in the Flat Gain EDFA Properties dialog box by clicking on Main/Operation Mode/Value. The first option is the Gain Control that maintains the gain constant and allows you to include (or not include) the amplified spontaneous emission in the calculations. In the second operation mode option, Power Control, the value of the output power is maintained constantly. The third operation mode, Saturation, considers the amplifier operating in a saturated condition — operating in an output signal power correspondent to a gain 3 dB lower than the saturated gain. Gain Control mode In this mode, you set the desired amplifier gain (in dB units), which is given by the ratio of the total output power (Pout) and total input power (Psin), including (or not including) the generated ASE (PASE), as given by Equation . There are no additional iterations or complicated equation solutions in this mode. The set amplifier input parameters as gain and noise figure give the performance of this sub-system to be inserted in the global system. P out – P ASE G = -----------------------------------P sin 1011 OPTICAL AMPLIFIER Power Control mode The value that you define in the power control mode is the desired amplifier output power (in dBm units), which is maintained constantly. If the gain required to keep the desired output power is higher than the value of the parameter Gain, the amplifier will saturate, and the maximum power will be determined by the input power amplified by the parameter Gain. Analogous with the gain-controlled mode, there is no additional calculation involved in the designed amplifier. The output power set as input parameter defines the amplifier performance to be considered in the system where this amplifier is inserted. The ASE, which basically computes the noise introduced by the amplifier into the system, can be included (or not included) in the amplifier performance. Note that the specified output power is not degraded by the ASE noise included in the amplifier subsystems — however, this noise source is computed in the global system analysis. Signal power control mode will not include the input noise into the calculated input power. Saturation mode In the saturation mode, it is assumed that the pump power is constant, causing the amplifier to operate in a saturated regime. The saturation power, gain, and noise figure are the parameters required by this mode. The saturation power is the input parameter maintained constant in this mode selection, and in an ASE-free model can be related with the gain (G), output power (Pout), and intrinsic saturation power (Psatint) by the expression: G – 1 P out G = G 0 exp – ------------- ----------int G P sat (2) where G0 is the small-signal gain or unsaturated gain. The intrinsic saturation power is written as: int Ahv P sat = ---------a (3) where A is the mode-field area, h is the Planck’s constant, is the frequency at the propagating signal, a is the absorption cross-section, and is the Er metastable lifetime in silica. These fiber specifications are not required in this amplifier module, since the intrinsic saturation power will be related to the amplifier saturation power under the gain compression condition. Under the 3 dB gain compression, the output power is proportional to the intrinsic saturation power. This relation is: P out 1012 3dB int = In 2 P sat Compressed OPTICAL AMPLIFIER (4) ASE calculation The ASE noise spectrum is built in this model from the noise figure provided as input parameter, considering the expression that relates spectral ASE noise with noise figure. The noise figure (NF) evaluated at a specific signal wavelength is: 1 S out NF = ---- + ---------G Ghv (5) The term 1/G corresponds to the shot noise, Sout is the output ASE spectral density at the signal wavelength, and h is the photon energy. In practical cases, there is ASE present at the input of the doped fiber so that the amplified input ASE must be added to the output ASE spectral density. The output ASE can be written as: S out = S amp + S in G (6) where Samp is the spectral density ASE generated by the doped fiber. Correcting for the input ASE gives the signal-spontaneous beat noise limited noise figure as a function of the signal gain, and input and output ASE spectral densities: 1 S out S in NF = ---- + ---------- – ------G Ghv hv (7) In the signal-spontaneous beat noise limited regime, with high gain and negligible input coupling, the noise figure of the optical preamplifier approaches a theoretical limit of [1]: 2 sig – sp NF opt = --------------------------------------- = 2n sp 2 2 sig – sh in G (8) where the spontaneous emission factor, nsp, is defined as: N2 z n sp v ,z = --------------------------------------------N 2 z – N 1 z v (9) where a v v = -------------e v (10) 1013 OPTICAL AMPLIFIER Since nsp 1, an EDFA at high gain has a minimum noise figure of 3 dB. This is derived by assuming that the input signal is shot noise limited and the output noise is signal-spontaneous beat noise limited. In practical situations, the noise figure is degraded by the amplifier input coupling loss. Noise figure This lists the signal-spontaneous beat noise limited noise figure. For each signal wavelength, the noise figure is: 1 S out s S in s NoiseFigure dB = 10 log 10 ---- + --------------------- – -----------------G Ghv hv (11) where S out s is the output ASE spectral density (W/Hz) at the signal wavelength, and S in s is the input ASE spectral density at the signal wavelength. Rewriting the ASE spectral density as a function of noise figure value, the noise spectrum can be generated considering the noise figure input parameter. Therefore, the ASE spectrum is obtained from the expression: S out s = G hv 10 NoiseFigure dB ------------------------------------10 1 S in s – ---- + -----------------G hv (12) References [1] T. Okoshi, "Exact Noise-Figure Formulas for Optical Amplifiers and Amplifier-Fiber Cascaded Chains," IEEE/OSA Topical Meeting on Optical Amplifiers and their Applications, Monterrey, PDP11, 1990. 1014 OPTICAL AMPLIFIER MEASURED Optical Amplifier Measured Enables you to design EDFAs considering pre-defined operation conditions that mean to specify previously the measured gain, noise figure, and amplifier output power. It is specially indicated for the prompt performance analysis of one or cascaded amplifiers present in a long-haul system. It can be also used for flat gain amplifiers. Ports Name and description Port type Signal type Input Input Optical Output Output Optical Parameters Main Name and description Default value Default unit Units Value range Measured gain and noise figure (nm dB dB) — — — GainAndNF.dat — — — 25 dBm W, mW, dBm [-100,+100] True — — True, False Wavelength, gain, and NF table with the measured data Gain and noise figure file name Filename with the measured data Max. output power Determines the total signal output power Include noise Determines if the component add noise to the output signal 1015 OPTICAL AMPLIFIER MEASURED Polarization Name and description Default value Units Value range Polarization filter None — None, Polarization X, Polarization Y Name and description Default value Units Value range Enabled Yes — [0, 0] Determines the polarization of the filter Simulation Determines whether or not the component is enabled Noise Name and description Default value Default unit Units Value range Noise center frequency 193.4 THz Hz, THz, nm [30, 30] 13 THz Hz, Thz, nm [1e-100, 1e100] 125 GHz Hz, GHz, THz, nm [1, 1] –100 dB — [-1e+100, 1e+100] 3 dB — [0, 0] Convert noise bins — — [0, 0] Name and description Default value Units Value range Generate random seed Yes — [0, 0] Determines the noise center frequency Noise bandwidth Bandwidth to increase noise bins Noise bins spacing Determines noise bins spacing Noise threshold Minimum value for adaptation of noise bins Noise dynamic Threshold ratio for adaptation of noise bins Convert noise bins Determines if the generated noise bins are incorporated into the signal Random numbers Determines if the seed is automatically defined and unique 1016 OPTICAL AMPLIFIER MEASURED Name and description Default value Units Value range Random seed index 0 — [0, 4999] User-defined seed index for noise generation Technical background The simulation of the EDFA Measured is performed in similar way to the Flat Gain EDFA. In this case, the desired amplifier performance given by the measured gain, noise figure, and maximum output power. Large and small input signals can be considered in this amplifier model. The concept of the measured amplifier enabling you to define the device performance makes this model flexible to design amplifiers for different applications in a system such as booster, in-line, pre-amplifier, gain flat, and noise flat. It can also load measurements from other software tools such as Optiwave's OptiAmplifier. This maximum output power can be limited when the total output power is greater then the parameter Max. output power. The calculation engine reduces the amplifier gain in order to have the total output power equal to the parameter Max. output power. ASE calculation The ASE noise spectrum is built in this model from the noise figure provided as input parameter, considering the expression that relates spectral ASE noise with noise figure. The noise figure (NF) evaluated at a specific signal wavelength is: 1 S out NF = ---- + ---------G Ghv (1) The term 1/G corresponds to the shot noise, Sout is the output ASE spectral density at the signal wavelength, and h is the photon energy. In practical cases, there is ASE present at the input of the doped fiber so that the amplified input ASE must be added to the output ASE spectral density. Therefore, the output ASE can be written as: S out = S amp + S in G (2) where Samp is the spectral density ASE generated by the doped fiber. Correcting for the input ASE gives the signal-spontaneous beat noise limited noise figure as a function of the signal gain, and input and output ASE spectral densities: 1 S out S in NF = ---- + ---------- – ------G Ghv hv (3) 1017 OPTICAL AMPLIFIER MEASURED In the signal-spontaneous beat noise limited regime, with high gain and negligible input coupling, the noise figure of the optical preamplifier approaches a theoretical limit of [1]: 2 sig – sp NF opt = --------------------------------------- = 2n sp 2 2 sig – sh in G (4) where the spontaneous emission factor, nsp, is defined as: N2 z n sp v ,z = --------------------------------------------N 2 z – N 1 z v (5) where a v v = -------------e v (6) Since nsp 1, an EDFA at high gain has a minimum noise figure of 3 dB. This is derived by assuming that the input signal is shot noise limited and the output noise is signal-spontaneous beat noise limited. In practical situations, the noise figure is degraded by the amplifier input coupling loss. Noise figure This lists the signal-spontaneous beat noise limited noise figure. For each signal wavelength, the noise figure is: 1 S out s S in s NoiseFigure dB = 10 log 10 ---- + --------------------- – -----------------G Ghv hv (7) where S out s is the output ASE spectral density (W/Hz) at the signal wavelength, S in s is the input ASE spectral density at the signal wavelength. Rewriting the ASE spectral density as a function of noise figure value, the noise spectrum can be generated considering the noise figure input parameter. Therefore, the ASE spectrum is obtained from the expression: S out s = G hv 10 NoiseFigure dB ------------------------------------10 1 S in s – ---- – -----------------hv G (8) 1018 OPTICAL AMPLIFIER MEASURED Measurements You can provide the measurements in the parameter Measured gain and noise figure. Alternatively, the measurements can be loaded from a file using the parameter Gain and noise figure file name. The gain and noise figure curves must be provided in the file containing three columns. The first column refers to the wavelength specified in [nm] units. The second column gives the gain noise curve in [dB] units. The third column gives the noise figure in [dB] units. Example of input file: Wavelength ([nm] Gain [dB] NF [dB] 1500.00 20.00 4.00 1510.00 20.00 4.00 1520.00 20.00 4.00 1530.00 20.00 4.00 1540.00 20.00 4.00 1550.00 20.00 4.00 References [1] T. Okoshi, "Exact Noise-Figure Formulas for Optical Amplifiers and Amplifier-Fiber Cascaded Chains," IEEE/OSA Topical Meeting on Optical Amplifiers and their Applications, Monterrey, PDP11, 1990. 1019 OPTICAL AMPLIFIER MEASURED Notes: 1020 OPTICAL FIBER AMPLIFIER Optical Fiber Amplifier This component simulates the propagation and amplification of optical pulses in a single-mode doped fiber amplifier. Ports Name and description Port type Signal type Input Input Optical Output Output Optical Parameters Main Name and description Symbol Default value Default unit Value range User defined reference wavelength - True - True, False 0 1550 nm [100, 2000] L 5 m [0, 500] - True - True, False - Constant - Constant, From File If TRUE, frequency value of “Reference wavelength” is used internally as ‘zero’ (or reference) frequency in spectrum of signal envelope. Values of parameters (attenuation, dispersion) are assumed to correspond to this frequency. If parameters are wavelengthdependent (from files), they are evaluated at this frequency. If FALSE, central frequency of simulated band is used. Reference wavelength Value of user defined/specified reference wavelength. Length Fiber length Attenuation effect If True, attenuation effect is enabled. Attenuation data type Defines the attenuation as a fixed constant value or as a wavelength dependent curve taken from a file. If ‘constant’, value from “Attenuation” tab is used. 1021 OPTICAL FIBER AMPLIFIER Name and description Symbol Default value Default unit Value range Attenuation 0.2 dB/km [0, 1010] - - - - Name and description Symbol Default value Default unit Value range Gain effect - True - True, False - Constant - Constant, Lorentzian, Parabolic, From file g0 0 dB/m [0, 1010] - 1550 nm [400, 2200] - 50 nm [0.5, 800] - gain.dat - - Es 1e-6 J [0, 10] - Bit rate Hz [103, 10100] Specified value is used if “Attenuation data type” is set to ‘constant’. If ‘from file’, the value is ignored. Attenuation vs. wavelength Defines the attenuation as a wavelength dependent curve in a file. Gain If True, gain effect is enabled. Gain profile Defines the gain profile as a fixed constant value or as a wavelength dependent curve taken from a file, or based on a Lorentzian, or parabolic profile. Gain Defines the small signal gain value. Gain peak wavelength Defines the wavelength for the gain peak (for parabolic and Lorentzian shape). Gain bandwidth Defines the gain bandwidth for parabolic and Lorentzian shapes Gain vs. wavelength Specifies the file containing the gain shape Saturation energy Defines the saturation energy due to limited pumping. Pulse repetition rate Defines the pulse repetition rate. 1022 OPTICAL FIBER AMPLIFIER Dispersion Name and description Symbol Default value Default unit Value range Group velocity dispersion - True - True, False - True - True, False - False - True, False - Constant - Constant, From File 2 -20 ps2/km [-10100, 10100] 3 0 ps3/km [-10100, 10100] D 16.75 — [-10100, 10100] If True, the GVD effect is enabled. Third order dispersion If True, the TOD effect is enabled. Frequency domain parameters Defines domain in which dispersion parameters are specified. If True, frequency domain is used and dispersion effect is specified in terms of 2 and 3 . Otherwise, wavelength domain is used ( D and S ). Dispersion data type Defines if dispersion parameter values are read from component tabs, or taken from a file Beta 2 Value of the GVD parameter in the frequency domain Beta 3 Value of the GVD parameter in the frequency domain Dispersion ps ----------------------- nm km Value of the GVD parameter in the wavelength domain Dispersion slope - [-10100, 10100] 0.075 ps -------------------------2 nm km Value of dispersion slope parameter. Dispersion file format - Dispersion vs wavelengtht - Dispersion vs wavelength, Group delay vs wavelength - Dispersion.dat - - Determines contents of dispersion file: group delay or dispersion vs. wavelength. If “Dispersion vs. wavelength” and “Frequency domain parameters” are selected, it is assumed that file contains 2 . If “Frequency domain parameters” is disabled, component assumes that file contains D . If “Group delay vs wavelength”, the file contains . 1 Dispersion file name Specifies file containing dispersion data The parameter “Frequency domain parameters” refers to the alternative definitions: 1 D D = --------- S = ------- (wavelength domain definition) 1023 OPTICAL FIBER AMPLIFIER and 1 2 2 = --------- 3 = --------- (frequency domain definition) of the dispersion parameters, but not to the argument of these functions, which is always assumed to be the wavelength. All the parameters in the component (including 2 and 3 ) are given as functions of wavelength (not frequency). This is also the case when 1 or 2 are specified from a file - the first column of the file contains wavelength values ( ) and the second column - the corresponding values of 1 or 2 . PMD Name and description Symbol Default value Default unit Value range Birefringence type - Deterministic - Deterministic, Stochastic Defines the birefringence. If “Deterministic”, both the strength of birefringence and principal axes are assumed constant, hence random mode coupling is disabled. If “Stochastic”, random mode coupling is enabled. Differential group delay If Birefringence type is “Deterministic”, this is the value of the differential group delay. If “Stochastic”, parameter is disabled. PMD coefficient Polarization mode dispersion coefficient. If Birefringence type is “Stochastic”, this is the value of the PMD parameter. If “Deterministic”, parameter is disabled. Mean scattering section length Averaged value of fiber length at which the polarization state of the signal is randomized by applying the scattering matrix. Scattering section dispersion Dispersion of the scattering section length. 1024 0 ps ------km Dp 0.5 ps ----------km L scatt 500 m scatt 100 m d----- d [-10100, 10100] [0,10100] [0,10100] [0,10100] OPTICAL FIBER AMPLIFIER Nonlinearities Name and description Symbol Default value Default unit Value range Self-phase modulation - True - True, False - Constant - Constant, From File A eff 80 - EffectiveArea.dat - - - Constant - Constant, From File Determines if the self-phase modulation (SPM) effect will be taken into account. If FALSE all the nonlinear effects self-steepening, SRS - are disabled. In the vector case enabling this effect enables also the cross-phase modulation between the orthogonal polarization components. Effective area data type Defines whether effective area parameter value is read from the component tab or from a file. If “Constant”, the value from the component is used. Effective area Defines the value of the effective area parameter. This value is used if “Effective area data type” is set to “Constant”. Otherwise, the value is ignored. Effective area vs. wavelength m 2 [0,1010] If “Effective area data type” is “From file”, this tab specifies the file containing the effective area data. n2 data type Determines if n 2 parameter (nonlinear index of refraction) value is read from the component tab or from a file. If “Constant”, value is taken from component. n2 The value of the n 2 parameter (nonlinear index of refraction). If data type is set to “Constant”, this value is used, otherwise the value is ignored. n2 Nonlinear coefficient 2.6 X 10-20 0.001317 Displays the nonlinearity parameter. Self-steepening 2 m -----W 1-------Wm [0,10100] - - False - True, False - False - True, False Specifies whether self-steepening effect is taken into account. Can be enabled only after enabling the SPM, and is taken into account only in the scalar case (if Model type is set to Scalar), and if Full Raman response parameter is FALSE. Full Raman response Defines the stimulated Raman scattering (SRS) effect representation in the model. If TRUE, SRS is represented through the convolution integrals of the fields with the Raman susceptibilities. Intrapulse Raman scattering is disabled. 1025 OPTICAL FIBER AMPLIFIER Name and description Symbol Default value Default unit Value range Intrapulse Raman scattering - False - True, False R1 14.2 fs R2 3 fs 0.18 - [0, 1] f 0.75 - [0, 1] Defines the stimulated Raman scattering (SRS) for. Can be enabled if Full Raman response is FALSE. If both Full Raman response and Intrapulse Raman scattering are FALSE, SRS effect is not taken into account in the simulation. Raman self-shift time 1 Value of the Raman self-shift time parameter associated with the parallel SRS effect [0,10100] R1 = dIm 1111 d = 0 Units are such that Re 1111 = 0 = 1 . Raman self-shift time 2 R2 = dIm 1122 d = 0 [0,10100] Units are such that Re 1111 = 0 = 1 . Fractional Raman contribution Fraction of the nonlinear polarization, related to the stimulated Raman scattering effect. Orthogonal Raman factor f = Re 1122 = 0 Units are such that Re 1111 = 0 = 1 . 1026 OPTICAL FIBER AMPLIFIER Numerical Name and description Symbol Default value Default unit Value range Model type - Scalar - Scalar, Vector - Exponential - Exponential, RungeKutta 4th order, RungeKutta 2nd order - Iterative - Iterative, Noniterative Number of iterations - 2 - [2, 1010] Step Size - Variable - Variable, Constant Defines model type used for simulation. Depends on polarization state of signal. If “Vector” selected, signal can have arbitrary polarization state and a system of two coupled equations (Equation 7) is solved. If “Scalar” selected, the signal preserves its polarization state and a single equation is solved (1). In the following cases, vector simulation is performed regardless of value of model type parameter: • • Two polarization components are detected at fiber input PMD effect is “Stochastic”. Propagator type Method used to apply nonlinear propagator in the split-step Fourier method. “Exponential” corresponds to standard implementation, “Runge-Kutta 4th (2nd) order” uses RungeKutta 4th (2nd) order to apply nonlinearity operator. Exponential cannot be used when Model type is set to Vector, and SRS effect is enabled. The default selection is Runge-Kutta 2nd order. Calculation type Specifies implementation of split-step Fourier method when Propagator type is “Exponential”. Specifies whether variable or fixed step-size simulation is used. If “Variable”, step size is adaptively changed depending on value of “Max. nonlinear phase shift” parameter, and solution itself. If “Constant”, step size is evaluated once at the beginning of simulation. In some cases, the fixed step size calculation executes faster, due to the smaller number of calculations per step, but the variable step size calculation is more flexible and can be faster if the peak power of the waveform varies considerably in z (for example, in the presence of strong attenuation). Max. Nonlinear phase shift Maximum (over the time window) phase shift induced by the self-phase modulation effect per step. NL max 3 mrad [0,10100] 1027 OPTICAL FIBER AMPLIFIER Name and description Symbol Default value Default unit Value range Boundary conditions - Periodic - Periodic, Absorbing - 0.05 - [0,10100] - [500, 2500] nm [100, 3000] Specifies type of boundary conditions used in simulation. Filter steepness If “Boundary conditions” option is set to “Absorbing”, the “Filter steepness” parameter determines the absorption/reflection properties of the time window boundaries. Lower/Upper calculation limit Set the spectral range in which the simulation is performed. Any spectral components outside the range is ignored. Graphs Name and description Symbol Default value Default unit Value range Calculate graph - False - True, False - 200 - [1, 100000000] - 200 - [1, 100000000] - True - True, False Enables/disables 3D graphs. If disabled, no graphs are plotted and no data are stored. Number of distance steps Number of snapshots used to construct a 3D plot. If this value is increased, the fidelity of the plot is improved only if the value is below the number of actual steps in z . The number of snapshots stored cannot be bigger than the number of steps in z taken by the simulation to obtain the solution. The latter is determined by the maximum nonlinear phase-shift parameter (numerical tab). Number of wavelength/time steps Number of stored points per snapshot. If this value is increased, the fidelity of the plot is improved only if the value is below the actual number of points in the time (frequency) domain used by the simulation to obtain the solution. The latter is related to the number of samples, which is a global parameter. Linear scale Determines axis type (linear or logarithmic) for the dependent variable. If TRUE, the axis type is linear. Note: The rest of the parameters in the Graphs tab of the component determine which graphs are plotted after the simulation is completed. 1028 OPTICAL FIBER AMPLIFIER Simulation Name and description Symbol Default value Default unit Value range Enabled - True - True, False Name and description Symbol Default value Default unit Value range Convert noise bins - False - True, False Name and description Symbol Default value Default unit Value range Generate random seed - True - True, False - 0 - [0, 4999] Determines whether or not the component is enabled. If FALSE, all input signals reach the output port of the component without any changes. Noise If TRUE, each noise bin within the bandwidth of the signal is converted to a Gaussian white noise, with the correct power spectral density, and the noise is added to the signal. Random numbers Determines how random number generator is initialized (seeded). If TRUE, the seed index used for the initialization is the random number itself. Otherwise, a user specified number is used. Random seed index If “Generate random seed” is FALSE, this value specifies the seed index. The generated pseudorandom sequence is the same if the seed index is not changed. The value of the “Random seed index” is ignored if “Generate random seed” is TRUE. Technical background Scalar approach Basic equation When the pulses propagating in the SMF gain fiber, it is assumed that the polarization is unchanged along the fiber length, and the evolution of the slowly varying electric 1029 OPTICAL FIBER AMPLIFIER field envelope can be described by the following equation (the scalar approach, Model type parameter from the "Numerical" tab is set to "Scalar") of the form: 2 3 2 2 2 E 3 0 E g i E E ------ + E + i 2 0 --------- – ----------------- --------- – --- E = i E E + ------- ------ E E – R1 E ------------ 2 3 2 0 T z 6 T T T (1) In Equation 1, E = E z T is the electric field envelope. A frame moving at the group velocity ( T = t – z v g t – 1 z ) is assumed. The derivatives of the propagation constant of the fiber mode , ( c is the mode effective index), with respect to frequency n n 2 0 = --------------------- n = 1 2 3 . n and 3 are the first and the second group velocity dispersion (GVD) parameters, respectively, and 0 is the reference frequency of the signal, related to the parameter "Reference wavelength" ("Main" category of the component properties) 2c through 0 = --------- with c being the light speed in vacuum. 0 The physical meaning of the terms in Equation 1 is the following. The first term takes into account the slow changes of the electric field along the fiber length. The second term takes into account the linear losses of optical fiber. The third term represents the (first-order) group velocity dispersion. This is the effect responsible for the pulse broadening. (See "Group velocity dispersion" in the Tutorials). The next term is the second-order GVD, known also as third-order dispersion (TOD). This effect becomes important for a signal with a broad spectrum (e.g. femtosecond pulses or WDM systems with many channels). The pulse shape becomes asymmetric due to the effect of TOD. (See "Third order dispersion" from the Tutorials). The parameters 2 and 3 are denoted as "frequency domain parameters" in the interface of the component (see the "Dispersion" category in the Parameters table). The following relations are used internally to convert between them and the commonly used wavelength domain parameters D (dispersion) and S (dispersion slope). d 1 2c D = --------- = – --------- 2 2 d 2 dD 3 = --------- S + 2D S = ------ 2c d 1030 2 (2) OPTICAL FIBER AMPLIFIER For gain fiber, the gain is defined by 2 d E g = g t 1 + T 22 2 dt (3) where T2 is the dipole relaxation time and g(t) is saturated gain according to g0 g t = ----------------------------------------------------------------------------2 2 1 + E x + E y dt E s (4) where g0 is the small signal gain and Es is the saturable energy. The parameter is given by: 0 n2 = ------------cA eff (5) In Equation 5, n 2 is the nonlinear refractive index coefficient and A eff is the fiber effective area. The first term in the right-hand side in Equation 1 accounts for the selfphase modulation effect. It is responsible for the broadening of the pulse spectra and, in the presence of anomalous GVD, for the formation of optical solitons (See "Selfphase modulation" and "Self-phase modulation and group velocity dispersion" from the Tutorials). The second term in the right-hand side of Equation 1 takes into account the self-steepening effect. It leads to an asymmetry in the SPM-broadened spectra of ultrashort (femtosecond) pulses [1] and is responsible for the formation of optical shocks (see "Self-steepening" in the Tutorials). This effect will be taken into account only if the "Full Raman response" parameter is set to False. The last term in Equation 1 accounts for the intra-pulse Raman scattering effect with the parameter R1 being the parallel Raman self-shift time. The intra-pulse Raman scattering is an approximation to the actual Raman response of the material which is valid provided that signal spectrum is narrow compared to the Raman-gain spectrum. The R parameter is related to the slope of the imaginary part of the Raman susceptibility Im 1111 at zero frequency offset [1]. The parameter is the fractional contribution of the delayed response of the material to the total nonlinearity [1]. The intra-pulse Raman scattering effect is responsible for the self-frequency shift i.e. energy transfer from higher to lower spectral components. It leads to a decay of higher order solitons into its constituents (see "Intrapulse Raman scattering" in the Tutorials). The intra-pulse Raman scattering plays the most important role among the higher order nonlinear effects [1]. Full Raman response The component can simulate the SRS effect without the requirement that the signal spectrum is much narrower compared to the Raman gain spectrum. Selecting the 1031 OPTICAL FIBER AMPLIFIER option "Full Raman response" from the Numerical tab can do this. In this case Equation 1 is replaced by: 2 i 2 0 E 2 E 3 0 3 E g 2 2 E ------ + E + ------------------------------ --------- – ------------------ --------- – --- E = i 1 – E E + E h 1111 s E T – s ds 2 3 2 z 2 6 T T 0 (6) In Equation 6, h1111(t) is the (time-domain) Raman response function [1][2]. It is the Fourier-transform of the of the Raman susceptibility 1111 . In this case the selfsteeping effect is neglected. Vector approach When the polarization state of the incident light is not preserved during its propagation inside an optical fiber the scalar approach is no longer applicable and Equation 1 is replaced by [1]: 2 3 E E X E i E 2 2 2 g ---------- + 1X ---------X- + -------2- ------------X- – --- E X – -----3- ------------X- = i 1 – E X + --- E Y E X 2 3 2 3 z t 2 6 t t + iE X 2 h1111 s EX t – s 2 ds + h 1122 s E Y t – s ds 0 0 + iE Y h 1212 s E X t – s E Y t – s ds 0 2 (7) 3 E E E i E 2 2 2 g ---------Y- + 1X ---------Y- + -------2- ------------Y- – --- E Y – -----3- ------------Y- = i 1 – E Y + --- E X E Y 2 3 3 2 z t 2 6 t t + iE Y h1111 s E t – s 0 2 2 ds + h 1122 s E X t – s ds 0 + iE X h 1212 s E t – s E X t – s ds 0 In Equation 7, hijkl(t) are the Raman response functions. The convolution integrals in Equation 7 are evaluated in the frequency domain, by multiplying the spectra of the electric fields with the Raman susceptibilities and then performing the inverse FFT. 1032 OPTICAL FIBER AMPLIFIER In case the SRS effect is represented by "Intrapulse Raman scattering", Equation 7 is replaced by [2]: 2 3 E X E gE i E E ---------- + 1X ---------X- + -------2- ------------X- – ---------X- – -----3- ------------X- = 2 3 z t 2 2 6 t t 2 2 1 +f EX EY 2 2 i E X + --- 1 – + -------------- E Y – R1 ---------------- – R2 ---------------- E X 3 t t 2 2 R1 – R2 E X E Y – i ------------------------ ------------------------- E Y 2 t (8) 2 3 E Y E i E gE E ---------- + 1Y ---------Y- + -------2- ------------Y- – ---------Y- – -----3- ------------Y- = 2 3 z t 2 2 6 t t 2 2 2 1 +f EY EX 2 i E Y + --- 1 – + -------------- E X – R1 ---------------- – R2 ---------------- E Y 3 2 t t 2 R1 – R2 E Y E X – i ------------------------ ------------------------- E X 2 t In the case of Equation 7 or Equation 8, due to the orthogonal Raman gain (the last terms in Equation 7 and Equation 8), the "Exponential" option for the "Propagator type" is not applicable. The component automatically selects "Runge Kutta 2nd order" when the model type is set to "Vector" and the Raman effect ("Intrapulse Raman scattering" or "Full Raman response" options are selected. Due to the increased number of convolutions performed at each step the fiber component can be slow when solving Equation 7 and Equation 8. For information, check the Optical fiber component technical background. 1033 OPTICAL FIBER AMPLIFIER Numerical solution For information about the numerical solution, check the Optical fiber component technical background. References [1] G. P. Agrawal, "Nonlinear fiber optics", Academic press, 3rd edition, 2001. [2] C.R.Menyuk, M.N.Islam and J.P.Gordon, Optics Letters, 16 566, (1991). 1034 OPTICAL FIBER AMPLIFIER Amplifiers Library Optical - Raman • Raman Amplifier-Average Power Model • Raman Amplifier-Dynamic Model 1035 OPTICAL FIBER AMPLIFIER Notes: 1036 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Raman Amplifier Component (Obsolete) This component is an obsolete version that is included with OptiSystem for backwards compatibility purposes - It was replaced by the Bidirectional Optical Fiber component. Ports Name and description Port type Signal type Input 1 Input Optical Output 1 Output Optical Input 2 Input Optical Output 2 Output Optical Parameters Fiber Name and description Default value Default unit Value range Fiber length 10 km [0, INF] Attenuation data type Constant — Constant, Wavelength Dependent /From File Attenuation – constant 0.25 dB/km [0, INF] Attenuation vs. wavelength AtnVsLambda.dat — [0, INF] Forward Input Coupling Loss 1 dB [0, 106] Forward Output Coupling Loss 0.022 dB [0, 106] Backward Input Coupling Loss 1 dB [0, 106] Backward Output Coupling Loss 0.022 dB [0, 106] Effective area data type Constant — Constant, Wavelength Dependent/From File Effective area – constant 72 µm2 [0, INF] Effective area vs. wavelength EffAreaVsLambda.dat — [0, INF] 1037 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Raman effect Name and description Default value Default unit Value range Peak Raman gain coef 9.9e-14 m/W [0, INF] Pump wavelength of peak Raman gain coef 1000 nm [0, INF] Raman gain spectrum vs. freq. RamanGainVsFreq.dat — — Raman gain polarization factor 0.5 — [0, INF] Temperature 300 K [0, INF] Name and description Default value Unit Value range Rayleigh coef. data type Constant — Constant, Wavelength Dependent/From File Rayleigh coef. — constant 5e-005 1/km [0, INF] Rayleigh coef. vs. wavelength RayleighGainvsLambda.dat — [0, INF] Name and description Default value Unit Value range Left end reflection data type Constant — Constant, Wavelength Dependent/From File Left end reflection — constant –30 dB [-INF, 0] Left end reflection vs. wavelength NearEndReflVsLambda.dat — [-INF, 0] Right end reflection data type Constant — Constant, Wavelength Dependent/From File Right end reflection — constant –30 dB [-INF, 0] Right end reflection vs. wavelength FarEndReflVsLambda. dat — [-INF, 0] Rayleigh effect Reflections 1038 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Other nonlinearities Name and description Default value Unit Value range Brillouin gain coef 5e-011 m/W [0, INF] Brillouin bandwidth data type Constant — Constant, Wavelength Dependent/From File Brillouin bandwidth — constant 40 MHz [0, INF] Brillouin bandwidth vs. wavelength FarEndReflVsLambda.dat — [0, INF] Brillouin Stokes shift 11 GHz [0, INF] Nonlinear refr. index data type Constant — Constant, Wavelength Dependent/From File Nonlinear refr. index — constant 3e-020 m2/W [0, INF] Nonlinear refr. index vs. wavelength N2VsLambda.dat — [0, INF] Raman-resonant n2 dispersion RealHiRezVsLambda.dat — [–INF, INF] Eff. refr. index vs. wavelength EffRIVsLambda.dat — [0, INF] Group velocity dispersion 5 ps/nm/km [0, INF] Dispersion slope 0.1 ps/nm2/km [0, INF] Effects on/off Name and description Value range Dependence Attenuation ON [ON, OFF] Rayleigh backscattering gain ON [ON, OFF] SRS gain ON [ON, OFF] OFF [ON, OFF] Pump depletion in SRS ON [ON, OFF] Double Rayleigh scattering OFF [ON, OFF] Left end reflection OFF [ON, OFF] Right end reflection OFF [ON, OFF] Polarisation maintaining fiber OFF [ON, OFF] (Stimulated Raman scattering gain) SpRS gain Spontaneous Raman scattering gain) 1039 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Simulation details Name and description Default value Unit Value range Enable ON — [ON, OFF] Parameter set Default — Default, Auto, User Upper Pump wavelength 1450 nm [0, INF] Power accuracy 0.001 — [0, INF] Max. number of iterations 100 — [1, 10000] Number of power iterations 4 — [1, 10000] ODE integration method 5th-order Runge-Kutta with step size control — 5th-order Runge-Kutta with step size control, Gear's stiff eq. solver with step size control ODE integrator accuracy 1e-006 — [0, 1] Max. number of steps per iteration 100000 — [1, 10000] Number of longitudinal points 256 — [10, 100000] Background noise PSD level 1e-100 W/Hz [0, 10000] Inphase noise ratio 0 — [0, 1] Calculate 3D graphics ON — [ON,OFF] 3D graphics resolution 10 — [1, 100] Noises Name and description Default value Default unit Unit Value range Noise center frequency 193.1 THz Hz, THz, nm [30, 3e+006] Noise bandwidth 30 THz Hz, THz, nm [0, INF] Noise bins spacing 1000 GHz Hz, GHz, THz, nm [0, INF] Noise threshold –100 dB — [-INF,+INF] Noise dynamic 3 dB — [0, INF] Convert noise bins Convert noise bins — — [ON, OFF] 1040 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Random numbers Name and description Default value Unit Value range Generate random seed ON — [ON,OFF] 0 — [0, 4999] Name and description Default value Unit Value range Lower limit of Region of Interest 1550 nm [0, INF] Upper limit of Region of Interest 1600 nm [0, INF] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Results 1041 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Graphs Name and description X Title Y Title Wavelength [nm] Power [dBm] Forward Output Gain [dB] Wavelength [nm] Gain [dB] Forward Output OSNR [dB] Wavelength [nm] OSNR [dB] Forward Output Multiple Rayleigh Scattering Spectrum [dBm] Wavelength [nm] Power [dBm] Backward Output Power Spectrum [dBm] Wavelength [nm] Power [dBm] Backward Output Gain [dB] Wavelength [nm] Gain [dB] Backward Output OSNR [dB] Wavelength [nm] OSNR [dB] Backward Output Multiple Rayleigh Scattering Spectrum [dBm] Wavelength [nm] Power [dBm] Forward Power Spectrum [dBm] Wavelength [nm] Fiber Length [km] Forward Gain [dB] Wavelength [nm] Fiber Length [km] Forward Gain Coefficient [dB/km] Wavelength [nm] Fiber Length [km] Forward OSNR [dB] Wavelength [nm] Fiber Length [km] Forward Double Rayleigh Scatt. Spectrum [dBm] Wavelength [nm] Fiber Length [km] Backward Power Spectrum [dBm] Wavelength [nm] Fiber Length [km] Backward Gain [dB] Wavelength [nm] Fiber Length [km] Backward Gain Coefficient [dB/km] Wavelength [nm] Fiber Length [km] Backward OSNR [dB] Wavelength [nm] Fiber Length [km] Backward Double Rayleigh Scatt. Spectrum [dBm] Wavelength [nm] Fiber Length [km] Forward Output Power Spectrum [dBm] When a parameter is defined as a curve loaded from a file, the format of the file is: Wavelength_1 ParameterValue_1 Wavelength_2 ParameterValue_2 Wavelength_3 ParameterValue_3 ...... Wavelength_N ParameterValue_N The unit of the wavelengths is always [nm]. The units of the parameter values are given in the table above, and are the same as the units of the respective Constant parameter. Arbitrary number of points (file lines) are allowed, except 0 (empty file). 1042 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Results The component produces the following results: • Maximum Forward Gain [dB] • Maximum Forward On/Off Gain [dB] • Forward Gain Flatness [dB] • Maximum Forward Power [dB] • Wavelength of Maximum Forward Power [dB] • Minimum Forward Effective Noise Figure [dB] • Forward Effective Noise Figure Flatness [dB] • Maximum Backward Gain [dB] • Maximum Backward On/Off Gain [dB] • Backward Gain Flatness [dB] • Maximum Backward Power [dB] • Wavelength of Maximum Backward Power [dB] • Minimum Backward Effective Noise Figure [dB] • Backward Effective Noise Figure Flatness [dB] These results are calculated for the wavelength range defined in the Results tab of the Component Properties dialog box. Forward and Backward are names used to distinguish the characteristics pertaining to the left and right ends of the fiber respectively. They have nothing to do with the frequently used terms forward / (backward) Raman amplification, meaning amplifier configuration having co-propagating / (counter-propagating) pump and signals. Graphics The Raman Amplifier presents the results of the calculations in a variety of both 2D and 3D graphics. 2D graphics The following 2D graphs are available: • Forward Output Power Spectrum [dBm] • Forward Output Gain [dB] • Forward Output On/Off Gain [dB] • Forward Output OSNR [dB] • Forward Double Rayleigh Scattering Spectrum [dBm] • Forward Eff. Noise Figure Spectrum [dB] • Backward Output Power Spectrum [dBm] 1043 RAMAN AMPLIFIER COMPONENT (OBSOLETE) • Backward Output Gain [dB] • Backward Output On/Off Gain [dB] • Backward Output OSNR [dB] • Backward Double Rayleigh Scattering Spectrum [dBm] • Backward Eff. Noise Figure Spectrum [dB] 3D graphics The following 3D graphs are available: • Forward Power Spectrum [dBm] • Forward Gain [dB] • Forward Gain Coefficient [dB/km] • Forward OSNR [dB] • Forward Double Rayleigh Scattering Spectrum [dBm] • Backward Power Spectrum [dBm] • Backward Gain [dB] • Backward Gain Coefficient [dB/km] • Backward OSNR [dB] • Backward Double Rayleigh Scattering Spectrum [dBm] 2D/3D graphics The following 2D/3D graphics are available: • Forward Power Spectrum [dBm] • Forward On/Off Gain [dB] • Forward Gain [dB] • Forward Gain Coefficient [dB/km] • Forward OSNR [dB] • Forward Double Rayleigh Scattering Spectrum Power [dBm] • Forward Eff. Noise Figure [dB] • Backward Power Spectrum [dBm] • Backward On/Off Gain [dB] • Backward Gain [dB] • Backward Gain Coefficient [dB/km] • Backward OSNR [dB] • Backward Double Rayleigh Scattering Spectrum Power [dBm] • Backward Eff. Noise Figure [dB] Forward and Backward are names used to distinguish the characteristics pertaining to the overall optical spectra propagating from the left end to the right end of the fiber respectively, and vice-versa. They have nothing to do with the frequently used terms 1044 RAMAN AMPLIFIER COMPONENT (OBSOLETE) forward / (backward) Raman amplification, meaning amplifier configuration having co-propagating / (counter-propagating) pump and signals. Technical background Introduction The most promising technology to support almost unlimited bandwidth employs the nonlinear effect of stimulated Raman scattering (SRS) in hybrid EDFA + Raman fiber amplifiers (HRA) or purely Raman fiber amplifiers (RFA) [1,2]. The most important advantage of this effect is that the pump wavelength p does not need to be tied to a particular energy level/absorption band, as it is in EDFAs. Raman amplification is readily obtainable in any spectral region and in any type of fiber, provided a practical pump source with wavelength 80-100 nm shorter than that of the signal and with sufficiently high power is available. Given the progress in the manufacturing of highpower pump lasers in the infrared [3] along with the seemingly limitless demand for amplification bandwidth, Raman amplification will play an increasingly important role in WDM networks. SRS is among the best-understood third-order nonlinear processes, observed experimentally for the first time in 1962 in bulk media [4] and in 1972 in optical fibers [5]. It manifests itself as an exponential growth of a signal (Stokes) wave in the field of a shorter wavelength-intensive pump. As mentioned above, SRS is a non-resonant effect with respect to pump wavelength, which may lie anywhere in the transparency windows of the medium. On the other hand, the frequency difference p-s between the pump and signal waves should be resonant with one of the vibrational modes R of the host. SRS does not require phase-matching, and for CW pumps, it allows both forward (pump and signal co-propagating) and backward (counter-propagating) pumping configurations. The most important characteristics of SRS in telecom-grade fibers are [6 (and references)]: • The SRS gain spectrum peaks at 13.2 THz ( 100 nm at p =1.55 m), but extends up to 30 THz. • The 3dB bandwidth of the gain spectrum is 6-7 THz ( 50 nm at p =1.55 m). • The peak gain gRpeak () coefficient is 6.4x10-13 m/W for p = 1.55 [m], and is inversely proportional to p. • Both the shape of the spectrum and the value of gRpeak () depend on the concentration of the dopants; the peak gain coefficient of pure GeO2 is 8 times larger than that of fused silica. Figure 1 shows the zero temperature Raman gain coefficient spectra of pure fused silica, pure fused GeO2, and silica doped with 25 mol.% GeO2. The spectra are scaled to the peak gain coefficient of silica. • The SRS effect is in principle highly polarization-dependent. Raman gain is negligible for orthogonal polarizations of the pump and signal. However, in nonpolarization maintaining fibers, the gain becomes polarization independent due to mode-scrambling. In this case gRpeak() is reduced by a factor of 2. 1045 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Figure 1 Zero temperature Raman coefficient spectra The arbitrary choice of pump(s) wavelength(s) allows for a key new feature in all types of hybrid and Raman fiber amplifiers: the possibility to arrange several pumps in a finite pump band and to amplify the WDM signals in their extended aggregate gain spectrum. Gain-equalization is achieved by a proper choice of the wavelengths and powers of the individual pumps. On the device level, the HRA and FRA come in a variety of configurations: backward-, forward- and bidirectionally pumped, discrete or distributed, single- or multi-stage. The ubiquitous nature of the Raman effect allows numerous types of fibers to be used as the SRS–active media — from standard transmission fibers in distributed FRA to short (5-8 km) DCFs or highly nonlinear heavily-doped fibers with small effective areas [9]. Typically, several hundred milliwatts of pump power are required. The challenges in modeling and optimizing FRAs are related mainly to the nonlinear, inefficient nature of SRS, requiring high pump powers and long fibers, and to the different pump mechanism. • All participating optical waves interact with each other. The shorter wavelengths transfer power to the longer wavelengths (all long wavelengths deplete all short wavelengths), resulting in a complex longitudinal distribution of gain coefficients and noise powers. • Other third-order nonlinear processes among the pumps take place — SPM and XPM, FWM, and stimulated Brillouin scattering (SBS). • Considerable noise powers and crosstalk are generated by multi-path Rayleigh scattering. An additional challenge is the requirement to build a model that is both quantitatively and qualitatively precise. While the general features of any of the effects above are 1046 RAMAN AMPLIFIER COMPONENT (OBSOLETE) well known [6], it is the complex interplay of the details that matters if such a model is to be used as a versatile design tool by the photonics industry. As a result, some of the simplifications (usually found in the literature) should be rejected: • The Raman spectrum of pure fused silica must be used with care. For discrete FRAs, the magnitude and the spectrum of the Raman gain coefficient must always be defined in dependence on the concentration of the dopants [14]. The dispersion of the real part of the Raman-resonant nonlinear susceptibility must also be accounted for [15]. • The assumption that the fiber parameters, such as effective areas/overlap integrals, losses, and Brillouin gain bandwidth, are constants. In the wavelength region of 1.4-1.65 [m], the effective areas of SMF-28TM and a typical DSF vary by 25% and 50% respectively. The comprehensive model described here uses the unified spectral signal representation illustrated in Figure 2. It features arbitrary number and location of pumps, signals and ASE bands, and complete forward / backward symmetry. Each forward propagating wave has a backward counterpart at the same wavelength and vice-versa. Figure 2 Unified spectral signal representation 1047 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Formulation of the model As an example, the power and the phase change of any type of wave (pump, signal, or ASE) with central carrier frequency k as PF,B(z, k) and F,B (z, k) respectively, where the subscripts F and B discriminate against the forward and backward propagating waves at the same wavelength. The system of coupled differential equations describing the operation of a FRA or the Raman sub-unit of a HRA has the form: dP F z , k ------------------------- = – k P F z , k dz + k P B z , k N + R sp g k , 1 P F z , 1 + P B z , 1 P F z , k + P 1 , k ,T ,B k l = k+1 k–1 – g R l , k P F z , l + P B z , l P F z , k l=1 sp – 2F total k ,T P F z , k Br Br Br sp Br B + --------------------------- g P B z , k + P F z , k + P k + , k ,T ,B k Br B + Bk Br Br Br sp Br B – --------------------------- g P B z , k – + P k , k – ,T ,B k P F z , k Br B + Bk 1048 RAMAN AMPLIFIER COMPONENT (OBSOLETE) N + N N R g l = 1m = 1n = 1 k k , l , m , n cos z – 4 k , l , m , n sin z = l + m – n x P F z , k P F z , l P F z , m P F z , n 1049 RAMAN AMPLIFIER COMPONENT (OBSOLETE) d F z , k -------------------------- = dz N k ,l ,k ,l 2 – kl PF z ,l + 2PB z ,l l=1 R g k , l , m , n - sin z + 2 k , l , m , n cos z + -------------------------------------------2 l = 1m = 1n = 1 N N N k = l + m – n P F z , l P F z , m P F z , n X ---------------------------------------------------------------------P F z , k The equations describing the evolution of P B z ,k and B z ,k are obtained by alternative interchanging of subscripts F and B. The notations are explained in Table 1. Table 1 Description of notations Notation Description N Number or pumps+signals+ASE bands in each direction 2N Total number of interacting waves k Total losses k Rayleigh scattering coefficient R R R g k , 1 = f k , 1 g peak 1 g norm 1 – k Raman gain coefficient R Peak Raman gain coefficient, depending on the frequency of the current pump wave. In fused silica, it is downshifted by = R = 13.2 THz from the respective pump. g norm R Normalized Raman gain spectrum of the fiber, as dependent on the type and concentration of the dopant. f l , k ;f k , l , m , n Mode overlap integrals; for definitions see, for example [6] (chap. 7 and 10) g peak 1 1050 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Notation Description sp P l , k ,T ,B = h 1 – k -------------------------- KT = 2h k B 1 + 1 e –1 sp F total k ,T = k 2h k 0 Power generated by spontaneous Raman and Brillouin scattering of the wave with carrier frequency 1 into the bandwidth of the wave with carrier k . Although the forms of these terms are identical, their values are different: sp P 1 , k ,T ,B 2h k B for SpRS, while sp P 1 , k ,T ,B » 2h k B for SpBS. A factor (with dimension of length) determining the integrated total power lost by the current wave via spontaneous Raman scattering into all possible lower frequencies, as depending on the Raman spectrum and the temperature. h k – ------------------------ KT g , k 1 + 1 e – 1 d R B Bandwidth of the respective wave. h, K, T Planck bar constant, Boltzmann constant, Temperature. gBr, BBr, Br Brillouin gain coefficient, line width, and Stokes shift. z = 1 z + m z – n z – k z – k .z Total phase difference between the nonlinearly mixed waves k Input phase mismatch lm Kroneker delta 1051 RAMAN AMPLIFIER COMPONENT (OBSOLETE) References [1] H. Masuda, S. Kawai, IEEE Photonics Technology Letters, Vol. 11, p. 647, 1999. [2] T. Nielsen, P. Hansen, A. Stentz, M. Aquaro, J. Pedrazzani, A. Abramov, and R. Espindola, IEEE Photonics Technology Letters, Vol. 10, p. 1492, 1998. [3] Laser Focus World, January 2000; SDL Press Release, http://www.sdli.com/investor/releases/19990630_BROADENS.html [4] E. Woodbury and W. Ng, Proc. IRE, Vol. 50, p. 2347, 1962. [5] R. Stolen, E. Ippen, and A. Tynes, Applied Physics Letters, Vol. 20, p. 62, 1972. [6] G. Agrawal, “Nonlinear Fiber Optics,” 2nd Edition, Academic Press Inc., San Diego, California, 1995. [7] F.L. Galeener, J.C. Mikkelsen Jr., R.H. Geils, and W.J. Mosby, Applied Physics Letters, Vol. 32, p. 34, 1978. [8] Y. Emori, K. Tanaka, and S. Namiki, Electronics Letters, Vol. 35, p. 1355, 1999. [9] T. Hosaka, S. Sudo, H. Itoh, and K. Okamoto, Electronics Letters, Vol. 24, p. 770, 1988. [10] H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photonics Technology Letters, Vol. 11, p. 530, 1999. [11] M. Nissov, K. Rottwitt, H. Kidorf, and M. Ma, Electronics Letters, Vol. 35, p. 997, 1999. [12] Y. Chen, Journal of the Optical Society of America, Vol. B7, p. 43, 1990. [13] B. Foley, M. Dakss, R. Davies, and P. Melman, Journal of Lightwave Technology, Vol. 7, p. 2024, 1989. [14] S. Davey, D. Williams, B. Ainslie, W. Rothwell, and B. Wakefield, IEE Proceedings, Vol. 136, p. 301, 1989. [15] R. Hellwarth, Progress of Quantum Electronics, Vol.5 , p. 1, 1977. [16] Y. Shen, “The Principles of Nonlinear optics,” J. Wiley & Sons Inc., 1984. [17] A. Uchida, M. Takeoka, T. Nakata, and F. Kannari, Journal of Lightwave Technology, Vol. 16, p. 92, 1998. [18] S. Evangelides, L. Mollenauer, J. Gordon, and N. Bergano, Journal of Lightwave Technology, Vol. 10, p. 28, 1992. 1052 RAMAN AMPLIFIER COMPONENT (OBSOLETE) Notes: 1053 RAMAN AMPLIFIER COMPONENT (OBSOLETE) 1054 RAMAN AMPLIFIER-AVERAGE POWER MODEL Raman Amplifier-Average Power Model This component simulates a Raman amplifier based on the average power approach [1], [2]. Ports Name and description Port type Signal type Input 1 Input Optical Output 1 Output Optical Input 2 Input Optical Output 2 Output Optical Parameters Main Name and description Symbo l Default value Default unit Value range Length L 10 km ]0; 1,000,000[ Constant — Constant, From File 0.2 dB/km [0,+INF[ - FiberLoss.dat nm - dB/km - - Constant — Constant, From File Amplifier length. Attenuation data type Defines if attenuation is entered as scalar, used for all wavelengths, or if it is wavelength dependent / downloaded from a file. Attenuation Constant attenuation value Attenuation file Attenuation value dependent on wavelength. Effective area data type Defines if effective area is entered as scalar, used for all wavelengths, or if it is wavelength dependent/ downloaded from a file. 1055 RAMAN AMPLIFIER-AVERAGE POWER MODEL Name and description Symbo l Default value Default unit Value range Effective interaction area A eff 72 µm2 [0, INF[ - EffectiveArea.dat nm - µm2 - - Raman gain - Raman gain, Raman gain efficiency - 1e-013 - [0,+INF[ - 1000 nm [0,+INF[ gr RG.dat THZ normalized Raman gain - Name and description Symbo l Default value Default unit Value range Temperature T 300 K [0,500] K eff 2 - [1,2] Constant effective area. Effective interaction area file Effective area dependent on wavelength. Raman gain type Defines type of Raman gain. If Raman gain efficiency is selected, effective area is disabled, and value is g r / A eff . Otherwise, it is normalized g r multiplied by Raman gain peak (see below). Raman gain peak Normalized Raman gain is multiplied by Raman gain peak. Formula is detailed later in this section. Raman gain reference pump Value used for Raman gain calculation. Formula is detailed later in this section. Gain X frequency File that defines Raman gain or the Raman gain efficiency. Enhanced Absolute temperature at which fiber is operating. Used for noise consideration. Polarization factor Actual value depends on relative polarization of fields of channels i and j. Equals 1 if fields of both channels are polarization-aligned, and 2 for totally scrambled polarization [4]. 1056 RAMAN AMPLIFIER-AVERAGE POWER MODEL Name and description Symbo l Default value Default unit Value range Rayleigh back scattering data type - Constant - Constant, From File - 5.0e-005 1/km [0, INF[ - Rayleigh.dat nm - 1/km - - 1450 nm [0,3000] - False - True, False - 16.75 ps/nm/km ]-INF,+INF[ - 0.075 ps/nm2/km ]-INF,+INF[ - 1550 nm [100,2000] Defines whether Rayleigh back scattering coefficient is entered as scalar, used for all wavelengths, or wavelength dependent/downloaded from a file. Rayleigh back scattering Constant Rayleigh back scattering. Rayleigh back scattering file Rayleigh back scattering dependent on wavelength. Upper pump reference Used for convergence test. All wavelengths below this value are considered pump, and are not taken into account for the convergence test. Enable dispersion Enables the linear chromatic dispersion application for the signals. Dispersion Value of the GVD (Group Velocity Dispersion) parameter in wavelength domain. Dispersion slope Value of the dispersion slope parameter. Reference wavelength Used internally as “zero” (or reference) frequency in spectrum of signal envelope. Attenuation value is assumed to correspond to this frequency. Numerical Name and description Default value Unit Value range Tolerance 0.01 - ]0,+INF[ Used to check convergence of the model. Based on gain of the signals. 1057 RAMAN AMPLIFIER-AVERAGE POWER MODEL Name and description Default value Unit Value range Number of divisions 50 - [1;50,000] 50 - [1;50,000] All signals - All signals, First signal Number of divisions (in space) of the fiber. Number of iterations Maximum number of iterations executed. If convergence is not reached in this number of iterations, model returns the calculated values anyway. Check convergence using: Defines if convergence is checked using “All signals” or “First signal”. Graphs Name and description Default value Unit Value range Calculate graphs False - True, False 20 - [1,1e8] 20 - [1,1e8] True - True, False -50 dBm ]-INF,+INF[ Defines if graphs are calculated or not. If False, component graphs are not represented. Number of distance steps Number of distance steps considered for graph generation. Number of wavelength steps Number of wavelength steps considered for graph generation. Linear scale Defines if a linear scale (Watt) or logarithmic one (dBm) is used. Minimum value If a logarithmic scale is used, this parameter defines the minimum value for the power that is displayed on the graph. Simulation Name and description Default value Unit Value range Enabled True - True, False Defines whether the component is enabled or not. 1058 RAMAN AMPLIFIER-AVERAGE POWER MODEL Noise Name and description Default value Default unit Unit Value range Noise center frequency 193.4 THz Hz, THz, nm [30, 30e5] 13 THz Hz, THz, nm ]0,+INF[ 125 GHz Hz, GHz, THz, nm [1,1000[ -100 dB — ]-INF,0[ 3 dB — [0,+INF[ Convert noise bins — — True, False Determines noise center frequency. Noise bandwidth Bandwidth to create noise bins. Noise bins spacing Specifies the noise bins spacing. Noise threshold Minimum value for adaptation of noise bins. Noise dynamic Threshold ratio for adaptation of noise bins. Convert noise bins Determines if generated noise bins are incorporated into the signal. Random numbers Name and description Default value Unit Value range Generate random seed True — True, False 0 — [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical Background In recent years, Raman amplifiers have become one of the most promising technologies for the next generation of fiber amplifiers, mostly due to their flexibility in bandwidth design. Nevertheless, the simulation techniques that are commonly used for RA's have demanded exhaustive computational time, mainly due to the use of direct integration of the coupled differential equations that describe the RA behavior [3]. The coupled differential equations have the shape observed in Equation 1. A similar set of equations, describing the backward propagation, is solved at the same time we solve the forward equations written below. 1059 RAMAN AMPLIFIER-AVERAGE POWER MODEL dP f z ---------------------- = P f z + P b z + dz P f z v h gr – --------------------- P z + P b z + K eff A eff f gr – P f + P b 1 + exp h – kT – 1 ---------------------A eff –1 – v P f z v gr – ---------------------- --- P f z + P b z – K eff A eff 2hP f z v gr – –1 --------------------- 1 + exp h – kT – 1 A eff where 1060 Symbol Definition frequencies (Hz) fiber attenuation [N/m] Rayleigh back scattering coefficient [N/m] gr – Raman gain coefficient for frequency difference ( – ) [m/W] P b z backward propagating power [W] A eff effective core area [m2] K eff polarization factor frequency interval h Plank’s constant k Boltzmann’s constant T temperature [K] (1) RAMAN AMPLIFIER-AVERAGE POWER MODEL In the equations, the following physical effects were taken into account: • pump-to-pump, signal-to-signal, and pump-to-signal Raman interactions • spontaneous Raman emission and its temperature dependency • stimulated Raman scattering • pump depletions due to Raman energy transfer • high-order Stokes generation • multiple Rayleigh back scattering • fiber loss • spontaneous emission noise A very interesting approach that considerably reduces the computational time for simulating RA is the one used for this component. The idea behind this technique is first to split the amplifier into a concatenation of small segments, and then to use the small-signal-traveling wave solution in each section (see Equation 3). In order to eliminate the z dependence in a small segment length, average powers in each section are introduced (see Equation 4). So, basically, we rearrange some terms of the original Equation 1 and reduce the propagation equations to a simpler form. This new form, suitable for the purpose of average power analyses, can be written as [2]: f z v dP -------------------- = A z v P f z v + B z v dz (2) where A z v = – + gr – gr – - P z + P b z – --- ---------------------- P f z + P b z -------------------- K eff A eff K eff A eff f v v gr – 1 – 2 h ---------------------- 1 + ---------------------------------------------------------–1 A eff exp h – kT – 1 (2a) v gr – 1 B z = P b z + h ---------------------- P f z + P b z 1 + ---------------------------------------------------------–1 A eff exp h – kT – 1 (2b) v if we substitute P f z , P b z , in (2a), (2b) in each lump by average powers in the lump, 1061 RAMAN AMPLIFIER-AVERAGE POWER MODEL coefficients A z v , B z v are independent of z (within the lump, A , B and the solution of Equation 2 can be written as: B P f z 0 + H = P f z 0 exp A H + ------------ exp A H – 1 A (3) where H is the length of the lumps. Within each lump, powers P f z , P b z must be replaced by average powers in G – 1 B v G – 1 P f b v = P f b ------------- + ----------- ------------- – 1 1nG A v 1nG (4) in where P f b are forward and backward propagating input powers to the lump, G = exp A H . The user is responsible to guarantee that the term A v does not become zero. For example, it is impossible to simulate the chromatic dispersion of just one signal if the attenuation is not considered, once the term A v will become zero. Numerical approach The relaxation method is used in order to satisfy the boundary conditions of the twopoint boundary problem with given accuracy. There are two different iteration procedures, for both forward and backward directions. Forward direction is from Input port 1 to Output port 1, and backward is from Input port 2 to Output port 2. The first procedure, the innermost one, is intended to evaluate the self-consistent convergence for the average powers used in Equation 4 for every amplified segment. When a certain tolerance is reached (10-12), the average powers are considered good enough to be used as an approximation of the desired functions. In the outermost one, or second procedure, the convergence is checked after the integration in forward direction is performed. If the variance in the gain is less than the tolerance desired (see “Numerical” on page 1057), the simulation is considered finished. Otherwise, the component runs for the maximum number of iterations set by the user. The reason for the reduction in computational time is that direct numerical integration of Equation 1 is replaced by algebraic operations. The user can choose the signals that will be used in the convergence checking. There are two available choices: All signals and First signal. When the First signal option is chosen, just the signal with the smallest wavelength is used in checking the convergence by the given tolerance. Otherwise, if the All signals option is chosen, 1062 RAMAN AMPLIFIER-AVERAGE POWER MODEL all signals are used in the checking. In the case where there a signal has not been transmitted, the convergence test is performed based on the pumps. Files Some data necessary for this model may be downloaded from a file. In general, these files are in the ASCII format and follow Optiwave's standard format. For clarity, the units of each column in the files are listed in the following table. Field First column Second column Attenuation Wavelength (nm) Attenuation (dB/km) Effective area Wavelength (nm) Effective area (µm2) Raman gain X frequency Frequency shift (THz) Normalized Raman gain 2 m -----W Raman gain efficiency X frequency Frequency shift (THz) Rayleigh back scattering Wavelength (nm) Raman gain efficiency 1 ------------Wm Back scattering (1/km) When a file with the normalized Raman gain is used, it must be provided values for the Raman gain peak and Raman gain reference pump to use in the calculation of the Raman gain used in the simulation. The following formula is used: PR g R = ------- g N p where g R is the Raman gain, P R is the Raman gain peak, p is the gain reference pump and g N is the normalized Raman Gain. m The unit of Raman gain is given in ----- . W Comparison As stressed in the beginning of the technical description, the average power model is intended to decrease the computational time required to solve the Raman Amplifier differential equations by simplifying the way the equations are written. In fact, the model shows a reduction in computation time of over two orders of magnitude [2] compared to the model using direct integration approach (fourth-order Runge-Kutta). However, in some cases, it is known that the model fails in converging (for example, when the total pump becomes very high). 1063 RAMAN AMPLIFIER-AVERAGE POWER MODEL Therefore, based on the characteristics presented, this model is very useful in getting a first approximation for a network under certain limits. Once the rough estimation is reached, the system could be generalized using the full steady state model. A validation example for this model is presented in Lesson: "Raman amplifier Average power model" in the tutorials section. 1064 RAMAN AMPLIFIER-AVERAGE POWER MODEL References [1] M. Karasek, M. Menif, "Protection of surviving channels in pump-controlled gain-locked Raman fibre amplifier", Optics Communications 210 (2002) 57-65. [2] B. Min, W. J. Lee, N. Park, "Efficient Formulation of Raman Amplifier Propagation Equations with Average Power Analysis", IEEE Photonics Technology Letters, Vol. 12, No. 11, November 2000. [3] E. Desurvire, "Erbium-doped fiber amplifiers: principles and applications", Wiley-Interscience, 1994. [4] S. Tariq, J.C. Palais, "A Computer Model of Non-Dispersion-Limited Stimulated Raman Scattering in Optical Fiber Multiple-Channel Communications", IEEE Journal of Lightwave Technology, Vol. 11, No. 12, December 1993. 1065 RAMAN AMPLIFIER-AVERAGE POWER MODEL 1066 RAMAN AMPLIFIER-DYNAMIC MODEL Raman Amplifier-Dynamic Model This component simulates a Raman amplifier using a dynamic model based on direct integration of the differential equations that describe it. Ports Name and description Port type Signal type Input 1 Input Optical Output 1 Output Optical Input 2 Input Optical Output 2 Output Optical Parameters Main Name and description Symbo l Default value Default unit Value range Length L 10 km ]0; 1,000,000[ — Constant — Constant, From file 0.2 dB/km [0,+INF[ — FiberLoss.dat nm - dB/km — Amplifier length. Attenuation data type Defines if attenuation is entered as scalar, used for all wavelengths, or if it is wavelength dependent / downloaded from a file. Attenuation Constant attenuation value Attenuation file Attenuation value dependent on wavelength. 1067 RAMAN AMPLIFIER-DYNAMIC MODEL Name and description Symbo l Default value Default unit Value range Effective area data type — Constant — Constant, From file A eff 72 µm2 ]0, +INF[ — EffectiveArea.dat nm - µm2 — — Raman gain — Raman gain, Raman gain efficiency — 1e-013 — [0,+INF[ — 1000 nm [0,+INF[ gr RG.dat THZ normalized Raman gain — Name and description Symbo l Default value Default unit Value range Temperature T 300 K [0,500] Defines if effective area is entered as scalar, used for all wavelengths, or if it wavelength dependent/downloaded from a file. Effective interaction area Constant effective area. Effective interaction area file Effective area dependent on wavelength. Raman gain type Defines type of Raman gain. If Raman gain efficiency is selected, effective area is disabled, and value is g r / A eff . Otherwise, is normalized g r multiplied by Raman gain peak (see below). Raman gain peak Normalized Raman gain is multiplied by Raman gain peak. Formula is detailed later in this section. Raman gain reference pump Value used for Raman gain calculation. Formula is detailed later in this section. Gain X frequency File that defines Raman gain or the Raman gain efficiency. Enhanced Absolute temperature at which fiber is operating. Used for noise consideration. 1068 RAMAN AMPLIFIER-DYNAMIC MODEL Name and description Symbo l Default value Default unit Value range Polarization factor K eff 2 — [1,2] — Constant — Constant, From file - 5.0e-005 1/km [0, +INF[ — Rayleigh.dat nm - 1/km — — 1450 nm [0,3000] — False — True, False — 16.75 ps/nm/km ]-INF, +INF[ — 0.075 ps/nm2/km -INF, +INF[ — 1550 nm [100, 2000] Actual value depends on relative polarization of fields of channels i and j. Equals 1 if fields of both channels are polarization-aligned, and 2 for totally scrambled polarization [4]. Rayleigh back scattering data type Defines whether Rayleigh back scattering coefficient is entered as scalar, used for all wavelengths, or wavelength dependent/downloaded from a file. Rayleigh back scattering Constant Rayleigh back scattering. Rayleigh back scattering file Rayleigh back scattering dependent on wavelength. Upper pump reference Used for convergence test. All wavelengths below this value are considered pump, and are not taken into account for the convergence test. Enable dispersion Enables the linear chromatic dispersion application for the signals. Dispersion The value of the GVD (Group Velocity Dispersion) parameter in the wavelength domain. Dispersion slope The value of the dispersion slope parameter. Reference wavelength This value is used internally as a “zero” or reference frequency in the spectrum of the signal envelope. The attenuation value is assumed to correspond to this frequency. 1069 RAMAN AMPLIFIER-DYNAMIC MODEL Name and description Symbo l Default value Default unit Value range Group delay data type — Constant — Constant, From file 1/Vg(v) 4900000 ps/km [0, 1010] — GroupDelay.dat ns—ps/km — Defines if the group delay is entered as a scalar used for all wavelengths, or if it wavelength dependent/entered from a file. Group delay Constant group delay Group delay file Numerical Name and description Default value Unit Value range Tolerance 0.01 — ]0,+INF[ 50 — [1;50,000] 50 — [1;50,000] All signals - All signals, First signal Used to check convergence of the model. Based on gain of the signals. Number of divisions Number of divisions (in space) of the fiber. Number of iterations Maximum number of iterations to be executed. If convergence is not reached in this number of iterations, model returns the calculated values regardless. Check convergence using: Defines if convergence is checked using “All signals” or “First signal”. Reference time Determines the instant of time used to take the powers to use as input powers in the fiber to solve the steady-state regime that will determine the initial values. Graphs Name and description Default value Unit Value range Calculate graphs False - True, False Defines if graphs are calculated or not. If False, component graphs are not represented. 1070 RAMAN AMPLIFIER-DYNAMIC MODEL Name and description Default value Unit Value range Number of distance steps 20 - [1,1e8] 20 - [1,1e8] True - True, False -50 dBm ]-INF,+INF[ Number of distance steps considered for graph generation. Number of wavelength steps Number of wavelength steps considered for graph generation. Linear scale Defines if a linear scale (Watt) or logarithmic one (dBm) is used. Minimum value If a logarithmic scale is used, this parameter defines the minimum value for the power that is displayed on the graph. Simulation Name and description Default value Unit Value range Enabled True - True, False Defines whether the component is enabled or not. Noise Name and description Default value Default unit Unit Value range Noise center frequency 193.4 THz Hz, THz, nm [30, 30e5] 13 THz Hz, THz, nm ]0,+INF[ 125 GHz Hz, GHz, THz, nm [1,1000[ -100 dB — ]-INF,0[ 3 dB — [0,+INF[ Convert noise bins — — True, False Determines noise center frequency. Noise bandwidth Bandwidth to create noise bins. Noise bins spacing Specifies the noise bins spacing. Noise threshold Minimum value for adaptation of noise bins. Noise dynamic Threshold ratio for adaptation of noise bins. Convert noise bins Determines if generated noise bins are incorporated into the signal. 1071 RAMAN AMPLIFIER-DYNAMIC MODEL Random numbers Name and description Default value Unit Value range Generate random seed True — True, False 0 — [0, 4999] Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Technical background It is widely believed that Raman Amplifier (RA) will play an increasing role in future optical fiber communication (OFC) systems [1]. They have already been widely utilized due to their fundamental advantages [1]: • there is amplification at any wavelength, provided the appropriate pump sources are available. • a fiber itself can be used as an active medium. • a pump spectrum determines a gain spectrum. The equations that describe a Raman amplifier are [2]: P z t - 1 ----------------------------P z t - ----------------------------= P z t P z t --------------z Vg t gr – P z t P ---------------------K eff A eff z t + P z t v h gr – P ---------------------A eff z t + P z t 1 + exp h – kT – 1 v P z t v gr – ------------------------ P z t + P z t K eff A eff 2hP z t v 1072 gr – –1 --------------------- 1 + exp h – kT – 1 A eff –1 (1) RAMAN AMPLIFIER-DYNAMIC MODEL where Symbol Definition frequencies (Hz) Vg frequency-dependent group velocity fiber attenuation [N/m] Rayleigh back scattering coefficient [N/m] gr – Raman gain coefficient for frequency difference ( – ) [m/W] P b z backward propagating power [W] A eff effective core area [m2] K eff polarization factor frequency interval h Plank’s constant k Boltzmann’s constant T temperature [K] In these equations, the following physical effects were taken into account: • pump-to-pump, signal-to-signal and pump-to-signal Raman interactions; • spontaneous Raman emission and its temperature dependency; • stimulated Raman scattering; • pump depletions due to Raman energy transfer; • high-order stokes generation; • multiple Rayleigh backscattering; • fiber loss; • spontaneous emission noise. In this component, the equations in Equation 1 (forward and backward) are solved spatially through direct integration using a standard classical fourth-order RungeKutta formula without adaptive step size [3]. Numerical approach The convergence of the model is checked in two directions: forward and backward. An iterative forward and backward integration of propagation equations must be applied because backward propagating ASE powers and a counter-directional pumping scheme may be defined, and the possibility of counter directional signal 1073 RAMAN AMPLIFIER-DYNAMIC MODEL propagation [2]. The forward direction is from Input Port 1 to Output Port 1 and backward is from Input Port 2 to Output Port 2. The iterative scheme is started with a forward integration of forward signals, propagating ASE spectral components, and pumps. The backward pumps and backward ASE powers are set to zero. At each backward integration, the final results + P z = L of the previous forward integration, together with the boundary conditions for the backward pump, backward ASE powers, and backward signals, are used as starting conditions. _ P z = 0 together with the boundary conditions for forward signal channels, pumps, and forward ASE, Similarly, the results of the previous backward integration are used as starting conditions for each forward integration [2]. The convergence checking is done after integration in the forward direction is complete. If the variance in the gain is less than the tolerance desired (see “Numerical” on page 1070) , the simulation is considered complete. Otherwise, the component runs for the maximum number of iterations set by the user. The user can choose the signals that will be used in the convergence checking. There are two available choices: All signals and First signal. When the First signal option is chosen, just the signal with the smallest wavelength is used in checking the convergence by the given tolerance. Otherwise, if the All signals option is chosen, all signals are used in the checking. In the case where there a signal has not been transmitted, the convergence test is performed based on the pumps. After the spatial integration is complete, the time evolution of pumps, signals, and amplified spontaneous emission waves is performed by direct integration with Equation 1, starting with the steady-state solution for longitudinal distribution of individual powers along the Raman fiber. To avoid possible oscillations of the solution in time domain, care must be taken in the selection of bin widths used in space ( z ), and time ( t ) discretization schemes. Stable solutions has been obtained when the time bin ( t ) is equal to or less than the propagation time through a space bin t z V g . In order to determine the rise/fall times of the surviving channel power transients with sufficient resolution, the ratio of time and space bins t z = 4 10 –9 s m should be independently kept for the Raman fiber length, as in the examples. Some data necessary for this model may be downloaded from a file. In general, these files are in the ASCII format and follow Optiwave's standard format. 1074 RAMAN AMPLIFIER-DYNAMIC MODEL For clarity, the units of each column in the files are listed in the following table. Field First column Second column Attenuation Wavelength (nm) Attenuation (dB/km) Effective area Wavelength (nm) Effective area (µm2) Raman gain X frequency Frequency shift (THz) Normalized Raman gain 2 m -----W Raman gain efficiency X frequency Frequency shift (THz) Rayleigh back scattering Wavelength (nm) Raman gain efficiency 1 ------------Wm Back scattering (1/km) When a file with the normalized Raman gain is used, it must be provided values for the Raman gain peak and Raman gain reference pump to use in the calculation of the Raman gain used in the simulation. The following formula is used. PR g R = ------- g N p where g R is the Raman gain, P R is the Raman gain peak, p is the gain reference pump and g N is the normalized Raman Gain. m The unit of Raman gain is given in ----- . W 1075 RAMAN AMPLIFIER-DYNAMIC MODEL References [1] E. M. Dianov, "Advances in Raman Fibers", Journal of Lightwave Technology, Vol. 20, No. 8, August 2002. [2] M. Karasek, M. Menif, "Protection of surviving channels in pump-controlled gain-locked Raman fibre amplifier", Optics Communications 210 (2002) 57-65. [3] W. H. Press, et al., "Numerical Recipes: The Art of Scientific Computing", 2nd Edition, Cambridge University Press, 1992. [4] S. Tariq, J.C. Palais, "A Computer Model of Non-Dispersion-Limited Stimulated Raman Scattering in Optical Fiber Multiple-Channel Communications", IEEE Journal of Lightwave Technology, Vol. 11, No. 12, December 1993. 1076 RAMAN AMPLIFIER-DYNAMIC MODEL Amplifiers Library Optical - Doped Fibers • Er Doped Fiber Dynamic • Er Doped Fiber Dynamic Analytical • Er Doped Fiber • Er-Yb Codoped Fiber • Er-Yb Codoped Fiber Dynamic • Er-Yb Codoped Waveguide • Pr Doped Fiber • Yb-Doped Fiber • Yb-Doped Fiber Dynamic • Tm Doped Fiber 1077 RAMAN AMPLIFIER-DYNAMIC MODEL Notes: 1078 ER DOPED FIBER DYNAMIC Er Doped Fiber Dynamic Incorporates time-varying input signal and pump powers that enable simulating dynamic effects presented by erbium-doped amplifiers inserted in a fiber link. This powerful tool solves the full rate and propagation equations in the time and spatial domain. The powers and population densities are calculated as a function of the time variation at each point of the z fiber. This model is specifically designed to simulate cascaded amplifiers in a long fiber link, considering multiple signal input. Ports Name and description Port type Signal type Input 1 Input Optical Input 2 Input Optical Output 1 Output Optical Output 2 Output Optical Parameters Main Name and description Default value Default unit Units Value range Length 5 m — [0, 1e4] 10 ms — ]0, +INF[ 0.01 dB/m — [0,100] 0.015 dB/m — [0,100] Fiber specification — — Fiber specification, Saturation parameter Specifies the doped fiber length Er metastable lifetime Specifies the Erbium metastable lifetime Loss at 1550 nm Determines the fiber loss at 1550 nm Loss at 980 nm Determines the fiber loss at 980 nm Input data Determines if saturation parameter is used or not 1079 ER DOPED FIBER DYNAMIC Name and description Default value Default unit Units Value range Saturation parameter 4.4e+015 1/(s.m) — [1e-10, +INF[ 0.24 — — [0.1,1] 1e+025 m–3 m–3~ppm-wt ~wt% [1,+INF[ 2.2 m — [0,1, 10] 2.2 m — [0.1, 10] Name and description Default value Units Value range OptiAmplifier format False — True, False nm — nm, m, Hz, THz Erbium.dat — — Name and description Default value Units Value range Relative error 0.0001 — ]0,1] 100 — [10,10000] 100 — [10,10000] Specifies value of saturation parameter Numerical aperture Specifies the numerical aperture of the Er-doped fiber Er ion density Specifies the Er doping in the Er-doped fiber Core radius Specifies the fiber core radius Er doping radius Species the Erbium doped radius Cross-sections Determines the format of the OptiAmplifier file File frequency unit Determines the frequency unit of the file with the measurements cross-section file name Determines the cross-section file Numerical Determines the relative error acceptable in each calculation for the steady-state solution used as initial condition for the dynamic behavior Max. number of iterations Specifies the maximum number of times to repeat the longitudinal integrations for the powers when solving the steady-state equations used as initial condition for the dynamic behavior Longitudinal steps Determines the number of longitudinal steps in the calculation 1080 ER DOPED FIBER DYNAMIC Name and description Default value Units Overlap factor data Calculate Calculate, Load from file LP01 Marcuse Gaussian, Whitley Gaussian, Desurvire Gaussian, Myslinski Gaussian, LP01 Determines whether the overlap factor values will be calculated by the component or it will be loaded from a file Geometrical model Determines whether the component will calculate the overlap factor using one of the gaussian approximations, or the LP01 mode Overlap factor file name Value range OverlapFactor. dat Specifies the overlap factor file name Reference time 0.5 / (Bit rate) s [0,1e10] Name and description Default value Units Value range Enabled True — True, False Determines the instant of time used to take the powers to use as input powers in the fiber to solve the steady-state regime that will determine the initial values Simulation Determines whether or not the component is enabled Noise Name and description Default value Default unit Units Value range Noise center frequency 193.4 THz Hz, THz, nm [30,30e5] 13 THz Hz, THz, nm ]0,+INF[ 125 GHz Hz, GHz, THz, nm [1,1000] –100 dB — ]-INF,0[ 3 dB — [0,+INF[ Determines the noise center frequency Noise bandwidth Bandwidth to create noise bins Noise bins spacing Specifies the noise bins spacing Noise threshold Minimum value for adaptation of noise bins Noise dynamic Threshold ratio for adaptation of noise bins 1081 ER DOPED FIBER DYNAMIC Name and description Default value Default unit Units Value range Convert noise bins Convert noise bins — — True, False Name and description Default value Units Value range Generate random seed True — True, False 0 — [0,4999] Determines if the generated noise bins are incorporated into the signal Random numbers Determines if the seed is automatically defined and unique Random seed index User-defined seed index for noise generation Graphs Name and description X Title Y Title Absorption parameters Wavelength (m) Cross-section (m2) Emission parameters Wavelength (m) Cross-section (m2) Average population density N2 Time (s) N2 1082 ER DOPED FIBER DYNAMIC Technical background Different solutions to the problem of transient fluctuations due to gain cross-saturation observed in EDFAs inserted in multi-wavelength networks have been suggested. Gain cross-saturation in fiber amplifiers induces transients in the surviving channels remaining as a consequence of the process of adding or removing channels in the network reconfiguration. Although this perturbation will be small in a single amplifier, it becomes considerable along cascaded amplifiers. As a result, a tool that enables analyzing the effects of addition and/or dropping wavelength channels in a multiwavelength optical network containing EDFAs is important. In opposition to the steady-state model (EDF module), the EDF Dynamic enables you to calculate the variation of signals and pumps power with the time when sampled channels are present in the layout. The dynamic behavior of cascaded EDFAs can be simulated as well. The results will help you design cascaded amplifier systems with suppression of both transient and steady state signal power fluctuations due to channel addition/removal. The numerical EDF Dynamic uses a two-level system approximation and is based on the solution of the propagation and rate equations for transitions between the upper and lower levels. These equations are given by Equation 1, Equation 2, and Equation 3, which are also in the technical background for the Er Doped Fiber [1]: N 2 z ,t N 2 z ,t 1 --------------------- = – ----------------- – -------t A eff N e a a n n + n N2 z ,t – n Pn + – z ,t + P n z ,t n=1 (1) N2 + N1 = 1 (2) P n z ,t e a a e ------------------------ = u n n n + n N 2 z ,t – n – P n z ,t + 2N 2 n n z (3) where the optical powers are expressed in units of number of photons per unit time, is the metastable spontaneous emission lifetime, N is the number of channels taken into account in the simulation (including signals, pumps, and ASE bins), is the number density of the active erbium ions, is the attenuation coefficient (which takes into account the background loss of the fiber), is the frequency step used in the simulation to resolve the ASE spectrum, and Aeff is the effective doped area given 1083 ER DOPED FIBER DYNAMIC 2 by b , where b is the Er doping radius (it is considered a uniform distribution of erbium ions in the area given by the Er doping radius region). The nth channel of wavelength n has optical power Pn(z,t) at location z and time t, e a with emission and absorption cross-section n and n respectively, and confinement factor n . The superscript symbols + and – are used to indicate channels traveling in forward (from 0 to L) and backward (from L to 0) directions, respectively. For beams traveling in the forward direction u n = 1 and for beams in the opposite direction u n = – 1 . The overlap integrals n between the LP01 mode intensity (which is used in this program) distribution doped region area are given by: b E r , 2 r dr n = ---------------------------------0 E r , 2 r dr 0 (4) where E(r, ) gives the electric field intensity. This model assumes that the signal and pump powers change slowly compared to the optical transit time in the fiber. This assumption is valid since the typical time that the light takes to pass by one 100 m fiber (one EDFA does not use fibers larger than that) is 500 ns. The time scales we deal with are always on the order of microseconds or longer. Numerical solution The solution of the time-dependent rate equations and the propagation equations is based on the assumption that the atomic populations remain constant during a time step t , typically microseconds. This assumption is acceptable since the metastable lifetime is relatively long (around 10 ms) and the transit time of photons through the Er3+-doped fiber is s
