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Chromatic and polarization mode dispersion monitoring for equalization in optical fiber communication systems

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Chromatic and polarization mode dispersion monitoring for equalization in optical fiber communication systems

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Content CHROMATIC AND POLARIZATION MODE DISPERSION MONITORING FOR EQUALIZATION IN OPTICAL FIBER COMMUNICATION SYSTEMS b y Seyed Mohammad Reza Motaghian Nezam A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2004 Copyright 2004 Seyed Mohammad Reza Motaghian Nezam Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3145249 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3145249 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedication To my beloved parents, sister, andfiance fo r their everlasting love and support. ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements I would like to acknowledge my aunt, Rafat Motaghian, and my cousins, Firuzeh and Negeen Mahmmoudi, for their support and helps throughout my graduate career. I would like to thank my academic advisor and dissertation committee chairman, Dr. Alan Eli Willner, for his support, guidance, and mentorship throughout my graduate school career. I would also like to extend my great appreciation to the other dissertation committee members, Dr. Robert Gagliardi, and Dr. Edward Goo. In addition, I would like to acknowledge Dr. William Steier, Dr. Vijay Kumar, and Dr. Robert Hellwarth for their encouragement and support during my graduate school career. I would also like to acknowledge those people who, not knowingly, have made invaluable contributions, which have allowed me to undertake the research projects presented in this dissertation. They are: C. Poole, H. Kogelnik, N. Gisin, G. Foschini, B. Heffner, F. Heismann, M. Karlsson, H. Gnauck, L. Moller, N. Kikuchi, R. Jopson, N. Bergano, A. Chraplyvy, H. Biilow, and C. Menyuk. I would like to pay my heartiest thanks to my colleague, John McGeehan, for his greatest support and invaluable help throughout my graduate career. I would like to thank my friend, Ehsan Pakbaznia, for his help during my dissertation submission. I would also like to thank my collaborators from Optical Communication Laboratory (OCLAB) for their helps in my graduate career. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Last but not least, I would like to thank those people who have contributed in some way to the success o f my academic endeavors. They are M illy Montenegro, Mayumi Thrasher, Tim Boston, and Diane Demetras. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Dedication.................................................................................................ii Acknowledgements................... H i List o f Tables................................................ x List o f Figures.................. xi Abbreviations................................................... xxvii Abstract..................................... xxxi Chapter 1............ 1 Introduction.......................... 1 Chapter 2 .......................................................................... 5 Background................................................................................................5 2.1 Signal Degradation Effects in Digital Optical Fiber Communication System s................................................................................................................................... 5 2.1.1 Chromatic Dispersion and Chromatic Dispersion Slope.................................5 2.1.2 Fiber Nonlinearities.............................................................................................. 11 2.1.2.1 Self-Phase Modulation.................................................................................12 2.1.2.2 Cross-Phase Modulation............................................................................. 14 2.1.2.3 Four-Wave M ixing....................................................................................... 15 2.1.2.4 Stimulated Scattering.................... 17 2.1.3 Polarization Impairments.................................................................................... 18 2.1.3.1 Mathematical Review o f Polarized Light...............................................120 2.1.3.1.1 The Polarization E lipse.....................................................................20 2.1.3.1.2 The Poincare Sphere...........................................................................25 2.1.3.1.3 The Stokes Polarization Parameters............................................... 27 2.1.3.1.4 The Stokes Vector.............................................................................. 29 2.1.3.1.5 The Muller Matrix Algebra.............................................................. 32 2.1.3.1.6 The Jones Matrix Algebra................................................................ 41 2.1.3.2 Polarization Mode Dispersion....................................................................49 2.1.3.2.1 PMD in the Jones S p ace...................................................................58 2.1.3.2.2 PMD in the Stokes Space..................................................................62 2.1.3.2.3 Higher-Order P M D ............................................................................67 2.1.3.2.4 The Autocorrelation Function o f PMD Vector............................71 2.1.3.3 Polarization Dependent Loss...................................................................... 72 2.1.3.4 Polarization Dependent G ain..................................................................... 74 2.2 PMD Em ulation...........................................................................................................75 2.3 Polarization Scram bling .......... 80 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.4 Fiber Bragg Grating ........................................... 84 2.4.1 Concept of Fiber Bragg Grating.........................................................................85 2.4.2 Chirped Fiber Bragg Grating.............................................................................. 86 2.4.3 Nonlinearly-Chirped Fiber Bragg Grating...................................................... 90 2.4.4 Sampled Nonlinearly-Chirped Fiber Bragg Grating..................................... 92 2.5 Chromatic Dispersion Mitigation and Monitoring in High-Speed Optical Fiber Communication Systems and Networks ...................... 94 2.5.1 Dispersion Maps....................................................................................................94 2.5.2 Corrections to Linear Dispersion M aps...........................................................96 2.5.3 Fixed Dispersion Compensation....................................................................... 98 2.5.3.1 Dispersion Compensating Fiber.................................................................98 2.5.3.2 Chirped Fiber Bragg Grating Compensators......................................... 100 2.5.3.3 Higher-Order Mode Dispersion Compensation Fiber......................... 102 2.5.3.4 Tunable Dispersion Compensation.........................................................103 2.5.3.4.1 The Need for Tunability..................................................................103 2.5.3.4.2 Approaches to Tunable Dispersion Compensation................... 106 2.5.4 Chromatic Dispersion Monitoring.................................................................. 108 2.6 Polarization Mode Dispersion Mitigation and Monitoring in High-Speed Optical Fiber Communication Systems and Networks.................................... 109 2.6.1 PMD Mitigation Techniques............................................................................ 110 2.6.1.1 Optical PMD Compensation.................................................................... I l l 2.6.1.2 Optical PMD Equalization........................................................................113 2.6.1.3 Electrical PMD Equalization.................................................................... 114 2.6.1.4 PSP Filtering................................................................................................115 2.6.1.5 Polarization Diversity Receivers..............................................................115 2.6.2 PMD Monitoring.................................................................................................115 2.6.2.1 Degree of Polarization................................................................................118 2.6.2.2 RF Spectrum Analysis o f the Detected Signal......................................121 2.6.2.3 Eye Opening.................................................................................................124 2.6.2.4 Phase Detection........................................................................................... 125 2.7 DGD and PMD Measurement ........................................... 126 2.7.1 Time Domain Measurements............................................................................127 2.7.1.1 Modulation-Phase-Shift Method............................................................. 127 2.7.1.2 Pulse-Delay Method................................................................................... 127 2.7.1.3 Interferometric M ethod............................................................................. 128 2.7.1.4 Polarization Optical Time Domain Reflectometry...............................130 2.7.2 Frequency Domain Measurements..................................................................130 2.7.2.1 The Poincare Sphere Analysis.................................................................. 130 2.7.2.2 The Poincare Sphere M ethod................................................................... 131 2.7.2.3 The Jones Matrix Eigenanalysis M ethod...............................................132 2.7.2.4 The Fixed-Analyzer M ethod.................................................................... 132 2.7.2.5 The Muller Matrix M ethod.......................................................................134 2.7.3 Designing the DGD/PMD Measurement Experiment................................. 134 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7.3.1 Spectral Efficiency o f the DGD/PMD Measurement.......................... 134 2.7.3.2 DGD/PMD Measurement Uncertainty................................................... 135 2.7.4 DGD/PMD Measurement Concerns............................................................. 135 Chapter 3......................................... 137 Chromatic Dispersion Monitoring in Digital Optical Fiber Communication Systems .................... 137 3.1 Chromatic Dispersion M onitoring Using Partial Optical Filtering and Phase Detection................................................................ 137 3.1.1 Theory o f Partial Optical Filtering and Phase Shift Detection o f Bit-Rate and Doubled Half-Bit-Rate Frequency Components.............................................139 3.1.2 Simulation and Experimental Results............................................................ 141 3.1.3 Chromatic Dispersion Compensation Results...............................................143 3.2 Enhancing Chromatic Dispersion Monitoring Range and Sensitivity Using a Dispersion-Biased RF Clock T one ..... 144 3.2.1 RF Clock Measurement Techniques for Chromatic Dispersion Monitoring ...........................................................................................................................................146 3.2.2 Dispersion-Biased RF Clock Tone Monitoring Concept........................... 146 3.2.3 Enhancing Chromatic Dispersion Monitoring Range and Sensitivity for Carrier-Suppressed RZ Signals..................................................................................148 3.2.4 Monitoring and Compensation Results for Carrier-Suppressed RZ Signals ...........................................................................................................................................151 3.3 Chromatic Dispersion M onitoring in Differential-Phase-Shift-Keyed System s........................................ 153 3.3.1 Chromatic Dispersion in DPSK and RZ-DPSK Systems........................... 154 3.3.2 Chromatic Dispersion Monitoring in DPSK and RZ-DPSK Systems Using RF Clock Tone.............................................................................................................. 155 Chapter 4 ........ 157 Polarization Mode Dispersion Monitoring in Digital and Analog Optical Fiber Comm unication Systems............................................... 157 4.1 Theoretical and Experimental Analysis of the Dependence of a Signal’s DOP on the Optical Data Spectrum ........................................................... 158 4.1.1 Theory of All-Order PMD Effects on the Signal’s D O P........................... 159 4.1.2 Effects o f DGD on the Signal’s DOP............................................................. 164 4.1.3 Effects o f Pulsewidth on DOP-Based DGD Monitors................................165 4.1.4 Effects o f Modulation Format on DOP-Based DGD Monitors................. 171 4.2 Enhancing the Dynamic Range and DGD M onitoring W indows in DOP- Based-DGD Monitors Using Symmetric and Asymmetric Partial Optical Filtering..................... 177 4.2.1 Theory o f Partial Optical Filtering Effects on the Signal’s DOP..............178 4.2.2 DGD Monitoring Results for Different Modulation Formats................... 183 vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2.2.1 RZ Signals....................................................................................................185 4.2.2.2 CSRZ Signals.............................................................................................. 189 4.2.2.3 ACRZ Signals............................................................................................. 191 4.2.2.4 NRZ Signals.................................................................................................195 4.3 Cancellation of Second-Order PMD Effects on First-Order DOP-Based DGD Monitors and Measurement of Depolarization Rate................. 197 4.3.1 First- and Second-Order PMD Effects on the Signal’s D O P.....................198 4.3.2 Cancellation of Second-order PMD on DGD Monitors............................. 200 4.3.3 Depolarization Rate Measurement..................................................................202 4.4 Accurate DOP Monitoring of Several WDM Channels for Simultaneous PMD Compensation..............................................................................................203 4.4.1 Concepts of WDM DOP Monitoring for Simultaneous WDM PMD Compensation................................................................................................................205 4.4.2 Demonstration o f Simultaneous WDM PMD Compensation Using Averaged DOP Monitoring .....................................................................................207 4.5 Link DGD Measurement without Polarization Scrambling Using DOP and Symmetric/Asymmetric Partial Optical Filtering.................................... 210 4.5.1 Theory o f DGD Measurement Using Partial Optical Filtering without Polarization Scrambling..............................................................................................211 4.5.2 Simulation Results..............................................................................................213 4.5.3 Experimental Results......................................................................................... 214 4.6 DOP-Based PMD Monitoring in Optical Subcarrier-Multiplexed Systems by Carrier/Sideband Equalization...................................... ...216 4.6.1 Theory o f PMD Effects on the Subcarrier’s DOP........................................219 4.6.2 Equalized Carrier-Sideband Filtering and DOP Measurement................224 4.6.3 Equalized Carrier-Sideband Filtering and DGD Monitoring...................226 4.6.4 PMD Compensation Using Equalized Carrier-Sideband Filtering Method .......................................................................................................................................... 231 4.7 PMD Monitoring for NRZ Data Using a Chromatic-Dispersion- Regenerated Clock ............... 234 4.7.1 Theory o f the Dispersion-Regenerated Clock in the Electrical Spectrum of NRZ Data.......................................................................................................................235 4.7.2 Effects o f PMD on the Regenerated RF Clock Tone..................................240 4.7.3 PMD Compensation Using the Dispersion-Regenerated Clock as a Control Signal...............................................................................................................................242 4.8 PMD Monitoring by RF Clock Regeneration Measurement Using Asymmetric Optical Spectrum Filtering Method .............. 244 4.8.1 Theory o f the Clock Regeneration Using Asymmetric Optical Spectrum Filtering Method............................................................................................................245 4.8.1.1 Asymmetric-Filter-Regenerated RF Clock Tone.................................246 4.8.1.2 Notch-Filter-Regenerated RF Clock Tone............................................ 248 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.8.2......PMD Compensation Using the Regenerated Clock Tone as a Feed Back Signal.............................................................................................................................. 249 4.9 Real-Time PMD Monitoring in Wavelength-Division-Multiplexed System Using in-Band Subcarrier Tone.. ...... 251 4.9.1 Concept o f Subcarrier Tone Fading Due to PMD in Time and Frequency Domain...........................................................................................................................251 4.9.2 PMD/DGD Monitoring Using Added Subcarrier in-Band T one............. 254 4.9.3 WDM PMD Monitoring and Compensation Using Added Subcarrier in- Band Tone .................................................................................................................... 254 4.10. Effects of XPM on the PMD Monitoring Parameters in Wavelength- Division-Multiplexed System...............................................................................256 4.10.1 XPM Induced DOP and RF Power Degradation in WDM System 257 4.10.2 Simulation Details........................................................................................... 258 4.10.3 Simulation Results................... 259 Chapter 5..... 263 Component DGD Measurement..................... 263 5.1 Measuring Component DGD Using Polarized Limited-Bandwidth ASE Noise and Monitoring the DOP........................................................................... 264 5.1.1 Theory o f Measuring the DOP o f a Spectrum-Shaped ASE Source 265 5.1.2 DGD Measurement Using a Band-Limited ASE Source...........................268 5.1.3 Effects o f Higher-Order PMD on DGD Measurement.............................. 270 5.2 Measuring Component DGD Using Polarized Fixed Optical Frequency Components and Monitoring the DOP............................................. ..272 5.2.1 DGD Measurement Concept and Setup.........................................................272 5.2.2 DGD Measurement for Different Limited-Bandwidth Optical Sources. 274 5.2.2.1 Subcarrier Tone-Based DGD Measurement.........................................274 5.2.2.2 Dual Laser Source-Based DGD Measurement..................................... 278 5.2.3 Discussion........................................................................................................... 279 References ...... 282 Alphabetized References....................................................................... 311 ix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables Table 2.1. The various methods fo r PMD/DGD measurement.................................... 136 Table 3.1. Relative RF clock power values fo r the positive (RF*) and negative (RF) bias taplines vs. dispersion. The sign o f the dispersion is indeterminate without dithering when both RF* and R F are between -2 .3 dB and 0 dB...............................150 Table 4.1. Summary o f the DGD monitoring range, D O P dynamic range, and optimal filter bandwidths for 40-Gbit/s, 12.5-ps pulsewidth RZ signals fo r various filter shapes............................................................................................................................ 194 Table 4.2. Summary o f the DGD monitoring range, DOP dynamic range, and optimal filter bandwidths for 40-Gbit/s, 12.5-ps pulsewidth CSRZ signals fo r various filter shapes............................................................................................................................ 194 Table 4.3. Summary o f the DGD monitoring range, D O P dynamic range, and optimal filter bandwidths for 40-Gbit/s, 12.5-ps pulsewidth ACRZ signals fo r various filter shapes............................................................................................................................ 194 Table 4.4. The value o f P, equal to [ l - ( DOPAsym)2 ] / [ l-(DOPsy m f ] , as the power splitting ratio at the transmitter changes (noted by the changing eyes) fo r a DGD value o f 74 ps. For a given DGD value, the value o f P remains fairly constant ....215 Table 5.1. Results fo r three o f our DGD measurement techniques (20-GHz DSB subcarrier tone, ASE noise using a 1.5 nm Gaussian filter, and dual laser source with 0.873 (for the first measurement) and 2.27 nm (for the rest) spacing) along with conventional JME measurement results when measuring the DGD o f three different spools o f fiber — one 1 km spool HNL fiber, a different 500 m spool o f HNL fiber, and one 4 km spool o f DSF. The “? ” entry refers to a DOP that is approximately 1 and thus the DGD cannot be m easured....................................................................................280 x Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures Fig. 2.1. Pulse broadening due to chromatic dispersion................................................... 6 Fig. 2.2. Transmission distance limitations due to uncompensated dispersion in SMF as a function o f data rate fo r intensity modulated optical signals [ 1 1 ] .........................8 Fig. 2.3. Dispersion parameter D vs. wavelength fo r different fib e r s........................... 9 Fig. 2.4. The polarization ellipse fo r the optical field......................................................23 Fig. 2.5. The Poincare sphere o f unit radius and Cartesian coordinates. The coordinates o f the point P are P(y/,x) ............................................................................... 26 Fig. 2.6. Normalized Stokes vectors fo r the six degenerate polarization states........32 Fig. 2.7. Propagation o f an input beam through a rotated polarizing element.........40 Fig. 2.8. Jones representation.............................................................................................. 44 Fig. 2.9. Pulse spreading due to PM D ............................................................................... 49 Fig. 2.10. Origin o f PM D ....................................................................................................... 51 Fig. 2.11. PMD fluctuations in a fiber due to (a) daily changes in temperature and (b) mechanical vibrations.....................................................................................................52 Fig. 2.12. (a) A histogram o f measured DGD data fo r a fiber link shows that it has a probability distribution that closely approximates a Maxwellian PDF and (b) a Maxwellian distribution with <dgd> -4 0 p s ..................................................................... 53 X I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.13. Measurement o f DGD o f a spooledfiber with 40-ps average DGD [42]. 54 Fig. 2.14. Conceptual illustration o f higher-order PM D effects on an optical pulse. ...................................................................................................................................................... 55 Fig. 2.15. PMD vector frequency ACF showing that the PMD o f wavelengths separated by more than ~ l/< dgd> become uncorrelated...............................................55 Fig. 2.16. BERfluctuations due to temperature changes................................................. 57 Fig. 2.17. Transmission distance limitations fo r a 40-Gbit/s NRZ system due to the combination o f fiber PMD and the PMD o f the cascaded in-line optical components found in amplifier sites............................................................................................................58 Fig. 2.18. Output polarization state evolution on the Poincare Sphere........................66 Fig. 2.19. Schematical diagram o f the PMD vector. Note that the angular rotation rate (dtp/dm) o f the PMD vector is 2 k .................................................................................. 69 Fig. 2.20. Measurement o f PCD o f a spooledfiber with 40-ps average DGD [42] . 70 Fig. 2.21. PDF o f (a) PCD fo r a 55.2-ps mean DGD, (b) depolarization rate fo r a 14.7-ps mean DGD, and (c) \Qm j\f o r a 14.7-ps mean DG D [42,48] ......................... 71 Fig. 2.22. Conceptual illustration o f the interaction between PMD and PDL. When PDL is present in a fiber link, the fiber PSPs are no longer guaranteed to be orthogonal................................................................................................................................. 73 Fig. 2.23. PDF o f 15 PMD sections: (a) without PDL and (b) with 15 PDL sections (PDL o f each section is 2.5 d B )............................................................................................ 74 xn Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.24. Three common emulator configurations constructed from a concatenation o f many birefringent elements (a) with uniformly-distributed polarization transformations (pol. controllers) between sections, (b) with rotatable sections, and (c) with fixed 45 angles between sections and variable birefringence elements, r is the DGD and y is its birefringence.......................................................................................79 Fig. 2.25. (a) A schematic diagram o f polarization scrambler and (b) Uniform distribution o f polarization state on the Poincare sphere (1000 samples) .................81 Fig. 2.26. Uniform and chirpedFBGs. (a) A grating with uniform pitch has a narrow reflection spectrum and a fla t time delay as a function o f wavelength, (b) A chirped FBG has a wider bandwidth, a varying time delay and a longer grating length 87 Fig. 2.27. Grating ripple effects on BER pow er penalty.................................................. 89 Fig. 2.28. Higher-order dispersion induced by nonlinearly-chirped FBG (NC-FBG) ......................................................................................................................................................90 Fig. 2.29. Tunable dispersion compensation using chirped FBG (a) LCFBG and (b) NC-FBG.....................................................................................................................................91 Fig. 2.30. Sampling a waveform in the real space leads to replicate spectra in the Fourier space. For an FBG, modulating the intensity o f the grating leads to multiple wavelength passbands.............................................................................................................93 Fig. 2.31. Dispersion map o f a basic dispersion managed system. Positive dispersion transmission fiber alternates with negative dispersion compensation elements such that the total dispersion is zero end-to-end.........................................................................95 Fig. 2.32. Various dispersion maps fo r SMF-DCF and NZDSF-SMF.........................96 Fig. 2.33. Typical DCF (a) refractive index profile and (b) dispersion and loss as a function o f wavelength. An is defined as refractive index variation relative to the cladding ...........................................................................................................................99 xiii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.34. The need for tunability. The tolerance o f OC-768 systems to chromatic dispersion is 16 times lower than that o f OC-192 systems. Approximate compensation by fixed in-line dispersion compensators fo r a single channel may lead to rapid accumulation o f unacceptable levels o f residual chromatic dispersion 104 Fig. 2.35. Tunable dispersion compensation at OC-768 (40 Gbit/s) is essential for achieving a comfortable range o f acceptable transmission distances (80 km for tunable, only ~ 4 km for fixed compensation)..................................................................104 Fig. 2.36. Accumulated dispersion changes as a function o f the link length and temperature fluctuation along the fiber link.................................................................... 105 Fig. 2.37. Architecture o f an all-pass filter structure fo r chromatic dispersion and slope compensation [ 1 0 6 ] .................................................................................................. 107 Fig. 2.38. (a) SEM image o f a photonic crystal fiber (holey fiber) and (b) net dispersion o f the fiber at 1550 nm as a function o f the core diameter [1 0 7 ]........... 108 Fig. 2.39. Schematic diagram o f an OPMDC and monitoring m odule..................... 112 Fig. 2.40. (a) Schematic diagram o f an optical PMD equalizer, (b) equalizer impulse response, and (c) measuredfiber-to-fiber transmissivity [1 4 5 ].................................. 113 Fig. 2.41. Conventional electrical equalizer (TF) .........................................................114 Fig. 2.42. (a) Feed back configuration and (b) fe e d forw ard and feedback configuration fo r optical PMD compensation.................................................................118 Fig. 2.43. (a) Fully polarized light, (b) partially polarized light, and (c) unpolarized light............................................................................................................................................119 Fig. 2.44. Measuring DOP using (a) the maximum and minimum optical signal’ s power and (b) a polarim eter................................................................................................120 xiv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.45. NRZ and RZ frequency components can be usedfor PMD m onitoring.. 121 Fig. 2.46. Received RF pow er variation vs. DGD fo r 1/8, quarter, half, and bit-rate frequency components.......................................................................................................... 123 Fig. 2.47. Eye monitor with analog integrator................................................................125 Fig. 2.48. Poincare sphere analysis...................................................................................131 Fig. 3.1. Conceptual diagram fo r the proposed chromatic dispersion monitor using phase comparison o f the bit-rate and frequency-doubled half-bit-rate frequency components..............................................................................................................................140 Fig. 3.2. Simulation results for 40-Gbit/s (a) NRZ (b) RZ, and (c) CSRZ dispersion monitoring using optical asymmetric Gaussian filtering...............................................141 Fig. 3.3. Experimental dispersion monitoring results fo r 10-Gbit/s (a) NRZ, (b) RZ, and (c) CSRZ signals. The NRZ and RZ monitors used an asymmetric 13.5-GHz FBG notch filter, while the CSRZ monitor used an 8-GHz Fabry-Perot fiber (FPF) filter with an FSR o f 750 GHz.............................................................................................142 Fig. 3.4. (a) 40-Gbit/s simulation and (b) 10-Gbit/s experimental results fo r CSRZ dispersion monitoring showing the effects o f filter detuning on dispersion sensitivity and monitoring windows. An 8-GHz FPF filter was used in (b )...............................143 Fig. 3.5. 40-Gbit/s CSRZ simulation results using symmetric optical filtering showing increased monitoring windows........................................................................... 143 Fig. 3.6. (a) Setup for 4-channel 10-Gbit/s CSRZ dispersion monitoring and compensation, (b) BER performance curves after compensation fo r the best and worst after transmission through 100 km SMF-28 fiber. The penalty fo r the worst channel is <0.5 d B ................................................................................................................ 144 xv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 3.7. (a) RF clock tone regeneration fo r CSRZ signals due to chromatic dispersion - the clock tone starts at a high pow er level and quickly reaches a maximum value, resulting in a limited monitoring range and low sensitivity, (b) Using a fixed dispersive element to “bias ” the RF clock power, we push the signal into the second monitoring window, extend the monitoring range and increase sensitivity.................................................................................................................................147 Fig. 3.8. Relative clock pow er as a function o f accumulated dispersion fo r (a) 10- and (b) 40-Gbit/s CSRZ signals..........................................................................................149 Fig. 3.9. Experimental setup fo r chromatic dispersion monitoring and compensation fo r 10-Gbit/s CSRZ signals. CSRZ generation is done via two cascaded EO modulators, and fixed 480 ps/nm dispersive elements are used to bias the dispersion. A NC-FBG is used as a dispersion compensator............................................................ 151 Fig. 3.10. (a) Relative RF clock pow er in the positive bias tapline and power penalty vs. accumulated dispersion in the link. As the RF clock pow er decreases (increased chromatic dispersion) the power penalty rises, (b) Dispersion compensation results after transmission through 40 km o f SMF. After compensation by maximizing the RF clock power, there is a 1.2-dB improvement in receiver sensitivity............................ 152 Fig. 3.11. Chromatic dispersion in DPSK and RZ-DPSK systems (a) Conceptual diagram o f chromatic dispersion and PMD effects on DPSK and RZ-DPSK signals and (b) DPSK/RZ-DPSKsystem configuration (T b'. Bit tim e)......................................155 Fig. 3.12. Clock tone power as a function o f chromatic dispersion fo r DPSK/RZ- DPSK signals (a) Simulation results o f chromatic dispersion effects on 40-Gbit/s DPSK and RZ-DPSK signals and (b) experimental and simulation results o f chromatic dispersion effects on 10-Gbit/s DPSK and RZ-DPSK system s................. 156 Fig. 4.1. (a) An RZ signal is completely depolarized (DOP = 0) after experiencing DGD equal to its pulse width (in this case, 50% o f the bit time). Thus the maximum DGD monitoring range o f a DO P-based DGD monitor changes as the RZ pulse width varies and (b) An NRZ signal, which to first-order can be considered a “100% duty cycle ” RZ signal, remains partially polarized even when the DGD exceeds a full bit duration.............................................................................................................................. 167 xvi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.2. Theoretical results o f minimum DO P vs. DGD (relative to the bit time, Tb) as the pulse width o f an RZ signal varies.......................................................................... 168 Fig. 4.3. Experimental setup fo r D O P-based DGD monitoring fo r varying data modulation form ats and pulse widths................................................................................. 169 Fig. 4.4. Experimental setup to generate variable-pulse-width RZ signals at 10, 20, and 40 Gbit/s. The resulting pulse width can be tuned by changing the bias o f the phase modulator and phase delay before i t ......................................................................169 Fig. 4.5. The minimum DOP vs. DGD curves fo r (a) a 20-Gbit/s 50% RZ (25-ps pulse width) signal, the maximum DGD monitoring range (first D O P minimum) occurs at ~ 25ps DGD and (b) a 40-Gbit/s 50% RZ (12.5-ps pulse width) signal, the maximum DGD monitoring range occurs at -12.5 ps D G D ........................................ 170 Fig. 4.6. Minimum DOP vs. DGD curves fo r (a), (b) 10-Gbit/s, (c), and (d) 20-Gbit/s signals. As the pulse width varies from (a) 25 p s to (b) 15 ps, the DGD monitoring range varies - from 25 ps to ~17 ps. For a bit rate o f 20 Gbit/s, as the pulse width varies from (c) 25 ps to (d) 12.5 ps, the D G D monitoring range changes from 25 ps to ~12 p s ...................................................................................................................................171 Fig. 4.7. Modified transmitters used to generate CSRZ (top) and ACRZ (bottom) data formats in our experimental setup fo r measuring the relationship between the DOP and DGD in an optical link..................................................................................................172 Fig. 4.8. Representative optical data spectra for 10-Gbit/s (a) NRZ, (b) RZ, (c) CSRZ, and (d) ACRZ signals...............................................................................................173 Fig. 4.9. Simulation results o f minimum DOP vs. DGD fo r 40-Gbit/s, equal-pulse- width (12.5 ps) data formats - RZ is dotted, CSRZ is solid, and ACRZ is dashed.... 174 Fig. 4.10. Simulation results o f minimum D O P vs. DGD fo r 40-Gbit/s (a) DPSK and (b) RZ-DPSK signals............................................................................................................ 176 Fig. 4.11. Experimental (dots) and simulated (line) results o f the minimum DOP vs. DGD fo r 10-Gbit/s 50 p s (a) CSRZ and (b) ACRZ signals........................................... 177 xvii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.12. Prior to optical filtering, an RZ signal that undergoes DGD equal to the pulse width is completely depolarized limiting the DGD monitoring range o f DOP- based DGD monitors. After filtering, the signal is partially polarized, allowing D O P-based monitoring o f the DGD................................................................................... 180 Fig. 4.13. Frequency-domain illustration o f the reduction o f depolarization via symmetric narrowband optical filtering. Short optical pulses have a wide optical spectrum, enhancing the effects o f DGD-induced depolarization. A narrowband filter shrinks the optical spectrum, reducing these depolarization effects and increasing the DGD monitoring range..............................................................................181 Fig. 4.14. Experimental setup fo r DGD monitoring using the DOP o f a partially- filtered optical spectrum. The transmitter configuration fo r the different modulation form ats (RZ, CSRZ, and ACRZ) is shown in Fig. 4.15................................................... 183 Fig. 4.15. Transmitter configurations fo r (a) 10-, 20-, and 40-Gbit/s tunable-pulse- width RZ generation, (b) 10-Gbit/s CSRZ generation, and (c) 10-Gbit/s ACRZ generation................................................................................................................................ 184 Fig. 4.16. Simulation results o f minimum DOP vs. DGD fo r electrically generated (a) 10-Gbit/s and (b) 40-Gbit/s, 50% RZ signals before and after partial optical filtering..................................................................................................................................... 185 Fig. 4.17. Experimental results o f minimum DOP vs. DGD before and after partial optical filtering fo r (a) 10-Gbit/s 15% RZ signals (including simulation results) and (b) 10-Gbit/s 50% RZ signals. The optical spectra fo r 10-Gbit/s 50% RZ signal (c) before, (d) after symmetric, and (e) after asymmetric partial optical filtering.........186 Fig. 4.18. Experimental results o f minimum DOP vs. DGD fo r 20-Gbit/s (a) 50% and (b) 25% RZ signals before and after symmetric optical filtering................................187 Fig. 4.19. Experimental results o f minimum DOP vs. DGD fo r 40-Gbit/s 50% RZ signals before and after asymmetric optical filterin g.....................................................188 Fig. 4.20. Simulation results o f minimum D O P vs. DGD fo r 40-Gbit/s 50% CSRZ signals before and after partial optical filtering..............................................................190 xvm Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.21. Simulation and experimental results o f minimum D O P vs. DGD fo r 10- Gbit/s 50% CSRZ signals (a) broadband filtering, (b) narrowband symmetric filtering, and (c) narrowband asymmetric filterin g ........................................................ 190 Fig. 4.22. Measured optical spectra fo r our CSRZ signal (a) before partial optical filtering, after (b) symmetric, and (c) asymmetric partial optical filtering................191 Fig. 4.23. Simulation results fo r minimum DO P vs. DG D fo r 40-Gbit/s, 50% ACRZ signals before and after partial optical filtering.............................................................. 192 Fig. 4.24. Simulation and experimental results o f minimum D O P vs. DGD fo r 10- Gbit/s, 50% ACRZ signals (a) broadband filtering, (b) narrowband symmetric filtering, and (c) narrowband asymmetric filterin g........................................................192 Fig. 4.25. Measured optical spectra fo r our ACRZ signal (a) before partial optical filtering, after (b) symmetric, and (c) asymmetric partial optical filtering................193 Fig. 4.26. Simulation results o f minimum DOP vs. D G D fo r (a) 10- and (b) 40-Gbit/s NRZ signals before and after asymmetric partial optical filterin g..............................195 Fig. 4.27. (a) Experimental and simulation results o f minimum D O P vs. DGD fo r 10- Gbit/s NRZ signals after symmetric and asymmetric partial optical filtering and the measured optical spectra fo r NRZ signal (b) before partial optical filtering, after (c) symmetric, and (d) asymmetric partial optical filterin g................................................196 Fig. 4.28. Conceptual diagram showing how to cancel the effects o f second-order PMD on DOP-based DGD monitors.................................................................................198 Fig. 4.29. Second-order PMD effects on first-order D O P-based DGD monitors for 40-Gbit/s RZ signals (a) DGD = Ops and (b) DGD = 25 p s ....................................... 200 Fig. 4.30. Second-order PMD effects on Fj-based DGD monitors fo r 40-Gbit/s RZ signals...................................................................................................................................... 202 xix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.31. F2 allows estimation o f the depolarization rate, 2k, in 40-Gbit/s (a) NRZ and (b) RZ signals even as the as total second order PMD, / Q m /, varies................203 Fig. 4.32. Conceptual diagrams o f optical WDM PMD compensation using a single compensator relied on (a) combined-DOP measuring and (b) averaging the individual D O Ps.................................................................................................................... 205 Fig. 4.33. Distribution o f measured combined-DOP, and averaged-DOP for 10- Gbit/s data streams with 1.6 nm channel spacing. Black-dotted and gray curves represent calculated single-channel D O P and combined-DOP o f 4 channels, respectively.............. 206 Fig. 4.34. Power penalty measurement with respect to DO P with the DGD values o f <Tb- In both (a) NRZ and (b) RZ data formats, the measured data points with the single-channel-DOP and the averaged-DOP have the similar trends as opposed to the combined-DOP method, which does not provide the monitoring functionality. D otted and solid curves represent fitted curves fo r single-channel DOP and averaged-DOP, respectively............................................................................................... 208 Fig. 4.35. Simulation results o f (a) averaged-BER curves with and without compensation, (b) compensated averaged-BER-curve compared with the BER-curves o f the worst and the best channels representing the significant improvement o f the highly impaired signals, and (c) averaged-DOP distribution o f four NRZ 10-Gbit/s WDM channels with 1.6-nm channel spacing with and without compensation 209 Fig. 4.36. Setup fo r DGD monitoring without polarization scrambling at the transmitter using partial optical filtering method...........................................................211 Fig. 4.37. Relationship between the DOP and the angle between the link PMD vector and the signal SOP fo r 40-Gbit/s (a) NRZ and (b) RZ sign als.................................... 213 Fig. 4.38. Relationship between (a) 1/P and (b) P and the angle between the link PMD vector and the signal SOP fo r 40-Gbit/s (a) NRZ and (b) RZ signals 214 Fig. 4.39. Simulation results showing the relationship between (a) 1/P and (b) P, as well as DOPAsym and DOPsym as functions o f DGD in 40-Gbit/s (a) NRZ and (b) RZ systems......................................................................................................................................214 xx Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.40. Fig. 4.40. P-DGD sensitivity curves fo r 10-Gbit/s (a) NRZ and (b) RZ systems without polarization scrambling at the transmitter.........................................216 Fig. 4.41. Conceptual diagram o f worst case DGD effects for (a) DSB and (b) SSB SCM signals in Jones space................................................................................................220 Fig. 4.42. Simulation results showing minimum DOP vs. DGD fo r a 20-GHz subcarrier with varying modulation depth....................................................................... 222 Fig. 4.43. (a) Optical spectrum for a 6.75-GHz DSB SCM signal when we increased the modulation depth until each sideband’ s optical pow er was 3 dB less than that o f the carrier and (b) experimental results fo r minimum D O P vs. DGD for this SCM signal........................................................................................................................................223 Fig. 4.44. Conceptual diagram o f our equalized carrier-sideband filtering (ECSF) technique................................................................................. 225 Fig. 4.45. Simulation results showing the optimum ECSF bandwidth fo r FPF filters and l st-order Gaussian filters as a function o f modulation depth and subcarrier frequency.................................................................................................................................226 Fig. 4.46. (a) Optical spectrum o f a 20-GHz, 30% modulation depth DSB SCM signal prior to ECSF, (b) optical spectrum o f the same signal after ECSF, and (c) minimum DOP vs. DGD curves before and after ECSF................................................227 Fig. 4.47. Theoretical, simulation, and experimental results fo r a 6-GHz, 40% modulation depth DSB SCM signal after ECSF.............................................................. 228 Fig.4.48. Simulation and experimental results fo r (a) 8- and (b) 10-GHz, 40% modulation depth DSB SCM signals before and after ECSF....................................... 229 Fig. 4.49. (a) Optical spectrum o f our 11- and 20-GHz, 30% modulation depth (per subcarrier) DSB SCM signals, (b) optical spectrum after ECSF, and (c) minimum DOP vs. DGD curves for this multi-subcarrier signal before and after ECSF 230 xxi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.50. RF pow er and minimum DOP (after ECSF) vs. DGD after transmission through 10 km o f SMF fo r a 20-GHz, 30% modulation depth DSB SCM signal 231 Fig. 4.51. Experimental setup fo r PMD compensation using ECSF to generate a feedback signal....................................................................................................................... 231 Fig. 4.52. (a) First- and (b) second-order PMD statistics o f the 30-section PMD emulator used in our PMD compensation experiment................................................... 232 Fig. 4.53. (a) Relative RF tone pow er distribution before and after compensation using ECSF as a feedback signal, (b) the D O P distribution o f the ECSF signals before and after compensation, and (c) measured BER vs. received optical power fo r a 20-GHz subcarrier BPSK modulated at 155 Mbit/s before and after compensation ................................................................................................................................................... 233 Fig. 4.54. RF clock tone cancellation in the NRZ electrical data spectrum after detection.................................................................................................................................. 236 Fig. 4.55. PMD effects on the dispersion-regenerated clock in the electrical spectrum o f NRZ data (Method 1 ) ....................................................................................................... 236 Fig. 4.56. Reflectivity and delay curves fo r the LCFBG used fo r RF clock regeneration........................................................................................................................... 238 Fig. 4.57. Clock power in NRZ data back-to-back (left) and after 1000 ps/nm o f dispersion (right).................................................................................................................. 239 Fig. 4.58. Fading and regeneration o f a dispersion-regenerated clock due to PMD (Clockpower @ 9.85 G H z)................................................................................................ 239 Fig. 4.59. Fading and regeneration o f the clock tone (9.85 GHz) due to P M D 240 Fig. 4.60. Relative regenerated clock pow er as a function o f DGD (worst case). In theory (dotted line) the curve reaches negative infinity at 50 p s DGD - in our simulations and experiments, we reached -3 0 d B ......................................................... 240 XXll Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.61. The power distribution o f the 2.5-, 5-, and 10-GHz frequency components due to PMD (<DGD>em u iator = 30 p s ) ...............................................................................241 Fig. 4.62. Experimental setup fo r PMD monitoring and compensation using dispersion-regenerated RF clock tone method................................................................ 243 Fig. 4.63. Power penalty as a function o f relative clock pow er.................................. 243 Fig. 4.64. Power penalty distribution (a) before and (b) after compensation using dispersion-regenerated RF clock tone.............................................................................. 244 Fig. 4.65. PMD effects on an asymmetrically-filtered-spectrum-regenerated-clock ................................................................................................................................................... 245 Fig. 4.66. (a) Regenerated RF clock pow er as a function o f filter type, order, and bandwidth and (b) regenerated RF clock pow er as a function o f the frequency detuning o f a filter centered on the optical clock sideband..........................................247 Fig. 4.67. Effect o f chromatic dispersion on the asymmetrically filtered spectrum regenerated clock...................................................................................................................248 Fig. 4.68. (a) Optical spectrum o f a typical NRZ signal prior to notch filtering with an FBG and (b) a close-up o f the electrical spectrum o f the same NRZ signal centered at ~10 G H z.............................................................................................................248 Fig. 4.69. (a) Optical spectrum o f an NRZ signal after notch filtering to remove one o f the optical clock sidebands and (b) the electrical spectrum o f the same signal after notch filtering - due to the filtering o f one o f the sidebands, the RF clock tone is regenerated..............................................................................................................................249 Fig. 4.70. Experimental setup fo r PMD monitoring and compensation using notch- filtered-regenerated RF clock tone.................................................................................... 250 Fig. 4.71. Power penalty distribution (a) before and (b) after compensation using our notch-filtering technique................................................................................................250 X X lll Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.72. Subcarrier tone pow er fading vs. DGD fo r different amount o f splitting ratio and subcarrier tone frequency.................................................................................. 252 Fig. 4.73. Monitoring window vs. subcarrier tone frequency...................................... 253 Fig. 4.74. Eye diagram and corresponding subcarrier tone pow ers..........................253 Fig. 4.75. (a) Q-penalty as a function o f subcarrier tone pow er and (b) subcarrier tone pow er vs. D G D ............................................................................................................. 254 Fig. 4.76. Experimental setup.............................................................................................255 Fig. 4. 77. (a) BER as a function o f subcarrier tone pow er and (b) channel-2 subcarrier tone power as a function o f channel-1 subcarrier tone pow er.................255 Fig. 4.78. Concept o f XPM-induced DOP and half-bit-rate frequency power degradation............................................................................................................................ 258 Fig. 4.79. Simulated optical transmission system ...........................................................259 Fig. 4.80. Variation o f (a,c) DOP and (b,d) RF pow er at half-bit-rate frequency fo r 10-Gbit/s (a,b) NRZ and (c,d) RZ signals fo r different total input powers, respectively. The x-axis shows the percentage o f samples...........................................260 Fig. 4.81. Variation o f the 10% tail o f the (a) half-bit-rate frequency pow er and (b) DOP as the number o f channels is varied.........................................................................261 Fig. 4.82. (a) Half-bit-rate frequency pow er and (b) D O P variation fo r different channel spacing fo r two 10-Gbit/s NRZ channels...........................................................262 Fig. 5.1. The DGD o f a D U T depolarizes the spectrum offiltered-and-polarized ASE noise. By measuring the DOP o f this depolarized signal an accurate DGD estimate can be obtained......................................................................................................................265 X X IV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 5.2. Theoretical results showing the relationship between minimum DOP, DGD, and filter bandwidth when (a) a Gaussian filter and (b) a FPF filter is used with our measurement technique. Wider filter bandwidths result in higher sensitivity but lower measurement ranges.............................................................................................................. 268 Fig. 5.3. Simulation results showing the relationship between minimum DOP, DGD, and filter bandwidth when (a) a Gaussian filter and (b) a FPF filter is used with our measurement technique, (c) The ejfects o f the Gaussian filter order on the monitoring range and sensitivity o f this DGD measurement technique..................... 269 Fig. 5.4. Experimental, simulated, and theoretical results when our measurement technique is applied using (a) a ~35-GHz Gaussian filter, (b) an ~8-GHz FPF filter, and (c) two cascaded FPF filters with an effective bandwidth o f ~5 GHz. In each case our technique matches up well with the theoretical and simulated results 270 Fig. 5.5. (a) The measurement o f DGD using minimum D O P is affected by higher- order PMD, (b) in the presence o f second-order PMD, the maximum DOP is not equal to one - maximum DOP can then be used to measure second-order-PMD, and (c) experimental data showing a relationship between second-order PMD and the maximum DOP allowing application o f this technique to second-order PMD measurement........................................................................................................................... 271 Fig. 5.6. Diagram o f four propose methods fo r DGD measurement using (a) a DSB subcarrier tone, (b) an SSB subcarrier tone generated using ECSF, (c) two polarized laser sources, and (d) a single polarized andfiltered ASE noise source................... 273 Fig. 5.7. (a) Optical spectrum o f a 6.75-GHz DSB subcarrier tone by increasing the modulation depth until each sideband’ s optical pow er was 3 dB less than that o f the carrier and (b) experimental results for minimum DOP vs. DGD fo r this subcarrier tone........................................................................................................................................... 276 Fig. 5.8. (a) Optical spectrum o f a 20-GHz, 30% modulation depth DSB subacrreir tone prior to ECSF, (b) optical spectrum o f the same signal after ECSF, and (c) minimum DOP vs. DGD curves before and after ECSF............................................... 277 X X V Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 5.9. (a) Simulation results o f minimum DOP vs. DGD fo r our dual laser source DGD measurement technique fo r varying laser spacings. The greater the laser spacing, the lower the measurements range but the greater the D O P sensitivity to DGD. (b) Simulation and experimental results fo r minimum DOP vs. DGD fo r two laser spacings......................................................................................................................... 279 xxvi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abbreviations ACF autocorrelation function AC RZ alternate-chirped retum-to-zero AM amplitude modulation BER bit-error-rate BPSK binary-phase-shift-keyed BW bandwidth CSRZ carrier-suppressed retum-to-zero DCF dispersion compensating fiber DFE decision feedback equalizers DGD differential-group-delay DOP degree of polarization DPSK differential-phase-shift-keyed DRA distributed Raman amplifier DSB double-sideband DSF dispersion-shifted fibers DUT device under test ECSF equalized carrier-sideband filtering EDFA erbium doped fiber amplifier EO electro-optic FBG fiber Bragg grating xxvii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FEC forward-error-correction FPF Fabry-Perot fiber FSR free spectral range FW HM full-width half-maximum FW M four-wave mixing HNL highly nonlinear HOM higher-order mode ISI inter-symbol-interference JME Jones matrix eigenanalysis LAN local-area network LCFBG linearly-chirped fiber Bragg grating LCP left circularly polarized LED light-emitting diode LHP linear horizontally polarized LP linearly polarized LVP linear vertically polarized MLD maximum likelihood sequence detection MPS modulation-phase-shift MMM Muller matrix method MZI Mach-Zehnder interferometer NC-FBG nonlinearly-chirped fiber Bragg grating NRZ nonretum-to-zero xxviii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NZDSF non-zero dispersion shifted fiber O AM operation/administration/maintenance OFF offset OOK on-off-keyed OPMDC optical PMD compensator OSA optical spectrum analyzer OSNR optical-signal-to-noise ratio OTDM optical-time-division-multiplexed PA Poincare analysis PBS polarization beam splitter PC polarization controller PCD polarization dependent chromatic dispersion PDF probability density function PDG polarization dependent gain PDL polarization dependent loss PER pseudo error rate PHB polarization hole burning PM polarization maintaining PMD polarization mode dispersion POTDR polarization optical time domain reflectometry PRBS pseudo-random bit sequence PSP principal state o f polarization xxix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RCP right circularly polarized RF radio frequency RZ retum-to-zero SBS stimulated Brillouin scattering SCM subcarrier-multiplexed SM F single mode fiber SNR signal-to-noise ratio SOP state o f polarization SPM self-phase modulation SRS stimulated Raman scattering SSB single-sideband TF transversal filter VIPA virtually imaged phased array W DM wavelength-division-multiplexed XPM cross-phase modulation XXX Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract Critical issues that severely hamper high-bit-rate (>10 Gbit/s/channel) and long-haul optical fiber communication systems include chromatic dispersion, polarization mode dispersion (PMD), and fiber nonlinearities. Optical fiber communication systems are designed such that these degrading effects are minimized. A key challenge is that there are several factors in which cause these fiber- based effects to vary with time, including: (i) temperature changes will cause a shift in the accumulated chromatic dispersion and affect any polarization based impairment penalties, (ii) reconfigurable optical networking will alter the signal path and thus the accumulation o f fiber-based effects, and (iii) periodic repair and maintenance o f the fiber plant will alter the fiber itself. These time varying degradation effects necessitate a monitoring unit in an optical network in order to either dynamically tune a mitigator or determine the network location that must be diagnosed or repaired. In addition, the main difficulty with managing and mitigating polarization effects in long distance fiber transmission systems is that they are stochastic processes. This means that a system can randomly wander in and out of high-penalty states. The goal, therefore, is to reduce the probability that the penalty will exceed an acceptable level to a negligible value (typically <1 minute per year). Outages caused by polarization effects are therefore non-catastrophic. This justifies the need for dynamic monitoring and mitigation techniques. xxxi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Therefore, for management, monitoring, and mitigation purposes in a robust system, simple, sensitive, flexible, and cost-effective chromatic dispersion and PMD monitoring technique may prove quite beneficial. Moreover, it may be highly desirable for component manufacturers and suppliers to be able to accurately measure the differential-group-delay (DGD) o f devices and components to ensure that they are compliant with customer specifications. In this dissertation, I propose and experimentally demonstrate several techniques to monitor these fiber dispersive effects (chromatic dispersion and PMD) by improving the monitoring control signal’s requirements. We apply the proposed monitoring methods to different types o f modulation formats and use some of them for optical compensation. In addition, we highlight two DGD measurement techniques. These techniques may potentially play key roles in future fiber-optic dynamic systems and reconfigurable optical networks. xxxii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1 Introduction Continuously, the demand for network bandwidth is outpacing even the astounding advances o f recent years. The ever-increasing fiber optic base and the acceptance of wavelength-division-multiplexed (WDM) as an established technology are waiting to fulfill the enormous future potential o f next-generation Internet services. The proliferation o f online services and network access providers coupled with low cost computers result in exponentially increasing numbers o f customers, with increasing bandwidth demands to support multimedia and other revolutionary applications. Faster processors fuel this demand, as today’s computers are outdated tomorrow. Because o f its high capacity and performance, optical fiber communications have already replaced many conventional communication systems in point-to-point transmission and networks and also have been considered as a good candidate for wireless backbone. Optical communication systems have grown explosively in terms o f the capacity that can be transmitted over a single optical fiber. This trend has been fueled by two complementary techniques, those being the increase in data-rate-per-channel coupled with the increase in the total number o f parallel wavelength channels. Due to the invention o f erbium doped fiber amplifier (EDFA) and distributed Raman amplifier (DRA) which have the wide gain bandwidth, the optical fiber transmission 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. systems are more enhanced with the simultaneous amplification, thereby, with the longer transmission without electrical regeneration in the link. However, there are many considerations as to the total number of WDM channels that can be accommodated in a system, including cost, information spectral efficiency, dispersions, nonlinear effects, mitigation and monitoring o f fiber-based effects, and component wavelength selectivity. Recent researches in the optical fiber communication fields are focused on how to mitigate bandwidth-limiting effects for network speeds up to 1-Tbit/s. However, in the not-too-far future, the speeds approaching 10-Tbit/s may be required as WDM optical networks encroaches the network environment widely. So far, there have been remarkable achievements in the optical fiber transmission systems. The bit-rates have reached 1.28-Tbit/s over 70 km for single-channel [1], and 3-Tbit/s (300 x 11.6-Gbit/s, C+L band) over 7,380 km, 1.28-Tbit/s (32 x 40-Gbit/s, C band) over 4500 km, 1.52-Tbit/s (38 x 40-Gbit/s, C band) over 6200 km, 10.2-Tbit/s (256 x 42.7-Gbit/s, C+L band) over 300 km, and 10.92-Tbit/s (273 x 40-Gbit/s S+C+L band) over 117 km for WDM systems [2 ,3 ,4 ,5 ,6 ]. The spectral efficiency has reached 1.6 (bits/s)/Hz [7], For higher capacities, in addition to the improvement o f single channel transmission characteristics, all the degrading effects on the WDM optical signals in the fiber or devices need to be addressed. The first stage towards optical transport networking is optical channel (wavelength) level reconfiguration, grooming and rapid protection/restoration. The goal is to provide a flexible, scalable, and robust 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. optical transport network, catering to an expanding variety o f client signals with equally varied service requirements. The challenges include managing optical channels, optical layer operation/administration/maintenance (OAM), and optical layer protection and automated provisioning & distributed restoration. In order to take full advantages o f the signal transmission through the optical fiber and achieve the high performance of optical fiber systems, several problems need to be solved. In general, optical signals suffer from many effects in the fiber including: chromatic dispersion, polarization mode dispersion (PMD), and fiber nonlinearities that cause degradation o f the transmitted signal, leading to system performance impairments. Moreover, there are system parameters that vary with time in dynamically configurable networks as well as in point-to-point links. These time-varying effects will degrade channel performance by generating nonlinearities, lowering signal-to- noise ratio (SNR), distorting the optical pulses, and introducing channel crosstalk and noises. Even if a lot of possible solutions have been investigated to solve these problems, still more enhanced solutions are needed to realize more effective optical communication systems with ultra-high capacity and performance. This dissertation is structured as follows: Chapter 2 presents a brief overview o f the signal degradation effects in the digital systems including: chromatic dispersion, nonlinearity, and polarization impairments and reviews mathematically polarization o f light and PMD. In addition, the topics o f emulation and generation of PMD, polarization scrambling, and fiber Bragg grating (FBG) are presented in this chapter. Moreover, the subject o f chromatic dispersion mitigation/monitoring, PMD 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mitigation/monitoring and differential-group-delay (DGD) measurement are discussed in this chapter. This is followed by a discussion in Chapter 3 o f several techniques for chromatic dispersion monitoring, improving and enhancing chromatic dispersion monitoring methods. In Chapter 4, some novel methods are depicted for PMD/DGD monitoring and control o f polarization-related impairments in digital and analog systems. Moreover, this chapter discusses a theoretical and experimental analysis o f different monitoring parameters and shows that these parameters are dependent on the nature o f signal (modulation format, pulse width, and etc.) and PMD and affected by nonlinearity. Chapter 5 presents two techniques for DGD measurement o f optical components. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 Background 2.1 Signal Degradation Effects in Digital Optical Fiber Communication Systems The optical signals degrade as travel down the optical fiber link due to the optical fiber properties such as chromatic dispersion, PMD, polarization dependent loss (PDL), polarization dependent gain (PDG), and various fiber nonlinear effects, which are considered as limitations in the high-speed, long-haul fiber communication systems. This section provides schematic understanding o f the fiber properties that induce the signal degradation effects and mathematical review on polarization of light and PMD. 2.1.1 Chromatic Dispersion and Chromatic Dispersion Slope In any medium other than vacuum and in any waveguide structure (other than ideal infinite free space), different electromagnetic frequencies travel at different speeds. This is the essence o f chromatic dispersion [8,9,10]. As the real fiber-optic world is rather distant from the ideal concepts o f both vacuum and infinite free space, dispersion will always be a concern when one is dealing with the propagation of electromagnetic radiation through fiber. The velocity in fiber o f a single monochromatic wavelength is constant. However, data modulation causes a 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. broadening of the spectrum of even the most monochromatic laser pulse. Thus, as shown in Fig. 2.1, modulated data spectrum has a non-zero spectral width, which spans several wavelengths, and the different spectral components o f modulated data travel at different speeds. In particular, for digital data intensity modulated on an optical carrier, chromatic dispersion leads to pulse broadening - which in turn leads to chromatic dispersion limiting the maximum data rate that can be transmitted through optical fiber. Modulated Data ol 1 1 lo Pulse Broadening 1 0 Optical Spectrum | jnt Fiber wIChromatic Dispersion M Vj I <pi* < P k Vk * f f Carrier f Fig. 2.1. Pulse broadening due to chromatic dispersion. Considering that the chromatic dispersion in optical fibers is due to the frequency dependent nature of the propagation characteristics for both the material (the refractive index o f glass) and the waveguide structure, the speed o f light of a particular wavelength A will be expressed as follows using a Taylor series expansion of the refractive index value as a function o f the wavelength [8]: 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Here, c0 is the speed of light in vacuum, X0 is a reference wavelength, and the terms in — and are associated with the chromatic dispersion and the dispersion 8X dA2 slope (i.e., the variation o f the chromatic dispersion with wavelength), respectively. Transmission fiber has positive dispersion, i.e., longer wavelengths see longer propagation delays. The unit o f chromatic dispersion is picoseconds per nanometer per kilometer (ps/nm/km), meaning that shorter time pulses, wider frequency spread due to data modulation, and longer fiber lengths will each contribute linearly to temporal dispersion. Higher data rates inherently have both shorter pulses and wider frequency spreads. Therefore, as network speed increases, the impact o f chromatic dispersion rises precipitously as the square o f the increase in data rate. The quadratic increase with the data rate is a result of two effects, each with a linear contribution. On one hand, a doubling o f the data rate makes the spectrum twice as wide, doubling the effect o f dispersion. On the other hand the same doubling o f the data rate makes the data pulses only half as long (hence twice as sensitive to dispersion). The combination o f a wider signal spectrum and a shorter pulse width is what leads to the overall quadratic impact. Moreover, different data modulation formats show different tolerance to the chromatic dispersion. For example, the common nonretum-to-zero (NRZ) modulation format, in which the optical power stays high throughout the entire time slot of a “1” bit, is more robust to chromatic dispersion than is the retum- 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to-zero (RZ) modulation format, in which the optical power stays high in only part of the time slot of a “1” bit. This difference is due to the fact that RZ data has a much wider optical power spectrum compared to NRZ data, thus incurring more chromatic dispersion. However, in a real WDM system, the RZ format increases the maximum allowable transmission distance by virtue of its reduced duty cycle (compared to the NRZ format) making it less susceptible to fiber nonlinearities. A rule for the maximum distance over which data can be transmitted is to consider a broadening of the pulse equal to the bit period. For a bit period Tb, a dispersion D value and a spectral width AX , the dispersion-limited distance is shown in Fig. 2.2 and given by Ld = ------ ------- = -------— ------— < x — (2.1.2) D .T b .AX D .T b .(cTb) Tb2 1000 i 400 NZDSF 4 ps/nm/km § 100 1Q 0 25 60 SMF 17 psInmSm 2.5 Bit-Rate (Gbit/s) Fig. 2.2. Transmission distance limitations due to uncompensated dispersion in single mode fiber (SMF) as a function of data rate for intensity modulated optical signals [l l ] . 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For example, for SMF (D = 17 ps/nm/km) and 10 Gbit/s data, the dispersion limited transmission distance is LD - 52 km. In fact, a more exact calculation shows that for 60 km, the dispersion induced power penalty is less than 1 dB. The power penalty for uncompensated dispersion rises exponentially with transmission distance, and thus to maintain good signal quality, dispersion compensation is required. Dispersion parameters can be changed by tailoring the waveguide profile. In dispersion-shifted fibers (DSF), X0 is in the neighborhood o f 1.5 pm and D usually between -2.5 and +2.5 ps/nm-km at 1.5 pm. The dispersion parameter, D as a function o f wavelength for both SMF and DSF is shown in Fig. 2.3. Negative D values are referred as normal dispersion, and positive D values are referred anomalous dispersion. E c w 3 c 0 e 0 1 Q , tfl 5 2 D 16 12 8 4 0 ■ A 1510 1530 1550 1570 1590 1610 Wavelength (nm) ■ SMF — ■ ■ — Alcatel-TeraLight •TrueWave RS — — ■ — ■ Corning E-LEAF — — — — -TrueWave Classic — — — DSF V __________________________________________________________ Fig. 2.3. Dispersion parameter D vs. wavelength for different fibers. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The wavelength dependency of D is usually considered through dispersion slope dD which is — = 0.08 ps/nm2 /km (for both SMF and for DSF around 1.5 pm). This dX wavelength dependence of chromatic dispersion is labeled second-order dispersion and is important in long-haul WDM systems because different wavelengths may need different dispersion compensation. To mitigate the effect o f fiber nonlinearities that will be explained in section 2 .1.2, the next generation o f fibers introduced small amounts o f dispersion in order to introduce enough dispersion to counteract nonlinear effects as well as to minimize the signal distortion from the chromatic dispersion. Non-zero dispersion-shifted fiber (NZDSF), was introduced by Coming - as large effective area fiber - LEAF-, and by Lucent - as TmeWave - in the mid 1990’s. The dispersion o f NZDSF is of the order o f 4 ps/nm/km, low enough to allow transmission over up to four times longer distances than SMF, but with a dispersion value large enough to reduce four-wave mixing (FWM) and cross-phase modulation (XPM). Both negative and positive dispersion cause pulse broadening at the output of the fiber. The broadening increases with the fiber length, imposing a limit on the maximum distance and/or data rate without regeneration. Therefore, chromatic dispersion must be mitigated for high-speed or long-distance systems. However, it is apparent by now that chromatic dispersion must be managed, rather than eliminated. Even though it is possible to manufacture fiber with zero dispersion, it is not practical to use such fiber for WDM transmission because o f large FWM induced penalties. 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Furthermore, even though the compensation o f chromatic dispersion for high speed or long-distance systems can be fixed in value theoretically, there are several important aspects o f optical systems and networks that make tunable dispersion compensation solutions attractive, especially in high-speed optical networks. 2.1.2 Fiber Nonlinearities There are two categories of fundamental optical nonlinear effects that can cause degradation o f the transmitted signal. They are refractive-index effects and stimulated scattering effects. Refractive index effects are associated with modulation of the refractive index due to changes in the light intensity. Stimulated scattering effects arise from parametric interactions between light and acoustic or optical phonons (due to lattice or molecular vibrations) in the fiber. The refractive index n of silica is not a constant but increases with power (or light intensity) according to the following relationship: n(co,P) = n0(co) + n2 (2.1.3) 4 // where n0(a))v$> the linear refractive index of silica, n2 is the intensity-dependent p refractive index coefficient, and I = is the effective intensity in the medium. 4 # The typical value o fn2 is 2.6 x 10'20 m2/W. This number takes into account the averaging o f the polarization states o f the light as it travels in the fiber. The intensity dependence o f the refractive index gives rise to three major effects [8,12]: (i) self phase modulation (SPM), (ii) XPM, and (iii) FWM. All these three nonlinear effects 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. can significantly degrade the performance of a WDM lightwave system [8,13], XPM and FWM are more severe in multi-channel WDM systems, while SPM can occur in both single channel and WDM systems. The relevant power-times-distance products for amplified transmission systems can be so large as to make fiber nonlinear effects the dominant factor in determining the design o f long-distance systems. System specifications such as the non-regenerated span length L , amplifier spacing lA, number o f WDM channels N, channel frequency spacing A f , and power per channel Pg are all affected. Understanding how system performance is degraded by fiber dispersion in the presence of fiber nonlinearities is crucial for designing amplified transmission systems. 2.1.2.1 Self-Phase Modulation A million photons “see” a different glass than does a single photon, and a photon traveling along with many other photons will slow down. SPM occurs because of the varying intensity profile o f an optical pulse on a single WDM channel. This intensity profile causes a refractive index profile and, thus, a photon speed differential. The resulting phase change for light propagating in an optical fiber is expressed as [8] NL = Y P L e ff (2.1.4) where the quantities y and Leff are defined as 7 = (2.1.5) 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where Aeff is the effective mode area of the fiber and a is the fiber attenuation loss. is the effective nonlinear length o f the fiber that accounts for fiber loss, and y is the nonlinear coefficient measured in rad/km/W. A typical range o f values for y is between 10-30 rad/km/W. Although the nonlinear coefficient is small, the long transmission lengths and high optical powers that have been made possible by the use o f optical amplifiers can cause a large enough nonlinear phase change to play a significant role in state-of-the-art lightwave systems. When an intensity-modulated signal travels through an optical fiber, the peak o f the pulse accumulates phase more quickly than the wings due to nonlinear refractive index. This results in a nonlinear chirping o f the signal. The SPM induced chirp may interact with dispersion induced chirp and can cause a totally different behavior depending upon positive or negative dispersion values [8,10], In the normal dispersion regime ( D < 0), the SPM induced nonlinear-chirp will add to the dispersion-induced linear-chirp, thereby causing not only the enhanced pulse broadening but also distorting the shape o f the pulse. In the anomalous dispersion regime ( D > 0), the SPM induced nonlinear-chirp will tend to partially negate the dispersion induced linear-chirp, thereby slightly reducing the pulse broadening, but still will distort the pulse shape. Therefore, SPM induced chirp can impose a limitation on bit rate and transmission distance in lightwave systems. The SPM induced chirp is dependent upon the power and the shape o f the optical pulse. Therefore, if the power and the shape o f the pulse are right, the SPM induced chirp and the dispersion-induced chirp can completely negate each other in anomalous 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dispersion regime ( D > 0) [9]. The pulse with the right shape and power is called soliton. 2.1.2.2 Cross-Phase Modulation When considering many WDM channels co-propagating in a fiber, photons from channels 2 through N can distort the index profile that is experienced by channel 1. The photons from the other channels "chirp" the signal frequencies on channel 1, which will interact with fiber chromatic dispersion and cause temporal distortion. This effect is called cross-phase modulation (XPM) [8,14], In a two-channel system, the frequency chirp in channel 1 due to power fluctuation within both channels is given by d 0 M ! r dP, „ r dPj „ ^ = — r = rL tr— + 2 ^ — (2 .1.6) dPI dP2 where — L and — - are the time derivatives o f the pulse powers o f channels 1 and dt dt 2, respectively. The first term on right hand side o f the above equation is due to SPM, and the second term is due to XPM. Note that the XPM-induced chirp term is double that o f the SPM-induced chirp term. This factor o f 2 arises from counting o f terms in the expansion of the nonlinear polarization inside the fiber [8,14], As such, XPM can impose a much greater limitation on WDM systems than can SPM, especially in systems with many WDM channels. However, fiber dispersion plays a significant role in the system impact o f XPM [8], Due to dispersion, pulses at different wavelengths travel with different speeds inside the fiber because of group 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. velocity mismatch. In normal dispersion regime ( D < 0), a longer wavelength travels faster while the opposite occurs in the anomalous-dispersion regime ( D > 0). This feature leads to a walkoff effect that tends to reduce XPM effect. 2.1.2.3 Four-Wave Mixing The optical intensity propagating through the fiber is related the electric field intensity squared. In a WDM system, the total electric field is the sum o f the electric fields o f each individual channel. When squaring the sum o f different fields, products emerge that are beat terms at various sum and difference frequencies to the original signals. Like SPM and XPM, FWM is also generated by the intensity-dependence of refractive index o f silica. However, impact o f FWM on performance o f WDM system is completely different. In FWM, the beating between two channels of a WDM system at their difference frequency modulates the phase of one o f the channels at that frequency, generating new tones as sidebands [15]. When three waves o f frequencies f , / . , and f k interact through fiber nonlinearity, they generate a wave o f frequency fijic = f i + f j - f k (2.1.7) Therefore, three waves give rise to nine new optical waves by FWM. For a WDM system with N channels, the number o f FWM products generated is M - ~ j ( N 3- N 2) (2.1.8) In WDM system with equally spaced channels, most o f the product terms are generated by FWM fall at the channel frequencies, giving rise to crosstalk. The 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. center channels are more vulnerable to this cross talk since the number of FWM products, which fall on center channels, is higher than those, which fall on end channels [10,15]. The efficiency of FWM depends on the channel spacing and the fiber dispersion. Increasing channel spacing or fiber dispersion will reduce mixing efficiency. High-speed WDM systems require simultaneously high launched power and low dispersion values. This greatly enhances the efficiency o f FWM, making FWM the dominant nonlinear effect in WDM lightwave systems. FWM can impose severe limitation on bit rate/channel, transmission distance, and number o f WDM channels [10]. While dispersion limits the maximum transmission distance and the bit rate, the effects o f XPM and FWM are reduced by dispersion because dispersion destroys the phase matching conditions. In order to achieve good system performance, it is important to consider the chromatic dispersion and the nonlinear effects o f the transmission fiber together. Dispersion management is a solution for this dilemma by using two different types o f fibers having opposite dispersions periodically. The total accumulated dispersion is zero after some distance, but the absolute dispersion is non-zero at all points along the link. The result o f this dispersion management scheme is that the total effect o f dispersion is negligible for all channels, and non zero dispersion causes phase mismatch between channels thereby destroying efficient nonlinear interactions. 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.1.2.4 Stimulated Scattering The nonlinear effects described above are governed by the power dependence of refractive index, and are elastic in the sense that no energy is exchanged between the electromagnetic field and the dielectric medium. A second class o f nonlinear effects results from stimulated inelastic scattering in which the optical field transfers part of its energy to the nonlinear medium. Two important nonlinear effects fall in this category [8]: (i) stimulated Raman scattering (SRS), and (ii) stimulated Brillouin scattering (SBS). The main difference between the two is that optical phonons participate in SRS, while acoustic phonons participate in SBS. In a simple quantum machanical picture applicable to both SRS and SBS, a photon o f the incident field is annihilated to create a photon at a downshifted frequency. The new photon is propagated along the original signal in the same direction in SRS, while the newly generated photon propagates in the backward direction in SBS. Furthermore, the downshifted frequency range where new photons can be generated is -3 0 THz in SRS and only -3 0 MHz in SBS. Therefore, SBS does not impose any significant limitations in high-speed (Gbit/s systems) digital lightwave systems. However, SRS can impose some limitations on WDM systems because the effect o f SRS is to deplete the energy o f some channels (higher frequency channels) on behalf of the other channels (low frequency channels). The effect o f SRS is not very significant unless the number o f channels is more than 100 [10]. On the other hand, SRS can be used for signal amplification in a fiber (so called Raman amplifier). Raman amplifier is becoming more and more cost effective now and is extensively 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. developed in recent years because o f some unique features. Indeed, unlike EDFA, Raman amplification can virtually occur at any wavelength by properly choosing the pump wavelength and a large bandwidth can be achieved by combing several pump wavelengths. 2.1.3 Polarization Impairments For many years, optical fiber communication systems were largely designed and operated with little concern for polarization effects. In fact, conventional optical fibers and some in-line components were assumed to be essentially polarization insensitive and parameters like PMD and PDL were typically not measured or specified. It was a time when chromatic dispersion, insertion loss and wavelength- dependent loss or gain was the main sources o f system penalties. However, many recent improvements in optical components and transmission system technologies have led to huge growth in the capacity o f long distance fiber systems. As carriers begin to employ higher data rate transmission systems (> 10-Gbit/s/channel), and especially when these systems are deployed over older fibers, the once-disregarded effects related to light-wave polarization become a significant source o f network impairments. Three o f the main sources o f polarization-related impairments are PDL [16], PDG [17-18], and PMD [19]. Each o f these phenomena may present a major limitation for a high data rate optical transmission system. PDL may cause optical power variations due to polarization fluctuations [16,20], PDG can induce SNR fluctuations due to gain variations [18] and PMD causes inter-symbol-interference 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (ISI) in digital systems and the radio frequency (RF) power fading in analog or subcarrier-multiplexed (SCM) transmission systems [19,21-22], PDL-induced intensity modulation is also a potentially system performance degrading effect [23- 24], Initially, these polarization effects were treated as separate phenomena. However, it has recently become clear that the interaction between PMD and PDL (or PDG) may cause added distortions and further broaden the distribution of system penalties [25-29], In general, many optical in-line components, such as optical amplifiers, WDM couplers, add-drop multiplexers, optical isolators, and circulators, often have some PDL (or PDG) that is typically small and negligible when considered alone. However, when these components are distributed throughout a fiber link, the combination o f their PDL (or PDG) and the PMD o f the fiber could lead to a mutual interaction that adds to greater system impairments than would be seen from either effect alone [25-28], A key difficulty with managing these polarization effects in long distance fiber transmission systems is that they are stochastic processes. This means that a system can randomly wander in and out of high-penalty states. The goal, therefore, is to reduce the probability that the penalty will exceed a certain level to a negligible value (typically <1 minute per year). Outages caused by polarization effects are therefore non-catastrophic, meaning that locating and resolving the cause o f a system outage due to a polarization-related effect is not as clear as locating a fiber cut or 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pump-laser failure. This could lead to the need for dynamic monitoring and mitigation techniques. A main source o f this randomness is non-idealities in the optical fiber. Ideally, the SMF core is circularly symmetric and the two polarization modes are degenerate, meaning that light in either mode propagates with the same speed. However, real SMFs possess some intrinsic birefringence due to random geometric and stress variations along the fiber core as a result o f the manufacturing process, cabling and laying processes. In combination with environmental perturbations, this generates PMD in the fiber that varies randomly with time and frequency [29-32], Additionally, the aggregate PDL value o f several in-line optical components in such a fiber link becomes a time-varying function due to random fluctuations o f the signal polarization states between each component. These time-varying degradations may require monitoring o f signal quality in some optical networks in order to either dynamically tune a PMD and/or PDL compensator or to determine the network location that must be diagnosed and repaired [33-34], This need has led to a growing field o f research on PMD and PDL monitoring techniques that are simple, sensitive, and, in some cases, able to distinguish polarization effects from other sources of distortion. 2.1.3.1 Mathematical Review of Polarized Light 2.1.3.1.1 The Polarization Ellipse The optical field in free space is described in a Cartesian coordinate system by the three dimensional wave equation, 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2.1.9) where V 2 is the Laplacian operator, c is the velocity of propagation o f the optical time, and r = r ( x ,y ,z ) . The equation (2.1.9) represents two independent wave equations for the field components Ex(r,t) and Ey(r,t). These two components are orthogonal to each other and lie in the same plane perpendicular to the direction o f propagation, that is, they are transverse to the longitudinal direction o f propagation and form a right hand coordinate system. Because the field consists o f only two transverse components, Ex(r,t) and Ey(r,t), it is convenient to select the direction o f propagation to be along the z-direction. For a monochromatic wave that propagates in the positive, the solution of (2.1.9) can be represented by where E^ , E^ , p , Sx and Sy are the maximum and minimum amplitude, propagation constant, and the phase o f each o f the components, respectively. These equations are said to be “instantaneous” in the sense that the time duration for a propagating optical wave to go through one period o f oscillation is of is the two-fold partial differential operator with respect to the Ex (z, t) = E0 xcos( co0t-f3 z + 5x) (2. 1.10) Ey (z, t) = EgyCosC c d 01 — j3z + Sy ) (2.1.11) order of 10'15 seconds. The time duration o f this magnitude cannot be observed or 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measured. In practice, it is found that observable or measurable representations can be obtained by taking time averages of the squares of the field components. By eliminating < x > 0t - ftz between (2.1.10) and (2.1.11), the dependence of optical field components EJz,t) and Ey(z,t) can be describe by E 2 (z ,t) E 2(z ,t) E (z,t)E (z,t) , + — — r ------- 2 ------------- -------- cos(8 ) - sin ( 5 ) (2 .1.12) p 2 p 2 F F ^ O x Oy Ox Oy where 8 = Sy - 8 x (0 < 8 < 2n). This equation is called the polarization ellipse and shows that at any instant o f time the locus o f points described by the optical field as it propagate is an ellipse; the ellipse does not change as the filed propagate. Fig. 2.4 shows the polarization ellipse for the optical field. Let Ox and Oy be the initial, un-rotated axes, and let 08, and Orj be the new set o f axes along the rotated ellipse. The angle between Ox and the direction o f 0% o f the major axis is called the orientation angle (0 < a/ / < t u ). This orientation angle o f the polarization ellipse is 2E E tan 2y/ = 0x 0y C os(8 ) (2.1.13) E 0X ~ E 0y 7Z 7 t The ellipticity angle % ( ----- < % < —) is the other parameter that is 4 4 2En En sin 2% -----— v — js in ( 8 ) (2.1.14) Eq x + E0y 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. All the parameters of polarization ellipse can be expressed uniquely in terms of the orientation angle y/ and the ellipticity angle x ■ 2E0x Fig. 2.4. The polarization ellipse for the optical field. The polarization ellipse (2.1.12) degenerates to special forms for different values of E 0 x > E o y , a n d 8 . 1. Efy = 0 . In this case, the oscillation o f the optical field is only along the x-axis. The light is then said to be linearly polarized in the x direction, and is spoken o f as linear horizontally polarized (LHP) light. 2. E0 x = 0 . In this case, the oscillation o f the optical field is only along the y-axis. The light is then said to be linearly polarized in the y direction, and is spoken of as linear vertically polarized (LVP) light. 3. 5 = 0 or 7t. In this case, the equation (2.1.12) can be described by, Ey(z ,t) = ± ( ~ L)Ex( z ,t) (2.1.15) Eq x 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Eo This equation is a straight line with slope ± (-—?-) and zero intercept. The light is E 0 x Eo then to be said linearly polarized ( .LP) with slope ± ( — - ) . The equation (2.1.15) E0x also shows that the value 5 = 0 yields a negative slope and the value 5 = n yields a positive slope. For the special case where E0 x = , (2.1.15) reduces to Ey(z,t) = ±Ex(z ,t) (2.1.16) The positive value is said to represent linear +45° (L+45P) polarized light, and the negative value is said to represent linear -45° (L-45P) polarized light. 7t 3 tc 4. 5 = — or — . In this case, the equation (2.1.12) becomes E* + (2.1.17) e 0x e 0; This is a standard form of an ellipse. to 3 tc 5. E0x= E 0y= Eg and 5 = — or — . In this case, the equation (2.1.12) becomes (2.U 8) F F ^o ^o This equation is a circle in which the light is either right circularly polarized (RCP) 7t 3n or left circularly polarized (LCP) ( 5 = — or 5 = -^-). 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.1.3.1.2 The Poincare Sphere The polarization ellipse is an excellent way to visualize the polarization behavior o f a propagating polarized optical beam. However, in dealing with the propagation of polarized light through polarizing elements, the orientation and the ellipticity angles o f the polarization ellipse change. Thus, the calculation to determine the new orientation and ellipticity angles o f the emergent polarization ellipse are long and tedious. In order to overcome the calculation difficulties, H. Poincare suggested in 1892 a geometrical representation in which a specific polarization state (ellipse) is mapped (in terms o f its orientation and ellipticity) as a point onto a sphere. A new polarization state (ellipse) is characterized by another point on the sphere with its new orientation and ellipticity. The arc length connecting the two polarization states then represents the effect o f polarizing elements. In an analogous manner, for polarized light, Poincare suggested that, given the initial orientation and ellipticity of a polarized beam on the sphere and the parameters o f the polarizing elements, one could determine a new point (its orientation and ellipticity coordinates) on the sphere. Conversely, given the orientation and ellipticity coordinates o f the initial and final points on the sphere (polarization states), the polarizing elements connecting the two points can be determined. In either case, the arc length between the two points could be determined by using the equations o f spherical trigonometry. After sixty years, H. G. Jerrard presented the theory o f Poincare polarization sphere, now known simply as the Poincare sphere. The basic idea behind the 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Poincare sphere is arise from a Greek astronomer Hipparchus around 150 BC. By series o f mathematical operations, Jerrard showed that by representing (2.1.10) and (2 .1.11) as a point in the complex plan, the initial point in the complex plane could be projected as another point onto the sphere { x 2 + y 2 + z 2 = / ). Any point on this sphere could be represented in terms o f the orientation and ellipticity angles y/ and X o f the polarization ellipse expressed by equations, x -c o s (2 x )c o s (2 y f) (2.1.19) y = cos( 2 x )sin( 2y/ ) (2 .1.20) z = sin (2x) (2 .1.21) These equations relate the Cartesian coordinates (x, y, z) to the spherical coordinates (\,y/ , x ) for a point on the Poincare sphere o f unit radius. On the Poincare sphere, the longitude lines represent the ellipticity angle ^ and the latitude lines represent the orientation angle y / . Fig. 2.5 shows the Poincare sphere. Z y Fig. 2.5. The Poincare sphere of unit radius and Cartesian coordinates. The coordinates o f the point P are P( % /). 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.1.3.1.3 The Stokes Polarization Parameters The description o f light in terms o f the polarization ellipse is very useful since it allows us by means o f a single equation (2 .1.12) to describe any state of completely polarized light. However, this representation is inadequate for several reasons. First, as the beam o f light propagates through the space, the light vector traces out an ellipse or some special form o f the ellipse, e.g., the circle or a straight line, in a time interval o f the order o f 10'15 seconds. This period is too short to allow us to follow the tracing o f the ellipse as the beam propagates and prevents us from following the polarization ellipse in the optical time domain. Second, the polarization ellipse is only applicable to describing light that is completely polarized and it cannot be used to describe partially polarized light and unpolarized light. Finally, the polarization ellipse is an amplitude description o f polarized light but the time average of the square of the field amplitudes, intensity, can be observed and measured. Therefore, the polarization ellipse must be transformed so that only intensities are present, that is, measurable and observable quantities. In order to transform (2.1.12) to an intensity or observable representation, we take a time average o f the time dependent quantities in (2 .1.12), < E x2(z,t)> < E 2(z,t)> < E J z , t ) E ( z , t ) > ,0 1 0 ^ — ;------- 1 -------------- -7------2 —— — — ------------cos(o) = sin ( o ) (2 .1.22) Eo? V W o , The time average o f the field components are defined by the equation 1 T < Ei(z,t)E,(z,t) >= Um — \E f z,t)Ej(z,t)dt i,j= x,y (2.1.23) 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where T is time o f the measurement. Using (2.1.10), (2.1.11), and (2.1.23), the time average in (2.1.22) are found to be (E o; + E0y2 / - (E0x2 - E0y2 / - (2E0xE0y cos(S))2 = (2E0xE0y sin(S))2 (2.1.24) The terms within the parentheses o f (2.1.24) can be written as S0 = E 0x2 +E0y2 (2.1.25) S , = E 0 2 - E 0y2 (2.1.26) 52 = 2E0xE0y cos 5 (2.1.27) 5 3 = 2E0xE0y sinS (2.1.28) Equation (2.1.24) can be then written as S02 = S 2 +S22 + S 2 (2.1.29) In 1852, G.G. Stokes introduced the four equations given by (2.1.25) through (2.1.28) that they are known as the four Stokes polarization parameters for a plane wave. Thus, the polarization ellipse transform to the Stokes relation, which is an intensity relation in the observable or measured domain. The first stokes parameter > S 0 is the total intensity o f the optical field. The second parameter S3 describes the preponderance o f the intensity o f linearly horizontal polarized light over linearly vertical polarized light. The third parameter S2 describes the preponderance of the intensity of linearly positive 45° polarized light over linearly negative 45°polarized light. The forth parameter Ss describes the 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. preponderance of the intensity of right circularly polarized light over left circularly polarized light. In order to obtain the stokes parameters o f a monochromatic optical wave, the time averaging process can be bypassed by representing the real optical amplitudes, (2 .1.10) and (2 .1.11), in terms o f complex amplitudes, Ex (z, t) = E0 xei(o,°l+SJ (2.1.30) E / z . t ^ E ^ ^ (2.1.31) The Stokes parameters for a plane wave are now defined by the following equations: (2.1.32) (2.1.33) S2 = 2R e (E ;E y ) (2.1.34) S, - 2 lm (Es'Ey ) (2.1.35) 2.1.3.1.4 The Stokes Vector Polarization o f optical field can be expressed in Stokes spaces. The Stokes vectors are real vectors that have unit magnitude. In this mapping, the optical phase is not included as shown in the next equations. The Stokes vector components depend on the magnitude o f x and y o f optical field components, and real and imaginary part of x and y o f optical field components products. The four Stokes parameter can be arranged in a column matrix and written in the following form: 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f e \ 5 = (2.1.36) The Stokes vector for a monochromatic elliptically polarized light (plane wave) is represented by S = f E 2 + E 2 ^ ^ O x ^ O y E o x - E 0y2 2 E 0X E 0y cos( 8 ) \ 2 E 0 x E 0 y sin(S) (2.1.37) The Stokes polarization parameters can also be expressed in terms o f the orientation and ellipticity angles o f the polarization ellipse y/ and x as S, = Sg cos(2x)cos(2yr ) S2 = S0 cos(2x)sin(2yr) S3 = S0 sin(2x) (2.1.38) (2.1.39) (2.1.40) These relations can be used to relate the Stokes parameters to the orientation and ellipticity angles o f the polarization ellipse as shown in the following equations: 5 , tan( 2y/)~ — 0<y/<7i (2.1.41) sin(2x) = ~ - 0 < x < ir (2.1.42) In addition, the normalized Stokes vector can be expressed in terms o f the orientation and ellipticity angles o f the polarization ellipse as 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. s = cos(2x)cos(2if/ ) cos( 2x ) sin( 2y/ ) sin( 2 x ) (2.1.43) The normalized Stokes vector for the six degenerate polarization states are as follows (see Fig. 2.6): a) LHP: E^^O. S = b )LVP:E0x=0. 1 o k Pj c) Linear +45° Polarized Light (L+45°): E0 x = E^ , 8 = 0. 0 s = s = 1 kOj d) Linearly -45° Polarized Light (L-45°): E0 x = E0y, 8 = n . f 1 ' 0 s = - 1 (2.1.44) (2.1.45) (2.1.46) (2.1.47) 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (0,0,1) Right hand circular (0,-1,0) -45° linear (-1,0 ,0) Vertical linear - ( 0,1,0) 45° linear (1,0 ,0)-------- Horizontal linear Left hand circular Fig. 2.6. Normalized Stokes vectors for the six degenerate polarization states. 2.1.3.1.5 The Muller M atrix Algebra Poincare attempted to solve the calculation difficulty due to interaction o f polarized light with elements that can change the state o f polarization (SOP) o f an optical beam by introducing his famous polarization sphere. However, the Poincare sphere received slight attention in the optical literature. In the late 1940, two new matrix algebras, Jones matrix calculus and Muller-Stokes calculus, for solving polarization 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. problem arose. The former is suitable for describing the polarization behavior in terms o f amplitude and phases and the latter for describing the polarization behavior in terms o f intensities. The use o f these algebras became even more attractive because high-speed computers were also becoming available. Nevertheless, the Poincare sphere is still very valuable because it allows a visualization o f the behavior of polarized light as it propagates through polarizing elements. At nearly the same time that Jones developed his matrix calculus, H. Muller (1943) independently developed another polarization calculus. Muller followed a line beginning with Stokes (1852) and F. Perrin (1942) and proceeded to express the Stokes parameters as a 1x4 column matrix and the polarizer element as 4x4 matrix. It appears that Muller was the first to determine the matrices that now bear his name for the polarizer, waveplate, and rotator. When the incident optical beam propagates through the polarizing element, it emerges with a new intensity and polarization state. Both the incident optical beam and the optical emerging beam are characterized by their four Stokes polarization parameters S, and.S)', respectively, where i = 0, 1, 2, 3. Since there are four input parameters that can influence each o f the four output parameters, the Stokes vector of the output beam S' can be linearly related to the Stokes o f the input beam S as, (2.1.50) ( c ^ 'mo o m0 l m0 2 f s } °0 s\ mI0 mu m!2 mis s , S'2 m2 0 m2 I m2 2 m2 3 s 2 U v ■ ™ 30 m3 2 m33y 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Equation (2.1.50) can be written as a matrix equation in terms o f the Stokes vectors as, S' = MS (2.1.51) where the 4x4 matrix represented by M is called the Muller matrix. The elements of the Muller matrix are real quantities. When an optical beam interacts with an optical polarizing element, such as polarizer, waveplate, and rotators, its polarization states always changes. The polarization states can be changed by: (i) changing the orthogonal amplitude(s), (ii) changing the phase(s), or (iii) changing the orientation o f the components. Now, we can drive the Muller matrices for each o f these following polarizing elements. a) Polarizer A polarizer is an optical element that attenuates the orthogonal components o f an optical beam unequally (anisotropically), so a polarizer is an anisotropic attenuator. Two orthogonal transmission axes can describe the polarizer. These axes are characterized, respectively, by transmission factors p x and p y whose magnitudes are unequal to each other. The components o f the incident optical beam are represented by Ex and Ey and the components o f the optical beam that emerges from the polarizer are E 'x and, Ey respectively. The output and input field components are then E'x = p xEx 0 <px < 1 (2.1.52) 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. E'=pEy 0 <Py < 1 (2.1.53) For complete transmission p x (or p y ) = 1, whereas, for complete attenuation p x (or p y) = 0. If one o f the axes has a transmission coefficient that is zero, the polarizer is called ideal linear polarizer. By substituting (2.1.52) and (2.1.53) into (2.1.32-2.1.35) and using (2.1.32-2.1.35), we can express the Stokes vector o f the output beam S' as, S' = M P0L( p x,py)S (2.1.54) The 4x4 matrix in (2.1.54) is written as M p0L(PX’Py) ( 2 2 Px P y 2 2 Px - Py 0 0 ] 1 2 2 Px - Py Px P y 0 0 2 0 0 2PxPy 0 0 \ 0 0 2P*Pyy (2.1.55) Equation (2.1.55) is the Muller matrix o f a polarizer. In addition the Muller Matrix o f polarizer can be expressed in trigonometric rather than algebraic form. In trigonometric form, we can write p x = p xcos(j3) (2.1.56) Py = Py cos(fi) (2.1.57) where 0 </3< it Substituting (2.1.56) and (2.1.57) into (2.1.55) we then have 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m P 0L(p,P) = - 1 cos(2/3) 0 0 cos(2P) 1 0 0 0 0 sin(2/3) 0 (2.1.58) 0 0 0 sin( 2 P )j For an ideal linear polarizer ( p x fO, p y = 0), The Muller matrix reduces to m p o l (1D = - '1 1 0 0' 2 P X 1 1 0 0 2 0 0 0 0 0 0 0, (2.1.59) For an ideal linear polarizer ( p xfO, p = 0), The Muller matrix reduces to M pol ( ^-) ~ ~ ' f 1 - 1 0 0 ' 2 Px - 1 1 0 0 2 0 0 0 0 , 0 0 0 0 , (2.1.60) b) Waveplate A waveplate is a polarizing element that introduces a phase shift < f > between two orthogonal components o f an optical beam. A waveplate is a phase shifter. Historically, in the filed of optics, however, it is also called a retarder or a compensator. The phase o f a propagating optical beam is given by , 2n < b = — z k (2.1.61) where X is the wavelength, and z is the distance that the wave propagates. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. /L 7t The distance of — corresponds to a phase o f — . Similarly, a propagation distance of 4 2 — corresponds to a phase shift o f n . Two orthogonal axes called the fast axis and the slow axis, respectively, characterize a waveplate. The phase shift along the fast axis is and along the slow axis is - - j , so the total phase shift between two axes is < f ) . The components o f the field o f the emerging optical beam are related to the incident field components by E ' = e 2 Er (2.1.62) E'y =e 2 Ey (2.1.63) By substituting (2.1.62) and (2.1.63) into (2.1.32-2.1.35) and using (2.1.32-2.1.35), we can express the Stokes vector of the output beam S' as, S' = M W P (0 )S The 4x4 matrix in (2.1.64) is written as ( 1 0 0 o ' 0 1 0 0 0 0 cos( < /> ) - sin( ( f > ) K 0 0 sin((f>) cos((j>) y Equation (2.1.65) is the Muller matrix o f a waveplate. 7t For a quarter-waveplate ( < f > = — ), the Muller matrix reduces to (2.1.64) (2.1.65) 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7t M W P( - ) = (1 0 0 0 ^ 0 10 0 0 0 0 - 1 0 0 10 (2 .1.66) The quarter-waveplate can be used to transform linearly polarized light to circularly polarized light or circularly polarized light to linearly polarized light. For a half-waveplate (< /> = it), the Muller matrix reduces to MffP ( ) ' ■ (1 0 0 0 ( 0 10 0 0 0 - 1 0 0 0 0 - 1 (2.1.67) The quarter-waveplate can be used to reverse the orientation and ellipticity o f the polarization state o f an optical beam. Another useful property o f waveplates is that their phases add, that is, if one waveplate is characterized by a phase shift o f (/> , and another by a phase shift < j )2, then the product o f the Muller matrices o f the two waveplates leads to a Muller matrix whose phase is the some o f the phases o f each waveplate so < j > = < /> , + < j )2, c) Rotator A rotator is a polarizing element that rotates the orthogonal components o f an optical beam ( Ex(z,tj and Ey(z,t) ) through an angle 6 . The angle 6 describes the rotation of Ex(z,t) to E'x(z,t) and Ey(z,t) to E'y(z,t) . The amplitude o f output and input field components are then E'x = Ex cos(6) + E v sin(0 ) (2.1.68) 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ey = - E x sin(0) + Ey cos(0) (2.1.69) By substituting (2.1.68) and (2.1.69) into (2.1.32-2.1.35) and using (2.1.32-2.1.35), we can express the Stokes vector of the output beam S' as, S ’ = M R0T( 6 )S (2.1.70) The 4x4 matrix in (2.1.70) is written as M r o t ( 9 ) = f1 0 0 0 0 cos( 26) sin( 20) 0 0 - sin(20) cos(26) 0 0 0 0 1 (2.1.71) Equation (2.1.71) is the Muller matrix o f a rotator. Note that a physical rotation through an angle 0 leads to the appearance o f 20 in the Muller matrix rather than 0 because we are working in the intensity domain, in the amplitude domain it appears as 0. Rotators are used primarily to change the orientation angle y/ o f polarization ellipse. Using (2.1.71), the orientation angle o f the emerging beam is, tan(2V ’) = (2L 72) Sj cos(26) + S2 sin(20) $ Substituting the orientation angle o f the input filed (tan(2y/) = — - ) into (2.1.72) tan(2y/')-tan(2y/ - 2 0 ) (2.1.73) so if/' = y/ - 0 (2.1.74) 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Equation (2.1.74) shows that a rotator rotates the polarization ellipse of the incident beam through an angle 9. The sign o f 6 is negative because the rotator is defined to be clockwise. If the rotation is counterclockwise, that is, 6 is replaced by - 6, and then we find the sign is positive (y/f = y/ + 9). d) The Muller Matrices for Rotated Polarizing Components All polarizing elements are rotated in an optical system. As shown in Fig. 2.7, the axes o f polarizing component are rotated through an angle 9 and are along the x - andy'-axes. The axes of the incident beam, however, are along the x- andy- axes. In order for the incident beam to interact with the rotating polarizing element, we must determine the components of the incident beam along the axes of the rotated polarizing axis. out Fig. 2.7. Propagation of an input beam through a rotated polarizing element. Then, after the beam has passed through it, we must determine the components of the emerging beam that are along the original x- andy- axes. It is clear that the components o f the Stokes vector S' o f the emerging beam can be expressed in terms o f the components of the Stokes vector S o f the incident beam as 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S' = M rot ( - 0 )■ M ■ M ro t (0 )S (2.1.75) where M is a Muller matrix characterizing the polarizing element, M R 0T (0 ) is the Muller matrix for rotation of the incident beam along the x'- and y'- axes, and M rot(~ 0) is the Muller matrix for rotation o f the emerging beam along the original x- and y- axes. Now, we show the Muller matrix for a rotated polarizer and a rotated waveplate. By substituting (2.1.58) and (2.1.71) into (2.1.75), the Muller Matrix for a rotated polarizer is Mp o l (0) = ^ j 1 cos( 2 p )cos( 29) cos( 2 P )sin( 26 ) 0 cos(2p )c o s(29) cos2(29) + sin (2 p )sin 2(2 6 ) (1 - sin 2 p )sin (2 6 )cos(26) 0 cos(2P ) sin(29) - (1 - sin 2 p )sin (2 6 )co s(20) sin2(2 6 ) + sin (2 p )co s2(2 9 ) 0 0 0 0 sin( 2P ) (2.1.76) Substituting (2.1.65) and (2.1.71) into (2.1.75), the Muller Matrix for a rotated wavepalate is M rot(0)-- ( 1 0 0 o ' 0 cos2 (2 6 ) + cos(<j>)sin2 (2 0 ) (l-cos< j> )sin(2d)cos(26) sin (^ )s in (2 0 ) 0 (l-cos< j> )sin(20)cos(20) sin 2 (2 6 ) + cos < j > cos2 (2 9 ) -sin((/> )cos(26) 0 - sin(<j>)sin(26) sin(<j>)cos(26) cos(f) (2.1.77) 2.1.3.1.6 The Jones M atrix Algebra As mentioned before, Poincare introduced his polarization sphere to overcome the difficult calculations, which were required to describe the propagation of polarized light through polarizing elements. In spite o f the elegance o f the Poincare sphere it was surprisingly difficult to apply. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In 1941 and 1942, R.C. Jones borrowed some o f the quantum mechanical mathematical developments and applied them to express the classical electric field components (amplitudes and absolute phases) in terms o f a 2 x 1 column matrix and the polarizing elements as a 2 x2 matrices. The Jones matrix has played a key role in the development of fiber optics. Most notably, because it describes the polarization in terms o f amplitude and phase that allow results obtained by Maxwell’s equation which are also explained as amplitudes and phases to be written as Jones Matrices. In addition, it is easy to find the eigenvalues and eigenvectors of these equations and, as shown later, much of the progress made in the study and understanding o f PMD has been done using the Jones matrix calculus. An optical filed propagating through either fiber or polarizer element can be expressed as a complex or real vector as show in the equations (2.1.78) and (2.1.79). E(x, y, z) = ej(^ 2){E 0xe ^ ex + E0yeiS’ ey } (2.1.78) E(x,y,z) = {E 0x cos(coct -/3z + 8x )ex + E0y cos(act - /3z + 8y )ey } (2.1.79) where cac, j3 , and 5 are optical frequency, optical phase, and propagation constant, respectively. Jones showed an optical filed can be mapped in 2D space that is called Jones space. The Jones vectors are complex vectors that have unit magnitude. This mapping expresses an optical filed in the complex domain using two main components (phase difference between x and y optical components and ratio x 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. component and envelop of optical field). The normalized Jones vector can be expressed as the following equation: f F ^ Z 'O x Jones j ( S r Sx ) (2.1.80) By using the following auxiliary relation, we can rewrite equation (2.1.80) as cos( a ) sin( a )ejS (2.1.81) where 8 - 8 - 8 X, and cos( a ) = u 0 x \E\ E0x - \E\ c o s ( a ) (2.1.82) E0y = |£j sin (a) (2.1.83) Substituting (2.1.82) and (2.183) into (2.1.32-2.1.35), the normalized Stokes vector can be expressed in terms of 8 and a as, c = Jones cos( 2 a ) sin( 2 a ) cos( 8 ) sin( 2 a )sin( 8 ) (2.1.84) Using (2.1.84) and (2.1.41-2.1.42), we can find the orientation angle y/ of polarization ellipse in terms o f 8 and a as, 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. y/ = ~ tan 1 (tan( 2 a )co s( 8)) X = ~jsin 1 (s^ n( )sin( 8)) (2.1.85) (2.1.86) The Jones representation has been shown in Fig. 2.8. Fig. 2.8. Jones representation. In addition, we can express the components Stokes vector S f in terms o f the components Jones vector using the Pauli spin matrices as Sj - S jonesG J o n e s where the Pauli spin matrices are defined as a l = (1 0 > '0 1 ) ' 0 - P i a . = » a , = ,0 - h 2 J 3 J o ) (2.1.87) (2.1.88) and while pauli spin vector in Stokes space is S = (a 1,(T2 ,a3 ^ (2.1.89) The normalized Jones vector for the six degenerate polarization states are as follows: a) LHP : E ^ = 0 . 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. b)LVP: E0 x = 0. Jones r a o' ' c) Linear +45° Polarized Light (L+45c ): E^ = E„ , 8 = 0 Jones 4 ~ 2 d) Linearly -45° Polarized Light (L-45°): E0 x - E^, 8 = n J o n e s 4~2 \ ~ b Q )RCP-E0x= E 0y, 8 = S - ± J o n es 42 u . f)LCP: £ ^ = £ ^ , 8 = 3 k T i 1 \ b (2.1.90) (2.1.91) (2.1.92) (2.1.93) (2.1.94) (2.1.95) J o n e s ^ Now, we can drive the Jones matrices for each o f these polarizing elements. In order to this, the Jones matrix calculus assumes that the components o f a beam emerging from polarizing component are linearly related to the components of the incident beam. This relation can be expressed as 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ' K ) J j u j a Y e .' ke ',J (2.1.96) y j l l J 2 2 ) \ E y Equation (2.1.96) can be written as a matrix equation in terms o f the Jones vectors as, C " _ TC 0 Jones ~ Jones (2.1.97) where J is the Jones matrix o f the polarization element. Now, we can drive the Jones matrices for each o f these following polarizing elements. a) Polarizer A polarizer is characterized by K = P*EX 0 <px< 1 E ' y = P y E y 0 < f y < 1 Using (2.1.98-2.1.99) and (2.1.96), the Jones matrix o f polarizer is r J P* p j For an ideal linear horizontal polarizer, this equation reduces to O 0^ J POL ~ K 0 0; J - u POL (2.1.98) (2.1.99) (2 .1.100) (2.1.101) For an ideal linear vertical polarizer, this equation reduces to (2.1.102) In addition, we can write the Jones matrix a homogeneous elliptical polarizer as 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. J E p x cos2 ( a ) + p sin2 ( a ) ( p x - p )sin (a )c o s (a )e - j S \ ( p x - p )sin (a )c o s (a )e +jS p x sin2( a ) + p cos2( a ) (2.1.103) where a and 8 determine the type o f polarizer, b) W aveplate As mentioned before, two orthogonal axes called the fast axis and the slow axis, respectively, characterize a waveplate. The phase shift along the fast axis is ^ and along the slow axis is - —, so a waveplate is characterized by E ' = e 2Er 2E> (2.1.104) (2.1.105) Using (2.1.104-2.1.105) and (2.1.96), the Jones matrix o f waveplate is J Wp — 0 K 0 e J^ (2.1.106) The two most common types of waveplates are the quarter-waveplate and the half- TC waveplate while ^ = — and n , respectively. The Jones matrices are J - e 4 J QWP e ( 1 0 y p - J 1 0 ' 0 - h (2.1.107) JHWP= i \ \ (2.1.108) In addition, we can write the Jones matrix a homogeneous elliptical retarder as 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. J R E T (2.1.109) r it _ it it -it ^ e 2 cos2( a ) + e 2 sin2( a ) ( e 2 - e 2 )sin (a)cos(a)e~ jS it -it it -it y( e 2 - e 2 )sin (a )c o s (a )e + JS e 2 sin2( a ) + e 2 cos2( a ) y where a and 8 , determine the type o f retarder. c) Rotator The Jones matrix form for a rotator is obtained from the familiar equations for rotation, E'x - Ex cos(9) + E sin(d) (2.1.110) E'y = - E x sin(6 ) + Ey cos(0) Using (2.1.110-2.1.111) and (2.1.96), the Jones matrix o f rotator is j _ COS( 0 ) Sin<0)' R O T {-sin(d) cos(9)y It is useful to find the Jones matrix for rotated polarizer and waveplate. For a rotated polarizer, using the following rotation transformation: J POL (6) = j(-e)jP O L j(9) we find (2.1.111) (2.1.112) (2.1.113) ^px cos2(9 ) + p y2 sin2(9 ) ( p x - p y )sin (9 )co s(9 ) ( Px - p y )sin (9 )co s(9 ) p x sin2(9 ) + p 2 cos2(9 ) J pol(0 ) = (2.1.114) For a rotated waveplate, using the following rotation transformation: J W P (9 ) = J ( - 9 ) J W P J ( 9 ) (2.1.115) we find 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Jwr(0) = cos(— ) + j sin(—)cos( 29) 2 j sin(—)sin( 29 ) 2 2 2 2 j sin(^) sin(29) c o s ( - j sin (^) cos(2 9 ) (2.1.116) r u . . A Ico s(2 9 ) sin(29) J W p (6 ) ~ c o s ( - ) I - ] sin(- ) (2.1.117) 2 2 \sin(29) - cos(2 9 ), 2.1.3.2 Polarization Mode Dispersion SMFs are actually bimodal, since they can support two perpendicular polarizations of the original transmitted signal (fundamental mode). In an ideal fiber (perfect) these two modes are indistinguishable, and have the same propagation constants owing to the cylindrical symmetry o f the waveguide. However, this birefringence (induced by core ellipticity and non-circularly symmetric stress) causes the power in each optical pulse to split between the two polarization modes o f the fiber and travel at different speeds, creating a DGD between the two modes that results in pulse spreading and ISI (see Fig. 2.9). This phenomenon is called PMD. Slow axis (ny ) Birefringence Fast axis (nx ) DGD Fig. 2.9. Pulse spreading due to PMD. 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In a short section of fiber (~ meters), the birefringence can be considered uniform. The difference between the propagation constants o f the slow and fast modes can be expressed as [35] con con f coAn A/3 = — - = (2.1.118) c c c where co is the angular optical frequency, c is the speed o f light, ns is the refractive index o f the slow mode, and nf is the refractive index o f the fast mode. The differential index o f refraction is a measure o f birefringence in the fiber, and is usually between 10'7 and 10"5. The time difference between two modes ( A t ) can be expressed from the frequency derivative o f thqA/3 . A t _ d L dco ' Anco'' I c An co dAn c dco (2.1.119) where the unit is picoseconds per kilometers (ps/lcm) o f fiber length. In a short fiber where the birefringence is uniform, the fiber length dependency of A t is linear. The two parameters PMD and DGD are closely related. However, they differ in that the DGD is always expressed in terms o f the time delay whereas the PMD can be expressed for short lengths o f fiber in units o f ps/km and for long lengths o f fiber in units o f ps/Vkm. Thus, we have two PMD measurement units but only one DGD measurement and we can write DGD( p s ) = PMD( p s /k m ) ’ lenght( km ) (2.1.120) D G D ( p s ) — P M D ( p s / -Jkm ) • -Jlenghtf 4km ) (2.1.121) 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The two major causes of PMD in an optical link are: (i) random geometric and stress variations along the fiber core and (ii) birefringence of in-line components. Ideally, the core o f a SMF would be circular, and remain so under stress. Yet in practice it is slightly elliptical, especially in older fibers that were manufactured and deployed in the 1980s, when bit-rates and distances were low enough for PMD to be disregarded as a significant issue. Even if the fiber core remains circular under stress, the refractive index profile may be altered giving rise to PMD. Fig. 2.10 shows the origin of the optical fiber birefringence. The intrinsic asymmetries o f the fiber remain fairly constant over time, while externally induced mechanical stress due to fiber movement and environmental perturbations lends a dynamic aspect to PMD. The mechanical stresses on an optical fiber can originate from a variety of sources including: (i) daily and seasonal heating and cooling [36] and (ii) nearby vibration sources. /intrinsic Birefringence} f Extrinsic Birefringence Elliptical geometry Stress Lateral stress Bending Twisting by non-circular core )[ Fig. 2.10. Origin o f PMD. Although much fiber is deployed in the ground and often within conduits, it is still subject to temperature variations and mechanical vibrations. For example, the data in Fig. 2.11(a) and (b) shows how the PMD of a 48.8-km buried fiber and 52-km fiber fluctuates due to temperature changes over night [37] and mechanical 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vibrations. [38]. As shown in this figure, PMD fluctuates in milliseconds to minutes scale due to mechanical vibrations however; it varies in hours to days scale because o f temperature changes. In addition, much fiber is deployed alongside railroad tracks because of the ease of right-of-way and construction. However, vibration from passing trains can contribute to stress on the optical fiber. Fiber that is not buried next to railways and highways may be deployed aerially; in this scenario, wind can cause swaying o f the fiber cable and can contribute to PMD. 0 2.0 1 1.5 O 18 o d 14 E £ 10 Slow Fluctuation 48.8 km buried cable E 3 O ( 400 800 Time (min) (a ) 15 F a s: F luctuation 52 km fiber <Yr >=2.8 p s 10 5 0 9.55 16.70 23.85 30.95 38.05 45.20 Time S p an (m s) (b) Fig. 2.11. PMD fluctuations in a fiber due to (a) daily changes in temperature and (b) mechanical vibrations. The most important aspect o f PMD is that it is a statistical process that causes a functioning system to always have some finite probability o f having an outage (an event when the power penalty exceeds some unacceptable level). Owing to the random variation in the local birefringence along a fiber span, the PMD o f a long fiber accumulates according to a three-dimensional random-walk process that leads to a square root o f transmission-length dependence, with units typically specified as ps/Vkm [31,39]. To first-order, PMD is simply described by the DGD and the 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. splitting ratio of the optical power launched into each principal states o f polarization (PSPs) (e.g. the worst case penalty occurs for a splitting ratio o f 0.5, meaning the power in each pulse is split equally between the two PSPs). It has been shown both analytically and by experiment that the DGD follows a Maxwellian distribution versus time or wavelength (see Fig. 2.12(a)), while the angle between the input SOP and the fiber PSP (related to the splitting ratio) is uniformly distributed [31,40-41]. In addition, the average DGD (<dgd> or < Ax > ) is a property o f the fiber that remains constant over time and wavelength and grows as the square root o f the fiber length. The probability density function (PDF) o f d g d = Ax is given by 32 dgd2 - 4 d g d 2 / d g d (dgd) = — — - J exP( , , , > n < dgd > 7t < dgd > Fig. 2.12(b) shows a Maxwellian distribution with < dgd >~ 40 ps. (2.1.122) 0.4 c 0.2 3 O o n Maxwellian fit i t 0 2 4 6 8 50 10 1 0.1 0 20 40 60 80 100 DGD[ps] dgd (a) (b) Fig. 2.12. (a) A histogram of measured DGD data for a fiber link shows that it has a probability distribution that closely approximates a Maxwellian PDF and (b) a Maxwellian distribution with <dgd> -4 0 ps. Moreover, environment changes cause PMD to vary stochastically in wavelength. Fig. 2.13 shows the wavelength dependence o f an optical fiber with < dgd > - 4 0 ps. 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 a o o 40 Eye clo su re Penalty (dB) 1530 1540 1535 X (n m ) Fig. 2.13. Measurement of DGD o f a spooled fiber with 40-ps average DGD [42]. In addition to first-order DGD, additional effects o f pulse spreading or compression and depolarization o f the input pulses can occur due to higher-orders of PMD. The frequency dependence o f both the magnitude (DGD) and direction (PSPs) o f the PMD vector lays the foundation for these higher-order effects [31-32], In the presence of higher-order PMD, an input pulse can spread and become depolarized, as the different frequencies making up the pulse spectrum will experience a slightly different polarization evolution as they propagate down the fiber, due to the frequency dependent nature o f PSPs. The conceptual illustration in Fig. 2.14 shows how these effects can be considered to arise from a concatenation o f many birefringent sections with randomly varying PSPs that split the main optical pulse into many optical replicas with orthogonal orientations and different relative time delays. The frequency-dependent nature o f higher-order PMD adds additional system impairments, especially after compensating for first-order PMD [43], and requires more complex monitoring and compensation techniques [44-45]. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Input Pulse Detected Pulse Random PSP orientation in each section Fig. 2.14. Conceptual illustration of higher-order PMD effects on an optical pulse. Another important statistical parameter describing the behavior o f the randomly varying PMD vector is the frequency autocorrelation function (ACF). This function establishes a PMD correlation bandwidth for an optical fiber with a given average DGD [46-47], Thus, two wavelength channels that are separated by more than this bandwidth will have uncorrelated PMD vectors. The ACF for a fiber with < dgd >=2.8 ps is shown Fig. 2.15. The autocorrelation bandwidth narrows as the average DGD o f the fiber link increases. Thus, for fibers with appreciable PMD, a separate PMD monitoring and compensation module will be required for each channel in a multi-channel WDM system, since PMD will affect each channel independently. It has been shown that the ACF o f the PMD vector plays a key role for WDM PMD monitoring, compensation, and emulation. ACF Bandwidth: Akc °c 1/ < d g d > <dgd> = 2.8 ps (127 km fiber) A X (n m ) Fig. 2.15. PMD vector frequency ACF showing that the PMD o f wavelengths separated by more than ~l/<dgd> become uncorrelated. 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The quantity o f bit errors encountered at the receiver is directly influenced by the amount o f PMD in a fiber optic transmission span. In digital optical fiber communication system, estimating the power penalty incurred can assess the PMD effects. The expression for the PMD induced power penalty is [36] £z= A ^ L j ( l z l l (2.1.123) T where s is the power penalty in dB, A t is the DGD, y is the power splitting ratio between the two component modes (0 < y < 1), and T is the full width at half m a x im u m o f the light wave pulse. The factor A is a dimensionless parameter determined by the pulse shape (NRZ, RZ, duty cycle) and receiver characteristics. Another relation that gives an estimate of the PMD induced limitation on the bit rate and the span of a digital optical fiber communication system is [35] (2.1.124) where B and L are the bit-rate (Gbit/s) and link length (km), respectively, and PMD has the units o f ps/Vkm. This relation was arrived at by considering the case that the PMD induced delay must be less than 14% o f the bit period in order to avoid incurring PMD-induced power penalty o f 1 dB or greater for a period o f 30 min per year [35], Fig. 2.16 shows the bit-error-rate (BER) fluctuations due to the variable nature o f PMD and the influence o f temperature on its variability. 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. § i 0 4 8 12 16 Elapsed time (hours) Fig. 2.16. BER fluctuations due to temperature changes. Additionally, in a cascaded fiber link, there may be many discrete components such as isolators, couplers, and wavelength multiplexers that are polarization sensitive because of intrinsic molecular asymmetries (anisotropy) in the optical materials or from asymmetries that were created in the waveguide during device fabrication. Although the PMD o f a single component may be negligible, the effect o f many cascaded components can add significantly to the PMD in a long fiber link. The combined PMD-induced broadening in a long link may be up to a few tens o f ps, which can degrade systems operating at > 10-Gbit/s. Fig. 2.17 shows a plot o f fiber PMD versus maximum transmission distance for a 40-Gbit/s NRZ system. Note that when the effects of the PMD o f the in-line components from the amplifier sites are added, there is now an ultimate distance limit o f -5 5 0 km even when there is no fiber PMD. Signal through fiber Signal through referenc^ J fiber | ■ ^S u n set ' Sunrise 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 E 0.8 it a 06 Q 2 0.4 Q . w © JO 0.2 E 0 0 100 200 300 400 500 600 Maximum Transmission Distance (km) Fig. 2.17. Transmission distance limitations for a 40-Gbit/s NRZ system due to the combination of fiber PMD and the PMD of the cascaded in-line optical components found in amplifier sites. 2 . 1 .3 .2 .1 PMD in the Jones Space The phenomenon of PMD in SMF was first recognized and measured by Rashleigh and Ulrich in 1978. They noted that in multimode fiber optical signal transmission, the maximum bit rate is limited by the difference in the group velocities o f the various exited modes o f the fiber. As a result, each pulse broadens so there must also exist a difference between the group velocities of the two modes (polarizations in SMF). They claimed without proof that in long fibers the statistical mode interchange due to non-uniform birefringence reduces and the delay difference is oc 4 l instead o f oc L as in the short fiber. In 1986, Poole and Wagner proposed a phenomenological mode o f PMD for long fiber lengths base on the observation that for a linear optical transmission medium in which there was no PDL. They showed that there exist two orthogonal input states o f polarization for which the output sates o f polarization are orthogonal and showed to first-order PMD no dependence on the wavelength. Based on this key 5 8 1 ps PMD in Amp. Sites No PMD in Amp. Sites No PMD In 1 ps PMD in Fiber , components components Old fiber PMD = 0.5 ps/km1 '2 26 26 New fiber PMD = 0.1 ps/km1 /2 625 320 Future fiber .PMD = 0.05 ps/km1 / 2 2500 480 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. observation in 5 km pieces o f SMF they proposed these states of polarization a convenient basis set for the characterization of PMD o f arbitrary lengths and configurations. They called these two orthogonal states o f polarization PSPs. In order to find these PSPs and DGD between them, we consider a linear medium described by a complex transfer matrix T (co). If we assume there is no PDL, then the Jones transfer matrix o f the fiber link can be modeled as T (c o )^ e ‘ }(m)U(co) (2.1.125) where j3(co), in general, is a complex constant and U(co) is the unitary matrix f Uj(co) u2(co)^ U ( g> ) = (2.1.126) K - u 2 (co) u ' ( g>) j We start from a general formula that relates the output optical field to a monochromatic input optical field E0 u , ( a}) - T ( co)Ein ( co) E o u t ( a > ) ~ e P (< a )U ( co)Ein ( co) (2.1.127) (2.1.128) where Ein(co) and E ^ c o ) are vectors representing the input and output fields, respectively. These fields can be written as E J c o ) = E in( co)ein(a>) (2.1.129) E o u , ( Q >) = ejK" ,(c o > E mt ( co) em l ( co) (2.1.130) 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where </>Jo)), < / > ou t(co), E J c o ), E0 J a ) , ein and e0 J a ) are the input and output phases, envelopes/amplitudes and normalized input and output states o f polarization, respectively. It is clear if PDL and the frequency dependent attenuation are negligible we can relates the input and output Jones vectors as So u t,J o n J c o ) = e > Ma)U (m )S in J o n J c o ) (2.1.131) where Sin J o n e s (co) = ein ( a ) and So u t J o m s (co) = ea u t (m). Equation (2.1.128) shows that the output SOP will vary with the frequency o f the input wave for an arbitrary but fixed input SOP. By taking the derivative o f (2.1.128) with respect to frequency and assuming all the frequency components o f the input optical field are parallel to each other ( --^ --6)~ - 0 ). This gives dco aL W , m a l J a , eK .,i[dJ(av^ m a ]i u(aj d A ^ lf(2 .u n ) dco da da da da (2-1.133) da da \Ein( a i da da In addition, we find the derivative o f the output optical field = < 2-L134> da da \Eoa(a^ da 1 1 da By substituting (2.1.128) in (2.1.134), we then have M J e L = [ 8 U U a » + Re{P(a>)}).... j ... 8\E j M ]e^ u(o))E. (a ) + e ^ > \ E da 1 8a \EJa)\ da J ' ' I 'I da (2.1.135) 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. By comparing equations (2.1.133) and (2.1.135) and in order to find output states of polarization that are invariant with frequency ( - o ), we then have dco [ dUM _ . 8 ( 4 ,( » ) - (co) - lm { / ) ( „ ) } ) u ( a ) ] K ( a ) = 6 (21136) dco dco By defining a new parameter “J c ” where k = d W o u t ( (° ) ~ b n , ( < * > ) - l m ( P ( a ) } ) dco or r± (co) = k± + + Im { j3'(co)} . dco It is clear that the eigenvectors - jkU (co)] are equal to the PSPs of the dco medium. We can show that the eigenvectors are e+ m(a>) = - 1 ■ u '2(a>) + jk +u2(co) -u'2(co) + jk +u '2( co) 1 ^- ju ’ 2( co) + k+u2(co)) (2.1.137) 1 (-u'j(co) + jk_u2(co) -u'2(co) + jk_u'2(co) ju'2(<o) + k_u2(co)) e i„(co) = - (2.1.138) where k± = ±^j\u',(co)\2 + \u '2(co)\2 . From (2.1.137) and (2.1.138), we see that e'in+(c o ) » e in~(co) = 0 e*in* (co) • ein ±(co) = 1 (2.1.139) (2.1.140) so (co) and ein (co) are orthogonal pair. However, the PSPs are generally frequency dependent due to the nature o f T (co). 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In addition, it is clear that the two corresponding output states ein +(co) and e - m (co) are also orthogonal to each other by applying (2.1.128) to the solutions (2.1.137) and (2.1.138) as shown in (2.1.139). The arrival times of the two pulses on the two PSPs are r± (co) = ±J\u'j (<otf + \u '2 (a>tf + — ( — + lm { J3'(co)) (2.1.141) v do) Equation (2.1.141) can be used to determine propagation delay difference between two replicas on the two PSPs so t ( co) = t + ( cd) - t ( co) = 2 ^ \ u '1 ( c o)\2 + \ u '2 ( 0))\2 = 2^jdet(U(co) (2.1.142) Equations (2.1.137-2.1.138) and (2.1.142) show that not only PSPs but also DGD are function of frequency resulting in higher-order PMD effects. 2.1.3.2.2 PMD in the Stokes Space The change o f polarization o f light on transmission through a fiber can be described as the rotation o f its Stokes vector. There are matrix forms that highlight these rotational properties (i.e. the rotational axis r and the rotation angle c f >). These matrices are basic for an understanding o f PMD fundamentals, and they have been used for the measurement of PMD vectors in the laboratory. In this section, we discuss several expressions for such matrices in the Jones and Stokes spaces, PMD effect in the 3D Stokes space, and the connection between the Stokes matrices and the Jones matrices. 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PMD can be explained as a rotation form in the Jones space. Generally, any unitary matrix U(co) can be expressed in the form U ( ( o ) - X,(co)rl (a>) + X2(oo)r2(co) (2.1.143) where Xj(co) , X2(co) , r,(co) , and r2(co) are its eigenvalues and column eigenvectors, respectively. Since eigenvalues and eigenvectors o f unitary matrix must be of unit magnitude and orthogonal to each other, the unitary matrix can be expressed in the rotational form z J l i t U ( m ) - e 2 r,(co)r*(co) + e 2 r2(a>)r2 (co) (2.1.144) As we discuss later, ( j) is the rotation angle in the 3D Stokes space. For showing analytical relationship between Jones space and Stokes space, we use equation (2.1.144) and express it in the alternate form U(a>) - 1 c o s ( ^ ) - j f • a s in ( ^ ) (2.1.145) U(co) = e 2 (2.1.146) where r is the rotation axis in the 3D Stokes space. As we discuss before, we can relate the input and output Jones vectors to the input and output Stokes vectors o f the light after passing through a fiber with PMD as $in!stokes = $ (2.1.147) ^ o J ,S to k e s = $ out, Jones O' t ^ O U f jo n e s (2.1.148) By substituting (2.1.131) into (2.1.148), we then have 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S ^ ,S lo k e s = S t in j o n e sU ^ ((a)alU((D)Sin J o n e s (2.1.149) We assume that the output Stokes vector can express in terms o f the input Stokes vector as $ out,Stokes = R ( in,Stokes (2.1.150) Using equation (2.1.147) and (2.1.150), we can relate the output Stokes vector to the input Jones vector as S out,Stokes = S in,Jones R ( (O )8S in J o n e s (2.1.151) By comparing (2.1.151) and (2.1.149), we can convert the rotational form of the Jones matrix U(co) into the isomorphic form for the matrix R(co) in Stokes space R (co)a = U* (oo)oU(co) (2.1.152) Using the equation (2.1.152), we can relate R(co) to the elements o f the Jones matrix U ( co ) as R(co) = 2 2 * * \u1(coj[ - \u 2(co)\ 2 R e { u fc o ) u 2 (co)} 2 Im{u,*(a>)u2(a>)} - 2 R e { u ,( a ) u 2(co)} R e { u / ( c o ) - u 22 ( a ) } - I m { u j 2 (<o) + u 22 (co)} - 2 I m { u j( a ) u 2( a ) } I m { u / (a > )-u 22 (a>)} R e { u 2 (co) + u 22 (co)} (2.1.153) Using equation (2.1.152), we can convert the rotational form o f the Jones matrix U ( co) into the isomorphic form for the matrix R(co) in Stokes space. U* (co)dU(co) = (cos( < j > ) ) a + ( 1 - cos( $ ))r( r » 6 -) + (sin( <f>))fxa (2.1.154) Using the spin vector rules and comparing o f (2.1.154) with (2.1.152) yields the rotational form o f R(co) in Stokes space R (co)~ rr + (sin(< / > ))r x -{cos(<f>))(r)x(rx) (2.1.155) 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R(co) = e _ j(f*) (2.1.156) ( 0 ~ r3 where rf = V 2ri V i r2r3 and r = r3 0 - n J i r3 r2r3 r3r3, C V 2 r l o J Equation (2.1.155) shows that for any input Stokes vector ( Sin S lo k e s ), Smt S to k e s represents a right-handed rotation of Sin S to k e s through an angle < f > about the direction r . As shown in Fig. 2.18 and in equation (2.1.150), if polarized light is launched into the fiber its output SOP will vary with frequency (<w). The following equations show how output SOP is related to the frequency derivation o f output SOP. By assuming that the input Stokes vector is invariant with frequency, we then have dS, in,Stokes dco = 0 (2.1.157) By taking the derivative o f (2.1.150) with respect to frequency, this yields a l J out,Stokes _ Q R ( c O ) n - I / ■K ( (OJoo v tS to k e s dco dco (2.1.158) Since dR(co) dco expressed as R~’(co) is an anti-symmetric matrix, equation (2.1.158) can be dS. out .Stokes dco - - Q (c o )x S i out,Stokes (2.1.159) 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 2.18. Output polarization state evolution on the Poincare Sphere. The vector, £2(co) , which is a three-component birefringence vector in 3D Stokes space is called PMD vector and can be expressed in terms of the rotation matrix in Stokes space as dR(co) Q (co)~ - dco -RT'fco) (2.1.160) By substituting Equations (2.1.155) into (2.1.160), we can express Q (co) in terms of the rotational variables r and < j > as D (co) - ^ - r + sin(<f>)^—-(l-c o s(< l> ))^ —y.r dco dco dco (2.1.161) In addition, by substituting (2.1.153) into (2.1.160), we can find Q (co) in terms of the unitary matrix U(co) elements as Q ( c o ) - 2 j ( u ’ l (co)u!' ' (co) + u '2( co)u2' ( co)) 2Im{u'J(co)u2(co)-u '2(co)uI(co)} 2 Re{u'1(co)u2(co)-u '2(co)u1( co)} (2.1.162) 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Moreover, by comparing equation (2.1.162) with (2.1.42) and (2.1.137- 2.1.138), we can find that the length of PMD vector is equal to DGD and PMD vector is a Stokes vector pointing in the direction o f the slow PSP with a length equal to DGD. Thus, we have DGD(a)) = |Q(co)\ = ^£2j (co) + Q 2 2 (<o) + Q ] (co) (2.1.163) Since each o f three components of PMD vector in 3D Stokes space is independent random Gaussian variable, the length o f PMD vector that is equal to DGD has a Maxwellian distribution. 2.1.3.2.3 Higher-Order PMD As shown in the previous section, PMD vector varies when the optical frequency changes. This variation results that different frequency components o f modulated signal experience different PSPs and different amount o f DGD since PSPs and DGD are frequency dependent. In optical fibers PMD is described as by the vector, Q (c o ), in Stokes space in the form Q(co) = | Q(co )\q(co) = D G D ( co )q(co) (2.1.164) where q(co)= is a unit Stokes vector pointing the direction of a PSP of the Q (aj^ fiber link and DGD(co) - 1 Q ( c o is the differential-group-delay. 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. By using the Tailor expansion, we can express PMD vector as the following equation: 18q(&) n(co) = DGD(m0 )q(mB ) + ( dDG®( a ) q(m) dm + DGD( m)- dm C O — (O q ) (m -m 0) + --- (2.1.165) when Q (m ) changes with m , the radiant frequency deviation from the carrier, additional impairment occurs, which, to the next order o f importance is described by high-order PMD vector. For example, we can describe the second-order PMD vector as It has been shown that the term = dDGpfaQ + D C D (m )d J M dm dm dm dq(m) ■ (2.1.166) dm induces depolarization and the dDGD(at) term causes polarization dependent pulse compression and pulse dm broadening [29]. Since q(a>) is a unit vector, is perpendicular to q(co), the first term on the dm right hand side o f (2.1.166) is — — - dm the component o f ^ ( a}) tfaat is parallel to dm f2(m ) , while the second term is dm , the component o f - - - - - -- that is dm perpendicular to Q (co) . Fig. 2.19 shows a vector diagram o f the principal of parameters and their interrelationships. 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T C C i I DGD(ao) ^ ( “ o) Fig. 2.19. Schematical diagram o f the PMD vector. Note that the angular rotation rate (5cp/5co) of the PMD vector is 2k. The parallel component o f causes polarization dependent chromatic 8a> dispersion (PCD). In accordance with the dispersion measure D , the PCD is given by P C D - ) d .B 9 P M . (2.1.167) X dco where c is the velocity of light, X is the wavelength, and PCD is expressed in ps/nm. The component o f that is perpendicular to Q (co) , rotates the PSP’s with dco frequency, as described by the derivative . As shown in Fig. 2.19, the angular dco rate o f rotation is , which we express in ps. In addition, it has been shown that da Q ((o) and are spherically symmetric random vectors [32], Using this fact, dco the statistical relation between DGD o f the fiber and the PCD is [42] 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 600 ? 3 00 c & 0 Q O Q--300 -600 <dgd> = 40(p l V ' : , i II, j ! i < 1 i > * * ti‘* 1 1 ' * ' v; tS ' " , J , i * ■ ■ •'(•V *.V 1 ':1 •! i * 1530 1540 1535 A . (nm) Fig. 2.20. Measurement of PCD of a spooled fiber with 40-ps average DGD [42]. (2.1.168) Moreover, it has been shown that PCD changes with wavelength (Fig. 2.20) and the d \D ( co )\ PDF o f -i-:----- , which is the p c d term, is given by [42] dco f pc d ( pcd ) : n l 2 / 7zpcd. ~— sech (— -j-) 4p 2p (2.1.169) where p depends on the fiber properties and can be related to the mean DGD by p = l^ E { \n \} (2.1.170) The PDF o f the zero mean random variable PCD has the functional form o f the energy density of a first-order soliton as shown in Fig. 2.21(a). Moreover, PDF of depolarization rate and \f2ai\ have been discussed in [48]. PDF o f depolarization rate and \£2m J\ for a 14.7-ps mean DGD have been shown in Fig 2.21(a) and (b). 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.0003 •r a <dgd> » 55.2 ps 1 0 '1 < * # 1 a | 1 °j 3 <dgd> = 14.7 ps Theory — ^ Simulation O Measurement— 10 * o >2000 ■ s q ; : i irK sf 10*2 H 4 1 0 1 4 ! '*-10* | x <dgd> - 14.7 ps Theory — — — Simulation o %Dj j M easurem ent-—— jijj^ 0 2000 0 20 40 60 80 0 200 400 600 |“ ia(ps2) i5h (p*) |£ m ii (ps2 ) (a) (b) (c) Fig. 2.21. PDF of (a) PCD for a 55.2-ps mean DGD, (b) depolarization rate for a 14.7-ps mean DGD, and (c) |Qf f iJ J for a 14.7-ps mean DGD [42,48], 2.1.3.2.4 The Autocorrelation Function of PMD Vector The PMD properties o f fiber are specified in terms o f the first-order PMD, which is equivalent to the time delay observed between two pulses propagating along the fast and slow axis of the fiber. This description is valid over a narrow bandwidth, as long as the system impairments caused by PMD can be described in terms o f the transmitted signal being split into two identical replicas that are merely delayed one relative to the other. However, the pulse distortions caused by higher-order PMD effects get to be significant long before the time delay associated with the first-order PMD becomes comparable with the pulsewidth o f the transmitted signal. As a result, when the transmitted bandwidth becomes large enough, the effect o f higher-orders o f PMD needs to be taken into account. Using the retarded plate model where the fiber is described in terms of a large number o f concatenated sections, which are statistically independent and whose birefringence vectors are Gaussian with independent components. Due to central limit theorem, the autocorrelation function (ACF) o f the PMD vector in the Stokes space is [46-47] 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ^ - T i A o r ^ R(Aco) = E{Q(co) • Q(m + Am )} = — [1 - e s< d g d > ! ] (2.1.171) Am2 where the < dgd > is the average length of the PMD vector. In addition, it has been shown [47] that the variances and correlations between all PMD orders as * d m n~k d c o n+k+1 7 V 7 E{d" . d 2 \ 9 ( .® ±A?2} = (_// (2n>! E{\o(co f } n + ‘ (2.1.173) dmn 'k dmn + k 3"(n + l )! 1 1 where ^ &(<*>) ^ g ^ g g ^ g / £ + order o f PMD or, the kth frequency derivative 8mk o f PMD vector evaluated at m = 0. As shown in Fig. 2.15,R(Aa>) decreases when Am increases and PSPs are become uncorrelated o f each other and different launched channels (even parallel to each other) experience different PMD vector (PSPs and DGD) in WDM systems. 2.1.3.3 Polarization Dependent Loss Polarization dependent loss (PDL) has been recognized as a critical issue because various inline optical components, such as switches, isolators, couplers, filters, and circulators, may have non-negligible PDL, i.e., >0.2 dB. When the optical pulse passes through an optical component with non-negligible PDL (by assuming negligible PMD and nonlinearity), it splits between two orthogonal polarization modes that attenuate each optical pulse replica differently. 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PDL can be expressed as the ratio o f the maximum to minimum transmission on a log scale, lO logt? - ^ ) , as the launch polarization is rotated through all possible ^m in states. Pure PDL can cause deleterious effects in a fiber transmission link including: (i) optical power fluctuations resulting from random optical-signal-to-noise ratio (OSNR) variations due to polarization state wandering during propagation [16-18], (ii) induced gain ripple [49], and (iii) limited PMD compensator performance [50]. Recent publications have also showed via theoretical and experimental results that the mutual interaction between PMD and PDL leads to a significant performance degradation in long-distance systems [25-28]. Note that when PDL exists in a fiber link also impaired by PMD, the PSPs o f the fiber are no longer orthogonal to each other, as shown in Fig. 2.22, and the probability distribution of the DGD degenerates from its Maxwellian shape, as shown in Fig. 2.23 [26,51]. The effects o f combined PMD and PDL on the BER o f a system show that when PDL is added to a link, P S P Fiber with high PMD m Polarization Mode Dispersion .PSP , Optical J L ti p o ti o n :a — D l = ? dB) PSP, Differential Group Delay PSP, X PS P, Different Attenuation PSP, X PSP Polarization Dependent Loss (PDL) Fig. 2.22. Conceptual illustration of the interaction between PMD and PDL. When PDL is present in a fiber link, the fiber PSPs are no longer guaranteed to be orthogonal. 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. several o f the BER data points cannot be explained by PMD alone and must result from some interaction between the two [25], In addition, it has been shown that in the presence o f PDL the DGD at a particular frequency can exceed that generated by PMD alone [28]. An additional concern for WDM systems is that the aggregate PDL o f a several in-line PDL components is wavelength dependent in the presence of PMD. As explained earlier, the PMD-induced randomization o f the polarization state is uncorrelated for different wavelength channels (outside the PMD correlation bandwidth). This will, o f course, cause the PDL seen by the WDM channels to become uncorrelated as well, generating a need for fast multi-channel PDL monitoring and dynamic compensation schemes [34], 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 DGD (ps) DGD (ps) (a) (b) Fig. 2.23. PDF of 15 PMD sections: (a) without PDL and (b) with 15 PDL sections (PDL of each section is 2.5 dB). 2.1.3.4 Polarization Dependent Gain Due to anisotropic gain saturation in fiber amplifiers, another polarization effect, polarization dependent gain (PDG), appears in amplified fiber links. The source o f PDG in EDFAs has been identified as polarization hole burning (PHB): signals with 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. orthogonal states o f polarization can utilize different subsets o f gain producing ions [17]. PDG can randomly degrade the OSNR, inducing significant fluctuations in the BER over time. Although the PDG from a single amplifier is quite small (almost negligible), the PDG effects from cascaded amplifiers in the overall optical link can result in a several-dB fluctuation in the received Q-factor. This impact arises from two competing phenomena: (i) PDG attenuates the signal power (and the noise power polarized parallel to the signal) and increases the orthogonal noise power, (ii) noise accumulation reduces the degree o f polarization (DOP) o f the light and, hence, the PDG differential gain. Since the dynamics o f EDFA gain are relatively slow, polarization scrambling of the signal at a rate faster than the response time o f the EDFA can eliminate any excess noise accumulation caused by PDG. 2.2 PMD Emulation The statistical probability distributions describing the first- and higher-order components o f PMD in long single mode fibers are well known at this point [52]. For example, both analytical and experimental results show that to first-order PMD can be described as a DGD between the two orthogonal polarization modes o f the fiber. This DGD follows a Maxwellian probability distribution and it is the high- DGD points in the distribution tail that are likely to cause system outages [53]. Additionally, due to the effects o f higher-order PMD, system outages may occur at low DGD values, or after the DGD has been compensated [54], In addition, although present-day fibers have low PMD values o f -0.1 ps/Vkm, much o f the fiber that was 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. previously installed in the 1980s has higher PMD values. A critical problem for designers o f newer high-performance transmission systems is to characterize potential degradations due to high-PMD fiber spans [55-57], Unfortunately, high- PMD transmission fiber is not commercially available and is rarely found in research laboratories. Moreover, even if it were available, it would be difficult to use it to rapidly explore a large number o f different fiber ensembles, as is required to determine the statistical distribution o f penalties due to PMD. This spurred the development o f several methods for rapidly emulating the statistical variations of PMD in real fibers as well as many techniques for generating specific components and combinations o f first and higher-order PMD in a predictable and repeatable way [58-69]. The function o f a PMD emulator is to accurately reproduce the statistical PMD variations o f real fibers in a short period o f time. Any PMD emulator should therefore meet the following key performance metrics: 1. The DGD should be Maxwellian-distributed over an ensemble of fiber realizations at any fixed optical frequency. 2. The emulator should produce accurate higher-order PMD statistics and should be able to reach any combination o f first and higher-order PMD values. 3. When averaged over an ensemble o f fiber realizations, the frequency ACF of the PMD emulator should tend toward zero outside a limited frequency range to provide accurate PMD emulation for WDM channels [46]. 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In addition to these performance requirements, the following features are desired to form a practical measurement tool: 1. Stability - the PMD of the emulator should remain stable over the measurement period, which may last minutes to hours. 2. Low loss - the emulator should ideally have low insertion loss and exhibit negligible PDL. 3. Simplicity - the implementation o f the emulator should allow easy control from one emulator state to the next. Such emulators are typically constructed from a concatenation o f several linear birefringent elements. These elements may be sections o f polarization maintaining (PM) fiber, birefringent crystals, or any other device that provides a DGD between the two orthogonal polarization axes (e.g., a polarization beam splitter (PBS) followed by two paths o f differing lengths and a polarization beam combiner). To achieve different PMD states, some property o f the emulator must be varied between samples, such as the polarization coupling between sections, the wavelength, or the birefringence o f each section. If enough sections are used, the PMD statistics o f the emulator will converge toward those o f a real fiber. Most PMD emulators can be classified into one o f four main categories: 1. Emulators with fixed orientations between the sections - this type o f emulator is typically constructed by splicing equal or unequal-length sections of PM fiber at either random or 45° angles. As explained in [59], using unequal lengths spliced at 45° angles will yield the most accurate statistics because the 45° angles 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. facilitate a rapid frequency decorrelation o f the resultant PMD vector and the use of unequal sections avoids an undesired periodicity in the frequency ACF. However, this emulator configuration has limited use since different PMD states can only be obtained by widely varying the wavelength or by slowly cycling through environmental changes. 2. Emulators with uniformly-distributed polarization transformations between sections (Fig. 2.24(a)) - these emulators are obtained by placing polarization controllers (PCs) between the birefringent sections to transform the polarization state according to a uniform distribution over the Poincare sphere [59,70]. 3. Emulators with rotatable sections (Fig. 2.24(b)) - the birefringent sections are randomly rotated relative to each other to obtain different PMD states. Examples include birefringent crystals mounted on rotation stages [60], PM fibers connected by rotatable connectors [61], and a long strand o f PM fiber with fiber-twisters placed periodically along it to vary the polarization coupling between sections [58]. 4. Emulators with tunable-bireffingence sections connected at fixed 45° angles (Fig. 2.24(c)) - for this type o f emulator, the orientation between sections remains fixed at 45° (to obtain rapid frequency decorrelation), while the birefringence o f each section is varied to obtain different PMD states. Examples of variable birefringence elements include voltage-controlled lithium-niobate crystals and PM fiber sections with small metallic heaters deposited on the fiber surface to temperature tune the birefringence [62]. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (C) Fig. 2.24. Three common emulator configurations constructed from a concatenation o f many birefringent elements (a) with uniformly-distributed polarization transformations (pol. controllers) between sections, (b) with rotatable sections, and (c) with fixed 45 angles between sections and variable birefringence elements, x is the DGD and y is its birefringence. For the latter three cases, statistical PMD samples are obtained at a given wavelength by randomly varying the polarization coupling between all sections for each measurement. A major limitation of PMD emulators is that the finite number o f sections puts a cap on the maximum DGD that can be obtained by the emulator. This peak value corresponds to the case when the birefringent axes the emulator sections become aligned. This peak DGD value is approximately equal to the product o f the rms DGD of the emulator and the square root of the number o f sections. A real single-mode fiber effectively contains hundreds to thousands o f birefringent sections [71], so emulators will always tend to have a maximum DGD that is much less than a real fiber, causing emulators to vary most from real fibers in the low-probability tail of the DGD distributions. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Early developments and investigations o f PMD emulators focused on the study o f the number sections required to produce accurate first- and higher-order statistics, on the differences between polarization scattering and simple polarization rotation between sections, and on obtaining a frequency ACF that quadratically falls to zero outside the PMD vector’s correlation bandwidth [56]. 2.3 Polarization Scrambling Scrambling the polarization state of a signal has been shown to be a valuable technique that can facilitate the compensation or reduction o f polarization-related impairments in a number of ways: (i) by enabling instantaneous DGD monitoring in both feedback and feed-forward PMD compensators [72-77], (ii) by enhancing PMD mitigation by using forward-error-correction (FEC) [78] and (iii) by significantly reducing signal fluctuations due to PDG or PDL-induced noise [79-83]. Typically, polarization-scrambling schemes are based on high-speed polarization modulators or relatively low-speed PCs such as LiNb03 devices (>1 MHz bandwidth) [81] or fiber-squeezer based PCs (up to 100 kHz bandwidth). Fig. 2.25(a) shows a schematic diagram o f an X-cut LiNb03 (variable linear phase retarder) polarization scrambler. LiNb03 polarization modulators have been used as bit-synchronous polarization scramblers to reduce PDG effects in undersea transmission systems where the scrambler output SOP is modulated along a great circle on the Poincare sphere at the bit rate [79]. When high-speed polarization scrambling is not required, sets o f polarization PCs are used as scramblers. Scramblers with different scrambling speeds and different output SOP distributions 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (corresponding to different reduced DOPs) may have different effects on system performance. - , PMF P d a r f z e r \ /N V(t) 45“ Linear Input SOP V > s * SMF Periodically varying m < outputSQP X-cutLiNbQ, y M /1 Variable Linear ^ t / C ^ Phase Retarder p |_ Q R (a) ' 0 > ) Fig. 2.25. (a) A schematic diagram o f polarization scrambler and (b) Uniform distribution of polarization state on the Poincare sphere (1000 samples). In ultra-long-haul systems, there may be hundreds o f cascaded EDFAs. PDL and PDG may cause the input signals to be attenuated or amplified in a way differing from that o f unpolarized noise, resulting in OSNR fluctuations at the end o f the link. Low frequency (-10 kHz) or bit-synchronous polarization scrambling has been shown to improve the performance o f ultra-long-haul transmission systems [79]. A typical demonstration o f polarization scrambling is reported in [83]. Note that the frequency o f polarization scrambling can affect the performance o f this scrambling system [24]. Although different approaches without polarization scrambling have been proposed for PMD monitoring, a major problem for such monitoring schemes is that the effective PMD value depends on both the DGD value and the PSPs o f the signal prior to transmission, thereby requiring the feedback loop to incorporate a complicated algorithm to control the polarization and compensator on a millisecond time scale. Moreover, the link DGD can be ambiguous under the circumstance in 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. which the transmitter SOP is aligned with one o f the link input PSPs, thereby causing feedback fading during the tracking procedure. Consequently, polarization scrambling o f the input signal’s SOP can be used to aid in PMD compensation schemes [84-89], as well as in monitors that can provide either DGD or PSP information [86-88], A key advantage of polarization scrambling at the transmitter is that it can decouple the dependence o f the monitored PMD on the input signal’s SOP, thus reducing the complexity and increasing the stability of the feedback control. In addition, polarization scrambling can be used to facilitate monitoring and compensation o f PDL since PDL-induced power fluctuation can be detected as long as the scrambling frequency is high enough to suppress the gain saturation in optical amplifiers [90]. In the aforementioned applications, it is often necessary that the scrambler output SOP is distributed, preferably uniformly, over the entire Poincare sphere for the purposes o f PMD and/or PDL monitoring and compensation on a millisecond time scale. For such applications, an output SOP distribution on the Poincare sphere (for an arbitrary input polarization state) using a fiber-squeezer-based polarization scrambler is shown in Fig. 2.25(b). Since this kind o f polarization scrambling is repeatable, periodic, and uniformly distributed, it is potentially an ideal technique for use in monitoring and compensation o f PMD effects. Moreover, in addition to other common sources o f signal distortion, such as noise, crosstalk, and nonlinearities, FEC coding has been shown to improve system performance in the presence o f PMD [84,91-93]. However, for worst case PMD 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (when there is equal power in each signal PSP), the PMD affects a large number of bits per FEC frame and error correction often fails. By utilizing polarization scrambling, the worst case PMD constellation can only affect a limited number of bits per FEC frame [78], Although polarization scrambling has a number o f advantages or applications that enhance the performance of signal transmission, we also note a potential problem that may occur due to polarization scrambling, especially for low-frequency (i.e. tens o f kHz) scrambling in the presence o f non-negligible PDL. Previous research concerning polarization scrambling o f a signal has concentrated on its effects in long-haul transmission where there are long cascades of EDFAs, typically on the order of hundreds o f amplifiers. It has been noted that PDL- induced intensity modulation is a potential system degrading effect [24], However, it has also been shown that this effect can be dramatically suppressed by the PDG that exists in a cascade of many (e.g. hundreds) saturated EDFAs using low frequency scrambling. PDG becomes effective in suppressing the PDL impairments because the scrambled signal gets partially polarized every time it passes through a PDL element. PDG therefore acts as feedback, which attempts to depolarize the signal and minimize the PDL-induced amplitude modulation (AM) [24], When the instantaneous PDL is high and the PDG effects are small enough to be considered negligible (e.g. in typical terrestrial systems where the number of EDFAs is on the order o f tens or less), the PDL-induced intensity modulation can become a problem. When the scrambling frequency is less than 1 kHz, the 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. scrambling effect is negligible since EDFAs operating in the saturated regime will alleviate PDL-induced low-speed power fluctuations, and the optical receivers usually cut out all fluctuations below their cut-off frequencies (kHz range). In contrast, if the scrambling frequency is beyond the kHz range, which is desired to provide better SOP coverage within a given period for applications in PMD monitoring and compensation [72,74,76,94], the optical intensity modulation will be detected at the receiver and cause eye closure. Given the above discussion, network designers may determine that polarization scrambling is necessary for PMD/PDL monitoring or PDG reduction. However this will require either the reduction o f PDL in in-line components or the use o f a simple PDL compensator [95]. 2.4 Fiber Bragg Grating Fiber Bragg gratings have emerged as major components for dispersion compensation because of their low loss, small footprint and low optical nonlinearity. Bragg gratings are sections of SMF in which the refractive index of the core is modulated in a periodic fashion, as a function of the spatial coordinate along the length of the fiber. When the spatial periodicity o f the modulation matches what is known as a Bragg condition with respect to the wavelength o f light propagating through the grating, the periodic structure acts like a mirror, reflecting the optical radiation that is traveling through the core o f the fiber. An optical circulator is traditionally used to separate the reflected output beam from the input beam. 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This section provides an overview on different types o f FBGs and their potential applications. 2.4.1 Concept of Fiber Bragg Grating FBGs are sections o f SMF in which the refractive index o f the core is modulated in a periodic fashion, as a function o f the spatial coordinate along the length o f the fiber [96-97]. When the spatial periodicity o f the modulation matches what is known as a Bragg condition with respect to the wavelength o f light propagating through the grating, the periodic structure acts like a mirror, reflecting the optical radiation that is traveling through the core of the fiber. For reflection-based gratings, an optical circulator is traditionally used to separate the input and the output ports and the transmitted part of the signal is simply discarded [98], An FBG is fabricated by a periodic modulation o f the index o f refraction in the core o f the fiber [98], In the most general case, the index perturbation Sn(z) takes the form o f a phase and amplitude-modulated waveform where z is the position along a grating, Sn0(z) is the maximum index modulation spatially averaged over a grating period, v is the fringe visibility o f the index change, A (z) is the local grating period including grating chirp, and $(z) describes phase changes in the grating. The grating filter characteristics can be analyzed by the coupled-mode theory [98] that describes the coupling between the forward- and (2.4.1) 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. backward-propagating waves at a given frequency. For uniform gratings, the index change takes the form The Bragg resonance wavelength, Xb, is proportional to the period o f the grating, where ne ff is the effective core index of refraction and it is a spatial average of n ( z ) . The periodic nature of index variations couples the forward- and backward- propagating waves at wavelengths close to the Bragg wavelength, and as a result, provides frequency-selective reflectivity to the incident signal over a bandwidth determined by the grating strength. 2.4.2 Chirped Fiber Bragg Grating When the periodicity of the grating is varied along its length, the result is a chirped grating which can be used to compensate for chromatic dispersion [99], The chirp is understood as the rate of change of the spatial frequency as a function o f position along the grating. In chirped gratings the Bragg matching condition for different wavelengths occurs at different positions along the grating length. Thus, the roundtrip delay o f each wavelength can be tailored by designing the chirp profile appropriately. Fig. 2.26 compares the chirped FBG with uniform FBG. In a data pulse that has been distorted by dispersion, different frequency components arrive with different amounts of relative delay. (2.4.2) Xb — 2neffA (2.4.3) 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Uniform FBG e © •43 8 5 3 & O S H 3 ft a » S T V ! Wavelength / l — „ d 1 M Uniform Pitch Chirped FBG e o 5 3 (2 -—c/ 3 Wavelength fl — fi- < 9 a < 9 S T • < ! (a) (njmmmwD Chirped Pitch (b) Fig. 2.26. Uniform and chirped FBGs. (a) A grating with uniform pitch has a narrow reflection spectrum and a flat time delay as a function of wavelength, (b) A chirped FBG has a wider bandwidth, a varying time delay and a longer grating length. Since the Bragg wavelength varies along the grating, different frequency components of an incident optical pulse are reflected at different points and have different time delays depending on where the Bragg condition is satisfied locally as shown in Fig. 2.26. Unlike a uniform grating which satisfies the Bragg condition for a specific wavelength, a chirped grating satisfies the Bragg condition for a range of wavelengths. By tailoring the chirp profile such that the frequency components see a relative delay which is the inverse o f the delay o f the transmission fiber, the pulse can be compressed back. The dispersion o f the grating is the slope o f the time delay as a function o f wavelength, which is related to the chirp. The measure o f grating chirp a is in units ofnm/cm a is defined as dX(z) a s = ' j dz The grating induced delay at position z is 2 I ( x )dx T(Z)= ^ ff (2-4.4) (2.4.5) 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The grating induced total dispersion can be determined as 1 d(T(z)) (2.4.6) Z d A j r Z - L , . where Lg is the length of the chirped grating. For linearly-chirped grating with reflection bandwidth AX , grating length Lg, and uniform effective core mode index ne ff (ne ff= 1.46), we have As an example, the accumulated dispersion after 100 km o f conventional SMF is about 1700 ps/nm. Let’s assume the bandwidth o f a grating is 0.2 nm (which is much larger than the 0.08 nm bandwidth o f a 10-Gbit/s optical signal), the required grating length is only 3.5 cm, the grating chirp is 0.057 nm/cm, and the grating However, the accumulated dispersion for a given channel may significantly vary in time for: (i) dynamically reconfigurable optical networks in which a given channel may originate locally or far away, and (ii) transmission systems having changing operating conditions. If dispersion changes, then dispersion compensation techniques must be flexible in order to track the accumulated dispersion as well as dynamically tune the compensator for new channel conditions. At present, there is (2.4.7) r(Lg) _ 2neff AX-Lg c-AX c-Lg -a g induced dispersion is 5 x 107ps/nm/km. 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. no method for tuning in situ the dispersion parameter o f dispersion compensating fiber (DCF). For the FBG, a recent report used 21 stretching segments to asymmetrically stretch a uniform FBG to produce different dispersion [100], However, there has been no reported system demonstration of dispersion compensation by dynamically tuning any o f the dispersive devices. The main drawback of Bragg gratings is that the amplitude profile and the phase profile as a function of wavelength have some amount o f ripple. Ideally, the amplitude profile o f the grating should have a flat (or rounded) top in the passband, and the phase profile should be linear (for linearly chirped gratings) or polynomial (for nonlinearly chirped gratings). The grating ripple is the deviation from the ideal profile shape (see Fig. 2.27). Considerable effort has been expended on reducing the ripple. While early gratings were plagued by more than 100 ps o f ripple, published results have shown vast improvement to values close to ±3 ps. Grating Ripple 0.08 nm Wavelength (nm) Fig. 2.27. Grating ripple effects on BER power penalty. Fig. 2.28 shows the grating induced high-order dispersion effect for 10-Gbit/s optical signal, which is the additional drawback o f chirped-FBG. The grating induced 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dispersion goes from 300 ps/nm to 1000 ps/nm in a 1-nm wavelength range. The average dispersion slope for this grating is about 700 ps/nm2. Hence, the grating induced dispersion differential for a 10-Gbit/s signal will be about 56 ps/nm. This high-order dispersion may distort the optical signal and give rise to power penalties. High Order Dispersion 0.08 [nm Wavelength (nm) Fig. 2.28. Higher-order dispersion induced by nonlinearly-chirped FBG (NC-FBG). 2.4.3 Nonlinearly-Chirped Fiber Bragg Grating In order to realize dynamic dispersion compensation, the amount o f dispersion o f the compensating grating should change as the grating is stretched. Fig. 2.29(a) shows a typical group delay curve versus wavelength for a linearly-chirped FBG (LCFBG). The slope o f the curve corresponds to the dispersion at a specified wavelength. For a linearly-chirped grating, the relative time delay decreases linearly as the wavelength increases, so the grating-induced dispersion is constant over the grating bandwidth. When the linearly-chirped grating is stretched, the time delay curve shifts to longer wavelengths, but the slope remains unchanged. At any given wavelength, the slope o f the time delay curve is constant, meaning that the grating-induced dispersion will not change whether the grating is stretched or not. Fig. 2.29(b) shows the time delay 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. No Slope Change at^o Slope Change atXp 1 k Stretch Relative Time Delay (ps) Wavelength (nm) Stretch,! Relative Time Delay (ps) Wavelength (nm) Linearly Chirped Nonlinearly Chirped (a) (b) Fig. 2.29. Tunable dispersion compensation using chirped FBG (a) LCFBG and (b) NC-FBG. curve o f a NC-FBG, whose grating parameter neff(z) - A (z) is a nonlinear function o f z. The time delay decreases nonlinearly versus the wavelength.Hence, the grating- induced dispersion (the slope o f the time delay curve) is different for different wavelengths within the grating bandwidth. As the grating is stretched, the accumulated delay curve shifts to longer wavelengths while maintaining its shape. At each wavelength, the slope o f the time delay curve (i.e. dispersion) increases from a shallow one to a much steeper one. Therefore, the amount o f dispersion increases as the grating is stretched to longer wavelengths [101], However, within the signal’s bandwidth, the dispersion is not constant. This intra-channel third-order dispersion of a NC-FBG can be appreciably large, especially when the NC-FBG has a relatively large tuning range. In order to tune the dispersion induced by a nonlinearly-chirped grating, a grating control should be implemented to control either the effective index neff( z ) or the pitch o f the grating A (z) . This allows for adjustment of the grating ne ff (z ) ’ M z ) and thus the relative delay for signals at different wavelength within 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the grating’s reflection bandwidth. A transducer, e.g. a piezoelectric element can be used as a control unit to compress or stretch a grating in order to produce a tunable dispersion profile. To control the effective core index neff( z ) , a temperature gradient, the electro-optic or magneto-optic effect could be implemented. These provide dynamically tunable relative delays o f different reflected spectral component. 2.4.4 Sampled Nonlinearly-Chirped Fiber Bragg Grating To achieve multiple channel operation, one solution is to sample (or modulate) the phase profile o f the single channel grating design. As known from Fourier analysis, sampling a function in the real space (here, along the length o f the grating, in real space) leads to repeated spectra in the Fourier space (here, in the wavelength domain) [102-103]. Sampled gratings can be written in a very short piece o f fiber. If the sampling technique is applied to the tunable single channel gratings, one can achieve both tunability and multiple channel operation. In practice, only the nonlinearly chirped, uniform strain grating can be used with multiple channel designs. On the other hand, for the nonlinearly chirped design the stretching is uniform, so the periodicity o f the sampling is maintained, as well as the channel spacing. The sampled gratings approach preserves all the advantages o f a single channel design, but allows multiple channel operation. In fact, the design o f the channel passband and the replication o f the channels for multi-channel operation can 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. be worked out separately. The design o f the chirp profile is responsible for the channel shape, and can be done the same way as for a single channel grating. By using an appropriate sampling function (shape, corresponding to a flat-topped shape in the Fourier domain), all channels can have equal amplitudes, as shown in Fig. 2.30. Frequency Space Grating axis (mm) Wavelength (nm) Fig. 2.30. Sampling a waveform in the real space leads to replicate spectra in the Fourier space. For an FBG, modulating the intensity o f the grating leads to multiple wavelength passbands. Thus, a multiple channel design can be reduced to two separate steps: design the chirp profile for the channel shape, and design the sampling function for the channel replication. One o f the major drawbacks o f the simple sampling approach is that the reflectivity o f the grating decreases with the number o f channels, because the active area (the portion o f the grating where the index is modulated) is reduced. In a system, the lower reflectivity translates to higher insertion loss. Thus it is important to manufacture gratings with the highest possible reflectivity [104]. 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.5 Chromatic Dispersion Mitigation and Monitoring in High-Speed Optical Fiber Communication Systems and Networks Dispersion is one o f the critical roadblocks to increasing the transmission capacity of optical fiber. The dispersive effect in an optical fiber has several ingredients including intermodal dispersion in a multimode fiber, waveguide dispersion, material dispersion, and chromatic dispersion. In particular, chromatic dispersion is one o f the critical effects in a SMF, resulting in a temporal spreading o f an optical bit as it propagates along the fiber. At data rates <2.5-Gbit/s, the effects of chromatic dispersion are not particularly troublesome. For data rates >10-Gbit/s, however, transmission can be quite tricky and the chromatic dispersion-induced degrading effects must be dealt with in some fashion, perhaps by compensation. Furthermore, the effects o f chromatic dispersion rise quite rapidly as the bit rate increases - when the bit rate increases by a factor o f four, the effects o f chromatic dispersion increase by a whopping factor o f 16! In this section, several solutions for chromatic dispersion mitigation and monitoring are discussed. 2.5.1 Dispersion Maps While zero-dispersion fiber is not a good idea, a large value o f the accumulated dispersion at the end o f a fiber link is also undesirable. An ideal solution is to have a “dispersion map,” alternating sections o f positive and negative dispersion as can be seen in Fig. 2.31. This is a very powerful concept: at each point along the fiber the dispersion has some non-zero value, eliminating FWM and XPM, but the total 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dispersion at the end o f the fiber link is zero, so that no pulse broadening is induced. The most advanced systems require periodic dispersion compensation, as well as pre- and post-compensation (before and after the transmission fiber). Positive Dispersion Negative Transm ission F iber Dispersion Element Dtotal"" 0 O 0 Distance (km) Fig. 2.31. Dispersion map of a basic dispersion managed system. Positive dispersion transmission fiber alternates with negative dispersion compensation elements such that the total dispersion is zero end-to-end. The addition o f negative dispersion to a standard fiber link has been traditionally known as “dispersion compensation,” however, the term “dispersion management” is more appropriate. SMF has positive dispersion, but some new varieties o f NZDSF come in both positive and negative dispersion varieties. Some examples are shown in Fig. 2.3. Reverse dispersion fiber is also now available, with a large dispersion comparable to that o f SMF, but with the opposite sign. When such flexibility is available in choosing both the magnitude and sign o f the dispersion of the fiber in a link, dispersion-managed systems can fully be optimized to the desired dispersion map using a combination o f fiber and dispersion compensation devices (see Fig. 2.32). 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. '+ SMF + ----------------- 1, High local dispersion: (D > 17) High SPM, L ow XPM, Low 3 D:stancc FWM 10 „ J ., ............L _ 20 30 2. Short compensation distance Non-Zero DSF + 1. Low Local Dispersion: (D - ±0.2) -D Distance 1 ■ ! Low SPM, Suppressed XPM, Suppressed FWM 2. Long compensation distance 100 • 200 300 Dispersion Values (in ps/nm /km ): SMF: ~ +17, DCF: - -85, M on-Z ero DSF: ~ ± 0 .2 k ............................................................ ... Fig. 2.32. Various dispersion maps for SMF-DCF and NZDSF-SMF. Dispersion is a linear process, so to first-order dispersion maps can be understood as linear systems. However, the effects o f nonlinearities cannot be ignored, especially in WDM systems with many tens o f channels where the launch power may be very high. In particular, in systems deploying DCF, the large nonlinear coefficient o f the DCF can dramatically affect the dispersion map. 2.5.2 Corrections to Linear Dispersion Maps Chromatic dispersion is a necessity in WDM systems to minimize the effects o f fiber nonlinearities. A chromatic dispersion value as small as a few ps/nm/km is usually sufficient to make XPM and FWM negligible. To mitigate the effects of nonlinearities but maintain small amounts o f chromatic dispersion, NZDSF is commercially available. Due to these nonlinear effects, chromatic dispersion must be managed, rather than eliminated. 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. If a dispersion-management system were perfectly linear, it would be irrelevant whether the dispersion along a path is small or large, as long as the overall dispersion is compensated to zero (end to end). Thus, in a linear system the performance should be similar, regardless of whether the transmission fiber is SMF, and dispersion compensation modules are deployed every 60 km, or the transmission fiber is NZDSF (with approximately % the dispersion value o f SMF) and dispersion compensation modules are deployed every 240 km. In real life, optical nonlinearities are very important, and recent results seem to favor the use o f large, SMF like, dispersion values in the transmission path and correspondingly high dispersion compensation devices. A recent study o f performance versus channel spacing showed that the capacity o f SMF could be more than four times that o f NZDSF. This is because the nonlinear coefficients are much higher in NZDSF than in SMF, and for dense WDM the channel interactions become a limiting factor. A critical conclusion is that not all dispersion compensation maps are created equal: a simple calculation o f the dispersion compensation to cancel the overall dispersion value does not lead to optimal dispersion map designs. Additionally, several solutions have been shown to be either resistant to dispersion, or have been shown to rely on dispersion itself for transmission. Such solutions include chirped pulses (where prechirping emphasizes the spectrum o f the pulses so that dispersion does not broaden them too much), dispersion assisted transmission (where an initial phase modulation tailored to the transmission distance 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. leads to full-scale AM at the receiver end due to the dispersion), and various modulation formats robust to chromatic dispersion and nonlinearities. 2.5.3 F ixed D ispersion Compensation From a system point o f view, there are several requirements for a dispersion compensating module: low loss, low optical nonlinearity, broadband (or multi channel) operation, small footprint, low weight, low power consumption, and clearly low cost. It is unfortunate that the first dispersion compensation modules, based on DCF only, met two o f these requirements: broadband operation and low power consumption. On the other hand, several solutions have emerged that can complement or even replace these first-generation compensators. 2.5.3.1 Dispersion Compensating Fiber One o f the first dispersion compensation techniques was to deploy specially designed sections o f fiber with negative chromatic dispersion. The technology for DCF emerged in the 1980s and has developed dramatically since the advent o f optical amplifiers in 1990. DCF is the most widely deployed dispersion compensator, providing broadband operation and stable dispersion characteristics, and the lack o f a dynamic, tunable DCF solution has not reduced its popularity. As can be seen in Fig. 2.33, the core o f the average DCF is much smaller than that of standard SMF, and beams with longer wavelengths experience relatively large changes in mode size (due to the waveguide structure) leading to greater propagation through the cladding o f the fiber, where the speed of light is greater than that of the 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DCF Design Performance DCF 1.5 1.0 c 0.5 < SMF 200 400 Radius (A.U.) £ -85 E -90 = -100 Q -110 (a) 1500 1520 1540 1560 1580 1600 Wavelength (nm) (b) Fig. 2.33. Typical DCF (a) refractive index profile and (b) dispersion and loss as a function of wavelength. An is defined as refractive index variation relative to the cladding. core. This leads to a large negative dispersion value. Additional cladding layers can lead to improved DCF designs that can include negative dispersion slope to counteract the positive dispersion slope o f standard SMF. In spite o f its many advantages, DCF has a number o f drawbacks. First, it is limited to a fixed compensation value. In addition, DCF has a weakly guiding 2 2 structure and has a much smaller core cross-section, 19 pm , compared to the 85 pm of SMF. This leads to higher nonlinearity, higher splice losses, as well as higher bending losses. Last, the length of DCF required to compensate for SMF dispersion is rather long, about one-fifth o f the length o f the transmission fiber for which it is compensating. Thus DCF modules induce loss, and are relatively bulky and heavy. The bulk is partly due to the mass o f fiber, but also due to the resin used to hold the fiber securely in place. One other contribution to the size o f the module is the higher bend loss associated with the refractive index profile o f DCF; this limits the radius of 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the DCF loop to 6-8 inches, compared to the minimum bend radius o f 2 inches for SMF. Traditionally, DCF-based dispersion compensation modules are usually located at amplifier sites. This serves several purposes. First, amplifier sites offer relatively easy access to the fiber, without requiring any digging or unbraiding o f the cable. Second, DCF has high loss (usually at least double that o f standard SMF), so a gain stage is required before the DCF module to avoid excessively low signal levels. DCF has a cross section four times smaller then SMF, hence a higher nonlinearity, which limits the maximum launch power into a DCF module. The compromise is to place the DCF in the midsection of a two-section EDFA. This way, the first stage provides pre-DCF gain, but not to a power level that would generate excessive nonlinear effects in the DCF. The second stage amplifies the dispersion compensated signal to a power level suitable for transmission though the fiber link. This launch power level is typically much higher than could be transmitted through DCF without generating large nonlinear effects. Many newer dispersion compensation devices have better performance than DCF, in particular lower loss and lower nonlinearities. For this reason, they may not have to be deployed at the midsection of an amplifier. The real demonstration results using the DCF have been shown in [105], 2.S.3.2 Chirped Fiber Bragg Gratings Compensators FBGs have emerged as major components for dispersion compensation because of their low loss, small footprint and low optical nonlinearity. Bragg gratings are sections o f SMF in which the refractive index o f the core is modulated in a periodic 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fashion, as a function o f the spatial coordinate along the length o f the fiber. When the spatial periodicity of the modulation matches what is known as a Bragg condition with respect to the wavelength o f light propagating through the grating, the periodic structure acts like a mirror, reflecting the optical radiation that is traveling through the core of the fiber. An optical circulator is traditionally used to separate the reflected output beam from the input beam. When the periodicity o f the grating is varied along its length, the result is a chirped grating which can be used to compensate for chromatic dispersion. The chirp is understood as the rate of change o f the spatial frequency as a function o f position along the grating. In chirped gratings the Bragg matching condition for different wavelengths occurs at different positions along the grating length. Thus, the roundtrip delay of each wavelength can be tailored by designing the chirp profile appropriately. Fig. 2.26 compares the chirped FBG with uniform FBG. In a data pulse that has been distorted by dispersion, different frequency components arrive with different amounts of relative delay. By tailoring the chirp profile such that the frequency components see a relative delay which is the inverse o f the delay o f the transmission fiber, the pulse can be compressed back. The dispersion of the grating is the slope of the time delay as a function o f wavelength, which is related to the chirp. The main drawback o f Bragg gratings is that the amplitude profile and the phase profile as a function of wavelength have some amount o f ripple. Ideally, the amplitude profile of the grating should have a flat (or rounded) top in the passband, and the phase profile should be linear (for linearly chirped gratings) or polynomial 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (for nonlinearly chirped gratings). The grating ripple is the deviation from the ideal profile shape. Considerable effort has been expended on reducing the ripple. While early gratings were plagued by more than 100 ps o f ripple, published results have shown vast improvement to values close to ±3 ps. 2.S.3.3 Higher-Order Mode Dispersion Compensation Fiber One o f the challenges of designing standard DCF is that high negative dispersion is hard to achieve unless the cross-section o f the fiber is small (which leads to high nonlinearity and high loss). One way to reduce both the loss and the nonlinearity is to use a higher-order mode (HOM) fiber (LPn or LP02 near cutoff instead o f the LP0 1 mode in the transmission fiber). Such a device requires a good quality mode converter between LP0 1 and LP02 to interface between the SMF and HOM fiber. HOM fiber has dispersion per unit length greater than six times that o f DCF. Thus, to compensate for a given transmission length in SMF, the length o f HOM fiber required is only one sixth the length o f DCF. Thus, even though losses and nonlinearity per unit length are larger for HOM fiber than for DCF, they are smaller overall, because o f the shorter HOM fiber length. As an added bonus, the dispersion can be tuned slightly by changing the cutoff wavelength o f LP02 (via temperature tuning). One soon to be released HOM fiber-based commercial dispersion compensation module is not tunable, but can fully compensate for dispersion slope. 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.53.4 Tunable Dispersion Compensation 2.5 3 .4.1 The Need for Tunability In a perfect world, all fiber links would have a known, discrete, and unchanging value o f chromatic dispersion. Network operators would then deploy fixed dispersion compensators periodically along every fiber link to exactly match the fiber dispersion. Unfortunately, several vexing issues may necessitate that dispersion compensators are tunability, that they have the ability to adjust the amount of dispersion to match system requirements. First, there is the most basic business issue o f inventory management. Network operators typically do not know the exact length o f a deployed fiber link nor its chromatic dispersion value. Moreover, fiber plants periodically undergo upgrades and maintenance, leaving new and non-exact lengths o f fiber behind. Therefore, operators would need to keep in stock a large number o f different compensator models, and even then the compensation would only be approximate. Second, we must consider the sheer difficulty o f 40-Gbit/s signals. The tolerable threshold for accumulated dispersion for a 40-Gbit/s data channel is 16 times smaller than at 10 Gbit/s. If the compensation value does not exactly match the fiber to within a few percent o f the required dispersion value, then the communication link will not work. Tunability is considered a key enabler for this bit rate (see Fig. 2.34 and 2.35). Third, the accumulated dispersion changes slightly with temperature, which begins to be an issue for 40-Gbit/s systems and 10-Gbit/s ultra long haul systems. 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Accumulated Chromatic DispersiotV k Partial compensation OC-192 OC-768 erfect compensation Distance (k m ) Fig. 2.34. The need for tunability. The tolerance o f OC-768 systems to chromatic dispersion is 16 times lower than that of OC-192 systems. Approximate compensation by fixed in-line dispersion compensators for a single channel may lead to rapid accumulation of unacceptable levels of residual chromatic dispersion. In fiber, the zero-dispersion wavelength changes with temperature at a typical rate of 0.03 nm/°C. It has been shown that a not-uncommon 50 °C variation along a 1000- km 40-Gbit/s link can produce significant degradation (see Fig. 2.36). Fourth, we are experiencing the dawn o f reconflgurable optical networking. In such systems, the network path, and therefore the accumulated fiber dispersion, can No Compensation , F|xed 80 km “ n X f i I | J | s^ff Cprfpjens m i 4 T O I 3 | 2 (ft o o 1 0) m Q [ _LA I if!. I f-i-l..... 1 i' OC-768 | i | ... I ... I i ^ a a ^ 4 « a ator Turiaft^ Co mpensator .felp-fel 0J ► p s/n m 0 20 40 60 80 100 120 140160 Distance (km) Fig. 2.35. Tunable dispersion compensation at OC-768 (40 Gbit/s) is essential for achieving a comfortable range of acceptable transmission distances (80 km for tunable, only ~ 4 km for fixed compensation). 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © O ) c (0 x: O c o e © Q . < / ) Q T5 0) + * JS 3 E 3 | ' ,u!2 M ) -30 -20 -10 0 10 20 30 40 Temperature Change, AT (°C) Fig. 2.36. Accumulated dispersion changes as a function of the link length and temperature fluctuation along the fiber link. change. It is important to note that even if the fiber spans are compensated span-by- span, the pervasive use of compensation at the transmitter and receiver suggests that optimization and tunability based on path will still be needed. Other issues that increase the need for tunability include: (i) laser and (de)mux wavelength drifts for which a data channel no longer resides on the flat-top portion o f a filter, thereby producing a chirp on the signal that interacts with the fiber’s chromatic dispersion, (ii) changes in signal power that change both the link’s nonlinearity and the optimal system dispersion map, and (iii) small differences that exist in transmitter-induced signal chirp. NRZ 4 0 G b it/s u n i t 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.S.3.4.2 Approaches to Tunable Dispersion Compensation A host o f techniques for tunable dispersion compensation have been proposed in recent years. Some of these ideas are just interesting research ideas, but several have strong potential to become viable technologies. Fiber gratings offer the inherent advantages o f fiber compatibility, low loss, and low cost. If an FBG has a refractive-index periodicity that varies nonlinearly along the length o f the fiber, it will produce a time delay that also varies nonlinearly with wavelength (see Fig. 2.26). Herein lies the key to tunability. When a linearly- chirped grating is stretched uniformly by a single mechanical element, the time delay curve is shifted towards longer wavelengths, but the slope o f the ps-vs.-nm curve remains constant at all wavelengths within the passband. When a nonlinearly-chirped grating is stretched, the time delay curve is shifted toward longer wavelengths, but the slope o f the ps-vs.-nm curve at a specific channel wavelength changes continuously. Ultimately, tunable dispersion compensators should accommodate multi-channel operation. Several WDM channels can be accommodated by a single chirped FBG in one o f two ways: fabricating a much longer (i.e., meters-length) grating, or using a sampling function when writing the grating, thereby creating many replicas o f transfer function o f the FBG in the wavelength domain (see Fig. 2.30). One ffee-space-based tunable dispersion compensation device is the virtually imaged phased array (VIPA), based on the dispersion o f a Fabry-Perot interferometer. The design requires several lenses, a movable mirror (for tunability), 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and a glass plate with a thin film layer o f tapered reflectivity for good mode matching. Light incident on the glass plate undergoes several reflections inside the plate. As a result, the beam is imaged at several virtual locations, with a spatial distribution that is wavelength-dependent. Several devices used for dispersion compensation can be integrated on a chip, using either an optical chip media (semiconductor-based laser or amplifier medium) or an electronic chip. One such technology is the micro-ring resonator, a device that when used in a structure similar to that o f an all-pass filter (see Fig. 2.37) can be used for dispersion compensation on a chip-scale. Although these technologies are not fully mature and not yet ready for deployment as dispersion compensators, they have been used in other applications and have the potential to offer very high performance at low cost. Channels Phase Shifter In Out H - >. re a > Q Channel Spacing a 3 o 0 ► Frequency (FSR) Fig. 2.37. Architecture o f an all-pass filter structure for chromatic dispersion and slope compensation [106], As the ultimate optical dispersion compensation devices, photonic bandgap fibers (holey fibers) are an interesting class in themselves (see Fig. 2.38). These are 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fibers with a hollow structure, with holes engineered to achieve a particular functionality. Instead of being drawn from a solid preform, holey fibers are drawn from a group of capillary tubes fused together. This way, the dispersion, dispersion slope, the nonlinear coefficients could in principle all be precisely designed and controlled, up to very small or very large values, well outside the range o f those of the solid fiber. | 500 1 0 = -500 a -1000 IT-1500 •2 -2000 fc -2500 a (A a \ V Second mode cut-off 0.4 0.6 0.8 1 1.2 1.4 Core Diameter (pm) (a) (b) Fig. 2.38. (a) SEM image of a photonic crystal fiber (holey fiber) and (b) net dispersion o f the fiber at 1550 nm as a function of the core diameter [107]. 2.5.4 Chromatic Dispersion Monitoring Another important issue related to dispersion management is dispersion monitoring techniques. In a reconfigurable system, it is necessary to reconfigure any tunable chromatic dispersion compensation modules on the fly as the network changes. Moreover, chromatic dispersion varies with temperature [108], a significant problem in >40-Gbit/s systems. In addition, periodic repair and maintenance o f the fiber plant can alter the properties of the link itself. These system scenarios require the ability to monitor the signal’s accumulated dispersion and feed the proper control signal to either chromatic dispersion compensator or equalizer. For management and 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. monitoring purposes, in a robust system, simple, sensitive, flexible, and cost- effective dispersion monitoring technique may prove quite beneficial. Several techniques for monitoring chromatic dispersion and signal quality in such systems have been previously reported including: (i) performance monitoring using the BER, an amplitude histogram [109], or eye opening [110], (ii) detecting the phase difference between two or more optical frequency components using narrowband optical filters [ 111], (iii) dithering the optical carrier frequency at the transmitter and measuring the resultant phase modulation o f the clock at the receiver using a phase-locked loop [112], (iv) comparing the phase between the upper and lower vestigial optical sidebands in the electronic domain [113-114], (v) partial optical filtering and phase shift detection o f bit-rate and doubled half-bit-rate frequency components [115], (vi) monitoring the intensity modulation induced by a phase modulation [116], (vii) monitoring the bit-rate frequency component o f the RF power (the “clock” tone) [117], (viii) monitoring a dispersion-biased RF clock tone [118-119], and (ix) inserting an in-band subcarrier tone at the transmitter and monitoring the subcarrier tone power degradation [120- 121]. 2.6 Polarization Mode Dispersion Mitigation and Monitoring in High-Speed Optical Fiber Communication Systems and Networks As is well known, high-bit-rate (> 10-Gbit/s/channel) transmission systems are highly susceptible to deleterious optical-fiber-based effects, such as chromatic dispersion, PMD, and nonlinearities. Systems must be designed such that these degrading effects are either minimized or mitigated. A key challenge is that there exist several 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. scenarios for which these fiber-based effects are not static but are time-varying, including: (i) small temperature changes will affect any polarization-dependent penalties, (ii) reconfigurable optical networking will change the signal path and thus the accumulation of fiber-based effects, and (iii) periodic repair and maintenance of the fiber plant will alter the fiber itself. These time-varying degradations require the monitoring of signal quality in an optical system in order to either dynamically tune a compensator or for network control and management. Monitoring that is simple, sensitive, and robust would facilitate proper system performance. In this section, I will highlight different types of PMD mitigation techniques and monitoring methods in optical fiber communication systems. 2.6.1 PMD Mitigation Techniques In digital communication systems, the effects o f PMD become important when the pulse splits and leaks into an adjacent bit. It has been shown in several reports that the acceptable average DGD varies between 10% and 20% o f a bit time depending mostly on the modulation format, outage probability and receiver architecture [122- 124]. Different PMD mitigation techniques have been proposed and fall into two main categories: (i) passive mitigation and (ii) active mitigation. Passive methods to mitigate PMD include the use o f novel modulation formats [122,125-133], FEC [78,91-93], new low PMD fibers, and soliton systems [85-89,134-137]. However, in some cases passive techniques are inadequate and active PMD mitigation techniques must be employed. These include: (i) optical PMD compensators [33,45,55,58,138-141], (ii) electrical equalizers [142-144], (iii) optical 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equalizers [145-147], (iv) PSP filtering, (v) PSP transmission [147-149], and (vi) polarization diversity receiver [150], Any active PMD mitigation scheme should be dynamically adaptive since the PMD drifts on a time scale o f milliseconds to days. While electronic equalizers are expected to be very cost-effective, can be integrated into the receiver, and can compensate for multiple distortion sources, they are only partial solutions as they may not be suitable for some high-PMD systems. Compared to optical compensators, the maximum or average DGD as demonstrated to date is fairly low, typically several tens o f ps. Additionally, since the optical phase information is lost after detection, electrical techniques cannot isolate the effects o f PMD from other fiber degrading effects, such as chromatic dispersion and nonlinearites. 2.6.1.1 Optical PMD Compensation Optical PMD compensator (OPMDC) is the most straightforward approaches to mitigate PMD since PMD is an optical property o f the fiber. All OPMDCs are composed o f a PC and a highly birefringent element(s) to apply the inverse transfer function o f the optical link as shown in Fig. 2.39. This birefringence can be a PM fiber, LiNb03 delay, FBG, bulk optic and combination o f polarization combiner, splitter or a free space optical time delay line. PC can be LiNb03 crystal, fiber squeezers, MEMs. The tunability o f the birefringence element depends on some technologies like FBGs, integrated optical crystals that increases cost and system complexity too. I l l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Polarization Controller Polarization dependent delay: sinale/multiole DGD — - . J i y Control Monitoring Algorithm Unit Fig. 2.39. Schematic diagram of an OPMDC and monitoring module. In addition, the global response time needed for PMD compensation depends on: (i) technology used for PC, (ii) speed o f tunability variable birefringence used for generating DGD, (iii) technology o f control signal, (iv) number of control signals, and (v) algorithm computation time. First and higher-order optical PMD compensation has been demonstrated using a number of control parameters. However, the most common OPMDCs employ only a few stages, as adding control parameters to enable many orders of PMD to be compensated increases the complexity of the system while lowering the response time. Single and double-stage OPMDCs with fixed and variable DGD components have been demonstrated for first and higher-order PMD compensation. Multi-stage compensators are able to mitigate first and higher-orders o f PMD for a single channel [55,140] or over a wide wavelength range in WDM systems [151]. However, tracking problems arise in compensators using more than two stages, due to too many control points and too little feedback. 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6.1.2 Optical PMD Equalization The performance of any digital data transmission can be characterized by the eye opening at the decision time ISI, which arises whenever two bits affect each other’s amplitudes, is a main contributor to receiver degradations. In a beat-noise-limited system, ISI on the spaces is much more problematic than ISI on the marks, because it both closes the eye and increases the detection noise. The main propose of the optical equalizer [145-147] is to eliminate ISI in the spaces. This is the reason makes the optical equalizers much more effective than electrical equalizers for many kinds of impairments such as PMD when it is too late to clean up the spaces in order to avoid signal spontaneous beat noise in the spaces after detection. Optical equalizers clean up the spaces by taking a controllable portion o f the energy at each time instant and with a controllable phase. A simple optical equalizer structure is consisting two identical Mach-Zehnder interferometers (MZI) connected in series with a single mode waveguide. Each MZI has variable couplers and a free spectral range (FSR) of 50 GHz as shown in Fig. 2.40. This structure has two to four control knobs and acts as a two tap linear equalizer in signal processing technology. Causd i i Cmaotft (a) (b) (c) Fig. 2.40. (a) Schematic diagram o f an optical PMD equalizer, (b) equalizer impulse response, and (c) measured fiber-to-fiber transmissivity [145]. 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6.1.3 Electrical PMD Equalization Equalizers in the electrical domain to mitigate various impairments in digital optical communication systems are well known and demonstrated [152-155]. Basically the electrical PMD equalization is achievable by inverting the nonlinear transfer function o f the system in the electrical domain. Two types of well known electrical equalizers are transversal filters (TF) [152] and decision feedback equalizers (DFE) [153-154] that are performing linear and nonlinear signal processing after detection. Although equalization in electrical domain reduces efficiency o f equalization compare to optical equalization since the information carried by the signal field in the output SOP and optical phase, both are random and varying with time, are lost due to square law detection. However, nonlinear processing schemes like feedback of sampled and decided signal in a DFE can be implemented, which have no counter part in the optical domain. In addition, sophisticated processing scheme like the maximum likelihood sequence detection (MLD) can be applied performing the decision not on a bit-by-bit but after collecting the distorted signal sequence over a few bit slots [155]. Fig. 2.41 shows a conventional electrical PMD equalizer. DGD • • Fig. 2.41. Conventional electrical equalizer (TF). 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Since in WDM systems, each channel needs to be equalized individually, it is highly desirable to have a compact realization o f such a system. Electronic PMD equalizers have the potential o f a compact integration within the electronics and optical receiver. 2.6.1.4 PSP Filtering In PSP filtering method, a polarizer selects the maximum optical power in the corresponding PSP and sends it to the receiver. Although the realization o f this technique is simple, however, it always looses 3-dB optical power. Moreover, the control signal is optical power that drifts and causes non-ideal performance in this method. In addition, this method is affected by higher-order PMD. 2.6.1.5 Polarization Diversity Receivers Two different polarization diversity receivers have been demonstrated including: (i) two arm receiver using one PBS, two detector, a electrical time delay line, electrical combiner, and a control signal to PC before PBS and (ii) N branches o f two arm receivers and N electrical combiner and equalizers [150]. In both technique it has been shown power penalty margin can effectively be increased. 2.6.2 PMD Monitoring PMD equalization and optical PMD compensation are the powerful techniques that potentially allow to upgrade the currently installed fiber links to high-bit-rate. Since PMD is a stochastic, time-varying and temperature-dependent process, the 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equalization and compensation o f the channel degradation induced by PMD must be adaptive to follow statistical variations o f PMD either in optical domain or electrical domain. The use of counteractive element called PMD monitor is the only way of managing accumulated PMD for the next generation o f telecommunication system [156-158]. Therefore it is imperative to implement some method o f rapid on-line dynamic monitoring of the accumulated PMD that does not interrupt the data transmission in high-speed optical systems and networks. In this section, the characteristic o f a PMD monitor, the different types o f PMD monitors and different PMD monitor configurations are explained. As PMD can vary on a millisecond time scale [38], both electrical and optical PMD equalizers, and OPMDCs must be dynamic, with a feed-forward [72,74-76] or feedback loop [33,73,159-160] that monitors the quality o f the incoming signal and provides a control signal to the compensator or equalizer. In addition, the independent effects of PMD on different wavelengths force an optical system to allocate a single compensator to each channel in WDM systems. They will thus require one or more monitoring modules to measure the effects o f PMD on multiple WDM channels [161], depending on the response time o f the module. PMD monitoring systems should meet the following requirements [156-157]: (i) simplicity, (ii) low cost, (iii) fast response time (monitoring speed < ms), (iv) control signal highly correlated to PMD, (v) high sensitivity [162-163], (vi) wide DGD monitoring range (-bit time) for the feed forward configuration [164-165], and (vii) low probability o f trapping in a local maximum [166]. 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A number o f monitoring signals appropriate for PMD mitigation include: (i) DOP [164-165,167-169], (ii) the power in the data’s spectral frequency components [33,58,75,138,170-174], (iii) the eye-opening penalty [160,175], (iv) measuring the phase difference between two frequency components located on orthogonal PSPs [176], (v) a subcarrier tone added to the data [177], and (vi) arrival time measurement of polarization-scrambled light [77], The three configurations that have been realized for optical PMD compensation include: (i) feedback, (ii) feed-forward, and (iii) feedback + feed forward. In the first configuration, shown in Fig. 2.42(a), one or more feedback signals align the incoming signal’s SOP to a fixed or variable DGD element that is controlled by another feedback signal. In the second technique, the addition o f a polarization scrambler at the transmitter allows a monitoring system in front o f the compensator to estimate both the DGD and PSP o f the PMD vector. This is important for avoiding the case when the DGD o f the link is high but the signal happens to be aligned with one of the fiber PSPs, which would cause a standard feedback system to see little penalty and assume there is little DGD. Thus, the feed forward signal can align and set the variable DGD element from its estimation o f the total PMD vector. Fig. 2.42(b) shows one of the feedforward configurations. In this configuration, a feed-forward signal sets a variable DGD element to the estimated DGD of the link and the feedback control signal varies the PC. 117 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fiber L in k w /PM D Sectricat m cak/.A i i«t# central signal Momto(wg [Variable DGO Component Monitoring: System Variable DSD Component Elactrteal control signal System if Electrical control signals Monitoring System I Fig. 2.42. (a) Feed back configuration and (b) feed forward and feedback configuration for optical The feedback configuration suffers from slow response time since it requires dithering of the signal to find an optimal point. However, feedback configuration has been successfully demonstrated with a large signal response o f 60 Hz and small signal response in excess of 300 Hz. On the other hand, the feed-forward configuration response time is fast without dithering, but requires polarization scrambling at the transmitter. One advantage o f the feed-forward configuration is that it is independent of the input signal’s SOP, and therefore, the OPMDC only tracks changes in the PMD vector, which fluctuates at half the speed of SOP variations [30], In summary, the performance o f different optical PMD equalization and compensation techniques depends on the monitoring signal, the control algorithm, and the configuration of the PMD compensator. The next several sub-sections describe different techniques for monitoring PMD. 2.6.2.1 Degree of Polarization Degree o f polarization (DOP) is the ratio o f the optical power o f the polarized component o f the signal (the difference maximum optical power and minimum optical power) to the total optical power. The value o f DOP = 1 indicates that the PMD compensation. 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. light is completely polarized (Fig. 2.43(a)); for 0 < D O P < 1 the light is partially polarized (Fig. 2.43(b)); and the value D O P - O shows that the light is unpolarized (Fig. 2.43(c)). ■ i i (b) (a) Fig. 2.43. (a) Fully polarized light, (b) partially polarized light, and (c) unpolarized light. By using a polarizer, rotator, and detector, we can measure the maximum and minimum polarized optical signal’s power (Fig. 2.44(a)) and determine the DOP of signal using the following equation: (jP max P m in ) D O P = - (2.6.1) ( P max + P m in ) In addition, we can measure the signal’s DOP using a polarimeter as shown in Fig. 2.44(b). The length o f the normalized Stokes vector is a measure o f the DOP. D O P J s f T s J T s f n - o - 2 + s 2 + s 2 (2.6.2) When the optical signal passes through the fiber with PMD, the “fast” and “slow” halves o f the signal have different speeds and thus less overlap. As this overlap decreases, the signal replicas on the two PSPs become more and more depolarized, and the measured DOP at the polarimeter is reduced. Thus, the effect o f PMD on the 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Frequency P C Photo - Detecto J 3 u L Polarizer (a) DOP Polarimeter (b) Fig. 2.44. Measuring DOP using (a) the maximum and minimum optical signal’s power and (b) a polarimeter. signal’s DOP can be used as an optical monitoring parameter to measure PMD. The use o f the DOP to monitor the effects of PMD has a number of advantages over other techniques, including: (i) there is no need for high-speed devices, (ii) it is simple, (iii) it is bit-rate independent, and (iv) it is unaffected by chromatic dispersion [178], Unfortunately, DOP measurements as a function of instantaneous DGD and the effectiveness o f a PMD compensation suffer from the following crucial disadvantages: (i) there is a small DGD monitoring window when measuring a short pulse RZ signal since the DOP is pulse-width dependent [162- 165], (ii) there is a lack o f sensitivity when measuring a NRZ signal [162,164- 165,178], and (iii) it is affected by nonlinearity (SPM, XPM) [178-182], 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6.2.2 RF Spectrum Analysis of the Detected Signal PMD causes any given optical frequency component to split between the two orthogonal PSPs and propagate down the fiber at different speeds. This speed differential de-phases the given frequency component on each PSP with respect to the carrier and generates a notch in the electrical spectrum after detection due to destructive interference. A number o f these notch components have been proposed as first-order PMD monitors in a link for RZ and NRZ modulation formats including: (i) the quarter-bit-rate frequency component, (ii) the half-bit-rate frequency component, and (iii) the bit-rate frequency component, as shown in Fig. 2.45. NRZ Power Spectrum NKZ*£ye • -a , fc / v . RZ Power Spectrum • |1*Ctock L 2* Clock ,-Q £ te r n o & V . Fig. 2.45. NRZ and RZ frequency components can be used for PMD monitoring. To show the first-order PMD effect on the electrical signal after detection, the output o f electric field can be expressed as dgd ^ , /77 , dSd Eoul(t) = A j y x ( t — )ex + A ^ ( l - y ) x ( t + — )ey (2.6.3) where A , y , x(t), d g d , ex , and ey are amplitude o f electric filed, optical power splitting ratio between two PSPs, the normalized pseudo-random bit sequence 1 2 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (PRBS), differential-group-delay, and the input Jones polarization states which depends on the azimuth and the ellipticity of the input SOP, respectively. After square law detection, the electrical signal simplifies to y (t) = \E0 jt) \ = A 2y + A2( i - r ) (2.6.4) By using the equation (2.6.5) that relates the power spectrum o f a random signal to its Fourier transform o f signal, we have S J f ) = U rn i £ ( F{\Eoul(t)\2} ) (2.6.5) T -*+ w T where E (•) and F{*} represent the expectation and Fourier transform operators and S (f ) is the power spectrum o f detected signal. Sy( f ) = U m ^ E ( r-> + c o i A2}F{ # - * f > 2 } ) (2-6.6) S y ( f ) = A4\cos(rfdgd) + j(l-2 y s in (r fd g d ))\2 U rn — E (F {\x (t)\2} ) (2.6.7) y r^ + co T The affected electrical power spectrum by PMD can be expressed as Sy( f ) = A4[ 1 - 4y( 1 - r ) sin2( nfdgd)]S^2 ( f ) For the worst case ( y = 0.5), the detected power spectrum is s y ( f ) = A* cos2(rfdgd)S^2 ( f ) (2 .6.8) (2.6.9) Equation (2.6.8) shows that the transfer function o f transmitter, fiber with first-order PMD, and receiver can be described as H ( f ) = cos( nfdgd ) + j ( l - 2ysin( rtfdgd ) (2.6.10) 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. As seen in the equation (2.6.10), the notch frequency depends on the link’s first- 2k +1 order PMD ( / = ---------, where k is an integer). However, higher-order PMD can 2dgd cause inconsistency in RF spectrum analysis-based first-order DGD measurement. Fig. 2.46 shows the RF power variation as a function of DGD for different frequency components. By measuring the RF power in the electrical spectrum at the chosen notch frequency, the effects of PMD on a data stream can be measured and can thus provide a control signal to a PMD compensator in a feedback [33,58,138,170-174] or feed-forward configuration [75,77]. Using the low frequency components for PMD monitoring has a number o f advantages in that they are not sensitive to higher-order PMD since they are closer to the center o f the optical spectrum, and they are more correlated to the BER when compared with the DOP method [183]. However, the RF power variation of these components (sensitivity) is less when compared to the higher frequency components. 1 0.8 0.6 < o 0.4 0.25R, 0 D G D / T b Fig. 2.46. Received RF power variation vs. DGD for 1/8, quarter, half, and bit-rate frequency components. 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6.2.3 Eye Opening Eye opening measurements are another electrical method for PMD monitoring that is based on an integrated sampling system. Since this technique evaluates the eye opening at the sample time, it needs a valid clock signal, called the synchronous control signal. The eye monitor is an integrated SiGe IC consisting o f two decision circuits in parallel instead o f a simple decision gate in a conventional receiver as shown in Fig. 2.47. The upper decision gate acts as active data channel; where as the lower gate is the monitor gate working with variable threshold to characterize the edge of the eye at variable phase. By dithering, the monitor threshold pseudo errors are generated. Using an EXOR these pseudo errors are detected and added within the integration time by an analog integrator. The eye opening is determined at a target integrator voltage which corresponds to a certain pseudo error rate (PER) in the monitor decision gate. In practice, a limited number o f points at the eye edges are measured by a PC controlled system with subsequent interpolation to determine the eye opening within 2 ms. If fluctuating signals are measured, the edges o f the eye and the slops are moving fast, which have to be tracked by the monitor. Due to analog integration o f error bits eye opening can be measured at PER > 10'4. The error rate fluctuates statistically with a Poisson distribution caused by optical noise. Due to integration o f a statistical signal the relative fluctuation (crre/) of eye opening signal at each point is given by 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where R is the transmission rate, PER is the pseudo error rate for measuring the eye opening, and Tjn t is the integration time. For a relative fluctuation o f integrator voltage o f 3.3% measurement within 0.1 ms are possible at PER> 10'3. Due to statistical limits, measurements at lower PER require increased integration times, which are not suitable for high-speed operation. The sensitivity o f eye monitor was determined by measuring the eye opening using degraded signals induced by noise (OSNR degradation) or PMD. yggg ip |gfc up p i p |. 2H jap. p i .gp ip. jpg jggf m p i m n pp .m > g jg * ; aeclioii circuits - " 1 1 - recovered data i i i i i I i i f I t-% -1 i 0 1 L & I M w i* «s s J w « Fig. 2.47. Eye monitor with analog integrator. Eye monitoring is typically used for electrical PMD equalization [128,175,184-185], though its application for optical PMD compensation also has been shown [160]. While the eye opening is tightly correlated to the BER, it is affected by other distortion sources such as chromatic dispersion and nonlinearities. 2.6.2.4 Phase Detection One other asynchronous method for DGD monitoring is the phase difference measurement o f a given frequency component after PSP filtering and electrical 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. detection [176], This method is not affected by other distortion sources such as chromatic dispersion however it requires PSP tracking at the receiver. This technique is fairly complicated and is also affected by higher-order PMD. 2.7 DGD and PMD Measurement Pulse broadening within optical fibers is very small, o f the order o f several picoseconds. Consequently, PMD is usually not a problem for transmission systems operating at 2.5 Gbit/s. Generally; the dominant source cause o f pulse broadening is chromatic dispersion in the SMF-based systems. However, PMD can be a crucial limitation in > 10-Gbit/s/channel fiber optical communication systems due to high- PMD legacy fiber and PMD o f many in-line components. Signal quality can be degraded by the PMD of components such as optical filters, FBGs, (de)multiplexers, and optical isolators, even in links where the inherent first-order PMD, i.e. DGD, of the fiber itself is negligible. For this reason, it is imperative for component manufacturers and suppliers to be able to accurately measure the DGD o f devices and components to ensure they are compliant with customer specifications. Some factors that play a key role in choosing a technique for DGD measurement include: (i) cost, (ii) speed, (iii) PSP measurement, and (iv) sensitivity to higher- order PMD effects. The variety o f PMD measurement techniques has been developed. These techniques can be categorized into two groups, including: (i) time domain measurements and (ii) frequency domain measurements. In this section, different types o f DGD/PMD measurements, advantages and disadvantages o f each proposed methods are discussed. 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7.1 T im e Domain Measurements In the time domain method, there are four basic measurements methods which are used, including: (i) the modulation-phase-shift (MPS) method [186-187], (ii) the pulse delay method, (iii) the interferometric method [188] and (iv) polarization optical time domain reflectometry (POTDR) [189-190], 2.7.1.1 Modulation-Phase-Shift Method In the MPS [186-187], a high frequency sinusoidally modulated signal is transmitted through the device under test (DUT). The DGD is determined from the difference in modulation phase between PSPs o f the DUT. In this measurement the input SOP is continuously changed in order to find the maximum and minimum delay times. When the maximum and minimum delay times are found the input SOP is aligned with the PSP’s o f the DUT. The phase difference between the maximum and minimum delay determines the amount o f PMD at the wavelength. The measure DGD is given by DGD = ^m a x ~ ^n in (2.6.12) where f m, < j )m ax, and < j > m in are the modulation frequency, the measured maximum phase, and the measured minimum phase (in radian), respectively. 2.7.1.2 Pulse-Delay Method In this method, the DGD at a given wavelength is obtained by launching sequentially two very short optical pulses into the fast and slow axes o f polarization (input PSPs) 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and then measuring the difference in the arrival time o f the two pulses that emerge from the corresponding output PSPs. For experimental measurement, a beam splitter is used to separate optical beam into two orthogonal PSPs and the PC brings the pulses into the desired PSPs of DUT. By adjusting the PC, The DGD o f DUT can be measured from less than 0.1 ps to several tens o f seconds. This method requires narrow pulses (pulse width < required resolution) and high-speed photo detector. 2.7.1.3 Interferometric Method The interferometric method can be used to test both individual components and long fibers [188]. However, the analysis of the data is different for these two configurations. If long fibers are tested then there is considerable mode coupling. Discrete components tend to exhibit little mode coupling whereas long fibers exhibit large mode coupling. Mode coupling length is the distance traveled for each of the two orthogonal modes where the energy in each mode becomes one half of the total energy. The objective o f the measurements is to obtain the mutual coherence function o f the two signals. As in the case o f the pulse delay the measurement is a direct measurement o f the time delay. The coherence function is directly related to the visibility function. Light from the optical source propagates into both arms o f the interferometer and light from the moving reflecting prism and the fixed prism is superimposed on the detector. The maximum visibility (u ) occurs when the lengths o f the two arms differ by less than the coherence length o f the source and when the 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. path lengths are equal. Straightforward analysis then shows that the time delay is given by 7 A x At = (2.6.13) c where Ax is the difference in path length between two arms o f the interferometer. A polarizer is used before the detector to allow the interference by coupling light from each o f the output PSPs of DUT into the photo detector with a common polarization. The interferometric method is applicable to optical components with well- defined eigenmodes, and to optical fiber in the “long-fiber” reghne, where the PSPs are dependent on the wavelength. For, a non-mode couple device the interferometer leads to a central peak surrounded by two adjacent peaks. The two outlying peaks are due to the “slow” mode and the “fast” mode o f the optical signals, respectively. The time separation between either o f the outlying peaks and the central peak is the differential-group-delay ( A t ). On the other hand the interferometric response for highly mode-coupled fiber with PMD is much greater than the coherence time o f the source consists o f an interferogram containing numerous components. The PMD is then determined by either a direct fitting o f a Gaussian curve or computation o f the photocurrent response. Interferometric measurements are extremely sensitive. Movement changes the details o f the interferogram but not its overall shape. Because interferometry measures large values of PMD quickly and the interferometric setup is easily split into source and receiver units, the method also lends itself to measure o f high-PMD installed fiber. 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7.1.4 Polarization Optical Time Domain Reflectometry This technique uses a polarization optical time domain reflectometer (POTDR), which is based on the analysis o f the SOP of the backscattered field [189-190]. By means o f a POTDR the local properties o f fiber birefringence can be characterized; preliminary results of laboratory tests performed on fibers tightly wound on drums can be found in [191]. This method has the following advantages over the other methods, including: DGD, Beat-length, and correlation length measurements using fiber end. 2.7.2 Frequency Domain Measurements Frequency domain measurements use either an optical source with a broad spectrum, a light-emitting diode (LED), or a tunable laser. These methods can measure over a wide range o f wavelengths. Mathematically, the measurement o f PMD over a wide range o f wavelengths is equivalent to measuring it at a single wavelength over a long period of time due to ergodicity. In other words, the value average will be identical. Five types o f measurements in the frequency domain are (i) the Poincare sphere analysis [192], (ii) the Poincare sphere, (iii) Jones matrix eigenanalysis (JME) [193], (iv) the fixed-analyzer measurement [194], and (v) the Muller matrix method (MMM) [195]. 2.7.2.1 The Poincare Sphere Analysis The Poincare sphere analysis is a wavelength dependent, fully polarimetric method to characterize the PMD o f an optical fiber within a given optical frequency range 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [192], It is based on the measurement of the change in three orthogonal Stokes vectors with frequency. In the absence of PDL, output polarization states rotates around the PMD vector and the motion equation o f the Stokes vector is described by dd - |i? | (2.6.14) dco where 0 is the rotation rate as shown in Fig. 2.48. The rotation rate and axis o f defined coordinate system yield DGD and PSP o f DUT a>, +o)7 . . at frequency —— —- , respectively. (ca) 'oul Fig. 2.48. Poincare sphere analysis. 2.12.2 The Poincare Sphere Method In the Poincare sphere (Poincare Analysis (PA), and SOP) techniques, if the light launched with equal power into both PSPs, then output SOP follows great circle on the Poincare sphere and equation (2.6.15) can be rewritten as — =< DGD > (2.6.15) Aa> Equation (2.6.15) is the defining relationship and the basis o f this method for the DGD measurement. In addition, this method is also suited to non-mode-coupled components. 131 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7.23 The Jones Matrix Eigenanalysis Method In this method, the complex 2x2 Jones transfer matrix T ( cd2 )T~l ( co, ) can be calculated by measuring two output states o f polarization at two launched wavelengths and three launched states o f polarization [193]. The eigenvalues and eigenvectors o f T(a>2 )T~’ (co,) yield DGD and PSP o f DUT at frequency °J/ + 0)2 , respectively. 2.T.2.4 The Fixed-Analyzer Method In this method the incident polarized light propagates through an optical fiber whereupon the emerging beam propagates a polarizer and is then spectrally analyzed using an optical spectrum analyzed using an optical spectrum analyzer (OSA) [194], The analyzers are used to select the orthogonal polarization modes. As the wavelength is changed the power transmitted through the fiber changes due to the PMD. Using this information the average PMD is determined by coming either the number o f exterema (peaks and valleys) or by counting the number o f zero crossing. In either case the test is actually measuring the rate at which the output SOP changes as the wavelength changes. From this data the PMD can be calculated. In the broadband source measurement the entire optical spectrum appears at the optical detector within the OSA. Thus, the OSA sweeps over the entire spectrum and data is acquired. With a tunable optical source only a single wavelength is used. Consequently, it is only necessary to use a power meter, this spectral behavior o f the fiber under test is obtained by spectrally varying the optical source, that is, the laser 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. can be tuned. The mean differential-group-delay over the spectra range (< A t >A) of DUT is kNX2X, < A t > ----------- — (2.6.16) k 4tv(X1- X 2)c where Xn X2, N e , and k are the initial and final wavelengths, the number of transmission extrema, and the factor appears to account the statistically for the effects of the wavelength dependence o f the PSPs . The factor k is called the mode- coupling factor and its value is 0.824 for randomly coupled fibers and 2.0 for non mode coupled fibers and devices. Another type of the fixed-analyzer method is to use a polarimeter rather than just a power meter. This provides several advantages over the use o f a single analyzer. The use o f three normalized Stokes parameter traces provides a full description o f the output polarization over wavelength. Each trace is analyzed by extrema counting (or Fourier analysis) and the resulting three mean DGDs are averaged. The measurement o f the three Stokes parameters is less dependent on the launch polarization. Another important advantage is that the normalized Stokes parameters are immune to changes in optical power. Finally, a Stokes parameter allows the user to view the output SOP on the polarization sphere for a sensitive indication o f the stability o f the test device. 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7.2.5 The Muller Matrix Method In the Miiller matrix method (MMM), the real 3x3 rotation transfer matrix R(co2 )R'(oij) can be calculated by measuring two output states o f polarization at two launched wavelengths and two launched states of polarization [195]. The rotation angle and axis of R(co2)R'(co, ) yield DGD and PSP of DUT at frequency 0)' + 0 )2 respectively. 2 2.7.3 Designing the DGD/PMD Measurement Experiment For DGD/PMD measurement, it is necessary to eliminate PMD in the measurement system by choosing short, and straight (no tight bends, radius o f bended fiber > 5 cm). In addition, we need to stabilize fibers and keep motion slow compare to “time condstant” because moving fibers modulates polarization states, adds noise, and errors proportional to DGD. Moreover, we need to either mitigate temperature 3/1T dynamics or keep rate o f temperature variation with time ( — — ) small. dt 2.7.3.1 Spectral Efficiency of the DGD/PM D M easurement SNR of DGD measurement depends on the frequency resolution ( Aco), DGD of DUT, and a (bandwidth efficiency factor) as it is described in SNR < aDGDAco (2.6.17) In DGD measurement, bigger bandwidth efficiency factor decreases the effect of polarization noise and improves SNR. In addition, the large step size ( Aco ) improves noise performance. However, aliasing and higher-order PMD limit maximum step 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. size. The inequality described in (2.6.18) gives a rule o f thumb for maximum step size in DGD/PMD measurement methods. DGDAco < n (2.6.18) 2.73.2 DGD/PMD Measurement Uncertainty The dominant uncertainty source depends on the DUT (mode-coupled, non-mode coupled). In non-mode coupled devices, measurement is dominated by fiber lead birefringence uncertainty (small PMD or broad bandwidth). However, the dominant uncertainty source is random noise (bandwidth efficiency factor) for big PMD or large frequency step size. In mode-coupled devices, measurement is dominated by statistical uncertainty. 2.7.4 DGD/PMD Measurement Concerns For a good measurement, we need to consider the following steps: 1. Appropriate measurement techniques • Cost • Spectral resolution • Speed • PSP measurement 2. Optimized measurement • PMD o f measurement system • Moving fibers • Multiple reflections 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3. Measurement parameters • Appropriate spectral resolution 4. Uncertainty The various methods for PMD/DGD measurement are summarized in Table 2.1. Methods Determines Light source Analyzer DGD Range MPS DGD/PSP Modulated Laser RF Spectrum Analyzer > 20 ps Pulse Delay DGD Short laser pulse Oscilloscope > 10 ps Interferometric DGD Broadband CW LED Interferometer <100 ps Fixed Analyzer DGD Narrowband Laser Polarizer/Power meter 0.1 ps-1 ns PSA DGD/PSP Polarimeter 0.1 ps-1 ns JME DGD/PSP 1 fs- 1 ns MMM DGD/PSP Table 2.1. The various methods for PMD/DGD measurement. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 Chromatic Dispersion Monitoring in Digital Optical Fiber Communication Systems In this chapter, we demonstrate two techniques for monitoring accumulated dispersion based on: (i) partial optical filtering and phase detection [115] and (ii) using a dispersion-biased RF clock tone [118-119], These methods allow determination o f both the sign and magnitude o f the accumulated dispersion by passively detecting RF component in the electrical spectrum without any modifications to the transmitter. 3.1 Chromatic Dispersion Monitoring Using Partial Optical Filtering and Phase Detection Phase shift detection techniques [113-115] have a key advantage over other dispersion monitoring techniques in that they are not easily affected by other distortion sources (such as first-order PMD). However, some demonstrated phase shift detection techniques require fast tuning o f an optical filter across the sidebands, a reference clock signal, synchronization between WDM channels, and multiple filters and/or receivers. In addition, the maximum dispersion range that conventional phase shift detection techniques can measure is limited by half o f the bit time phase difference induced by group velocity delay [115], However, in long haul 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. transmission, the residual dispersion in each WDM channel may exceed the allowable dispersion range of a practical system due to dispersion slope mismatch. Also, the sign o f accumulated dispersion may introduce different pulse spreadings among WDM channels when they interact with nonlinearities. So, it would be highly desirable to have a dispersion monitor that extends the dispersion monitoring range beyond that o f conventional techniques and that can determine the sign o f the dispersion. In this section, we demonstrate a new chromatic dispersion monitor that uses phase detection to enable flexible wide range dispersion monitoring. We filter the optical signal asymmetrically by placing an optical filter offset from the center o f the optical data spectrum, then compare the phase o f the RF component at the bit rate (e.g. 10 GHz for 10-Gbit/s data) with the phase o f the generated bit-rate RF component, which we create by frequency-doubling the half-bit-rate RF component (e.g. 5 GHz doubled to 10 GHz for 10-Gbit/s data) from the detected data spectrum. This phase shift is correlated to dispersion because dispersion causes a phase shift between these two frequency components. Moreover, Asymmetric filtering isolates only one sideband’s optical frequency components, cancels fading effects, and makes the phase shifts observable. We apply this technique, via simulation, to 40-Gbit/s NRZ, RZ and carrier-suppressed RZ (CSRZ) signals and show that our technique results in a near quadrupling o f the monitoring range compared to other monitoring techniques that has ability to determine sign o f dispersion (i.e. from ±40 to ±160 ps/nm for RZ and CSRZ signals, and from ±40 to ±120 ps/nm for NRZ signals). We 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. also found that the monitoring window increases from +40 ps/nm to +350 ps/nm for 40-Gbit/s CSRZ signals when the symmetric filtering (i.e. centering the filter on the optical spectrum) is used. In additioin, the optimal filter is found for each configuration. This technique was verified experimentally for 10-Gbit/s NRZ, RZ and CSRZ signals and we found that the monitoring range is increased from +640 to +1600 ps/nm for RZ and CSRZ signals, and from 640 to 800 ps/nm for NRZ signals (Increases are limited due to the lack of an optimal filter for both cases). Using this monitoring technique, we also demonstrate 10-Gbit/s CSRZ, four-wavelength tunable dispersion compensation using a nonlinearly chirped, sampled FBG. We achieved <0.6-dB power penalty for all CSRZ data channels after compensation. 3.1.1 Theory of Partial Optical Filtering and Phase Shift Detection of Bit- Rate and Doubled-Half-Bit Rate Frequency Components When a data modulated signal passes through a SMF fiber, chromatic dispersion causes the various optical frequency components within the data spectrum to travel at different speeds down the fiber, as shown in Fig. 3.1. After detection, this phase match appears as RF power variation A conceptual diagram for our technique is shown in Fig. 3.1. In the monitoring tapline at the receiver, after asymmetric filtering, the beat term between these optical components with the strong optical carrier results in sinusoids (with varying envelopes due to the data modulation) that can be extracted using a narrowband RF filter. We take the bit-rate RF component and the half-bit-rate RF component, frequency-double this half-bit-rate RF component, compare their phases, 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and use the resulting phase differential as a monitoring signal for chromatic dispersion compensation. H Tunable CDC Phase Detector TTA2 (fc )^ D L 2C O M i : Mixer Optical Asymmetric Filtering @ R b -Ib p f K 0 /e Asymmetric .• • . Optical spectrum;;:: ■ Frequency Doubler ;. -M -1* 9 .10 M . Frequency.: ■ , (GH*)' ; CD Monitor Fig. 3.1. Conceptual diagram for the proposed chromatic dispersion monitor using phase comparison of the bit-rate and frequency-doubled half-bit-rate frequency components. Because the spacing between two extracted original RF components is four times smaller than the corresponding RF components from the conventional method, the monitoring range is extended by factor o f four regardless to modulation formats theoretically. But in CSRZ system, symmetrical filtering further increase the monitoring window to ~ 8 x those of conventional phase-detection techniques, but lose the ability to discern the sign of dispersion in the process. In this system, there is no carrier component, however, after filtering (and removing the 1.5Rb ( Rb: bit rate) components), the half-bit-rate optical frequency components beat each other at the receiver to generate RF component at bit rate, and this is not sensitive to dispersion. However, half-bit-rate RF component from the data spectrum is sensitive to dispersion. By doubling this frequency component, and comparing the phase o f this doubled frequency component with the bit-rate frequency component, we can monitor chromatic dispersion. 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.1.2 Simulation and Experimental Results We apply this technique, via simulation, to 40-Gbit/s NRZ, RZ, and CSRZ signals for varying amounts of chromatic dispersion, and the results are shown in Fig. 3.2. The dispersion - v s .- phase curve changes as the modulation format changes. It is clearly seen that dispersion is well correlated with the phase shift. Also, from the figure, it is obvious that this technique can determine the sign o f the dispersion by measuring whether the phase differential is positive or negative. The monitoring windows are +120, ±160, and ±160 ps/nm for NRZ, RZ, and CSRZ signals, respectively. We found that the bandwidth and the position o f optical filter should be optimized to maximize the monitoring window. The optimal optical filter bandwidth (BW) and offset (OFF) are BW = 0.5Rb , OFF = 0.5Rh for NRZ, BW = 0.8Rb , OFF = 0.5Rh for RZ, and BW = 0.5 Rb, OFF = 0.25Rb for CSRZ. 180 Q 4 Z !E W •90 -180 NRZ 40 Gb/s Asymmetric filtering BWr ,„«=20 GHz ■160 -80 0 80 Dispersion (ps/nm) 180 RZ 40 Gb/s 2 -90 Asymmetric filtering BWQ « 32 GHz -180 • S O 0 Dispersion (ps/nm) 80 (ps/nm) 160 -160 CSRZ 40 Gb/s Asymmetric filtering B W „_ » 20 GHz -160 -80 0 80 Dispersion (ps/nm) (a) (b) (c) Fig. 3.2. Simulation results for 40-Gbit/s (a) NRZ (b) RZ, and (c) CSRZ dispersion monitoring using optical asymmetric Gaussian filtering. 141 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 180 120 180 $ 100 0 )1 3 5 Ui 135 80 300 600 900 1200 1500 200 400 600 800 800 1200 1600 400 10 Gb/s CSRZ Asymmetric filtering BWfpf= 8 GHz J O f f l h 10 Gb/s NRZ ^ Asymmetric filtering BWrea= 13.5 GHz OB' Asymmetric filtering BWrae= 13.5 GHz . 10 Gb/s RZ Dispersion (ps/nm) Dispersion (ps/nm) Dispersion (ps/nm) (a) (b) (c) Fig. 3.3. Experimental dispersion monitoring results for 10-Gbit/s (a) NRZ, (b) RZ, and (c) CSRZ signals. The NRZ and RZ monitors used an asymmetric 13.5-GHz FBG notch filter, while the CSRZ monitor used an 8-GHz Fabry-Perot fiber (FPF) filter with an FSR o f 750 GHz. Fig. 3.3 shows our experimental results for phase shift versus dispersion for 10- Gbit/s NRZ, RZ, and CSRZ signals for varying filter types and bandwidths. Due to equipment limitations, only positive dispersion is demonstrated in this experiment. The monitoring windows are ~80Q, -1500, and -1300 ps/nm for NRZ, RZ, and CSRZ signals, respectively. This is an increase by a factor o f -2.5 for RZ and CSRZ signals, and the monitoring windows for all three would be extended further with the use o f an optimal optical filter. Fig. 3.4(a) and (b) show the 40-Gbit/s simulated and 10-Gbit/s experimental results for phase shift versus dispersion for a number o f filter offset points from the center of the optical spectrum. There is a tradeoff between sensitivity and monitoring range as the offset changes. Note that for the optimal filter offset (0.25Rb), a good balance between the two is obtained. If we switch from using asymmetric filtering to using symmetric filtering, we achieve the simulation results shown in Fig. 3.5 for 40-Gbit/s CSRZ signals, with Gaussian filter bandwidths between 10 and 40 GHz. With this filtering, we could more than double the monitoring range with the cost o f losing the ability to determine the sign o f the dispersion. It is clear from Fig. 3.5 that there is 142 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the tradeoff between the monitoring range and sensitivity as the filter bandwidth is varied - as filter bandwidth increases, sensitivity increases. 180 f Af a +20 GHz 40 Gb/s 180 r j CSRZ " a T lir £ 90 1 Af = +10GHz / / 0 b . o> 9 90 0 Q Q a 0 5 " z 0( . e (O \ Af « 0 GHz (/> 9 VI C O -90 S X*. > 1 * ^ "X . ^ 4> (0 (0 -90 JC x Af=0G H z J Z A . ----- b w g *,„ = 20 G H z\ £ L -180 - - b w ^ . w g h z 180 0 10 Gb/s A f = +4 GHz 0 A f « +2 GHz \ vAf = +6 GHz S s '' A f a O G H z ^ ^ x \ BWpP c= 8 GHz V ° £ - 90 *£-180 i/i 10 1 • " / / \ \ ............. A y / i f V N 2 0 f i f V ' G H z / 11 V \ ' ’ v i f \ \ rS ‘ j j 4 0 G b /s C S R Z V \ . 2 Q f j S y m m e tric F ilte rin g y \ G H z / / \ \ * • ' / \ *" BW oe„ „ .,« 4 0 GHz, 0 90 180 270 360 Dispersion (ps/nm) •400 -200 0 200 400 D ispersion (ps/nm ) (a ) Dispersion (ps/nm) ( b ) Fig. 3.4. (a) 40-Gbit/s simulation and (b) 10-Gbit/s experimental Fig. 3.5. 40-Gbit/s CSRZ results for CSRZ dispersion monitoring showing the effects o f simulation results using symmetric filter detuning on dispersion sensitivity and monitoring optical filtering showing increased windows. An 8-GHz FPF filter was used in (b). monitoring windows. 3.1.3 Chromatic Dispersion Compensation Results Using our technique as a dispersion monitor, we set up the 4-channel 10-Gbit/s CSRZ transmission system shown in Fig. 3.6(a) using a nonlinearly-chirped, sampled FBG (with a dispersion range from -600 to -1900 ps/nm) for tunable dispersion compensation. A FPF filter is used for asymmetric filtering (8 GHz bandwidth, 750 GHz FSR) to select a single channel. We then set the compensator for the appropriate amount o f dispersion and used that compensator for all four channels. After compensation using our monitoring technique, we achieved a near back-to- back receiver sensitivity (at 10" 9 BER) for the best o f the four channels, and <0.5-dB power penalty for the worst channel (shown in Fig. 3.6(b)). Residual power penalties may arise from the measured 50 ps peak-to-peak ripple o f the FBG. 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ib e r t M r x I— © nn- m>- [ S - |X 4|~ b h i H S ) \ SMF, 50 k NRZ CSRZ E? F A A / 10 Gb/s <5> 5 GHz 1 0 -a . \# — — Back-to-Back 1Q-9 1® 1553.4 nm (W/Comp.) : K 1555.0 nm (W/Comp.) 1 ^ — -21 -20 -19 -18 -17 Receiver Sensitivity (dBm) (a) (b) Fig. 3.6. (a) Setup for 4-channel 10-Gbit/s CSRZ dispersion monitoring and compensation, (b) BER performance curves after compensation for the best and worst after transmission through 100 km SMF-28 fiber. The penalty for the worst channel is <0.5 dB. 3.2 Enhancing Chromatic Dispersion Monitoring Range and Sensitivity Using a Dispersion-Biased RF Clock Tone One o f the simplest techniques for chromatic dispersion monitoring in standard RZ and NRZ signals is measuring the RF power o f the bit-rate frequency component (“clock”) after detection [117]. However, it is unclear how well this method of dispersion monitoring responds to nonstandard modulation formats. In addition, the monitoring range and sensitivity to dispersion may change as the modulation format changes. It has been previously shown that CSRZ signals are significantly more robust to fiber nonlinear effects and chromatic dispersion [196] when compared to standard RZ and NRZ signals due to the compact spectrum and altemate-phase reversal feature. In addition, CSRZ signals have a simple and stable zero-dispersion- compensation characteristic when compared to NRZ signals [196]. The chromatic dispersion tolerance for 40-Gbit/s CSRZ signals (defined as the 1-dB power penalty point) occurs at -2 5 ps/nm o f residual dispersion, and current techniques for monitoring, such as the RF power, have a severely limited monitoring range (-30 ps/nm). 144 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We demonstrate a technique o f dispersion monitoring for CSRZ signals using the RF clock tone power that has significantly enhanced monitoring range and sensitivity when compared to conventional RF tone power monitoring techniques. We show that standard RF power monitoring techniques, for CSRZ signals, have minimal sensitivity (<0.0048 dB/ps/nm for 10-Gbit/s CSRZ signals) and a small dispersion monitoring range. We use fixed positive and negative dispersion elements to “bias” the RF power to a maximum value in the monitoring tapline, after which our experiments show the monitoring range is extended from 480 ps/nm to -752 ps/nm, and the sensitivity is increased from 0.0048 dB/ps/nm to 0.0106 dB/ps/nm for 10- Gbit/s CSRZ signals. We also show simulation results for 40-Gbit/s signals, with the monitoring range extended from 30 to 48 ps/nm, and sensitivity increased from 0.0476 dB/ps/nm to 0.1667 dB/ps/nm. These monitoring ranges exceed the highest previously reported CSRZ monitoring ranges by 20% (640— >752 ps/nm for 10-Gbit/s signals, and 40— >48 ps/nm for 40-Gbit/s signals) [114], This technique does not require dithering o f the signal to determine the sign o f the dispersion when the dispersion exceeds the 0.6 dB penalty tolerance value. In addition, this technique can be applied to WDM systems by sweeping an optical filter across the WDM channels and using multichannel dispersion elements, such as a sampled LCFBG or FBG array. Using this technique to monitor dispersion in a CSRZ transmission link with different lengths o f SMF (20, 25, ..., 40 km), we demonstrate adaptive dispersion compensation using a NC-FBG, and <0.2 dB o f power penalty (at 10'9 BER) is achieved after compensation. 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.1 RF Clock Measurement Techniques for Chromatic Dispersion M onitoring It is w ell known that the electrical power spectrum of an NRZ signal does not contain any power at the clock frequency (i.e., a 10-Gbit/s data rate stream will not contain any RF power in the 10 GHz region, where there is a null in the spectrum o f the signal). However the effect o f dispersion is to induce an increase in the power in the spectral region of the clock. Within a range o f values of the signal dispersion, the power is proportional to the amount o f accumulated dispersion. Beyond this distance, the clock power fades again, and then continues to change periodically with the distance. As opposed to NRZ systems, RZ data contains a clock component, and within a range of values of the signal dispersion, the clock power is gradually faded away. Based on these effects, the measurement ranges are ±900 ps/nm for NRZ signals and ±640 ps/nm for RZ signals at 10 Gbit/s. 3.2.2 Dispersion-Biased RF Clock Tone Monitoring Concept A conceptual diagram of our dispersion monitoring technique for CSRZ signals is shown in Fig. 3.7. While the bit-rate frequency component is present in the electrical data spectrum o f a CSRZ signal after detection, this tone is not as useful for dispersion monitoring as similar tones in RZ or NRZ signals as it has low monitoring range and sensitivity. Fig. 3.7(a) shows that at the zero dispersion point, the RF clock power is fairly high (relative to the maximum clock power as dispersion varies). This RF clock power reaches a maximum level (and thus the edge o f the first dispersion monitoring window) after a minimal amount o f chromatic dispersion 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. has accumulated in the signal. After this maximum point, however, the RF clock power fades rapidly due to dispersion. We take advantage o f this fact by placing a dispersive element in the monitoring tapline at the receiver, biasing the CSRZ signal with enough positive and/or negative dispersion to reach the maximum clock power value (reference level), creating a second “dispersion monitoring window” located between the first maximum point of the RF clock power (reference level), and the next minimum power point, shown in Fig. 3.7(b). The signal after transmission (to which this bias dispersion is applied) will show RF clock tone fading from this maximum power value corresponding to the link dispersion, allowing large monitoring windows and a high sensitivity. We stress that the dispersive element is added only in the monitoring tapline, and thus does not distort the data signal. Small Clock Regeneration CSRZ Data Electrical Spectrum w/ Dispersion Clock SQ / Large Clock Fading Dispersive element Small Dispersion Monitoring Range . & Sensitivity t 7 _ . Clock „ First power [window (a) Disp. Large Dispersion Monitoring Range & Sensitivity I — S Clock power tap line at the receiver window Fig. 3.7. (a) RF clock tone regeneration for CSRZ signals due to chromatic dispersion - the clock tone starts at a high power level and quickly reaches a maximum value, resulting in a limited monitoring range and low sensitivity, (b) Using a fixed dispersive element to “bias” the RF clock power, we push the signal into the second monitoring window, extend the monitoring range and increase sensitivity. 147 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.3 Enhancing Chromatic Dispersion Monitoring Range and Sensitivity for Carrier-Suppressed RZ Signals To determine the amount o f chromatic dispersion bias required to reach the maximum RF clock power and the dispersion monitoring range and sensitivity of our second monitoring window, we simulated 10- and 40-Gbit/s CSRZ signals after varying amounts o f link dispersion using LCFBGs to bias the signal dispersion. In addition, we set up a simple CSRZ transmission system using varying lengths of SMF and DCF to bias the RF power and measured the RF clock tone power for the 10-Gbit/s CSRZ signal, and the results are shown in Fig. 3.8. Fig. 3.8(a) shows our simulated and experimental results for relative RF clock tone power versus chromatic dispersion at 10 Gbit/s for both positive and negative dispersion values with the monitoring windows (after biasing) shaded. The maximum RF clock tone power comes with a positive or negative dispersion value o f ~48Q ps/nm with a RF power differential o f only 2.3 dB from the 0-dispersion point. The RF power minimum comes at -1232 ps/nm of dispersion, and is down by ~8 dB from the RF power maximum. The dispersion difference between the maximum and minimum power levels is -752 ps/nm. Thus, by biasing the CSRZ signal by -4 8 0 ps/nm, the dispersion monitoring range can be extended by over 50%, and the sensitivity more than doubled from 0.0048 dB/ps/nm to 0.0106 dB/ps/nm. Our simulation results for 40-Gbit/s signals are shown in Fig. 3.8(b) - the RF power maximum comes at -3 0 ps/nm, with the minimum at -7 8 ps/nm. Thus, with 30 ps/nm biasing, the dispersion monitoring range is again extended by over 50%, to -4 8 ps/nm, and the sensitivity is more than tripled from 0.0476 dB/ps/nm to 0.1667 dB/ps/nm. 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -1400 -700 0 700 1400 Dispersion (ps/nm) (a ) -100 -50 0 50 100 Dispersion (ps/nm) (b) Fig. 3.8. Relative clock power as a function o f accumulated dispersion for (a) 10- and (b) 40-Gbit/s CSRZ signals. Note that in Fig. 3.8 we show RF clock tone power for both positive and negative dispersion values. This technique can be used for monitoring both positive and negative dispersion by switching between two monitoring taplines, one with a positive dispersion bias, and a second with a negative dispersion bias (or a single dispersive element that can provide positive and negative dispersion by switching between input ports). At first glance, as the RF power curve is symmetric around the zero-dispersion point, it seems difficult to determine the sign o f the measured dispersion. However, the sign of dispersion can be determined without dithering as long as the accumulated dispersion (for a 10-Gbit/s signal) is more than ~320 ps/nm. This is usually not a hindrance as this dispersion value is under the 0.6-dB penalty tolerance level for 10-Gbit/s CSRZ signals. By measuring o f the amount o f RF clock power variation relative to the defined reference level at biased dispersion point (±480 ps/nm for 10-Gbit/s CSRZ signals), we can estimate the accumulated dispersion in the link, as summarized in Table 3.1. When 320<D <752 ps/nm, the 149 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. relative RF power of the positive bias tapline is always between -2.3 dB and - 8 dB, while the negative bias tapline power is between 0 dB and -2.3 dB, while when - 752< D < -320 ps/nm, the relative RF power in the negative bias tapline is always between -2.3 dB and -8 dB, while the positive tapline power is between 0 dB and - 2.3 dB. Using these facts, the sign o f the dispersion can be determined as long as the absolute dispersion value is greater than 320 ps/nm. When the relative RF power level for both the positive and negative bias taplines ranges between -2.3 dB and 0 dB (0<| D |<320 ps/nm), the sign of the chromatic dispersion can be determined by dithering that tapline’s dispersive element and looking at one o f the bias taplines and the trend o f the RF power as the dispersion increases. For example, in the positive monitoring tapline, when the link dispersion is positive and we positively dither the dispersive element, the RF power will decrease. However, if the link dispersion is negative when we positively dither the element, the RF power will increase. In this maimer, we can determine the sign of the link dispersion. -2.3 < RF* < 0 dB -8 < RF* <-2.3 dB -2.3 < R F < 0 dB 0 < | D | < 320 ps/nm 320 < D < 752 ps/nm -8 < R F < -2.3 dB -752 < D < -320 ps/nm Table 3.1. Relative RF clock power values for the positive (RF4 ) and negative (RF ) bias taplines vs. dispersion. The sign of the dispersion is indeterminate without dithering when both RF+ and RF" are between -2.3 dB and 0 dB. 150 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.2.4 Monitoring and Compensation Results for Carrier-Suppressed RZ Signals To verify our monitoring technique, we take measurements for single channel CSRZ transmission over 20 to 40 km SMF (step size o f 5 km) followed by an FBG dispersion compensator. Fig. 3.9 shows the experimental setup for CSRZ transmission. Two cascaded electro-optic (EO) modulators, one driven by a 10- Gbit/s 21 5 -1 PRBS and the other by a 5-GHz clock, were used to generate the CSRZ signal. We added a dispersion compensator consisting o f a computer-controlled mechanically-stretched NC-FBG for which the dispersion can be adjusted from -300 to -7 0 0 ps/nm and used our monitoring signal as feedback to control the grating dispersion. CSRZ EO EO 40 km SM F L D _ _ — — • r; 10 G b it/s P R B S 2*5-1 NRZ it/s i , EDFA - £ > - D is p e rs io n C o m p e n s a to r (N o n lin e a r c h irp e d FBG) C h ro m a tic D isp ersio n M onitor - 4 ?0 I-dH+dI + 4 , s o p s /n m L .—* L _ J p s/n m vS C o u p le r > ,/r [bert] E D F A -------1 — O B P F Fig. 3.9. Experimental setup for chromatic dispersion monitoring and compensation for 10-Gbit/s CSRZ signals. CSRZ generation is done via two cascaded EO modulators, and fixed 480 ps/nm dispersive elements are used to bias the dispersion. A NC-FBG is used as a dispersion compensator. Generally, in the feedback configuration method, dispersion compensators work near the zero dispersion point (total dispersion including dispersion o f link and compensator). In this method, we offset the zero dispersion point to ±480 ps/nm in the monitoring tapline. When the accumulated dispersion in the link changes, the measured biased RF power in two monitoring taplines, one with +480 ps/nm o f 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dispersion (positive bias), and the other with a -480 ps/nm bias varies and estimates the dispersion variation in the link and adjusts FBG to maximize the biased RF power. The relative biased clock power as a function o f accumulated link dispersion and the system power penalty to receiver sensitivity (at IQ" 9 BER) as the dispersion is varied is shown in Fig. 3.10(a). This system shows that with the bias in place, the monitoring range is extended to -8 0 0 ps/nm with a sensitivity o f -0.0075 dB/ps/nm. Fig. 3.10(b) shows the BER curves before and after dispersion compensation. Prior to dispersion compensation using this grating and our monitor, the CSRZ system shows 1.2 dB o f penalty to receiver sensitivity after transmission through 40 km of SMF (the worst scenario after compensation for different transmission distance). However, after compensation, the power penalty is 0.2 dB when compared to the back-to-back receiver sensitivity. We believe the residual penalty results from the ripple o f the FBG (-50 ps peak-to-peak). In addition, this method is able to be 2 „ 200 400 600 800 1000 Dispersion (ps/nm) (a) 0 - Back-to-Back - S -w/DC - w/o DC c e 10'6 1.2 dB -22 -21 -20 -19 -18 -17 Received Optical Power (dB) (b ) Fig. 3.10. (a) Relative RF clock power in the positive bias tapline and power penalty vs. accumulated dispersion in the link. As the RF clock power decreases (increased chromatic dispersion) the power penalty rises, (b) Dispersion compensation results after transmission through 40 km of SMF. After compensation by maximizing the RF clock power, there is a 1,2-dB improvement in receiver sensitivity. 152 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. applied to feed forward configuration by direct estimation o f chromatic dispersion in the link. 3.3 Chromatic Dispersion Monitoring in Differential-Phase-Shift- Keyed Systems Fiber nonlinearities, such as SPM and XPM, arise from data-dependent instantaneous power modulation and tend to be the main causes o f transmission impairments in WDM systems [8-9], In differential-phase-shift-keyed (DPSK) optical signals, the “l ”s and “0”s are represented by the phase (0 or n ) of the optical wave. Since the optical intensity of DPSK signals remains constant in the fiber, it is expected that this format may minimize fiber nonlinearities as well as optical-amplifier-based saturation effects [197]. Moreover, the receiver sensitivity quantum limit for a DPSK system is improved by about 3 dB compared to on-off- keyed (OOK) systems [198,199]. Previously reported results on DPSK signals show extended transmission distances and have included the combination of DPSK with intensity-modulated RZ channels [200-202], In the RZ-DPSK signal, an optical pulse appears in each bit slot, with the binary data encoded as either a 0 or n phase shift between adjacent bits. For example, 3.2-Tbit/s RZ-DPSK data has been transmitted over 5200 km [202]. Given that a key application o f optical DPSK is long-distance non-repeatered transmission, periodic monitoring o f the data may be valuable for fault location, guaranteed QoS, and network control and management. Moreover, monitoring of signal integrity for DPSK may prove even more important than in OOK systems 153 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. since DPSK has been shown to be: (i) more sensitive to the accumulated chromatic dispersion than OOK [203] and (ii) comparably sensitive to PMD as OOK [204], To date, there has been no report o f an optical monitoring technique for DPSK. In this section, we demonstrate chromatic dispersion monitoring by measuring clock tone power for DPSK and RZ-DPSK signals [205]. We show the monitoring sensitivities before differential decoding are better than after decoding. The unambiguous measurement ranges at 10 Gbit/s are 600 ps/nm for DPSK signals and 900 ps/nm for RZ-DPSK signals. In these monitoring windows, the clock power changes by more than 20 dB. 3.3.1 Chromatic Dispersion in DPSK and RZ-DPSK Systems Fig. 3.11(a) shows the impact of chromatic dispersion on DPSK and RZ-DPSK signals. Since chromatic dispersion can induce phase modulation to amplitude modulation (PM-to-AM) conversion [116]— a limiting effect for DPSK signals— after transmission' through dispersive fiber the DPSK signal is no longer constant amplitude. This causes power fluctuations or pulse distortions in DPSK and RZ- DPSK signals, degrading system performance. Thus these fluctuations can be used to monitor chromatic dispersion in a fiber link. Fig. 3.11(b) shows the typical setup o f DPSK and RZ-DPSK systems. An optical phase modulator is driven by differentially coded data to generate the optical DPSK signal. An intensity modulator is added to produce the RZ-DPSK signal. At the receiver, the MZI, with one arm delayed by the bit time Tb, converts the DPSK data 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. into OOK data. A standard optical receiver then detects the OOK signals. Equivalently, a simple bandpass filter can replace the demodulating MZI to perform the conversion. 3.3.2 Chromatic Dispersion Monitoring in DPSK and RZ-DPSK Systems Using RF Clock Tone As stated previously, chromatic dispersion-induced amplitude fluctuations can be used to monitor the dispersion o f a fiber link. Since these amplitude fluctuations [DPSK' 1 1 0 1 0 0 RZ-DPSK 1 1 0 1 0 0 J I [Pulse appears in every bitj XORj Dispersive Fiber P P M -A M conversion D epolarization (a ) : Receiver End I a SOP// S O P 1 ; P ir n t;r 11 u r i u a t io n j ► S O P //..................................i iA SO P// SOP.L j Pulse Distortion Data | Laser[- . J j |ciock r Phase Intensity Modulator Modulator Fiber I .ink CKZ-DPSK DPSK Decoding Direct I —| .Detection < H > W ] Rx Fig. 3.11. Chromatic dispersion in DPSK and RZ-DPSK systems, (a) Conceptual diagram of chromatic dispersion and PMD effects on DPSK and RZ-DPSK signals and (b) DPSK/RZ-DPSK system configuration (Tt,: Bit time). occur at the same period as the data rate, they affect the magnitude o f the extracted clock tone. Fig. 3.12(a) and (b) shows the clock power as a function of chromatic dispersion. The clock tone power is calculated both before and after MZI filtering. It is clear that the chromatic dispersion monitoring sensitivity is better when measuring the clock power before MZI filtering. For dispersion from 0 to 60 ps/nm, the clock 155 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. power changes by over 40 dB for DPSK and by over 20 dB for RZ-DPSK. In general, PMD has a similar impact on both DPSK and RZ-DPSK signals. 40 Gbit/s DPSK '/ RZ-DPSK s — i ^ ^ ~ Z Before MZI Filtering After MZI Filtering 0 20 40 60 80 100 Residual Dispersion (ps/nm) (a ) 10 Gbit/s rcn-a- h -10 2 -20 2 -30 ? -SO DPSK, Simulation ■ DPSK, Experiment RZ-DPSK, Simulation □ RZ-DPSK, Experiment 0 200 400 600 800 1000 Chromatic Dispersion (ps/nm) (b) Fig. 3.12. Clock tone power as a function o f chromatic dispersion for DPSK/RZ-DPSK signals (a) Simulation results o f chromatic dispersion effects on 40-Gbit/s DPSK and RZ-DPSK signals and (b) experimental and simulation results o f chromatic dispersion effects on 10-Gbit/s DPSK and RZ- DPSK systems. The DPSK and RZ-DPSK experiment was conducted at 10-Gbit/s signals. Additionally, a 7.5-GHz bandpass filter replaced the demodulating MZI to convert DPSK to OOK. For dispersion from 0 to 1000 ps/nm, the clock power changes by over 40 dB for DPSK and by over 20 dB for RZ-DPSK. The measured system penalties and clock-power changes agree well with the simulation results. 156 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4 Polarization Mode Dispersion Monitoring in Digital and Analog Optical Fiber Communication Systems The following techniques to monitor DGD/PMD for equalization and improvement of monitoring requirements are presented in this chapter: (i) theoretical and experimental analysis o f the dependence o f a signal’s DOP on the optical data spectrum, (ii) enhancing the dynamic range and DGD monitoring windows in DOP- based-DGD monitors using symmetric and asymmetric partial optical filtering method, (iii) cancellation o f second-order PMD effects on first-order DOP-based DGD monitors and measurement o f depolarization rate, (iv) accurate DOP monitoring o f several WDM channels for simultaneous PMD compensation, (v) link DGD measurement without polarization scrambling using DOP and symmetric/asymmetric partial optical filtering method, (vi) DOP-based PMD monitoring in optical SCM systems by carrier/sideband equalization, (vii) PMD monitoring for NRZ data using a chromatic-dispersion-regenerated clock tone, (viii) PMD monitoring for RZ and NRZ data by RF clock regeneration measurement using asymmetric optical spectrum filtering method, (ix) real time PMD monitoring in WDM systems using in-band RF tone, and (x) effects o f XPM on the PMD monitoring parameters in WDM systems. 157 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.1 Theoretical and Experimental Analysis of the Dependence of a Signal’s DOP on the Optical Data Spectrum The use of the DOP to monitor the effects o f PMD has a number o f advantages over other techniques, including: (i) there is no need for high-speed devices, (ii) it is simple, (iii) it is bit-rate independent, and (iv) it is unaffected by chromatic dispersion [178]. However, while there are a number of previously demonstrated PMD monitors that involve the DOP as a monitoring signal, a given monitor may not be suitable for all systems [162-163], In fact, the DOP is highly sensitive to the shape o f the optical data spectrum, and even if the pulse widths are identical (in the time domain) between two data formats, the sensitivity and DGD monitoring range may be substantially different when applied to DGD monitors. In this section, we show the theory behind the effects o f all-order PMD on the DOP in a system. We show via simulation and experiment that the DOP is highly dependent on the pulse width and data modulation format used in a system. Additionally, we show that the DGD monitoring range in RZ systems is limited by the pulse width o f the signal. We test our theory on a number o f modulation formats, including NRZ, RZ, CSRZ, alternate-chirped RZ (ACRZ), and DPSK and find that even though the bit-rates are identical (10 Gbit/s), the DGD monitoring range is 100 ps, 25 ps (for 25% RZ), 50 ps, and 70 ps, respectively, due to the varying optical power spectrum resulting from the changing data modulation format. 158 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.1.1 Theory o f All-Order PMD Effects on the S ign al’s DOP The relationship between the DOP and first-order PMD in a system with a finite- linewidth source has been previously reported [206-208], We will first explore the general relationship between the DOP, all-order PMD, and the optical power spectrum in Jones space. We assume that there is no fiber nonlinearity and no PDL. In this scenario, the Jones transfer matrix o f the fiber link can be modeled as T(co) = e(-a((0)L-fp(m)L)U ( a ) (4.1.1) where a(co), fi(co), and L are the attenuation, the mean propagation constant and the length o f the fiber respectively and U(a>) is the unitaiy matrix f u^co) u2(a> U(co) = (4.1.2) - U j(c a ) u* ( co) j To determine the analytical relationship between the DOP, the optical power spectrum, and all orders o f PMD, we start from a general formula that relates the output electric field to the input electric field Eo u t (< °)~ T ( o))Ein ( a>) (4.1.3) where Ein (co) and Em t (co) are stationary random vectors representing the input and output fields, respectively. These fields can be written as E Joo) = e ^ ^ E J c o ^ e J c o ) (4.1.4) Eo j 0 i ) = (4.1.5) 159 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where < j > in ( co) , < / > o u t ( co) , Ein ( co) , Eo u t ( co) , ein, and eo u t ( co) are the input and output phases, envelopes/amplitudes, and normalized input and output SOPs, respectively. We note that all input frequency components are parallel to each other after data modulation since the modulator polarizes the light; thus ein ( c o ) - e jn ( ein is frequency independent). However, as all-order PMD is expressed by the unitary matrix U (co), the output eout(co) will become a function o f frequency (i.e., it is frequency dependent). The DOP is calculated by using equation (2.6.1) [206-208] DOP = < ? ™ - M . (4.1.6) ( ! ' max + P mir) where Pm m and Pm m are the maximum and minimum optical power measured after a PC and polarizer (given free reign to change the input SOP to the polarizer using the PC). An ideal elliptical polarizer can be modeled in Jones space as ^cos2 (Q) sin(§)cos(G)e jS ' A = (4.1.7) sin(Q)cos(Q)e+ JS sin2 (Q) J where 0 is the angle of incidence to the polarizer (measured with respect to its polarizing axis) and S is equal to zero in the ideal linear polarizer case. After the ideal linear polarizer, the polarized electric field can be expressed by Epoiout ( co ) = A T ( co)Ein ( co) (4.1.8) 160 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The average (and expected value, due to the pseudorandom nature o f the data) of the optical power o f the output electric field is P = U rn ^ -- E {P T( s ,) } = Jim E {± - \ E o li; ( t , s i) » E out( t > s i )d t} (4-1-9) T ~ ± + Q 0 / J T-*-Ho r-H -a 0 T ± T where PT( s i) is a random variable, E { .} represents the expectation operator (ensemble averaging), and Eo u t ( t.si) is a random vector. This integral results in the time-averaging o f the inner product o fE out(t,si) , which, after resolving the inner product o f Eg u t (t.si) and extending the integral bounds (due to taking the limit), becomes 1 + ° ° 2 2 Pa re = U rn E { - l[\Ex, ou t(t,Si)\ + \E ^ t(t,Si)\ ]d t} (4.1.10) T-++oo I J 1 — co By using Parseval’s theorem, the average power expression becomes j 2 P «. = Hm E { ~ - ~ \ [ \ E x^ (< x > .s, )\ + \E yAU t ( a , s t )\2 ] d t } (4 1 -H) r-+ + « 2xT J 1 1 — o o We now switch back to using the vector inner product o f Eo u l ( t,s<) and moving the expectation operator inside the integral, leading to j +GO P«. = - f E t f E ° 2 ( c0’s i ) * E o Ut(<°’s i)]}dco (4.1.12) -CO Resulting in the following expression for the average optical power after the ideal linear polarizer (after plugging (4.1.8), the expression for Eo u t ( t, st) , into (4.1.12)) is Pm e = ^ H m \E{[ EitJ (o},Si)T* (o))A2T(co)Ein (a>,Si)]do)} (4.1.13) 2m c J 161 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We choose a three-dimentional coordinate system such that the input (postmodulator) field is polarized parallel to the x-axis = (4.1.14) 0 v and by plugging (4.1.1), (4.1.4), and (4.1.14) into (4.1.13), we obtain the following expression for the average optical power: + O C 1 p - f U m ------E{\Ein(eo,si f } [(0.5 + 0.5cos(26)(\u}( c o f - I u2( w f )~ sin (2 @ )R e(u }( co)u2( co))]dco 2kT 1 (4.1.15) As we can write the polarimeter input optical power spectrum as S(co) = lim - E{\Ein (a, st f } (4.1.16) T — »+co 'J' and assuming attenuation over desire bandwidth is frequency independent, our average optical power becomes ( —2 a L ) + ■ » +« +•» Eve = \S ( a ) d m + 0.5cos(2e) j(\u 2(co)\2 ~ \u 2( o i) f )S(co)dco-sin(20) JR e (u l(co)u2(co))S(co)dco} (4.1.17) Using (4.1.17), we find the maximum and the minimum average optical power to be J-2 a L ) +• r2Z ; « Pm m a x = (— ------) { 0 . 5 ^S(co)dm + 0.5 Jf ( Y |« / co - \u2(a>)\‘ )S(co)dm ] 2 + 4[ j " R e(u ,(m )u 2(co ))S (to )d m ]2 } (4.1.18) ( — 2 aL ) +® j +« ^ ’ +« Eve m, ~ (— ^-----)(0. J ( S ( co)do> - 0.5 J f \(\u ,(o i_ )|* - \u2(a>)\ )S (m )d co ]2 + 4[ j " R e ( u ,(m )u 2(co))S(m )dco]2 } (4.1.19) 162 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. By plugging (4.1.18) and (4.1.19) into (4.1.6) (the expression for the DOP) we obtain (4.1.20) D O P = I + q o + o o If J V |u/co)\2 -|u2(C 0 ) \ 2 )S ( co)dco]2 + 4 [ jW u,(co)u2(a > ) ) S ( co)d(o]2 ^ j - Jsf co )da> By comparing this equation with the Stokes vector definition o f the DOP Jsf + s~ + s 2 3 (a , DOP = — — ------ (4.1.21) We can see that S0 (the optical power) is equal to + 0 0 Js( a )dco (4.1.22) — 0 0 S, is equal to j (| Uj( c o )\2 - | u2( 0) )\2 )S ( c o )dco (4.1.23) -00 and S2 is equal to + - C C j2 Re(uI(a>)u2(co))S(co)dco (4.1.24) —CO S3 equals zero as we used an ideal linear polarizer. Were this not the case (using an ideal elliptical polarizer modeled in the equation (4.1.7)), S3 would be equal to +oo ^2Im(ul(eo)u2(a> ))S( co )da> (4.1.25) -co These equations (4.1.22-4.1.25) show the effect of all-order PMD and the optical spectrum on each individual Stokes vector. 163 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.1.2 Effects of DGD on the Signal’s DOP To first-order, PMD is a frequency-independent time delay (DGD) between two orthogonal PSPs within an optical fiber. Taking into account only DGD, the unitary transform matrix (4.1.2) described in section 4.1.1 can be simplified to U ((o)~ RD(co)R~! (4.1.26) where R is the rotation matrix that aligns the input SOP into the first-order PSPs o f the fiber model by f / / i R = cos( < j)) - sin( < j)) sin( (p ) cos( (j)) (4.1.27) and D(o>) is a diagonal matrix that takes into account the time delay between the two PSPs, described by D (w ) ( gjoxigd / 2 0 ^ 0 e - jw d g d / 2 (4.1.28) We can relate the unitary matrix U(co) to the azimuth one o f the PSPs and to the DGD via the following: codgd codgd U (co) - cos( ) I — js in ( ) 2 2 f cos(2(j>) sin(2<j>) ^ (4.1.29) \sin(20) - cos(2$) y where cos(2(p) - 2 y - 1 , sin(2(p) = *Jy( 1 - y ) , y is the power splitting ratio between the two PSPs, and I is the identity matrix. 164 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. By expanding U(co) and extracting Uj(a>) and u2(co) (see formula (4.1.2)) from the result, we can plug the result into (4.1.20) so we can express the DOP as the following function o f the DGD and power splitting ratio: D O P ( dgd, y ) ~ -t-oo jcos( codgd)S( c o )dco I - 4 y (l - y ) + 4 y ( l - y ) [ —----- — ---------------------] 2 (4.1.30) jS(co)da> For this special case of first-order PMD, this formula matches the DOP formula for the effects o f first-order PMD on a finite line-width source derived in [206-208], By taking the inverse Fourier transform o f the above formula, the DOP can be related to the ACF o f the received optical signal Rin by D O P (d g d , y ) = J - 4 y ( l - y ) + 4 y ( l - y ) [ ^ ^ M ...^ ± j2 (4.1.31) V ZKm ( For the worst case ( y = 0.5), this results in the following expression for minimum DOP as a function of first-order: I cos( codgd) S(co )deo D O P ( d g d ) - _____________ = R J dgd ) + R J - d gd) (4.1.32) J s ( a ) d a 2R i J ° ) This formula gives a simple relationship between the DOP and the signal (as a function o f DGD). 4.1.3 Effects of Pulse Width on DOP-Based DGD Monitors However simple the above relationship involving Rjn (the ACF of the optical spectmm), may seem, there are a number o f challenges faced by DOP-based DGD 165 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. monitors. One in particular is that as the ACF is dependent on the pulse width o f the signal, the DGD monitoring range and DOP sensitivity vary as the pulse width o f an RZ signal changes (note that for this theoretical analysis, an NRZ signal is generalized as an RZ signal with a duty cycle equal to one). A general expression for the ACF for an RZ signal (assuming ideal rectangular pulses) is A T m=+°° _ _ ryiT R j T ) = ^ [ a ( w ) + J l A ( ~ ~ ^ )] (4X 33) where A refers to the triangle function, a (— ) - • W ’ ( 1 - ^ - ) Id < W { w ' II o Id > w where A , W , and Tb are the pulse amplitude, pulse width, and bit duration, respectively. When we plug this equation (4.1.33) into (4.1.31), we obtain (4.1.34) for the effects o f first-order PMD on an RZ (or NRZ) signal for any generic pulse width and splitting ratio. DOP(dgd , r ) = ^ i - 4 Y( i - r ) + r d - 2 (4-1 -34) If we assume the worst case {y = 0.5), we obtain the following result for minimum DOP, which can also be obtained by inserting (4.1.33) into (4.1.32): DOP(dgd) = L w H s L , + j A f i d - p l L ) ] (4. ,.35) This expression shows the effect of signal pulse width on the minimum DOP. Fig. 4.1(a) and (b) are conceptual diagrams illustrating the reason for this pulse-width dependence. Fig. 4.1(a) shows a 50% RZ pulse as it is affected by DGD 166 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50% RZ DOP = 1 DOP = 0 T J2 Slow axis “ DGD 4 5 ” Fast axis C onstant Poia rization Total De-polarization Fig. 4.1. (a) An RZ signal is completely depolarized (DOP = 0) after experiencing DGD equal to its pulse width (in this case, 50% o f the bit time). Thus the maximum DGD monitoring range o f a DOP- based DGD monitor changes as the RZ pulse width varies. NRZ DOP = 1 0 < DOP <1 45° 45° Slow axis ' | DGD Fast axis Constant Polarization At - DGD Partial De-polarization Fig. 4.1. (b) An NRZ signal, which to first-order can be considered a “ 100% duty cycle” RZ signal, remains partially polarized even when the DGD exceeds a full bit duration. ( DGD = 0.5 *Tb). As the signal (launched at 45° with respect to the PSPs o f the DGD element or fiber link) passes through the DGD element, the “fast” and “slow” halves o f a given pulse travel at different speeds and thus no longer overlap. As this overlap decreases, the signal replicas on the two PSPs become more and more depolarized, and the measured DOP at the polarimeter is reduced. If the signal experiences DGD equal to or greater than half o f the bit time, but less than the full bit duration (for 10 Gbit/s, this would be 50 ps), the two signal replicas no longer coincide in any way, and the measured DOP is zero. Thus for RZ signals there is a 167 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. defined limit to the monitoring range o f a DOP-based DGD monitor - once the DGD equals or exceeds the pulse width (regardless o f the bit rate) the measured DOP will reach its first minimum point. Fig. 4.1(b) shows a similar diagram for an NRZ signal. An NRZ signal, to first-order, can be considered a “100% duty cycle” RZ signal and never completely depolarizes, even after experiencing >1 bit duration’s worth o f DGD - due to the pseudorandom nature o f the data, the minimum DOP is 0.5 [164-165,178]. Fig. 4.2 shows a plot o f equation (4.1.35) the theoretical results o f minimum DOP versus DGD (relative to the bit time - this figure is general for any given bit rate) as the pulse width ( W ) varies. As the pulse width increases from 0.1 *Tb (corresponding to a 10% duty cycle RZ signal) to Tb (a full bit time, corresponding to an NRZ signal), the DGD monitoring range (the point at which the DOP reaches its first minimum value) increases. In each case, the maximum DGD monitoring range is precisely equal to the pulse width. Note that the for the NRZ case, the DOP does not reach a minimum of zero, but rather 0.5. 0 0.2 0.4 0.6 0.8 1 DG D/Tb (ps) Fig. 4.2. Theoretical results of minimum DOP vs. DGD (relative to the bit time, Tb ) as the pulse width of an RZ signal varies. 168 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DGD Broadband _ . . , EDFA PC Element ASE filter Polanm eter TX~J{> A n 0-50 ps II Fig. 4.3. Experimental setup for DOP-based DGD monitoring for varying data modulation formats and pulse widths. Fig. 4.3 shows the experimental setup we used to verify our theoretical results on minimum DOP versus DGD and pulse width. After generating the RZ or NRZ signal, we pass the signal through a variable DGD element at an angle o f 45° with respect to the PSPs o f the DGD element, and then into a polarimeter to measure the DOP. We generate our variable-pulse-width RZ signals at different bit-rates using the transmitter setup shown in Fig. 4.4. We first generate 10-Gbit/s RZ data (223-l PRBS) with 50% duty cycle using two cascaded EO modulators. The pulse width is then compressed by adjusting the bias and phase delay o f a phase modulator followed by a spool o f SMF with a dispersion value o f 80 ps/nm. 2 stage MUX LD Bias NRZ RZ EDFA T P>-[PM EO Data EO SMF 80 ps/nm 10 z !< J ) Gb/s Clock PPG / 3.2 n s delay / X 10-to-20 G b/s C h irp ed P u lse C o m p re ssio n 1.6 n s d elay 20-to-40 Gb/s data 40 Gb/s 20 Gb/s - * 10 Gb/s Fig. 4.4. Experimental setup to generate variable-pulse-width RZ signals at 10, 20, and 40 Gbit/s. The resulting pulse width can be tuned by changing the bias o f the phase modulator and phase delay before it. 169 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A two-stage optical multiplexer is used to generate 20- and 40-Gbit/s data streams. The results showing the minimum DOP versus DGD for 20- and 40-Gbit/s 50% RZ signals are shown in Fig. 4.5(a) and (b). While both o f them are 50% RZ signals, the DGD monitoring range changes from -2 5 ps to -12.5 ps as the pulse width changes from 25 ps (20 Gbit/s) to 12.5 ps (40 Gbit/s), respectively. A more interesting case is when the bit rate remains constant, but the pulse width is varied. 40 Gb/s RZ (50%) 0.8 CL O Q 0.4 0.2 DGD (ps) 20 Gb/s RZ (50%) 0.8 0.6 CL 0.4 0.2 DGD (ps) (a) (b) Fig. 4.5. The minimum DOP vs. DGD curves for (a) a 20-Gbit/s 50% RZ (25-ps pulse width) signal, the maximum DGD monitoring range (first DOP minimum) occurs at -25 ps DGD and (b) a 40-Gbit/s 50% RZ (12.5-ps pulse width) signal, the maximum DGD monitoring range occurs at -12.5 ps DGD. Fig. 4.6(a) and (b) show the minimum DOP versus DGD results for 10-Gbit/s 25% (25 ps) and 15% (15 ps) RZ, while (c) and (d) show the results for 20-Gbit/s 50% (25 ps) and 25% (12.5 ps) RZ signals. Even for cases when the bit rate remains constant, as the pulse width changes, the maximum DGD monitoring range changes as well - always equal (or close to) the pulse width o f the signal. 170 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a. O Q 1 ' 10 Gbit/s RZ (25%) 1 ~ J' 1 | 1 I I ! | 1 1 1 1 | 1 1 1 1 \ 10 Gbit/s RZ (15%) : 0.8 \ 0.8 0.6 \ O . 0 6 O 0.4 \ 0.4 V 0.2 0.2 \ Y n . 1 . 1 1 I . 1 ................................... . 1 .................... ..... 0 . . - I I i i i . 1 I i i . I...I . ,i ..r. . 10 20 30 40 50 DGD (ps) (a) 10 20 30 40 50 DGD (ps) (b) a. O Q 1 20 Gb/s RZ (50%) 0.8 0.6 0.4 0.2 0 10 20 30 40 50 0 DGD (ps) (c) 20 Gb/s RZ (25%) 0.8 0.6 Q . O Q 0.4 0.2 20 30 DGD (ps) 40 (d) Fig. 4.6. Minimum DOP vs. DGD curves for (a), (b) 10-Gbit/s, (c), and (d) 20-Gbit/s signals. As the pulse width varies from (a) 25 ps to (b) 15 ps, the DGD monitoring range varies - from 25 ps to -17 ps. For a bit rate of 20 Gbit/s, as the pulse width varies from (c) 25 ps to (d) 12.5 ps, the DGD monitoring range changes from 25 ps to -12 ps. 4.1.4. Effects of Modulation Format on DOP-Based DGD Monitors The data modulation format also has a significant effect on DOP-based DGD monitors. While such a revelation may seem obvious, as a change in the data modulation format will often result in a change o f pulse width (and thus a change in DOP sensitivity and DGD monitoring range as explained in the above section), this effect is not limited to pulse width - in fact, the DOP/DGD relationship can be 171 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. significantly different between two equal-pulse-width modulation formats (such as 50% RZ and 50% ACRZ) due to the DOP dependence on S(co) (the optical spectrum) shown in (4.1.32). We modified our experimental setup in Fig. 4.3 to allow for generation o f two new data formats: CSRZ and ACRZ. The transmitter configurations for each o f these two modulation formats are shown in Fig. 4.7. EO EO LD _ _ 10 Gbit/s PRBS21 5 * NRZ „ .T t ! -i © C SRZ (a ) DGD OBPF _ , . . EDFA PC Elem ent 0.35 nm Po,anm eter ..... PM LD FPF 8 GHz 0-100 p s EO jit/s I 10 Gbit/s . PRBS2'=-1 ' ACRZ NRZ (b) I Fig. 4.7. Modified transmitters used to generate CSRZ (top) and ACRZ (bottom) data formats in our experimental setup for measuring the relationship between the DOP and DGD in an optical link. In the CSRZ modulation format, in addition to modulating the amplitude of the optical signal in a manner similar to RZ signal, a second modulator is driven with a half-bit-rate clock, resulting in adjacent bit positions undergoing a n phase shift relative to each other [209], In the ACRZ modulation format, the combination o f a phase modulator and narrowband optical filter prior to the data modulator results in a signal for which the phase varies sinusoidally with time (at a period o f 2 * Tb) [210]. The measured optical data spectra for generic NRZ, RZ, CSRZ, and ACRZ signals are shown in Fig. 4.8(a)-(d), respectively. 172 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Gbit/s NRZ £ -20 -30 -50 L 1549.8 1550.1 1550.3 10 Gbit/s RZ -20 tn -30 -50 — 1549.7 1549.9 1550.2 X (nm) (a) X (nm) (b) 10 Gbit/s CSRZ £ -20 ■ £ -10 U L -50 1554.7 1555.3 1555.0 10 Gbit/s ACRZ S -10 -20 « -30 -50 1552.9 1553.5 1555.0 X (nm) (C) X (nm) (d) Fig. 4.8. Representative optical data spectra for 10-Gbit/s (a) NRZ, (b) RZ, (c) CSRZ, and (d) ACRZ signals. The simulation results detailing the differences in the minimum DOP/DGD relationships for equal-pulse-width (40-Gbit/s 50% RZ, 12.5-ps pulse width) signals are shown in Fig. 4.9. The RZ curve differs from those shown in earlier figures as an alternate method o f RZ generation was used in this simulation. As seen in the theoretical results (Fig. 4.2), the minimum DOP/DGD relationships look like the triangle function; however, this relationship becomes more smooth and sinusoidal in Fig. 4.9. As we explained in equation (4.1.32), the DOP is optical ACF dependent (i.e. pulse shape dependent). In our theoretical results in Fig. 4.2, we assume RZ signals with ideal rectangular shapes, while in our simulation, we generated RZ using two cascaded modulators, resulting in sinusoidally-shaped bits - this accounts for 173 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 Gb/s 0.8 \ RZ 0.6 CL o Q 0.4 0.2 20 30 DGD (ps) Fig. 4.9. Simulation results of minimum DOP vs. DGD for 40-Gbit/s, equal-pulse-width (12.5 ps) data formats -R Z is dotted, CSRZ is solid, and ACRZ is dashed. the differences between the theoretical curve and the simulation results for the RZ signals.The DGD monitoring range (location o f minimum DOP) and DOP sensitivity (value of minimum DOP) vary widely as the data format (and thus the optical spectrum) changes, even though the pulse widths are identical - the minimum DOP for this type o f RZ signal is ~0.4, while for ACRZ it is ~0, and the DGD monitoring range is -12.5 ps for RZ, while it is 20 ps for ACRZ. As such, an identical monitoring system and feed-forward configuration cannot be used for DGD estimation when the data format changes, even if the pulse width remains the same. A more “physical” explanation o f why the DGD monitoring window for ACRZ signals is greater than that for CSRZ signals may be useful. The DOP as a function o f DGD is optical spectrum dependent and stronger optical frequency components play a key role in this mechanism. While there are two equally strong half-bit-rate optical frequency components around the central optical frequency in the CSRZ spectrum, there are three equally strong optical frequency components in the ACRZ spectrum-the center frequency and the two half-bit-rate optical frequency 174 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. components. While the optical center frequency component and frequency sidebands have the same SOP at the transmitter, after propagation through the fiber link, PMD induces a phase delay between the two PSPs for the optical center frequency component and for each o f the frequency sidebands. In general, these phase delays are not equal to each other. These phase differences manifest themselves as an “SOP walkoff” between the optical sidebands and the optical center frequency. In Stokes space, this walkoff angle is equal to 2n * f * D G D radians on the Poincare sphere. In the first-order worst case (D G D - —— , with equal power in each PSP), the half- 2R b bit-rate optical frequency components rotate ±45° (±90°) relative to the center frequency component in Jones space (Stokes space). In this case, CSRZ signal totally become depolarized and its DOP becomes zero; however, ACRZ signal partially become depolarized and its DOP remains nonzero due to the strong optical carrier component. Additional DGD is required to reduce the ACRZ signal’s DOP to zero. The fact that the DOP o f the optically generated RZ signal does not reach zero can be attributed to the fact that noncarrier optical components (including the optical clock components) are at a much lower power level relative to the carrier compared to CSRZ and ACRZ. The simulation results for 40-Gbit/s DPSK and RZ-DPSK are shown in Fig. 4.10(a) and (b). These figures show that it is best to place the monitoring tap-line prior to the optical decoder to obtain the best DOP sensitivity and DGD monitoring windows. When compared to our results in Fig. 4.9, we again see that the monitoring range and 175 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0.8 „ 0-6 Q- 8 . . 0.2 0 o 10 20 30 40 50 0 10 20 30 40 50 DGD (ps) DGD (ps) (a ) (b ) Fig. 4.10. Simulation results of minimum DOP vs. DGD for 40-Gbit/s (a) DPSK and (b) RZ-DPSK signals. DOP sensitivity to DGD are markedly different due to the changing shape o f the optical spectrum caused by this modulation format, even though the bit rate remains at 40 Gbit/s. Our experimental and simulation results measuring the minimum DOP versus DGD for 50-ps pulse width 10-Gbit/s CSRZ and ACRZ signals are shown in Fig. 4.11(a) and (b). For equal pulse widths, the minimum DOP versus DGD curves for the CSRZ and ACRZ formats are different - the ACRZ signal shows a ~20% increase in DGD monitoring range (from 50 to 70 ps) when compared to the CSRZ signal despite the pulse widths being identical in the time domain. In addition, after reaching a DOP minimum, the CSRZ signal begins to rise almost immediately, while the ACRZ signal remains low for a wide DGD range after reaching its minimum. These results are consistent with the simulation results shown in the figure. 40 Gbit/s RZ-DPSK K After optical yv decoding After optical decoding \ BefoiWptical ^ decoding 40 Gbit/s DPSK \ \ Before optical decoding 176 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CL o Q u ™ , . . . T . . . T . _ T _ - T . t - t — , —l-.-r .- T — r.-r .-T _-r— r— r . 1 1 " ' c 1 ' • < "J" ! ...-r ,.....f — 'r T " 10 G bit/s CSRZ Ii \ 10 Gb/s ACRZ : 0.8 0.8 0.6 a . 0-6 O 0.4 \ ° 0 .4 d \ / 0.2 0.2 •v n m J_±- I 1 I I I 1 I I 1 1 I I 1 1 1 0 i i p i i , . i i ! i i i • i ^ i i i i 0 20 40 60 80 100 u 20 40 60 80 100 DGD (ps) DGD (ps) (a) (b) Fig. 4.11. Experimental (dots) and simulated (line) results of the minimum DOP vs. DGD for 10- Gbit/s 50 ps (a) CSRZ and (b) ACRZ signals. 4.2 Enhancing the Dynamic Range and DGD Monitoring W in d o w s in DOP-Based-DGD Monitors Using Symmetric and Asymmetric Partial Optical Filtering It has been shown that the use o f a signal’s DOP has some advantages over other techniques for PMD monitoring. Unfortunately, DOP measurements as a function of instantaneous DGD suffer from the following crucial systems disadvantages: (i) there is a small DGD monitoring window when measuring a short pulse RZ signal [162- 165], and (ii) there is a lack o f sensitivity when measuring a NRZ signal [162,164- 165,178]. It would be highly desirable to have a PMD monitor for which the DOP can be measured to obtain wide DGD monitoring windows and wide dynamic range for both RZ and NRZ signals. In this section, we demonstrate a technique o f partial optical filtering that can dramatically enhance the DGD monitoring range and/or DOP dynamic range/sensitivity to DGD in DOP-based DGD monitors. We apply this technique to 177 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RZ, CSRZ, and ACRZ and conclude that the use o f symmetric and asymmetric filtering using a optical filter can offer significant increases in the DGD monitoring range. However, given equal bit rate and pulse width, the filter shape, order, and bandwidth required to obtain maximum DGD monitoring range and DOP dynamic range can vary as the modulation format changes. We apply this technique to 10- Gbit/s CSRZ and ACRZ signals for which the pulse widths are half of the bit time and show that the monitoring range can be extended from 50 to 70 ps and from 70 to 100 ps, respectively. Moreover, the monitoring range o f 25-ps pulse 20-Gbit/s RZ signals is extended from 26 to 45 ps. We also apply our technique to NRZ signal and show that using asymmetric optical filtering in NRZ systems can double the DOP dynamic range without any reduction in DGD monitoring range. These results show that this technique is ideal for the DGD monitoring signal required in feed-forward OPMDCs, but may also be applicable (with some limitations) to feedback OPMDCs. 4.2.1 Theory of Partial Optical Filtering Effects on the Signal’s DOP The use o f the DOP is a popular method for monitoring PMD/DGD within an optical link, and numerous PMD monitors have been shown to use the DOP as a control signal in both feed-forward and feedback OPMDC configurations. However, there are a number o f drawbacks to these monitors - when monitoring RZ signals, the maximum DGD monitoring range is limited by the pulse width o f the signal [162- 165], and when monitoring NRZ signals, the DOP dynamic range to DGD is halved [162,164-165,178] - the DOP varies from 1 to 0.5; it varies from 1 to 0 in RZ 178 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. monitors. In addition, as the modulation format changes, the optical spectrum, pulse shape, and phase change, and thus the minimum DOP versus DGD curves change. We solve these problems using a single added optical element, an optical filter placed in the monitoring tap-line, centered either on the optical spectrum (“symmetrically”) or offset from the center o f the spectrum by the bit-rate frequency - i.e. for 10-Gbit/s data, offset by 10 GHz (“asymmetrically”) . We measure the DOP o f the portion of the optical spectrum that is passed through the filter - performing a “partial signal spectrum” DOP measurement. As multiplication in the frequency domain corresponds to convolution in the time domain, a narrowband optical filter (with a broad time domain response) can be used to broaden a pulse in time via convolution. When taking into account the effect o f the optical filter to the expression for the DOP in systems with finite linewidth sources [206-208] we obtain where H(f) is the optical filter transfer function, fg is the frequency offset o f the filter from the center o f the optical spectrum, S(f) is the optical spectrum, and y is the optical power splitting ratio between the two PSPs. In the worst case, when the splitting ratio {y ) is equal to 0.5, using Parseval’s theorem and taking the inverse Fourier transform, we can simplify the above expression for minimum DOP as a function o f DGD, resulting in \\H (f ~ ft, f\ S (f)c o s (2 7 tfd g d )d f j2 (4.2.1) D O P (d g d ,y)= l-4y(l-y) + 4y(l-y)[- 179 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DOP( dgd) = F-'{\H(f-fo)\2 }*R(t) r - v + F - ^ H t f - f r f r R ( z ) t = - d g d 2xF~1{\H (f-fo)\2 }*R(t) T = 0 (4.2.2) where R ( t ) is the optical autocorrelation function, * is the convolution operator, and F~J is the inverse Fourier transform operator. The effect of this filter on a 50% RZ signal in the worst case (y = 0.5) is shown in Fig. 4.12. In a standard monitoring configuration for pulsewidth < 0.5 * Tb, when the DGD is greater than or equal to the pulse width and less than 1 bit duration the optical pulse replicas on the two orthogonal PSPs no longer coincide with each other and as such the signal is completely depolarized - the minimum DOP is zero. The point at which the signal reaches this complete depolarization is the maximum DGD monitoring range, and is typically equal to the pulse width o f the signal regardless o f the bit rate (i.e. a 10-Gbit/s 25% RZ signal and a 20-Gbit/s 50% RZ signal will have similar maximum DGD monitoring ranges due to the identical pulse width irrespective o f the change in the data rate). 50% RZ DOP - 1 J b /2 . DOP = 0 DOPt Slow axis 4 Optical 4 1 * 45° t P G D ' ' "I Filter ^ / j .Z ( f a Fast axis ^ V ' ■ / ___ - V Constant At = DGD = T„/2 d g d Polarization b DtaD A t = DGD = Tb/2 Total De-polarization DGD Partial De-polarization Fig. 4.12. Prior to optical filtering, an RZ signal that undergoes DGD equal to the pulse width is completely depolarized limiting the DGD monitoring range of DOP-based DGD monitors. After filtering, the signal is partially polarized, allowing DOP-based monitoring of the DGD. 180 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. After adding the optical filter, the narrow transfer function o f the filter has a wide response time and convolves with the short pulses (in the time domain) results in a broadening o f the signal replica pulses. These broadened pulses may overlap where they did not before, thus shifting upward the minimum DOP versus DGD curve and extending the DGD monitoring window. The firequency-domain explanation for this re-polarization is shown in Fig. 4.13. The link DGD causes the SOP o f frequency components within the optical spectrum to rotate with respect to the central optical frequency by an amount ± 2n *A f * DGD (in Stokes space), where Af is the frequency offset of a given component from the center o f the optical spectrum. This is known as the “SOP walkoff’ effect. As short optical pulses in time have a wide optical spectrum, depolarization effects are much more pronounced for short pulse- width signals. A narrowband optical filter shrinks the optical spectrum, reducing the depolarization effect. Optical Spectrum JlflL Slow axis Optical 4 J k .F A A . . rA Constant SOP V / ^ \ J Frequency dependent ' Canceling De-polarization effects Fig. 4.13. Frequency-domain illustration of the reduction of depolarization via symmetric narrowband optical filtering. Short optical pulses have a wide optical spectrum, enhancing the effects of DGD- induced depolarization. A narrowband filter shrinks the optical spectrum, reducing these depolarization effects and increasing the DGD monitoring range. This limiting of DGD monitoring range is present in short pulse-width CSRZ and ACRZ systems as well. In the CSRZ modulation format, in addition to 181 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. modulating the amplitude of the optical signal in a manner similar to RZ signal, a second modulator is driven with a half-bit-rate clock and at a bias o f vx , resulting in adjacent bit positions undergoing a n phase shift relative to each other. In the ACRZ modulation format, the combination o f a phase modulator (driven with a half- bit-rate clock with a peak-to-peak voltage o f V x) and narrowband optical filter prior to the data modulator results in an RZ signal with a sinusoidal chirp (with a period of 2 * Tb). Since the optical spectrum for ACRZ and CSRZ signals differs from that of RZ signals, when this technique of partial optical filtering is applied to these signals, the shape, order, and bandwidth of the filter must be optimized for the individual data modulation format to ensure the maximum DGD monitoring range and DOP dynamic range. We believe this technique to be ideally suited for the DGD monitoring portion o f a feed-forward OPMDC, as it gives an accurate representation o f the DGD and is less sensitive to higher-order PMD effects than other DGD monitors - resulting in a monitoring signal that is highly correlated to system performance (as first-order PMD (i.e. DGD) is usually the most significant PMD contribution to performance degradation). Such a feed-forward OPMDC would also require a monitoring signal to set the PC - two such techniques are shown in [74-76]. References [74-75] also show that it is possible to use the DOP and a measurement o f the normalized SOPs to measure the PMD vector in a feed-forward OPMDC to estimate the PMD vector (and thus control the PC and DGD element together). As our technique requires monitoring the DOP anyway, simply measuring the SOPs as 182 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. well will enable generation o f both monitoring signals required in a feed-forward OPMDC. We believe that this technique can be applied in feedback OPMDCs as well, with the limitation that due to a slight reduction in DOP sensitivity to DGD the monitoring signal may be slightly less accurate at very low DGD values (commonly the “tracking area” for feedback OPMDCs). However, by filtering the high frequency components, we reduce the sensitivity to higher-order PMD. As first- order PMD is the most significant contributor to performance degradation, we believe that this makes our control signal much more correlated to system performance than a DOP-based feedback signal without filtering (that may take into account more higher-order effects). 4.2.2 DGD Monitoring Results for Different Modulation Formats Fig. 4.14 shows the experimental setup for our DGD monitoring system. The transmitter generates 10-, 20-, or 40-Gbit/s RZ, CSRZ, or ACRZ data modulated. dg d o b pf PC Element (8 GHz- 40 GHz) Polarimeter — c s i b — 1*1-------------- n n T X T " 0-100 ps 1 1 Fig. 4.14. Experimental setup for DGD monitoring using the DOP of a partially-filtered optical spectrum. The transmitter configuration for the different modulation formats (RZ, CSRZ, and ACRZ) is shown in Fig. 4.15. with a 21 5 -1 PRBS. The transmitter configurations required generating these formats are shown in Fig. 4.15. The resulting signal is passed through a PC and tunable DGD element at an angle o f 45° with respect to the PSPs o f the element. The DGD element in our RZ setup was the computer-controlled programmable element 183 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. described in [211] with a DGD range from 0 to 50 ps. In our ACRZ and CSRZ setup, we used a simpler first-order PMD emulator with a DGD range from 0 to 100 ps. After passing through the DGD emulator, we either send the signal directly through a broadband ASE filter and a polarimeter, or through an optical filter (placed either symmetrically or asymmetrically) then to the polarimeter, to measure the DOP. We used both Gaussian and FPF filters with bandwidths from 8 to 40 GHz in this experiment. In an actual system, the optical filter and polarimeter would act only on a tapped-off portion o f the data, and not on the data path itself, and thus wouldnot distort the transmitted data. 2 stage M UX NRZ RZ EDFA l i c T H E O H EO h f x H PM Data 10 Gb/s PPG k Q . Clock A < i> SM F 80 ps/nm 3.2 ns delay ZA 10-to-2Q G b/s 1.6 n s delay ZA 20-to-40 G b/s data ► 40 Gb/s -► 20 Gb/s -►10 Gb/s Chirped Pulse Compression (a) LD i i I 10 Gbit/s 1 PRBS 21 5 -1 EO ■ e NRZ CSRZ PM LD FPF 8 GHz E0 Q ) 5 GHz 10 Gbit/s PRBS 21 5 -1 NRZ J A CRZ (b) (c) Fig. 4.15. Transmitter configurations for (a) 10-, 20-, and 40-Gbit/s tunable-pulse-width RZ generation, (b) 10-Gbit/s CSRZ generation, and (c) 10-Gbit/s ACRZ generation. 184 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2.2.1 RZ Signals We first applied our technique of partial optical filtering to RZ signals. In a standard RZ system, the DGD monitoring range o f a DOP-based PMD monitor is approximately equal to the pulse width o f the RZ signal. We first simulated our DGD monitor using electrical 50% RZ generation techniques at 10 and 40 Gbit/s and obtained the minimum DOP versus DGD curves shown in Fig. 4.16(a) and (b). In these simulations, we used l st-order Gaussian filters with a bandwidth o f 0.8 * Rb (which we found to be the optimum filter bandwidth when electrical RZ generation is used) positioned both symmetrically and asymmetrically. In each case, the DGD monitoring range is doubled - from ~50 to 100 ps for 10 Gbit/s, and from 12.5 to ~25 ps for 40 Gbit/s. Asymmetric Filtering — - Broadband Symmetric Filtering ■ ■ ■ ■ ■ ■ Symmetric V \ Filtering..-- Asymmetric Filtering Broadband Symmetric Filtering Symmetric Filtering DGD (ps) DGD (ps) (a) (b) Fig. 4.16. Simulation results of minimum DOP vs. DGD for electrically generated (a) 10-Gbit/s and (b) 40-Gbit/s, 50% RZ signals before and after partial optical filtering. For our experimental results, we generate our RZ data using the setup shown in Fig. 4.15(a) - we begin by generating 10-Gbit/s RZ data with 50% duty cycle 185 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Gbit/s RZ (15%) W/ Filtering o-W/o Filtering 10 20 30 40 50 DGD (ps) (a) 10 Gbit/s RZ (50%) Asymmetric Sym m etric' 20 40 60 80 100 DGD (ps) (b) m 2--10 E 2 -20 O 0 ) tfi -30 3 “ -10 a O -50 10 Gbit/s 0 C O 10 Gbit/s Symmetric -20 ST 10 Gbit/s Asymmetric ; m A . 2 . .1 0 RZ f t Filtering T 3 , RZ Filtering Optical Spectrum S k S o ■ I | -30 © * A . 1549.7 1549.9 1550.2 1549.7 X (nm) 1549.9 1550.2 1549.7 1549.9 1550.2 X (nm) X (nm) (c) (d) (e) Fig. 4.17. Experimental results of minimum DOP vs. DGD before and after partial optical filtering for (a) 10-Gbit/s 15% RZ signals (including simulation results) and (b) 10-Gbit/s 50% RZ signals. The optical spectra for 10-Gbit/s 50% RZ signal (c) before, (d) after symmetric, and (e) after asymmetric partial optical filtering. using two cascaded EO modulators. Our 10-Gbit/s 50% RZ data was pulled from this output. The pulse width is then compressed to 12.5 ps and 25 ps by adjusting the bias and clock phase delay o f a phase modulator followed by a spool of SMF with a dispersion value o f 80 ps/nm. A two-stage optical multiplexer is used to generate 20- and 40-Gbit/s data streams. Our results for 10-Gbit/s 15% and 50% RZ signals are shown in Fig. 4.17(a) and (b). This figure shows the experimental minimum DOP versus DGD curves for these two pulse widths before and after partial optical filtering using an 8-GHz FPF filter with an FSR o f 750 GHz. 186 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a. O o 1 0.8 0.6 0.4 0.2 0 20 Gb/s RZ (50%): 1 .T ,.r ..j...,... — ,— ,— r— r , i i , , 20 Gb/s RZ (25%) : - W/ filtering/ 0.8 - \ \ W / filtering / \ \ - o - W/o filtering r V -o - W/o filtering ; ' \ N- «L °'6 \ ® \ \ - \ k \ A I O Q \ \ v «. P 0.4 \ O M Y j T u 0.2 vVX .............................................Y / .................................................. 0 o o I 1 | . 1 , 1 1 1 1 1 1 . . 1 . 1 1 1 1 . . 1 . 10 20 30 40 DGD (ps) (a ) 50 10 20 30 40 50 DGD (ps) (b) Fig. 4.18. Experimental results of minimum DOP vs. DGD for 20-Gbit/s (a) 50% and (b) 25% RZ signals before and after symmetric optical filtering. Simulation results are also shown for the 50% RZ case. Before filtering, the monitoring range is limited to -1 7 ps for the 15% RZ case. However, after partial optical filtering, for the 15% RZ case, the monitoring range is extended to beyond 50 ps as the pulse is expanded in time via the narrowband optical filter. For the 50% RZ case, the monitoring range is only extended to -6 0 ps after symmetric filtering (from the 50-ps value prior to filtering) as we did not have a FPF filter o f the optimal bandwidth for this type o f signal. After asymmetric filtering, we increased the DGD monitoring range to -100 ps (Tb) but with a loss o f DOP dynamic range due to the nonoptimal filter bandwidth. Fig. 4.17(c)-(e) show the measured optical spectrum of the 10-Gbit/s 50% RZ signal before and after symmetric and asymmetric optical filtering. For our optical spectrum measurements, we used an OSA with a resolution o f ~l-GHz. Fig. 4.18 shows our minimum DOP versus DGD results for 50% and 25% (25-ps and 12.5-ps pulse width) 20-Gbit/s RZ signalbefore and after symmetric 187 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. partial optical filtering. Prior to symmetric partial optical filtering using a 36-GHz l st-order Gaussian filter, the DGD monitoring ranges are limited to the pulse width o f the signal (despite both being 20 Gbit/s) - -2 5 ps for the 50% RZ case and -12.5 ps for the 25% RZ case. However, after partial optical filtering, the DGD monitoring ranges are extended by -2 5 and -3 5 ps (to around Tb) for the 50% and 25% RZ cases, respectively. Fig. 4.19 shows our minimum DOP versus DGD curves for 12.5-ps pulse width (50%) 40-Gbit/s RZ signals. Prior to asymmetric partial optical filtering with a 36- GHz l st-order Gaussian filter, the monitoring range is limited to -1 3 ps. However, after asymmetric partial optical filtering, the DGD monitoring range is extended to a full bit time, 25 ps. It is clear that partial optical filtering allows significantly enhanced DGD monitoring ranges while keeping the DOP dynamic range high. 1 ................................... 40 Gb/s RZ (50%); o s ? \ | W / filtering W/o filtering 0.6 Q . o > ° 0 . 4 0.2 i 0 0 5 10 15 20 25 DGD (ps) Fig. 4.19. Experimental results of minimum DOP vs. DGD for 40-Gbit/s 50% RZ signals before and after asymmetric optical filtering. 188 40 Gb/s RZ (50%) ?v -m— W/ filtering W/o filtering Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.2.2.2 CSRZ Signals Fig. 4.20 shows the simulated results for DGD monitoring for 40-Gbit/s, 12.5-ps pulsewidth CSRZ signals before and after partial optical filtering. In these simulations, the optical filters are Gaussian filters (both 1st- and 2n d -order) with bandwidths of 23.6 GHz for symmetric filtering and 42 GHz for asymmetric filtering. We calculated these to be the optimal bandwidths for ensuring maximum DOP dynamic range and DGD monitoring range. This simulation makes it clear that for CSRZ systems, symmetric filtering provides the greatest increase in DGD monitoring range while keeping the minimum DOP dynamic range high. Asymmetric filtering results in a slight increase in the DGD monitoring range at the cost o f DOP dynamic range. Also note that prior to optical filtering, the peak of the minimum DOP curve is at -0.85 even when the DGD is equal to zero. This is due to the presence o f residual unpolarized ASE noise in the system. However, after partial optical filtering, we remove the majority o f this noise and the peak reaches ~ 1, almost eliminating the effect o f ASE on this measurement. One point o f interest is that the monitoring window is much larger when a 2n d -order Gaussian filter is used than when a l st-order Gaussian filter is used. This is due to the fact that while the bandwidths o f these filters are the same, the higher-order Gaussian filter has a steeper rolloff after the 3-dB bandwidth point, leading to a greater broadening in the time domain after filtering (as shown in (4.2.2)). Our experimental and simulation results for a 10-Gbit/s, 50 ps pulsewidth CSRZ signal are shown in Fig. 4.21(a)-(c). 189 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Q. o a 0.8 0.6 0.4 0.2 \ , -----Broadband symmetric filtering \ V -. Symmetric filtering (1 8 1 Order) Symmetric filtering (2 "dOrder) ----Asymetric filtering - \ V X \ \ \ * * " * * " * •« . \ \ : \ \ \ \ / ' CSRzl / ' V / / \ 40 Gb/s 0 10 20 30 40 50 DGD (ps) Fig. 4.20. Simulation results of minimum DOP vs. DGD for 40-Gbit/s 50% CSRZ signals before and after partial optical filtering. Fig. 21(a) shows the DGD monitoring results when the signal is broadband filtered (to remove some ASE noise, but retain the entire signal spectrum). This results in a DGD monitoring range limited by the pulse width (~50 ps). After narrowband symmetric filtering using an 8-GHz FPF filter, the monitoring range is extended by -2 0 ps with no loss o f DOP dynamic range. Our simulations show that 2n d -order Gaussian filtering actually results in the widest DGD monitoring range (-twice the bit duration) - however, we did not have this type o f optical filter available. Broadband symmetric filtering \ 9 / CSRZ \ / _ R b= 10 Gb/s \ / BW9ao8 = 36 GHz a 0 20 40 60 80 100 DGD (ps) (a) Narrowband symmetric filtering CSRZ Rfi* 10 Gb/s BV\A.= 8 GHz 0 20 40 60 DGD (ps) (b) 0.6 a. o a asymmetric filtering 0.2 100 DGD (ps) (c) Fig. 4.21. Simulation and experimental results of minimum DOP vs. DGD for 10-Gbit/s, 50% CSRZ signals (a) broadband filtering, (b) narrowband symmetric filtering, and (c) narrowband asymmetric filtering. 190 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S' T O . -1 0 ¥ 1 -2 0 -3 0 8 £ -4 0 o -5 0 10 Gbit/s 0 S" 10 G bit/s Sym m etric 0 S ' 10 G bit/s A sym m etric ; : CSRZ f t f t 2 - -io CSRZ Filtering H. -io CSRZ ft Filtering : u \ E I U A E i ; / \ 2 -20 n t -20 /M ; J \ W -30 / \ W -30 \ f \ / \ 8 N \ I \ 5 = -40 N \f t S -40 : ** '■ *« r o / \ o J u -50 .......* ....... ....... X.......... -5 0 .... iir...............lUi......... 1554.7 1555.3 1555.0 1555.3 1554.7 1555.0 1555.3 1554.7 1555.0 X (nm) X (nm) X (nm) (a) (b) (c) Fig. 4.22. Measured optical spectra for our CSRZ signal (a) before partial optical filtering, after (b) symmetric, and (c) asymmetric partial optical filtering. Asymmetric filtering results in an increase in monitoring range similar to that of symmetric filtering, but with a halving o f minimum DOP dynamic range. The measured optical spectra o f these CSRZ signals before and after filtering are shown in Fig. 4.22(a)-(c). 4.2.2.3 ACRZ Signals Fig. 4.23 shows our simulation results for minimum DOP versus DGD for 40-Gbit/s, 12.5-ps pulsewidth ACRZ signals. Prior to optical filtering (solid line), the DGD monitoring range is limited to -1 8 ps. However, after symmetric or asymmetric filtering using l st-order Gaussian 60- and 6 8-GHz filters, respectively, the DGD monitoring range is extended by - 1 0 ps, to 28 ps (-1 bit duration) with little change in DOP dynamic range. Note that unlike the CSRZ modulation format, for ACRZ, the minimum DOP versus DGD curves are almost identical for both symmetric and asymmetric filtering. 191 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 -----Broadband symmetric filtering 0.8 \ \ • — Symmetric filtering \ \ 0.6 - u \ \ ~ 0.4 : \ \ \ \ / / 0.2 ACRZ 1 A . / / - 40 Gb/s 0 , , , . i , , . ? i . > ' - .................... 10 20 30 40 50 DGD (ps) Fig. 4.23. Simulation results of minimum DOP vs. DGD for 40-Gbit/s, 50% ACRZ signals before and after partial optical filtering. Our experimental and simulation results for 10-Gbit/s, 50 ps pulse width ACRZ signals are shown in Fig. 4.24. Fig. 4.24(a) shows our results prior to narrowband optical filtering, with a monitoring range o f -7 0 ps. After narrowband symmetric filtering using an 8-GHz FPF filter, the monitoring range is extended to > lOOps (-a full bit duration). Using a narrowband asymmetric filter increases the monitoring range similarly to that of symmetric filtering, with a slight decrease in minimum DOP dynamic range. Fig. 4.25(a)-(c) shows the measured optical spectra o f our ACRZ signal before and after filtering. Broadband sym m etric filtering ACRZ Rb= 10 Gb/s BWa = 3 6 GHz 0 20 40 60 80 100 DGD (ps) (a) Narrow band sym m etric filtering ACRZ R„ = 10 Gb/s BW w= 8 GHz Narrowband asym m etric filtering ACRZ ® Rb= 10 Gb/s B W ^ - 8 GHz @ -5 GHz 0 20 40 60 80 100 DGD (ps) 0 20 40 60 80 100 DGD (ps) (b) (c) Fig. 4.24. Simulation and experimental results of minimum DOP vs. DGD for 10-Gbit/s, 50% ACRZ signals (a) broadband filtering, (b) narrowband symmetric filtering, and (c) narrowband asymmetric filtering. 192 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m TP a. O 0 ■1-niTn-nTrr........... 0 -r-H — r t — m i ■ ■ ■ . . | i i ■ j . ■ . T-r'T1 '1 0 10 Gbit/s ST 10 Gbit/s Sym m etric ST 10 Gbit/s Asym m etric -10 ' A C R Z A A A S -1 0 ACRZ A Filtering B -10 ACRZ ft Filtering J v l f l £ m E i n -20 i \ 1 " 20 M 1 ’20 A -30 f \ a. O T -30 / 1 W * -30 I ■ . / [ 8 1 \ 8 r \ ■ 4 0 m V *5 -*o C L I \ I - 40 I M ^ -50 M ........................JL o -50 . tfclUlW.................................W i l k . 0 -50 J b f , . , ............ ....... 1552.9 1553.5 1555.0 1553.5 1552.9 1555.0 1553.5 1552.9 1555.0 X (nm) X (nm) X (nm) (a) (b) (c) Fig. 4.25. Measured optical spectra for our ACRZ signal (a) before partial optical filtering, after (b) symmetric, and (c) asymmetric partial optical filtering. Tables 4.1-4.3 show a summary o f our simulation results listing the optimal filter shapes and bandwidths for each modulation format for the feedforward configuration considering first-oredr PMD. A key to these results is that a given filter shape, order, bandwidth, and position (placed at the center o f the optical spectrum, or offset from the center) will affect these different modulation formats in different ways. Thus, a single DOP-based DGD monitoring module must be calibrated to a given system depending on the filter types available, the pulsewidth, and the data modulation format. To maximize the DGD monitoring range in 40-Gbit/s RZ systems, a FPF filter placed symmetrically is the optimum choice - however to obtain maximum DOP dynamic range, a Gaussian filter placed asymmetrically is required. Similarly, in 40-Gbit/s CSRZ systems, the maximum monitoring range (46 ps) is obtained by using a 2n d -order Gaussian filter. The performance o f a DOP-based DGD monitor will always depend on the data modulation format, the pulsewidth, and the filters available, and no single filter shape, bandwidth, or position on the spectrum results in ideal performance for all three modulation formats. 193 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RZ Broadband Symmetric Filter Symmetric Optical Filter Asymmetric Optical Filter Filter Gaussian (1s t) FPF Gaussian (1s t) Gaussian (1s t) Monitoring Range (DGD-ps) 16 38 38 36 DOP Dynamic Range 95% 39% 97% 48% 97% 50% 92% 37% Optimal BW (GHz) 144 47 60 32 Table 4.1. Summary of the DGD monitoring range, DOP dynamic range, and optimal fdter bandwidths for 40-Gbit/s, 12.5-ps pulsewidth RZ signals for various filter shapes. CSRZ Broadband Symmetric Filter Symmetric Optical Filter Asymmetric Optical Filter Filter Gaussian (1s t) FPF Gaussian (1st) Gaussian (2n d ) Gaussian (1st) Monitoring Range (DGD-ps) 14 26 26 46 38 DOP Dynamic Range 95% 0% 97 % 1% 97% 2% 97% 0% 97% 47% Optimal BW (GHz) 144 15 23.6 23.6 42 Table 4.2. Summary of the DGD monitoring range, DOP dynamic range, and optimal fdter bandwidths for 40-Gbit/s, 12.5-ps pulsewidth CSRZ signals for various filter shapes. ACRZ Broadband Symmetric Filter Symmetric Optical Filter Asymmetric Optical Filter Filter Gaussian (1st) FPF Gaussian (1s t) FPF Gaussian (1st) Monitoring Range (DGD-ps) 18 26 26 32 30 DOP Dynamic Range 99% 2% 99% 1% 99% 0% 99% 11% 99% 9% Optimal BW (GHz) 144 54.4 60 62 68 Table 4.3. Summary of the DGD monitoring range, DOP dynamic range, and optimal filter bandwidths for 40-Gbit/s, 12.5-ps pulsewidth ACRZ signals for various filter shapes. 194 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.1.2.4 NRZ Signals The monitoring range in NRZ systems is limited by the pulse width (i.e. the bit duration). However, the DOP dynamic range is limited in NRZ systems to 50% (the DOP varies from 1 to 0.5) as when the DGD is greater than or equal to the bit duration, the two optical signal replicas on the different PSPs have shifted by >1 bit time with respect to each other, and there is (given random data) a 50% chance that the adjacent bit position has a “1” bit. Fig. 4.26 shows the simulation results for 10- and 40-Gbit/s NRZ signals after broadband symmetric (conventionally used to remove the effects o f ASE on the DOP measurement) and narrowband asymmetric filtering. The optical filter that we used in these simulations was a l st-order Gaussian filter with a bandwidth of 0.8* Rb , which we have found to be the optimum bandwidth for these NRZ signals. C L o Q 1 0.8 0.6 0.4 0.2 0 \ — Asymmetric Filtering 1 s r i— '— i i'--. - .... i i i i \ -----------Asymmetric Filtering ; \ \ ■ — ■ Broadband 0.8 V . ----------Broadband J \ V^Symmetric Filtering \ \ : \ s : \ ■ * » .___ Symmetric Filtering Q . o 0.6 : K ; Q 0.4 ■ \ - " — ■ : 10 Gb/s \ : NRZ ... U..J----1 --- 1 ----1 --- 1 ----1 ----J . .. J _ . . . .L_J------------ 1 ---- 0.2 0 40 G b /s \y r \ ■ NRZ. T .............. Y . . Y ' 50 100 150 DGD (ps) (a) 200 20 40 60 80 100 DGD (ps) (b) Fig. 4.26. Simulation results of minimum DOP vs. DGD for (a) 10- and (b) 40-Gbit/s NRZ signals before and after asymmetric partial optical filtering. 195 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.8 Symm etric 0.6 a. o Q Asymmetric 0.4 0.2 10 G b it/s NRZ 100 D G D (p s ) (a) m 10 Gbit/s 10 Gbit/s Sym m etric NRZ ......Y u •20 C Q ■ u C O a O 10 G bit/s A sym m etric NRZ Filtering 1549.8 1550.1 1550.3 1549.8 1550.1 X (nm) X (nm) (b ) (c ) 1550.3 1549.8 1550.1 1550.3 X (nm) (d) Fig. 4.27. (a) Experimental and simulation results of minimum DOP vs. DGD for 10-Gbit/s NRZ signals after symmetric and asymmetric partial optical filtering and the measured optical spectra for NRZ signal (b) before partial optical filtering, after (c) symmetric, and (d) asymmetric partial optical filtering. Without asymmetric filtering, the DGD monitoring range for the 10-Gbit/s NRZ signal is -1 0 0 ps, but the DOP dynamic range varies from 1 to 0.5. However, after asymmetric filtering using the optimal filter, the monitoring range remains -1 0 0 ps, but the DOP dynamic range is almost doubled. Fig. 4.27 shows the simulation and experimental results and measured optical spectra for a 10-Gbit/s NRZ signal with symmetric and asymmetric filtering. Fig. 4.27(a) shows the DGD monitoring results. Our simulations show that prior to filtering, the minimum DOP varies from -1 to -0.5 (Fig. 4.26). However, after asymmetric filtering using our 8-GHz FPF filter, 196 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. our experimental and simulation results (Fig. 4.27(a)) show that the minimum DOP ranges from 1 to -0.35. Had a filter of optimal bandwidth (0.8* Rb, for l st-order Gaussian filters) been available, the DOP dynamic range for asymmetric filtering would have been extended to the full limits o f the graph (from 1 to 0). Fig. 4.27(b)- (d) show the measured optical spectra without filtering, and after symmetric and asymmetric filtering. Note that for NRZ signals, narrowband symmetric filtering actually reduces the DOP dynamic range (compared to using a broadband ASE filter), due to the canceling o f depolarization effects. 4.3 Cancellation of Second-Order PMD Effects on First-Order DOP- Based DGD Monitors and Measurement of Depolarization Rate It has been shown that a key disadvantage in the use o f the DOP for monitoring in feedback [212] or feed-forward PMD compensator configurations is that it is highly susceptible to higher-order PMD effects. It would be highly desirable to have a DGD monitor for feed-forward compensator configurations in which the errors in the DOP/DGD relationship caused by second-order PMD are minimized or eliminated. In this section, we present a theoretical analysis o f the effects o f second-order PMD (which consists o f the depolarization rate, 2k, and PCD) on the first-order DOP-based DGD monitors [213], Moreover, we show that through the use o f an optical filter, asymmetrically centered at the lower, then the upper, optical sidebands (via tuning the filter) and measuring the maximum and minimum o f the upper and lower filtered spectrum’s DOP, we can cancel out the effects o f second-order PMD 197 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. on the measured DGD value (Fig. 4.28) [213], In addition, this technique can measure the depolarization rate, 2k [213], Fig. 4.28. Conceptual diagram showing how to cancel the effects of second-order PMD on DOP- based DGD monitors. 4.3.1 First- and Second-Order PMD Effects on the Signal’s DOP When PDL and nonlinear effects are negligible the output electric field after first- and second-order PMD effects is given by [214] where R is the rotation matrix that aligns the input SOP into the fiber model by (4.1.27) and R}(co) is the frequency-dependent rotation matrix (that takes into account the fact that the depolarization rate {2k) makes the PSPs frequency dependent) defined by Fiber with PMD PMDC Polarization Scram bler j U U r MAX, Upper ; i , J DOP Min, Upper . j DOP m ax, Lower q lD 0P L ° « s ! > T unable A 'g o r.th rr / * -0 0 A " DGD-Based J \ Poiarim eter DOP m onitor DGD-Based DOP m onitor -olarimetor Emt(co) = e(- ^ (^ )R-1R - , (co)D(ci})RI(co)REln(a)) (4.3.1) V 2 2 J (4.3.2) 198 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and D(co) is the dispersive matrix that takes into account first-order DGD and the frequency dependence of DGD introduced by second-order PMD D(co) = where j is defined by rejx 0 ^ 0 (4.3.3) , , ,, . ® ddgdf co) WQ C O ^ 7 (4.3.4) where in this Taylor series expansion we set co0 to be the center frequency o f the optical spectrum, and the differential term refers to PCD. Using these equations, we obtain the following expressions, which relate the maximum and minimum DOP to the received optical spectrum and the first- and second-order PMD [213]: DOP + 0 0 I + 0 0 + 0 0 JS(a>)cos2 (x )d ai+ \ ( js(a> )sin2(x )co s(2 kco )d a )f + ( jS (w )s in 2(x)sin(2ka)da> )2 5) js(co)d(0 DOP,„ = ■ js(c o )co s2(x )d c o - ( jS (a ))sin 2(x)cos(2kco)da>)2 + ( JS ( a ) s in 2(x)sin(2kco)dao)2 ( ^ 2 6 ) .« ■ < V -on -00 ^ ' Jsf" co)da> In these equations, S(co) refers to the input optical spectrum to the polarimeter. Note that after taking into account second-order effects, the maximum DOP is no longer equal to one and the minimum DOP no longer occurs when we launch at 45° with respect to the first-order PSPs (in Jones’ space). This happens due to the frequency-dependent nature of the PSPs caused by second-order PMD. 199 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Equations (4.3.5) and (4.3.6) show that the minimum DOP cannot be used to accurately estimate DGD in feed-forward compensation configurations in the presence of second-order PMD. To find the relationship between the DOP, first- and second-order PMD, we assume a Gaussian pulse with a fiill-width half-maximum (FWHM) equal to the half bit time for RZ signals. Fig. 4.29(a) and (b) show the effects of second-order PMD on a first-order DOP-based DGD monitor for 40-Gbit/s RZ signals, respectively, when the first-order DGD is equal to 0 ps and 25 ps. These figures show that the PCD and depolarization rate make the DGD estimates unreliable. DGD = Ops 0.8 DGD * 2 5 ps a. § 0.90 a 0.65 : s 0.55 0.80 RZ 4C Gbit/s — y , • to. a mm , s* 0.45 ' i t s pi GwssianPuls** - -ou ■ _ -ou ft 0 1S 30 ^ 0 ' 15 800 «V^ 8 0 o v . IPS * (a) (b) Fig. 4.29. Second-order PMD effects on first-order DOP-based DGD monitors for 40-Gbit/s RZ signals (a) DGD = 0 ps and (b) DGD = 25 ps. 4.3.2 Cancellation of Second-Order PMD Effects on DGD Monitors We propose two new parameters, which we call “ F, ” and “ F , ”, which are based on the maximum and minimum DOP of the upper and lower sidebands after asymmetric filtering. Parameter F, can be used to cancel the effects of second-order PMD on 200 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the DGD estimate provided by a first-order DOP-based DGD monitor, and can be described as [213] Fj = 4 - (DOPm a x u p p e r + DOPm a x lo w e r + D O P min u p p e r + DOPm in _ la w e r ) (4.3.7) F, is unaffected by second-order PMD as the summation of the maximum and minimum DOPs (for a given sideband) cancels the depolarization effect, and the summation of the upper and lower filtered DOPs cancels the effect of PCD. Note that in equations (4.3.5) and (4.3.6) the received optical spectrum is S ( co ) \H ( a > - o )J\ after asymmetric filtering, where the H (a>) is the optical filter transfer function and coc is the filter’s frequency offset from the center of the optical spectrum. By assuming a Gaussian pulse with an FWHM equal to the bit time and half bit time for NRZ and RZ signals, the optimum filter offset is calculated to be R h and 0.125 * R b for NRZ and RZ, signals, respectively, and the optimal filter bandwidth is calculated to be R b and ~ 0.6 * R b . Fig. 4.30(a) and (b) show the Fb parameter as a function of the effective second-order PMD, \£2a\ for 40-Gbit/s RZ signals. This figure shows that Fb is fairly insensitive to second-order PMD - for a given DGD value, the Ft parameter remains fairly constant, and thus the parameter can be used to monitor DGD without significant interference from second-order PMD. The upward trends in the graphs for low DGD values are due to residual second-order PMD effects after filtering. 201 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DGD = 25 ps NRZ 40 Gbit/s 0.6 0.5 0.4 F1 0.3 0.2 0.1 0 DGD = 25 p s; 20 p s ; - RZ 40 Gbit/s 10 ps- 0 . , _ps: 0 200 ,400 , 600, 800 I a© I (ps2 ) (a) 200 4,00 , I Q© | (ps2) (b) f 0 ° 800 Fig. 4.30. Second-order PMD effects on F r based DGD monitors for 40-Gbit/s RZ signals. 4.3.3 Depolarization Rate Measurement After DGD estimation using this technique, we can estimate the depolarization rate (2k) using parameter F2, which is described as [213] F2 =DOPm a x u p p e r + DOPm a x lo w e r (4.3.8) Parameter F2 only takes into account the effects of DGD and the depolarization rate as the summation of the maximum DOP of the lower and upper asymmetrically filtered spectrum averages over the positive and negative frequency components relative to the central frequency of the optical spectrum (removing the effects of PCD). Thus, knowing the DGD estimate found using parameter F2, we can estimate the depolarization rate using F2 . Fig. 4.31(a) and (b) show the depolarization rate as a function of F2 and total second-order PMD, 1/2 I, for a DGD value of 25 ps for 40-Gbit/s NRZ and RZ 202 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. signals, respectively. Note that for a given depolarization rate, 2 k , the value of F2 remains fairly constant as the total second-order PMD changes. 2.1 F2 1.9 1.8 DGD = 2 5 p s k = 0 p s 2 ps 6 ps 4 ps 8 ps 10 ps 400 800 1200 I Qc d | (ps2) (a) D G D = 2 5 p s k= 0 ps 4 0 0 8 0 0 1 2 0 0 I Q© I (PS2) (b ) Fig. 4.31. F2 allows estimation o f the depolarization rate, 2k, in 40-Gbit/s (a) NRZ and (b) RZ signals even as the as total second order PMD, | | , varies. 4.4 Accurate DOP Monitoring of Several WDM Channels for Simultaneous PMD Compensation As PMD varies through time [38], an OPMDC is required to monitor the PMD of the link in order to control a feedback loop. The compensator in the feedback loop rotates the incoming optical signal’s SOP and adjusts a DGD element to optimally compensate for the estimated PMD. Given that PMD is uncorrelated between different wavelengths, each WDM channel would require its own expensive compensator, in order to optimally compensate for the PMD in each channel [215], This is obviously not a cost-effective solution. It is possible to alleviate this problem by using one compensator for several WDM channels simultaneously. Published results have shown that using a single RF control signal for several channels to tune a 203 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. compensator, such that the channel most affected by PMD is also the channel most compensated, is one effective solution to this problem [216]. Such a scenario may degrade the other channels with lower PMD while improving the channels with higher PMD. However, the monitor continuously directs the compensator to act on the “newer” worst channel, thereby reducing the probability that an outage will occur on any single channel. Because network outages generally occur for DGD values on the tail of Maxwellian distribution, this technique can be effective, since the probability of two channels being highly affected simultaneously by PMD is much lower than the probability of a single channel. A key challenge in the implementation of the above technique is to monitor all the WDM channels collectively and feed a single control signal to a single OPMDC. In this section, we show via simulation and experiment that the system limitations of all-optical monitoring of several WDM channels in order to drive a single OPMDC [161], We focus on the utility of measuring the DOP for each WDM channel and taking the average of the DOPs to provide the single monitoring signal. We demonstrate multi-channel PMD compensation based on an averaged-DOP parameter in 4-channel 10-Gbit/s NRZ and RZ transmission systems. Using a single OPMDC for four WDM channels, we achieve a significant power penalty reduction more than 10 dB and 3 dB for NRZ and RZ, respectively, in the worst case of first- order PMD emulation. The 2% worst-case performance of the averaged-BER is improved by two orders of magnitude and averaged-DOP is enhanced by 20%. 204 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4.1 Concepts of WDM DOP Monitoring for Simultaneous WDM PMD Compensation For multi-channel PMD compensation, we consider two optical monitoring techniques. First, we consider a simple combined-DOP method (Fig. 4.32(a)). All channels are tapped and sent to the monitoring unit. The monitoring unit measures the overall DOP of all the channels and provides a single monitoring signal for the single WDM OPMDC. In the second technique (averaged-DOP method depicted in Fig. 4.32(b)), we use the averaged-DOP of the channels to drive the compensator. Combined-DOP Technique IQ Single compensator T Single monitoring [signal ^ , Rx ^ -2 , Rx A, , Rx Rx M onitoring (a) Averaged-DOP Technique IQ Single compensator Single monitoring signal Rx n A 2 Rx R x K h Rx s r i" _______I L er. M onitoring (b) Fig. 4.32. Conceptual diagrams o f optical WDM PMD compensation using a single compensator relied on (a) combined-DOP measuring and (b) averaging the individual DOPs. The DOP of each individual channel is measured by sweeping the filter across each WDM channel. The results for four channels are then averaged to yield a single monitoring signal to OPMDC. The prerequisite condition for the combined-DOP 205 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. method is that the SOPs of all channels should be maintained the same through out the transmission. While intra-channel SOPs rotate due to DGD, the inter-channel SOPs alternate relative to each other as a function of the channel spacing and DGD. Due to this fact the DOP fades with respect to the DGD in a WDM system. Fig. 4.33(a) and (b) describe the DOP fading effects for both NRZ and RZ modulation formats, respectively. The fading periodicity is inversely proportional to the channel spacing. Using the combined-DOP method, measured data points (hollow circles) are matched with the DOP-fading simulation (solid gray line). As a result, the combined-DOP method cannot be implemented in a multi channel system due to the periodic fluctuation of DOP. On the other hand, using the averaged-DOP measurement technique (solid triangles) ensures the functionality of the monitor. As shown in Fig. 4.33, the distribution of the measured averaged-DOP values with respect to DGD is well matched with the calculated single-channel DOP curve (dotted line). The monitoring range and the sensitivity are 100(50) ps and 45%(65%) for an NRZ(RZ) signal. Averaged Tejch. 0.8 0.6 o P 0.4 0.2 0 'A.T < a (measured) Combined Tech. (measured) 'D Single chann O ■ ; (simulated)* el 0 20 40 60 80 100 DGD (ps) (a) 0.8 I Pm o.6 O P 0.4 0.2 0 fh. Combined Tech. A-., (simulated) 0 20 40 60 80 100 DGD (ps) (b) Fig. 4.33. Distribution of measured combined-DOP, and averaged-DOP for 10-Gbit/s data streams with 1.6 nm channel spacing. Black-dotted and gray curves represent calculated single-channel DOP and combined-DOP o f 4 channels, respectively. 206 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4.2 Demonstration of Simultaneous WDM PMD Compensation Using Averaged DOP Monitoring Simultaneous WDM PMD compensation based on the averaged-DOP technique is experimentally demonstrated for 4-channel 10-Gbit/s NRZ and RZ transmission systems with 1.6 nm channel spacing. Before demultiplexing the channels, we add a fixed DGD element to emulate first-order PMD. After tapping off the power of each channel for monitoring, all DOPs are separately measured by sweeping the optical filter across WDM channels, and averaged to obtain a single feedback control signal for the single WDM OPMDC. An OPMDC is located after the emulator (see Fig. 4.32(b)). One of the channels is filtered out to measure the power penalty after the demultiplexor. DOPs and power penalties are measured with DGD values less than T>- In the proposed averaged-DOP method, the contribution of DOP from each channel to the overall averaged-DOP is independent from channel to channel. When the worst case of each channel is considered (i.e. all channels are launched at 45° to the first-order PMD emulator), the averaged-DOP distribution of the 4 channels is consistent with that of a single channel. Fig. 4.34 shows the power penalty performance when the monitoring is performed by the combined-DOP method (solid up-triangles), by the averaged-DOP method (hollow down-triangles), and shows the compensated performance (hollow circles). It is clearly seen that all the data points of averaged-DOP are re-distributed in the narrow area near 100% of DOP and ~ 0-dB power penalty after PMD 207 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. compensation showing significant power penalty reduction. The maximum improved values are more than 10 dB and 3 dB for NRZ and RZ signals, respectively. We also show simulation results for a real transmission link by using a 7-section PMD emulator with an average DGD value of 40 ps. We take 300 independent samples. Even if all SOPs of the input channels are not parallel to each other, the averaged- DOP still provides a good single control signal for a single OPMDC that is designed to optimize the overall performance of a WDM system by reducing the highly deleterious impact of the DGD distribution tails and decreasing the probability of a system outage. to -a-, GA-t-A-V- • Single-ch a Combined v Averaged u « - 7; o Com pensated - o< 0 i — • - ..... 0.7 0.75 0.8 0.85 0.9 0.95 1 DOP (a) i f A A:—- A - ’ V 7 ™ "--T — - " f Combined-Tech doesn’t function • Single-ch a Combined v Averaged Com pensated 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 DOP (b) Fig. 4.34. Power penalty measurement with respect to DOP with the DGD values o f <T( ) . In both (a) NRZ and (b) RZ data formats, the measured data points with the single-channel-DOP and the averaged-DOP have the similar trends as opposed to the combined-DOP method, which does not provide the monitoring functionality. Dotted and solid curves represent fitted curves for single-channel DOP and averaged-DOP, respectively. Fig. 4.35(a) illustrates that the averaged-BER distribution of the four-channel NRZ system is significantly improved using the single first-order-PMD compensator with DGD value of 40 ps. The 2% worst-case performance of the averaged-BER is improved by two orders of magnitude after compensation. Fig. 4.35(b) depicts the 208 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. effectiveness of the averaged-DOP method by comparing the averaged - log( BER ) values after compensation with the average - log( BER ) values before compensation for the worst and the best channels. The worst BERs occur for DGD values located in the tail of the Maxwellian distribution. These DGD values have the largest effect on system outage. It can be observed from Fig. 4.35(b) that for these DGD values a significant improvement in BER is obtained using our proposed averaged-DOP monitoring technique, therefore reducing overall system outage. Fig. 4.35(c) illustrates that the averaged-DOP is also improved significantly using the same compensator, resulting in an improvement of the 2% worst-case performance of the averaged-DOP values by 20%. 9 9 . 9 9 i.■ ■ ■ ■ ..■ ..i------- --------- - ■ ■ i ~ 9 9 . 9 } - 9 9 - W/O I ■ £ 8 8 : Compensation Jj : ' t % W > 5 0 2 1 8 \ ^ y \ a iq o ; > -" r ""Pr ^ C .i . 0 1 W/Compensation > 4 6 8 10 Averaged (-log(BER)) (a) 9 9 . 9 9 r 9 9 . 9 ^ 9 9 8 8 r * 8 6JJ 50 & a S3 IQ © : .i .01 w /o Compensation 9 9 . 9 9 9 9 . 9 /-n 9 9 ^ 9 5 9 0 5 0 W orst Channel W/O Comp. 1 . 1 .01 Best Channel / W/O Comp. J Averaged-BER‘ W/ Comp. 2 4 6 8 1 0 -log(B E R ) (b) W / Compensation 0 .6 5 0 .7 0 .7 5 0 .8 0 .8 5 0 .9 0 .9 5 1 A v era g ed -D O P (c) Fig. 4.35. Simulation results of (a) averaged-BER curves with and without compensation, (b) compensated averaged-BER-curve compared with the BER-curves o f the worst and the best channels representing the significant improvement o f the highly impaired signals, and (c) averaged-DOP distribution o f four NRZ 10-Gbit/s WDM channels with 1.6-nm channel spacing with and without compensation. 209 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.5 Link DGD Measurement without Polarization Scrambling Using DOP and Symmetric/Asymmetric Partial Optical Filtering Both electrical and optical techniques are available for mitigating PMD in an optical link. These mitigators must be dynamic, as PMD can vary on a millisecond time scale - with a feedback or feed-forward loop that can monitor signal quality and provide a control signal to the OPMDC. The feed-forward configuration for PMD monitoring/compensation has been shown to have a number of advantages over feedback configurations [74], However, feed-forward PMD monitors/compensators based on the DOP typically require polarization scrambling at the transmitter. This scrambling has become an important tool for PMD monitoring and compensation in terrestrial transmission links because it provides a means of monitoring the instantaneous DGD values and thus reduces the feedback tracking complexity [73], However, polarization scrambling results in a number of systems disadvantages including: (i) it requires modification of the transmitter and (ii) polarization scrambling has been shown to have a number of deleterious system effects [24], As such, it would be convenient to have a DOP-based DGD monitor that did not require polarization scrambling at the transmitter yet it still provides a DGD measurement result. In this section, we show a technique for DOP-based DGD monitoring that is independent of the input SOP to the fiber link [217], This technique measures the DOP when a narrowband optical filter is placed at the center of the optical spectrum (“symmetrically”), and when the filter is centered at one of the optical clock 210 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sidebands (“asymmetrically”) [163-165]. Using these two DOP values, we can calculate the DGD (and thus generate a monitoring signal) independent o f the input SOP [217]. A diagram of the setup for the proposed DGD monitor is shown in Fig. 4.36. This technique is simple and requiring only a single optical filter and polarimeter. This technique can also be applied to WDM systems by sweeping the filter across each channel. However, this technique cannot be applied in situations where the DGD = 0, or when the input SOP is lined up to the fiber PSPs - however, in these cases, PMD mitigation is not necessary. with PMD Tundhto: h J i Symmetric N o P o la riza tio n Scrambler ____ ; T i J _____________ Fig. 4.36. Setup for DGD monitoring without polarization scrambling at the transmitter using partial optical filtering method. 4.5.1 T h eo ry of DGD Measurement Using Partial Optical Filtering without Polarization Scrambling The DOP of a modulated signal is a function of the received optical spectrum, link PMD (first- and higher-orders), and the input signal’s SOP. The dependence of DOP on the input SOP makes DOP-based DGD measurement unreliable. To solve this problem, most systems use polarization scrambling at the transmitter - by scrambling the input signal’s SOP over the Poincare sphere and continuously monitoring the signal’s DOP, we can estimate the link’s DGD. However, using our technique, we 211 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. extract information about the optical spectrum’s DOP to measure DGD without the need for scrambling. To explore the analytical relationship to show that DGD can be measured without polarization scramblingin feed-forward configuration, we start from a general formula described by [206-208] where S(co) is the received optical spectrum and y is the power splitting ratio between the two PSPs (which is related to the angle between the link PMD vector and the input signal’s SOP) - showing that the DOP is dependent on the received optical spectrum and power splitting ratio. Fig. 4.37(a) and (b) show this dependence on the power splitting ratio - these figures show our simulation results relating the DOP as a function of the angle between the link’s PMD vector { Q ) and the input signal’s SOP for 40-Gbit/s NRZ and RZ signals. They show that the signal’s DOP is related to the DGD and the input signal SOP. In this simulation, an optical filter (with bandwidth 4* Rb) was placed before the polarimeter to filter out any ASE effects. Via symmetric and asymmetric filtering of the received optical spectrum, we can obtain the following equation for a new term that we call “ P ” [217]: D O P (dgd,y) = 1 - 4/(1 - y) + 4y( 1 - y)[- jc o s ( a > d g d ) S ( w ) d a » (4.5.1) p _ 1 — DOP2 Asym 1 — DOP2 Sym (4.5.2) 212 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 p s 0.8 0.6 a. § 0 .4 DGD = 12.5 ps 0.2 4 0 G b/s R Z 6 0 1 2 0 <n, S O P ,n > ° 1 8 0 5 ps 0.8 12.5 ps 0.6 0. § DGD = 25 ps 0 .4 0.2 4 0 G b/s N R Z 1 8 0 (a) (b) Fig. 4.37. Relationship between the DOP and the angle between the link PMD vector and the signal SOP for 40-Gbit/s (a) NRZ and (b) RZ signals. where DOPA and DOPS y m are the DOPs when a narrowband optical filter is offset from the optical spectrum by the bit-rate frequency (i.e. 10 GHz offset in a 10-Gbit/s system) and when it is centered on the spectrum, respectively. Equation (4.5.2) arises from (4.5.1) - by squaring the right-hand-side and rearranging terms, a (1 -DOP2) term can be isolated. By taking two measurements (in this case DOPA and DOPS y m ), and dividing the two, the splitting ratio, y , drops from the equation. 4.5.2 Simulation Results Fig. 4.38(a) and (b) show the simulation results for — (NRZ) and P (RZ) as a function of the angle between the link PMD vector and the input signal SOP for 40 - Gbit/s NRZ and RZ signals, respectively. These figures make clear that P (and hence — ) is independent of this angle and thus the input signal SOP. The filter P bandwidth was 0.7Rb ( 0.8Rb) for the NRZ (RZ) simulation. 213 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1-D O P Sym. 1 0.8 0.6 0.4 0 .2 0 , D G D = 25 ps 12 .5 ps 40 G b /s NRZ 5 ps 1-DOP2 a s , 1-DOP2 8 y 45 90 135 180 <ft, SO Pin > ° 1.2 1 0 .8 0 .6 0.4 0.2 0 D G D — 25 ps 12.5 ps 5 ps 40 Gb/s RZ (50%) 0 45 90 135 180 <0, S O P ,n > ° (a ) (b ) Fig. 4.38. Relationship between (a) 1/P and (b) P and the angle between the link PMD vector and the signal SOP for 40-Gbit/s (a) NRZ and (b) RZ signals. Fig. 4.39 (a) and (b) are the simulation results showing the relationship between -—(NRZ), P (RZ), DOPA s y m , and DOPS y m as function of DGD in 40-Gbit/s systems. These figures show that the DGD monitoring range of this technique is not limited by the pulse width of the signal - for both the NRZ and the RZ cases, the monitoring range is at least one full bit time. Sym. 0.8 0 .4 s ASym. 0.2 " t r • 40 Gb/s NRZ DGD (ps) (a) \ / .ASym. 1-D O P 1-D O P2 s. ^ Sym. N f 40 Gb/s RZ (50%) 0«- 1 0 20 3 0 4 0 5 0 DGD (ps) (b ) Fig. 4.39. Simulation results showing the relationship between (a) 1/P and (b) P, as well as DOPA sy m and DOPsym as functions of DGD in 40-Gbit/s (a) NRZ and (b) RZ systems. 4.5.3 Experimental Results Using a first-order PMD emulator, we took 4 points (23, 40, 50, and 74 ps) and varied the splitting ratio in 10-Gbit/s RZ systems. To perform the filtering, we used 214 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. an 8-GHz FPF filter, centered at either the center of the optical spectrum, or at the bit-rate frequency (in this case -10 GHz). Table 4.4 shows the corresponding eye diagram and value for P for RZ signals as they are launched with different SOPs into this first-order PMD emulator. This table shows that for the same amount of DGD, as the splitting ratio changes 1 — D O P 2 a (shown by the varying eye diagrams), P , equal t o , and remains fairly 1 —D O P 1 Sym constant. Thus this technique is a good method for measuring DGD without the use of polarization scrambling. Eye ■ ■ ■ * % • - - r r , t * A * h ' - p - k DGD 74 ps Different input signal’s SOP P | 0.4975 0.5000 0.5154 | 0.4854 Table 4.4. The value o f P, equal to [l-( DOPA sy m )2 ]/ [l-(D O PS y m )2], as the power splitting ratio at the transmitter changes (noted by the changing eyes) for a DGD value o f 74 ps. For a given DGD value, the value o f P remains fairly constant. Fig. 4.40(a) and (b) show the simulated and experimental DGD sensitivity curves for “jL” and P ” in a 10-Gbit/s (a) NRZ and (b) 50% RZ system, respectively. These demonstrate that by using “ P ” and “ — related to the DOP of a filtered optical spectrum when the filter is centered on the spectrum, and offset by the bit-rate frequency, we can obtain DGD information about a link without requiring polarization scrambling at the transmitter. 215 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.8 0.6 1 — D O P sy m . "I — O O P 2 Asym. 0 .4 0.2 0 20 4 0 60 8 0 1 0 0 0 20 40 60 8 0 1 0 0 DGD (ps) DGD (p s) (a ) (b) Fig. 4.40. P-DGD sensitivity curves for 10-Gbit/s (a) NRZ and (b) RZ systems without polarization scrambling at the transmitter. 4.6 DOP-Based PMD Monitoring in Optical Subcarrier-Multiplexed Systems by Carrier-Sideband Equalization Optical subcarrier multiplexing has been shown to be a useful technique for reliably transmitting both analog and digital signals over fiber. It has seen application to analog cable television, and future applications may include antenna remoting, local- area network (LAN) traffic, and header control for optical packet-switched networks. In addition, due to its high bandwidth granularity, it may see application in high- bandwidth, multiuser, reconfigurable digital transmission systems. Chromatic dispersion PMD have long been considered limitations to high speed and/or long-distance transmission over fiber, and much research has been devoted to combating these effects. However, SCM signals can be made relatively robust to chromatic dispersion through use of single-sideband (SSB) generation [218-222], However, SSB generation does not prevent PMD from degrading an SCM signal - indeed, it has been reported that the transmission of analog and digital SCM signals over fiber can be severely affected by PMD [21-22,223-227], PMD has 216 10 Gb/s NRZ 10 Gb/s RZ (50%) \ — — S im u latio n ^ ------Sim ulation / ■ * E x p erim en tal / 0.6 ■ Experim ental / 1 — D O P 2 A a y m . / / ' 1 - d o pV . - S / • ■ 0.4 . a y s ' • 7" ■ ■ .................... 0 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a statistical behavior, since (i) the relative orientation between the SOP of an input signal and the PSPs of a fiber link is a uniformly distributed random variable and (ii) the DGD between the fast and slow PSPs is a random process with a Maxwellian probability distribution due to the random orientation of the PSPs of sections of fiber birefringence within the link. For example, in 40-GHz optical SCM systems, the RF power after detection is completely faded over a fiber link with an average DGD of only 5 ps when the instantaneous DGD is only 12.5 ps, near the tail of the Maxwellian DGD distribution. A key point is that there is always a finite probability of RF fading in an SCM system due to PMD. To ensure robust transmission of SCM signals through long fiber links, PMD mitigation may be necessary. While both electrical and optical techniques for PMD mitigation have been demonstrated, electrical equalization [185] is not effective in SCM systems as it is based on canceling ISI, which does not recover a PMD-faded RF tone. Thus, OPMDC, in either the feedback or feed-forward configurations, is required, along with PMD/DGD monitoring to provide a compensator control signal. Some previously reported control techniques for optical PMD mitigation in SCM systems use the RF signal power as a feedback control signal [22,228-229]. Flowever, this technique suffers from a number of disadvantages, including: (i) poor reliability due to the effects of chromatic dispersion on double-sideband (DSB) signals, (ii) it requires high-speed electronics, and (iii) it is affected by nonlinearities, FWM in particular [230-231], As feed-forward OPMDCs have been shown to have a number of advantages over feedback OPMDCs [74-76], a monitor that can be used 217 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. in both feed-forward and feedback OPMDCs provides increased flexibility to a system. The technique of monitoring a signal’s DOP and using it as a control signal for a PMD mitigation is popular in digital transmission systems because: (i) there is no requirement for high-speed electronics, (ii) it can be applied to both feed-forward and feedback OPMDCs, and (iii) it is unaffected by chromatic dispersion. However, this technique has yet to be implemented for DGD/PMD monitoring for SCM signals due to the low sensitivity of DOP to DGD in SCM systems resulting from low modulation depths commonly required to keep the modulator operating in its linear region [232], In this section, we demonstrate a unique DOP-based PMD monitor for SCM systems that has significantly enhanced DOP sensitivity to DGD/PMD [168,233]. We show that the DOP sensitivity to DGD/PMD in an SCM system is typically negligible, due to the high optical power of the carrier compared to the subcarrier(s), and is dependent on the modulation depth of the SCM signal. The use of optical filtering to improve the performance of DOP-based DGD monitors for digital transmission ofNRZ signals has been previously demonstrated [163-165]. We apply a similar technique to these SCM signals - using a narrowband optical filter; we equalize the optical power of the carrier and one of the sidebands, often more than tripling the DOP sensitivity to DGD/PMD [168,233], The proposed technique can be applied to both SSB and DSB SCM signals, and can be applied to single- or multiple-subcarrier systems. We demonstrate our technique for both single and dual- 218 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. subcarrier systems and show a tripling of the DOP sensitivity (in single-subcarrier systems) and more than doubling of the DOP sensitivity (in the dual-subcarrier system). Using this technique as a feedback signal to an OPMDC, we improve the 5% RF power distribution tail by 11 dB, from -17 to -6 dB, and improve the receiver sensitivity by 12.5 dB. 4.6.1 Theory of PMD Effects on the Subcarrier’s DOP The relationship between the DOP and the PMD of an optical link is well understood in digital transmission links, and this technique has received much recent attention for use for DGD and/or PMD monitoring. However, it has been shown that the DOP in an SCM system has low sensitivity to PMD, making it less suitable as a PMD monitoring control signal [232]. While the optical carrier and sidebands have the same SOP at the transmitter, after propagation through the fiber link, PMD induces a phase delay between the two PSPs for the optical carrier and for each of the sidebands. In general, these phase delays are not equal to each other. These phase differences manifest themselves as an “SOP w alkoff ’ between the optical sidebands and carrier. In Stokes space, this walkoff angle is equal to ±2n* f * D G D radians on the Poincare sphere. Fig. 4.41 shows a conceptual diagram illustrating the first- order worst case {dgd - — — , with equal power in each PSP) in both DSB and SSB ^ f s SCM systems, corresponding to an optical sideband rotation of ± 90(±180 ) relative to the carrier in Jones space (Stokes space). In this case, in the electrical domain, the subcarrier signal completely fades. Fig. 4.41(a) shows a diagram of this worst case 219 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for a DSB SCM signal before and after a fiber link with PMD. Notice that when there is an intra-subcarrier SOP walkoff due to PMD, the effects of this walkoff are minimal due to the typically low data rate on the subcarrier. Otpetmriza&in L S B U S B / « - / , L / « + / , J e o p s f v. a itcMsattm ■ ■ * a p iic a l sto e u a r SSB i k L S B I f r f i J fiber with PMD D S B i ... \ J \ U S B / . * /> f + r ® % V J * * } I Veferfewfer j a i JT]__J g f | • • • • • - I 0® » (a) DOP * 1 D*poi*rit*tion Fiber with PMD S S B i X 1 ; + x in POP OOP - 1 (b) Fig. 4.41. Conceptual diagram of worst case DGD effects for (a) DSB and (b) SSB SCM signals in Jones space. In a standard digital transmission system, since the optical data spectrum consists of many frequency components, the unequal rotation of these frequency components relative to each other results in significant depolarization and a corresponding reduction in the DOP. However, for SCM signals, due to the high optical power of the carrier compared to the sidebands (a result of the low modulation depths commonly used in SCM systems due to the need to operate in the linear region of the modulator), even in the worst possible depolarization case (when the optical carrier and sidebands are orthogonal to each other, in Jones space), at the 220 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. end o f the link, the DOP change is negligible. Fig. 4.41(b) shows a diagram of the worst case for SSB SCM signals. Similarly to DSB systems, even in this worst depolarization case, the optical power of the carrier makes any change in DOP due to sideband depolarization negligible. The relationship between the DOP and first-order PMD in a system using a finite linewidth source has been previously reported [206-208], Applying the expression for the optical spectrum of an SCM signal to the formula derived in [208], we obtain [168,233] DOP ( y , dgd ) = n - +oo x — i 7 J L f¥ l X J n ( —~ )co s( 2 - m f d g d ) 2 $ 1 - 4y(l - y) + 4y(l - y)[- n — +oo I J 2 n ( 7 C f ) n — — o o (4.6.1) where m is the modulation depth ( _), f s is the subcarrier frequency, y is the power splitting ratio between the two PSPs, and j n is a Bessel function of order n . If we assume the worst case (y = 0.5) then the relationship becomes one of minimum DOP to DGD, and is equal to [168,233] DOP ( dgd ) n — +oo Z J 7 T C W l n ( ---- )c ° s ( 2 rntf dgd ) 2 $ n — -oo n = +°° _ Z J 2 n ( ^ ) n 2 = — o o (4.6.2) When the modulation depth is low, the zero-order Bessel function dominates this summation ( « = 0 ), forcing the cosine term to equal one, canceling the 221 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. numerator and denominator and resulting in a minimum DOP of one regardless of the DGD. The relationship between the minimum DOP and the DGD of a link is closely related to the modulation depth and subcarrier frequency of the SCM signal (shown in (4.6.2)). An increase in the SCM modulation depth results in a corresponding increase in the minimum DOP variation due to DGD. As the modulation depth increases, the first-order Bessel function in (4.6.2) becomes comparable in magnitude to the zero-order Bessel function and an increase in minimum DOP variation to DGD is observed, as shown in Fig. 4.42 for a 20-GHz DSB SCM signal with modulation depths of up to 30%. As SCM systems typically use low modulation depths, the DOP variation as a result of DGD remains negligible. Were the subcarrier frequency to change, the periodicity of the curve would also change, as the first minimum value always occurs at . 2f, 0.9 0.8 Q. O Q 0.7 m = 10% - - m=20% m = 3 0 % 0.6 fs= 20 GHz 0.5 20 100 DGD (p s) Fig. 4.42. Simulation results showing minimum DOP vs. DGD for a 20-GHz subcarrier with varying modulation depth. 222 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. If the optical power of the carrier is reduced such that the optical power of the sidebands is equal to the optical power of the carrier, then the depolarization effects on the sidebands (relative to the carrier) as a result of DGD significantly alter the DOP of the SCM signal. To verify this hypothesis, we increased the modulation depth of a 6.75-GHz DSB signal high enough that the combined optical power of the two sidebands was approximately equivalent to the carrier power (i.e. each sideband was 3 dB lower than the carrier). The resulting optical spectrum is shown in Fig. 4.43(a). We measured the spectrum using an OSA with ~l-GHz resolution. At this power level, the square of the zero-order Bessel function is equal to twice the square of the first-order Bessel function. We then launched this signal at 45° relative to the PSPs of a first-order PMD emulator for which we varied the DGD, and measured the resulting DOP using a polarimeter, which is shown in Fig. 4.43(b). In this case, with the much-increased optical sideband power levels, the DOP reaches -4.7 £ C Q - I -28.7 S I *3 Q. o C O -52.7 1531.17 6.75 GHz 1531.42 1531.67 0.8 q. 0.6 O D 0.4 0.2 f„ = 6.75 GHz 100 20 D G D (p s ) (b) Fig. 4.43. (a) Optical spectrum for a 6.75-GHz DSB SCM signal when we increased the modulation depth until each sideband’s optical power was 3 dB less than that o f the carrier and (b) experimental results for minimum DOP vs. DGD for this SCM signal. 223 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. zero at -74 ps (~_L_), making this a useful tool for enhancing the DOP sensitivity 2f, to DGD for use in PMD and DGD monitors. 4.6.2 Equalized Carrier-Sideband Filtering and DOP Measurement We combat this minimal DOP sensitivity to DGD in SCM systems by using an optical filter centered on one of the optical sidebands such that the carrier is on the edge of the filter. This allows us to equalize the optical power levels of the carrier and sideband (and filter out one of the sidebands of a DSB signal). A diagram of this technique is shown in Fig. 4.44. In such a case, for a splitting ratio ( y ) of 0.5 (the worst case, when there is equal optical power in each PSP) the minimum DOP becomes [168,233] DOP (d g d ) = n — +oo Z J 2 n ( ~ - ) n ~ ~oo \2 H ( » f s - f Q 7 c o s( 2 jm f^ d g d ) n = +oo Z j K ^ ) n = -oo H ( n f - f ) s 2 (4.6.3) where H(f) is the optical filter transfer function, f 0 is the frequency offset of the filter from the optical carrier. 224 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Depolarization ^op!tc*rf swtaljasd F i b e r w i t h P M D f s J a f r o w - h a i K * *V*» \ ECSF f D O P . * 1 Eqw affeed C a r r tv & s ls j e t r a w i p o w e r Fig. 4.44. Conceptual diagram o f our equalized carrier-sideband filtering (ECSF) technique. The optimal 3-dB bandwidth of this filter is a key issue when using this technique as it directly affects the amount of carrier suppression. The bandwidth depends on the subcarrier frequency, the filter shape, and the modulation depth of the SCM signal, as shown in Fig. 4.45 for ( l st-order) Gaussian and FPF filters. For example, using a tunable FPF filter (with an FSR of 750 GHz), for a 40-GHz, 20% modulation depth subcarrier the bandwidth of the filter should be -12 GHz to achieve maximal canier/sideband power equalization. However, increasing the subcarrier modulation depth to 50% changes the optimal filter bandwidth to almost 40 GHz. The use of ECSF does not change the maximum DGD monitoring range, which remains at — . 2 fs However, as the relationship between DGD and RF power is a periodic function, maximizing the DOP will always result in minimizing RF power fading regardless of the actual DGD value (assuming no higher-order PMD). 225 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■•O- m=50% G auss. - O - m=50% FPF -® - m=20% Gauss. - * - m=20% FPF I 50 E 20 fs (GHz) Fig. 4.45. Simulation results showing the optimum ECSF bandwidth for FPF filters and l st-order Gaussian filters as a function o f modulation depth and subcarrier frequency. 4.6.3 Equalized Carrier-Sideband Filtering and DGD Monitoring To demonstrate the effectiveness of this technique for DGD/PMD monitoring, we applied our ECSF technique to a tapped-off portion of an optical SCM signal, generating a PMD monitoring signal that can be applied to both feedback and feed forward OPMDC configurations. We generated DSB SCM signals with modulation depths of 30%, and 40% (other modulation depths were not possible in our experiment due to the lack of sufficiently varied optical filters) at 155 Mbit/s using a 2,5-l PRBS and sent them at 45° with respect to the PSPs of our first-order PMD emulator. The optical spectrum for a 20-GHz, 30% modulation depth DSB SCM signal generated via externally modulating a 1531.4 nm carrier prior to ECSF is shown in Fig. 4.46(a). After using a filter to perform ECSF and equalize the optical power of the carrier and one of the sidebands, we obtain the spectrum shown in Fig. 4.46(b). The filter used in this experiment was a voltage-controlled FPF filter with 8-GHz bandwidth and an FSR o f -750 GHz. Note that one of the sidebands is almost completely removed in this process, meaning that the ECSF technique can be 226 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. applied to both DSB and SSB signals, as the resulting spectra are virtually identical (only a SSB remains) after ECSF. We measure the DOP of the signal (with and without ECSF) as a function of DGD using a polarimeter, and the result is shown in Fig. 4.46(c). The simulated results are also shown in the figure, and the experimental results match well with the simulation. Note that prior to ECSF, the minimum DOP varies only from 1 to -0.8, making it difficult to use it as a control signal for a DGD/PMD monitor, while after ECSF, the minimum DOP varies from 1 to ~0. W /o E C S F m = 3 0 ” / U+20 G H z f,-2 0 G H z O ,9- -30 1531 1531.2 1531.4 1531.6 1531.8 X (nm) (a) W / E C S F m = 3 0 % r f^ + 2 0 G H z O -20 r-20 G H z 1531 1531.2 1531.4 1531.6 1531.8 X (nm) (b) 0.2 ' I VII E C S F \ , U \ 1 I I m = 3 0 % ' I f,» 2 0 G H z 6 1 0 20 40 60 80 100 DGD (ps) (c) Fig. 4.46. (a) Optical spectrum of a 20-GHz, 30% modulation depth DSB SCM signal prior to ECSF, (b) optical spectrum of the same signal after ECSF, and (c) minimum DOP vs. DGD curves before and after ECSF. 227 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.47 shows theoretical, simulation, and experimental results for minimum DOP versus DGD for a DSB 6-GHz, 40% modulation depth signal after ECSF. Note the agreement between the three data sets. Fig. 4.48 shows the simulation and experimental results for minimum DOP versus DGD for 8- (Fig. 4.48(a)), and 10-GFlz (Fig. 4.48(b)), 40% modulation depth DSB SCM signals. For both the 8- and 10-GFlz DSB signals, the DOP prior to ECSF varies from 1 to 0.7, however, after ECSF it varies from 1 to 0. Note in figures 4.47 and 4.48 that the point at which the DOP first reaches zero changes as the subcarrier frequency changes - this point is equal to — — , and thus increases as the subcarrier frequency decreases. 1 0.8 £ L 06 o ° 0.4 0.2 0 0 20 40 60 80 100 DG D (p s ) Fig. 4.47. Theoretical, simulation, and experimental results for a 6-GHz, 40% modulation depth DSB SCM signal after ECSF. This technique can also be applied to multisubcarrier systems. In such systems, the first notch in the minimum DOP curve is limited by the highest subcarrier frequency. We used a multi-subcarrier DSB signal with modulation depth of 30% (per subcarrier) and subcarrier frequencies of 11 and 20 GHz. The optical 228 Theory Sim ulation y • Experim ental m = 40% f = 6 GHz Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0.8 W /o E C S F 0.6 a. O a 0.4 \W / E C S F 0.2 m = 4 0 % f,= 8G H z 100 DGD (ps) W /O E C SF 0.8 0. 0.6 O Q 0.4 \ W / EC SF / 0.2 m = 40% f„= 1 0G H z 20 40 60 80 100 0 (a) DGD (ps) (b) Fig.4.48. Simulation and experimental results for (a) 8- and (b) 10-GHz, 40% modulation depth DSB SCM signals before and after ECSF. spectrum of these DSB signals prior to ECSF is shown in Fig. 4.49(a). After ECSF using our 8-GHz FPF filter, we get the optical spectrum shown in Fig. 4.49(b). In this case, there are two subcarriers in each sideband. To equalize the total sideband and carrier power, each subcarrier should, after ECSF, be -3 dB down from the optical carrier power (so the combined power of the two optical subcarriers is equal to the optical carrier power). Due to the lack of a filter of the exact proper bandwidth, we could only bring the carrier/sideband differential to ~5 dB, preventing the minimum DOP notch from reaching a value of zero. The simulation and experimental results for the minimum DOP sensitivity curves before and after ECSF are shown in Fig. 4.48(c). Even with a nonideal filter (our 8-GHz FPF filter), the minimum DOP sensitivity to DGD is more than doubled (from -0.8 to -0.3). The first minimum point on the curve is -25 ps, equal to the first minimum point of a 20- GHz DSB SCM signal (shown in Fig. 4.46). 229 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -1 0 m = 3 0 % W /o E C S F fc + 1 1 G H z / fc + 2 0 G H z £ 0 3 -40 -60 1531 1531.2 1531.4 1531.6 1531.8 W / E C S F m = 3 0 % N + 1 1 G H z c+ 2 0 G H z Q . O .9- -50 X (nm) (a ) 1531 1531.2 1531.4 1531.6 1531.8 X (nm) (b) CL o Q 0.6 0.4 0.2 0 W /o E C S F \ ■ \ \ \ o/ \^o ^ / W / E C S F m = 3 0 % fs 1 = 1 1 G H z M ultiple subcarrier f!, = 2 0 G H z signal 20 40 60 80 100 DGD (ps) (c) Fig. 4.49. (a) Optical spectrum of our 11- and 20-GHz, 30% modulation depth (per subcarrier) DSB SCM signals, (b) optical spectrum after ECSF, and (c) minimum DOP vs. DGD curves for this multi subcarrier signal before and after ECSF. To demonstrate the robustness o f our ECSF technique to chromatic dispersion and its advantages when compared to conventional DSB SCM PMD monitoring method using RF tone power, we generated a 20-GFIz, 30% modulation depth DSB SCM signal and transmitted it first through our first-order PMD emulator (at 45° with respect to the PSPs), and then through 10 km of SMF to induce chromatic-dispersion-related RF power fading. With this amount of chromatic dispersion, the 20-GHz DSB subcarrier is almost completely faded and thus is not sensitive to variations in DGD (PMD). Fig. 4.50 shows the RF tone power and 230 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. minimum DOP of the DSB SCM signal after ECSF as a function of DGD on the minimum DOP versus DGD curves, the circles are data points taken without chromatic dispersion and solid squares are after transmission through 10 km of SMF. It is clear that DOP is not sensitive to chromatic dispersion while RF power is. -20 m = 30% f„ = 20GHz 0.8 -40 - 5 -50 0.2 ' — i* -60 100 40 60 DGD (ps) Fig. 4.50. RF power and minimum DOP (after ECSF) vs. DGD after transmission through 10 km of SMF for a 20-GHz, 30% modulation depth DSB SCM signal. 4.6.4 PMD Compensation Using Equalized Carrier-Sideband Filtering Method To demonstrate the effectiveness of our ECSF technique in generating a DOP feedback signal for PMD compensation, we set up an OPMDC using a feedback OPMDC configuration, which is shown in Fig. 4.51. SSB Transmitter OBP ' 30-s«tton PMD Emulator 1 .0 ‘ S ttb ea rrierf ® a t a J [f^=20 GHz 1S S J f^ #si , BPSK i EO Filter i E D F A . - ^ r - ^ - - x - ------------------ y eDFA H> : 9iA*- 0 <DGD> = 40 ps <\QJ >*900 ps7 RX j Feed back j Signal to PC Poiarim eter ■ j ECSF N-OBPF PMD Monitor \ Fig. 4.51. Experimental setup for PMD compensation using ECSF to generate a feedback signal. 231 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We generated a 20-GHz SSB signal with a modulation depth of 30% with 21 5 -1 PRBS by externally modulating a 1531.4 nm optical carrier and filtering out the lower sideband using a 9-GHz FPF filter with an FSR of 78 GHz. We propagate this signal through an electrically controlled 30-section PMD emulator with an average DGD value of -40 ps and average second-order PMD of -900 ps2 [62], The first- and second-order PMD statistics of this emulator are shown in Fig. 4.52. We performed ECSF on a tapped-off portion of the SCM signal using a voltage-controlled FPF filetr with an 8-GHz bandwidth. We measured the DOP of the ECSF signal using a poiarimeter, and used the resulting DOP value as a feedback signal to a PC to adjust the OPMDC, which consisted of a PC and a single section of PM fiber with a DGD value of 23 ps. 1 2 0 1 0 0 *-» c 8 0 3 O 6 0 i o 4 0 ■ 2 0 0 ^ E x p e r i m e n t - 8 5 0 S a m p l e s / \ \ Maxwellian <DGD> = 4 0 p s 2 5 4 5 6 5 8 5 1 0 5 D G D (p s ) (a ) 180 160 140 120 ** £ 100 3 O 80 o 60 40 20 0 <DGD> = 40 ps |nj> = 900 PS2 200 1000 1800 2600 3400 4200 |O J (ps*) (b) Fig. 4.52. (a) First- and (b) second-order PMD statistics of the 30-section PMD emulator used in our PMD compensation experiment. Fig. 4.53 shows our experimental results when using our technique as a feedback control signal in the PMD compensation setup shown in Fig. 4.51. Fig. 4.53(a) shows the RF power fading distribution after the PMD emulator before and after compensation. We took 300 independent samples in this measurement for each case 232 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (before and after compensation). After compensation, the 5% worst-case RF tone power tail is increased by 11 dB from -17 dBm to -6 dBm. Fig. 4.53(b) shows the ECSF DOP distribution before and after compensation. Prior to compensation the feedback signal (DOP) varies, but after compensation the maximized DOP is always greater than 0.9, corresponding to minimized RF fading. Full compensation is not possible as the OPMDC uses a fixed, 23 ps DGD component, and due to higher- order PMD effects. Using a 155 Mbit/s binary-phase-shift-keyed (BPSK), 20-GHz SSB SCM signal, we measure the BER before and after compensation. Fig. 4.53(c) shows the measured BER as a function of received optical power for an arbitrary sample in which the RF power fading is about 22 dB after the emulator and prior to compensation. Using the DOP of the ECSF signal as a feedback control, we choose an arbitrary sample point before compensation for which the receiver power is -10 dBm at BER 10~9. After compensation, the receiver sensitivity increases by about 12.5 dB at a BER 10~9. WI Comp. (ECSF) 5% tail I W/o Comp. \ N •30 -25 -20 -15 -10 4 0 R e la tiv e R F S ig n al P o w er (d B ) Maximizing DOP ~ for Comp. (ECSF) • DOP Before Comp. CL 0.4 0.6 0.8 1 0 W/ Comp W/o Com p.' D O P 5 ' 6 7 8 9 1 0 f •27 -24 -21 -18 -15 -12 -9 R eceiv ed O p tic a l P o w er (d B m ) ^ 12.5 dB (a) (b) (c) Fig. 4.53. (a) Relative RF tone power distribution before and after compensation using ECSF as a feedback signal, (b) the DOP distribution of the ECSF signals before and after compensation, and (c) measured BER vs. received optical power for a 20-GHz subcarrier BPSK modulated at 155 Mbit/s before and after compensation. 233 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.7 PMD Monitoring for NRZ Data Using a Chromatic-Dispersion- Regenerated Clock Tone A number of monitoring techniques appropriate for OPMDCs have been proposed. A method was reported that tracked the effects of PMD on an optical-time-division- multiplexed (OTDM) signal by measuring the power of the RF clock tone that automatically appears in the electrical spectrum after detection [171]. Generally, PMD causes the carrier and optical clock tone power to split between the two PSPs and travel at different speeds down the fiber. This speed differential de-phases the optical clock tones and carrier on the two PSPs, reducing the recovered RF clock tone power due to destructive interference. It has been shown that NRZ signals suffer greater degradation in receiver sensitivity due to PMD than RZ signals [126], Thus, the need for efficient PMD monitoring techniques for NRZ signals is much greater than that for RZ signals. However, in the NRZ electrical data spectrum, in the absence of chromatic dispersion, there is no RF clock tone present after detection as the upper and lower optical clock sidebands beat with the carrier and cancel each other out at the receiver. In this section, we propose a PMD monitoring technique for NRZ signals by measuring the effect of PMD on a RF clock tone that has been regenerated via the application o f chromatic dispersion to the signal. [170,172] As it has been demonstrated that chromatic dispersion regenerates the clock in the electrical spectrum of NRZ signals, we introduce FBG-based chromatic dispersion in the monitoring tap-line of the OPMDC to generate a RF clock tone at the bit-rate- frequency within the NRZ electrical spectrum. The added dispersion is equal to -630 234 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ps/rnn for 10-Gbit/s data. This regenerated clock tones will show PMD effects similar to RZ clock tones, and thus can be used as a PMD monitoring signal. Advantages of the proposed monitoring method include: (i) they do not require modification at the transmitter, (ii) a wide dynamic range (>30 dB), (iii) low cost when used in WDM systems, and (iv) they add an extra parameter that can be used with the 'A and 1 4 bit-rate frequencies to determine higher order PMD. Using this techniques along with a PMD-emulated link, we implement PMD monitoring and compensation and reduce the 1% power penalty tail by 6 dB. 4,7.1 Theory of the Dispersion-Regenerated Clock in the Electrical Spectrum of NRZ Data In theory, there is no clock component in the optical NRZ spectrum since the Fourier transform of a rectangular pulse with a pulsewidth of Tb is a sine function that is equal to zero at any frequency components that are multiples of the bit mrate. However, in practice, the nonzero rise and fall times generate residual optical components at these frequencies. In addition, the nonlinear transfer function of EO modulators may generate frequency components at or near the optical clock frequency. These components, however, are not present after detection, as the beat terms between the optical clock sidebands and carrier are out of phase and thus cancel each other out after detection, as shown in Fig. 4.54. Chromatic dispersion can change the phase difference between these two optical clock sidebands, and thus after transmission through a dispersive network, 235 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. OptimS Spectrum Time Domain LSB - Clock USB-Clock Square D e t e c t i m Frequency Domain Carrier & LSB-CSoefc Seat term No Clock Fig. 4.54. RF clock tone cancellation in the NRZ electrical data spectrum after detection. some RF clock component may be detected. This component has been used in the past to monitor chromatic dispersion in NRZ systems [234-235], We take advantage of this regeneration effect to monitor PMD in dispersion-compensated systems. In this technique, a dispersive component (such as a LCFBG) makes the beat terms in phase and thus regenerates the post-detection-clock in the electrical NRZ spectrum. We use this element in the monitoring tap-line to ensure that we do not adversely affect the received data. This element is used to maximally regenerate the clock so that the dephasing effects of PMD on the clock become observable, as seen in Fig. 4.55. Depolarized NRZ Optical Spectrum Depolarized & D ispersed NRZ Optical Spectrum Fiber with PMD (8®**-® carrier Dispersive Element DGD * O ps DGD ■ 0.5If, p s t— a k*. L|| Clock Fading • V .4 | due to PMD Fig. 4.55. PMD effects on the dispersion-regenerated clock in the electrical spectrum of NRZ data. 236 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. First-order PMD effects on the detected electrical power of a dispersion-regenerated clock in NRZ systems can be described by 7 V C /~) ^ P ( d g d ,y ) = [ 1 - 4y(l - y ) sin2 ( n R h d g d )] s in 2 ( ------■ —— ) (4.7.1) f c where y is the power splitting ratio between the two PSPs, D is the total dispersion in the link added to the dispersion of our dispersive element, c is the speed of light and Rb and fc are the bit-rate and carrier frequencies, respectively. Theoretically, the total amount of dispersion required to obtain maximum clock regeneration using this monitoring technique is equal to D = ( ^ — ) (4 .7 .2 ) 2cR b Plugging this expression in for D in (4.7.1) forces the second sine term to one, leaving an expression for the maximized regenerated clock power that is independent of the link dispersion and dependent on the DGD, splitting ratio, and the bit rate P(dgd ,y) = [1 -4y(l - y) sin 2 ( nRbdgd )] (4.7.3) This formula illustrates that the amount of dispersion required to maximally regenerate the NRZ clock tone depends on the bit rate - at 10 Gbit/s, for example, -630 ps/nm of dispersion results in a maximally regenerated clock and makes PMD effects most visible. We used a LCFBG to provide the dispersion necessary to regenerate the clock. The delay and reflectivity curves for this FBG are shown in Fig. 4.56. 237 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 2 0 0 0 -5 •200 -600 9 * -15 £ ' 2 0 -800 -25 -1000 -30 L u 1542 -1200 1543 1545 1546 1544 X (nm) Fig. 4.56. Reflectivity and delay curves for the LCFBG used for RF clock regeneration. To ensure that this grating did not significantly affect our PMD measurements, we measured the PMD and PDL of this FBG using a polarization analyzer, and found that the average DGD of the grating was <1 ps and the PDL was negligible. To minimize the effects of FBG ripple on our regenerated clock, we performed our experiment at 1544 nm, which we experimentally determined to be the point with the lowest ripple, thus minimizing the effect of ripple on the upper and lower clock sidebands. We generated 10-Gbit/s NRZ data using a 22 3 -l PRBS and modulated it onto a 1544 nm source. Prior to the receiver, a tap-line is used as the monitoring path so our monitoring methods did not adversely affect the data. The receiver in the tap- line was a 10-GFlz square-law detector and the receiver was attached to an electrical spectrum analyzer. To calibrate our monitor, we first did a back-to-back measurement without any DGD elements in the system, and determined that 1000 ps/nm of dispersion (from our FBG) regenerates the clock by ~30 dB, from -56 dB to -26 dB, as shown in Fig. 4.57. 238 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. D is p e r s io n Ojgs^^ -56 dBm -26 dBm % \ \ ! \ J s Fig. 4.57. Clock power in NRZ data back-to-back (left) and after 1000 ps/nm of dispersion (right). To measure the effects of first-order PMD on the regenerated clock, we used a first-order PMD emulator and set it to various values of DGD (from 0 to 74 ps) before the LCFBG. By adjusting the PC to set the input SOP to 45° relative to the PSPs of the emulator, we generate worst-case first-order PMD, the effects of which we can monitor via the RF clock tone. Fig. 4.58 shows the effects of PMD on the RF clock tone. The PMD effect is periodic - after reaching a minimum power level, additional PMD will then regenerate the RF clock (in Fig. 4.58, 74 ps DGD results in a regenerated RF clock tone when compared to 50 ps DGD). This method for monitoring works best in the feedback configuration where the system is typically operating near the zero-DGD point (post-compensator). However, in a feed-forward DGD monitoring configuration [72], the monitoring window (in a 10-Gbit/s system) is limited to 50 ps without additional control signals. Clock power = >26 dBm Clock power = >36 dBm DGD = 40 ps Clock power ~ -56 dBm DGD = 50 ps -*/ Clock power ~ -30 dBm Fig. 4.58. Fading and regeneration of a dispersion-regenerated clock due to PMD (Clock power @ 9.85 GHz). 239 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In addition, we used a narrowband 10-GHz amplifier (to isolate the clock tone) after detection and fed the amplified sinusoidal signal to a 50-GHz oscilloscope. Fig. 4.59 shows the effects of the different amounts of DGD on the amplitude of the clock tone. After 23 ps of DGD, the clock amplitude has decreased by ~60 mV, but after 40 ps of DGD, it has fallen by ~230 mV. IA V ~ 59 m v DGD = 23 p s •"'/V ...... /A ....... ...... T V '" J V V \ / \ v V = 304 m v DGD - 50 p s /■ A A A \ 229 m v j V N. ........... T / V / W \ / v G ' DGD = 40 p s > V V ?XI pV= 12Tm v DGD = 74 p s Fig. 4.59. Fading and regeneration of the clock tone (9.85 GHz) due to PMD. 4.7.2 Effects of PMD on the Regenerated RF Clock Tone Fig. 4.60 shows the simulated, theoretical and experimental results for clock fading and regeneration as a function of DGD for a 10-Gbit/s NRZ signal. As seen in this CO 2 , I*. 0 > 5 o CL -10 -20 . > -40 J 2 ( £ -50 .. ... Clock | Fading V ? r d t r ciock f Regeneration Clock Power @ 9.855 GHz - ‘ " U a e iy s tiumikitim. b Bjpeiinmual 20 40 60 80 100 DGD (ps) Fig. 4.60. Relative regenerated clock power as a function of DGD (worst case). In theory (dotted line) the curve reaches negative infinity at 50 ps DGD - in our simulations and experiments, we reached - 30 dB. 240 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. figure, for a 9.855-GHz clock tone, the dispersion-regenerated clock fades from 0— >50 ps of DGD, and is regenerated from 50— >100 ps. Fig. 4.61 shows simulated distributions of the 2.5- and 5-GHz frequency components and the 10-GHz regenerated clock component in an emulated PMD environment (30-section PMD emulator) for a 10-Gbit/s NRZ data. This simulation consists of 2000 statistically independent samples to emulate a Maxwellian distribution with an average DGD of 30 ps. The tail end of each distribution shows the monitoring sensitivity using that frequency component - the power variation of the 10-GHz regenerated clock in Fig. 4.61 shows that the 10-GHz component has a higher sensitivity than either the 2.5- or 5-GHz components as the much lower variation of the 2.5- and 5-GHz components (when compared to the 10-GHz component) due to PMD increases the inaccuracy of the measurement due to noise. However, the 2.5 and 5-GHz RF components are less affected by higher-order PMD than the 10-GHz RF component due to their close proximity to the optical carrier in .0 1 . . . ...I . . ‘....... I . ..... i --------------------. . . - -25 -20 -15 -10 -5 0 R elative C lock P o w er (dB) Fig. 4.61. The power distribution of the 2.5-, 5-, and 10-GHz frequency components due to PMD (< D G D > e m u i a t o r = 30 ps). 99.99 p - ,-.-,- ,-, , , , 99.9 - lOGHzRegern 99 - - 0 - 5 GHz Freq. Cor ** 90 : 2 . 5 GHz Freq. G <DGD> = 30 p s 10 5 .1 241 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the optical domain - while the optical carrier and optical data for in-band frequencies have the same SOP at the transmitter, after propagation, PMD induces a phase delay between the two PSPs for the carrier and for all in-band frequencies. In general, these phase delays are unequal, manifesting themselves as an “SOP walkoff’ between the carrier and frequencies within the optical spectrum. This walkoff angle is equal to ±2n* f * DGD (f ) radians (in Stokes space) on the Poincare sphere, where / is distance of a chosen frequency from the optical carrier, and DGD is a function of frequency. Looking at the Taylor expansion of the effects of higher- order PMD on DGD (considering the frequency-dependent of time delay between first-order PSPs, such as PCD), it is seen that optical frequency components closer to the carrier are not depolarized as much as those farther away (for any arbitrary DGD value) thus lower-RF components are less affected by these higher-order PMD effects. 4.7.3 PMD Compensation Using the Dispersion-Regenerated Clock as a Control Signal Using our dispersion-regenerated RF clock tone as a control signal, and a PC followed by a fixed 31-ps DGD element as a compensator, we performed PMD monitoring and compensation, the experimental setup for which is shown in Fig. 4.62. We used the same LCFBG used when characterizing the monitor as the dispersive element used in regenerating the clock. To make sure the effects of higher-order PMD are taken into account, we used a PMD emulator consisting of 10 sections of PM fiber with 9 PCs distributed between the sections to realize a 242 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154 nr LI PMD Monitor L inearly Chrped F B G (1 0 0 0 ps/nm ) 1 O itp c 's iv c d em o n * (c Iock reg e 'io i3 ;.o n ) 10 Gbit/s PRBS 223-1 NRZ 10-Section * I e o p a Em ulator il-g — h > —A -0 ‘ ‘ * — * ^ Feed back Signal to PC <DGD> = 32 p s i DGD = 31 ps | s ? Q j Fig. 4.62. Experimental setup for PMD monitoring and compensation using dispersion-regenerated RF clock tone method. Maxwellian DGD distribution (the measured average DGD was ~32 ps) [59], Using our monitor and this emulator to take 300 independent samples, we show in Fig. 4.63 the correlation between power penalty (without compensation) and the regenerated clock tone power affected by PMD. The distribution of the points is due to the effects of higher-order PMD. The 1-dB power penalty point corresponds to -4.5 dB of clock fading. We compensated for PMD by maximizing the regenerated clock and using that signal as a feedback control signal for a PC. Using this technique, the 1% worst case of the power penalty distribution tail for the channel is reduced from 8.4 dB to 2.4 dB as shown in Fig. 4.64. S T o le ra b le P o w e r p e n a lty § 4 -25 -20 -15 -10 -5 0 R elative C lock P o w e r (dB) Fig. 4.63. Power penalty as a function of relative clock power. 243 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. W I Com pensation W/O C om pensation C om pensation Pow er Penalty (dB) Pow er Penalty (dB) (a ) (b) Fig. 4.64. Power penalty distribution (a) before and (b) after compensation using dispersion regenerated RF clock tone. 4.8 PMD Monitoring by RF Clock Regeneration Measurement Using Asymmetric Optical Spectrum Filtering Method By using an optical filter offset from the optical carrier (“asymmetric filtering”), an RF clock tone is generated within the NRZ electrical spectrum. In this section, we propose two ways, first by using a standard optical filter to isolate the carrier and a single sideband, and second by using an FBG as a notch filter to remove a sideband. These regenerated clock tones will show PMD effects similar to RZ clock tones, and thus can be used as a PMD monitoring signal. The approporiate filter bandwidth depends on the type of filter used and the bit rate (e.g. a bandwidth of -0.08 nm works well for 10-Gbit/s data if the filter is a l st-order Gaussian). There are no stringent requirements on filter stability as the amount of filter detuning can be determined by measuring the optical power at the output of the filter. Advantages of this monitoring method are the same as the proposed method in the section 4.7. In addition, it is unaffected by chromatic dispersion and nonlinear effects. Using this technique along with a PMD-emulated 244 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. link, we implement PMD monitoring and compensation and reduce the 1% power penalty tail by 6 dB. 4.8.1 Theory of the Clock Regeneration Using Asymmetric Optical Spectrum Filtering Method Since the effect of first-order PMD on the upper and lower sideband optical clocks is the same, instead of regenerating the clocks using a dispersive element explained in the section 4.7, an optical filter centered on either the upper or lower sideband clocks that isolates one of the optical clock tones and the carrier will allow that beating term to be used to monitor PMD effects. This technique for PMD monitoring involves optical filtering (centering an optical filter within the monitoring path on either the upper or lower optical clock) enables us to view the clock in the electrical spectrum and thus monitor PMD, as shown in Fig. 4.65. This has some advantages over our first technique in that the monitoring sensitivity is unaffected by link chromatic dispersion, nonlinearity and the non-zero chirp of the modulator. D G D -O p s A sym m etric Depolarized Optical Spectrum Depolarized Optical Spectrum Fiber with PMD Square D etection A sym m etric Filtering DGD = 0.SH, p s \ Clock Fading d ue to PMD Fig. 4.65. PMD effects on an asymmetrically-filtered-spectrum-regenerated-clock. 245 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. After filtering, with one of the optical clock tones removed, the effect of first- order PMD on the detected electrical power of the asymmetric-filtered-regenerated- clock can be described by P(dgd ,y) = [ ! ~ 4r(I - r ) f ’ (*R»dgd >]\H (R l # (4.8.1) where H is the optical filter transfer function. The division by 2 is due to the removal of one of the sidebands via filtering (ideally, there would be no residual power in the removed sideband), and H ( R b) arises due to the carrier suppression induced by the optical filter. We stress that the dispersive component/optical filter/FBG notch filter is added only to the monitoring path, which is a tap-line used for PMD monitoring at the receiver, and not on the main data path, preventing the added dispersion, and any distortion due to the asymmetric filtering from affecting the received data. 4.8.1.1 Asymmetric-Filter-Regenerated R F Clock Tone The first technique for PMD monitoring involves asymmetric filtering of the optical data spectrum to regenerate the RF clock tone. Fig. 4.66(a) shows the simulation results showing that the regenerated RF clock tone power depends on the optical filter’s bandwidth and shape. This figure shows that as the order o f a Gaussian filter increases, the power of the regenerated clock also increases. This is due to the fact that the sharp edges of the higher-order filter passes one of the optical sidebands while maintaining the carrier/sideband power ratio, and almost wholly canceling the second optical clock sideband. Clock regeneration using a l st-order Gaussian or a 246 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FPF filter is about 10 dB less than the higher-order Gaussian filters due to this effect. In addition, Fig. 4.66 shows that the optimal filter is a Gaussian filter centered at the optical clock frequency (with the sensitivity improving as the order of the Gaussian filter increases). Fig. 4.66(a) also shows the optimum filter bandwidth necessary to achieve maximum RF clock regeneration for various types of filters. The FSR of the FPF filter is ~750 GHz and the filter was centered at either the upper or lower optical clock sideband at the bit-rate frequency. Fig. 4.66(b) shows how the regenerated RF clock power varied as we detuned the filter. Gauss. 5th " G auss. o- 20 G auss 5 10 15 20 25 30 BW (GHZ) (a) Gauss. 3rd 30 FPF 20 Gauss. 1st 10 0 ■ 2 0 2 4 6 -6 -4 Frequency Detuning (G H z) (b) Fig. 4.66. (a) Regenerated RF clock power as a function of filter type, order, and bandwidth and (b) regenerated RF clock power as a function of the frequency detuning of a filter centered on the optical clock sideband. Fig. 4.67 shows how the filter-regenerated (as opposed to the FBG- dispersion-regenerated) RF clock is affected by link dispersion - demonstrating that this technique can be used for chromatic-dispersion-insensitive PMD monitoring. Prior to filtering using a l st-order Gaussian filter, chromatic dispersion in a link (generated via 10, 20, or 40 km of SMF) has a significant effect on the RF clock 247 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. power at the receiver. After filtering, however, the effect of chromatic dispersion is minimal for a given value of DGD (<2-dB fluctuation). W/o filtering 20 km C O ■O 40 km 10 km 0 ) 5 o C L -20 W/ filtering 1 o 8 -40 £ 10 G bit/s NRZ -60 100 DGD (p s) Fig. 4.67. Effect of chromatic dispersion on the asymmetrically filterd spectrum-regenerated clock. 4.8.1.2 Notch-Filter-Regenerated RF Clock Tone As an alternative, the use of a standard optical filter to isolate one of the optical clock sidebands and the optical carrier, an FBG used as a notch filter can remove one of the sidebands while leaving the rest of the spectrum intact. Fig. 4.68(a) shows the optical spectrum of a typical NRZ signal prior to notch filtering, and 4.68(b) shows a 10 GHz O ptical C lock NRZ (10 G bit/s) -1549.85 1 5 5 0 .1 1550.35 X (nm ) (a) Fig. 4.68. (a) Optical spectrum of a typical NRZ signal prior to notch filtering with an FBG and (b) a close-up of the electrical spectrum of the same NRZ signal centered a t-10 GHz. W/o Filtering 0 ) - 6 5 9.985 f (GHz) 10.01 248 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. close-up of the electrical spectrum centered at -10 GHz. There is no RF clock tone present prior to notch filtering. However, after using a narrowband FBG with a 10-dB bandwidth of 15 GHz in the transmission mode as a notch filter to remove the upper optical clock sideband, we obtain an optical spectrum as shown in Fig. 4.69(a). After filtering, the electrical clock tone is regenerated by 28 dB, as shown in Fig. 4.69(b), and can be used for PMD monitoring. Asymmetric Notched Filtered Spectrum* I 2 - -20 10 GH z Optical Clock- a ® O T -40 -50 E -55 m H . -60 | -65 O -70 ■g -75 g -8 0 -1549.85 1550.1 1550.35 X (nm) (a) -85 9.9 W/ Asymmetric ■ f 1 Filtering ■ m i T J | O O ! CM i 1 1 I,.-. U . A . . .4 hi 1 . Jj.ft.kj d j 9.985 f (GHz) ( b ) 10.01 Fig. 4.69. (a) Optical spectrum of an NRZ signal after notch filtering to remove one of the optical clock sidebands and (b) the electrical spectrum of the same signal after notch filtering - due to the filtering of one of the sidebands, the RF clock tone is regenerated. 4.8.2 PMD Compensation Using the Regenerated Clock Tone as a Feed Back Signal Using our notch-filter-regenerated RF clock tone, we performed PMD monitoring and compensation for a PMD-emulated link. The experimental setup for this PMD monitoring case is shown in Fig. 4.70. Using this alternate technique for PMD monitoring, with a 30-section electrically controlled programmable PMD emulator 249 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Gb/s PRBS 21 5 -1 NRZ EDFA , LD 30-Section PMD Emulator AnOll^lcoC. Peed buck Signal to PC .''■ Is ) V o PD FBG Notch-Filter BERT <DGD> = 40 ps Att. g - i l DGD = 50 ps | <gQ Fig. 4.70. Experimental setup for PMD monitoring and compensation using notch-filtered-regenerated RF clock tone. that has an average DGD of 40 ps [62], we took 300 samples and using a PMD compensator consisting of a PC and a single piece of PM fiber with a DGD value of 50 ps, again achieved a 6-dB reduction in the 1% power penalty tail, from 8 dB to 2 dB, as shown in Fig. 4.71. o O > 1 1 1 1 I 1 1 1 1 1 j 1 1 1 1 1 1 1 1 6 0 r j" '" '" " 'r " 1 — r " i — i — | — i — i — > — | — < — i — i — , — i — i — r — : _ W/o Compensation 1401 W/ Compensation : : f c 8 d B 1 2 0 1 2 d B i 1% v 1 0 0 L 1% ^ r * 1 !-► : ° 6 0 i-.! i i 1 4 0 i ! ; t • i H h T . 1 -■•Mj 0 ■ * » f ■ i 1 J i 1 i 1 ■ Pow er Penalty (dB) (a) Power Penalty (dB) (b) Fig. 4.71. Power penalty distribution (a) before and (b) after compensation using our notch-filtering technique. 250 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.9 Real-Time PMD Monitoring in Wavelength-Division- Multiplexed System Using in-Band Subcarrier Tone One o f the critical limitations in each of the previously reported monitoring techniques is the need for a separate monitoring module for each WDM channel, increasing both system cost and complexity. It would be highly desirable if a single module could provide PMD monitoring for many WDM channels simultaneously and independently. In this section, we present a technique for simultaneous and independent PMD monitoring of WDM channels using a single module that measures the subcarrier tone power added to each of the WDM channels [177]. The subcarrier tones have the same power but slightly different frequencies. We show through statistical measurements that this monitoring technique, which uses only a single photodetector and does not need demultiplexing of the individual channels, monitors the PMD within each channel. For 500 independent samples, we find that the subcarrier tone power fading due to PMD is strongly correlated to the PMD-induced degradation on that channel. 4.9.1 Concept of Subcarrier Tone Fading due to PMD in Time and Frequency Domain Due to first-order PMD, a subcarrier tone (SSB or DSB) power launched into the fiber splits into two PSP’s and each of the subcarrier tone polarization components travels at a different speed. When the subcarrier tone polarization components are out 251 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o f the phase at the receiver, power fading occurs. Theoretically, the subcarrier tone power fading is proportional to P(dgd ,y ) = 1 - 4y(l - y ) sin 2 (nfsdgd ) (4.9.1) where y and f s are the splitting ratio and subcarrier tone frequency, respectively. The effects of the DGD and splitting ratio for 6- and 9-GHz subcarrier tones are shown in Fig. 4.72(a) and (b). As the spilliting ratio approaches 0.5, the subcarrier tone power fading increases while the DGD notch remains unchanged. Thus the subcarrier tone frequency plays a key role in determining the monitoring window and sensitivity of the monitoring system. o 3 . -10 -20 ■ S -30 I -40 9.0 GHz y = 0.5 i.O GHz -50 100 0 40 60 80 20 \y v y 9.0 GHz 6.0 GHz -14 40 0 20 60 80 100 DGD (ps) DGD (P8 ) (a) (b) Fig. 4.72. Subcarrier tone power fading vs. DGD for different amount of splitting ratio and subcarrier tone frequency. At first, we measure the frequency of maximum fading due to DGD by using an optical free-space variable time delay that provides DGD values ranging from 53 to 103 ps. The monitoring window and the corresponding subcarrier tone frequency are shown in Fig. 4.73. Thus, by changing the subcarrier tone frequency it is possible to select the maximum measurable PMD value. 252 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 5 6 7 8 9 10 Subcarrier Frequency (GHz) Fig. 4.73. Monitoring window vs. subcarrier tone frequency. This method can be applied to a WDM system. When the PMD correlation bandwidth is less than the WDM channel spacing, the PMD of each channel is independent of the other channels [46]. Because of this fact, traditional multiple- channel PMD monitoring systems must measure an electrical or optical parameter of each channel by demultiplexing and then detecting all channels separately. However, as shown in Fig. 4.74, if subcarrier tones with different frequencies are added to the WDM channels, then each subcarrier tone will fade in correspondence with the PMD on that channel [21], independently from the other channels. A single detector can therefore be used to monitor the performance of all channels simultaneously. This technique is extremely useful for in-line monitoring where optical demultiplexing may be unnecessary and expensive. M 5.9 GHz ---------------- f *t 19 dB m I 1 . ! & • < ---- ----------- ^ ^ 6.0 G H z j Fig. 4.74. Eye diagram and corresponding subcarrier tone powers. 253 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.9.2 PMD/DGD Monitoring U sing Added Subcarrier in-Band Tone A 5.5-GHz subcarrier tone added to 10 Gbit/s, chirp-free NRZ signal is lunched into a 30-section PMD emulator with an average DGD value of 20 ps, random DGD value and a random PSP orientation for each data point. For a given sample, the PMD-induced Q-factor penalty is calculated from BER simulations, where we assume that ASE is the dominant noise source. In our simulation, we filter out the 5.5-GHz component of the photodetected signal for 10000 statistically independent samples. As shown in Fig. 4.75 (a), there is a good correlation between Q-factor penalty and subcarrier tone power. Fig. 4.75 (b) shows the result of the subcarrier tone power as a function of DGD. 2.5 £ ■ 0.5 -2 1 0 ■ 5 -4 ■ 3 Relative Sub carrier Power (dB) (a ) » 2 0 3 1 48 S O C l D GD (ps) (b) Fig. 4.75. (a) Q-penalty as a function of subcarrier tone power and (b) subcarrier tone power vs. DGD. 4.9.3 WDM PMD Monitoring and Compensation Using Added Subcarrier In-Band Tone Our experimental setup is shown in Fig. 4.76. 5.9- and 6.0-GHz subcarrier tone frequencies used enable us to monitor a maximum DGD of 83 ps, which is within the 254 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. upper 1% probability tail of the Maxwellian distribution of the PMD emulator with an average DGD value of 38 ps [59], 10 Gb/s Data 1550.0nm -» { + )» -( 7 ) fsl 1551.5nm LD OD E/O pr Modulator LD E/O pr f , = 5.9GHz s l Control tone #1 50/50 PMD Emulator 10G Optical Filter Att. HX EDF. Spectrum Analyzer BERT i - A lOGb/s Data f = 6.0GHz s2 Control tone #2 Fig. 4.76. Experimental setup. Fig. 4.77(a) shows the results of our BER measurements (500 independent samples for one channel) as a function of the subcarrier tone power. As seen in this figure, there is excellent correlation between the PMD-induced BER and the detected subcarrier tone power. To demonstrate simultaneous and independent PMD monitoring, we consider the simple case of a 2-channel system. Fig. 4.77(b) shows the subcarrier tone power on channel-2 as a function of the subcarrier tone power on channel-1 (500 independent samples). It is clearly seen that the subcarrier tone powers are independent, as expected. tt 10 ■ ff< * -60 -58 -56 -54 -52 -50 -48 -46 Subcarrier Power (dBm) -50 -55 w ■ 60 -65 -68 -64 -60 -56 Subcarrier Power - Channel #2 dBm -52 (a) (b) Fig. 4.77. (a) BER as a function of subcarrier tone power and (b) channel-2 subcarrier tone power as a function of channel-1 subcarrier tone power. 255 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.10 Effects of XPM on the PMD Monitoring Parameters in Wavelength-Division-Multiplexed System All PMD monitors and compensators assume that the system is linear and PMD effects do not change faster than on a millisecond time scale. However, it has been shown for 2-channel system that XPM induces a change of the SOP of each channel, even when there is no PMD. This effect changes on a nanosecond time scale and degrades the signal’s DOP when there is not a significant walkoff between channels. In addition, the presence of other channels rapidly alters a signal’s SOP and dramatically reduces the effectiveness of a PMD compensator in a WDM system [179]. The effects of SPM and XPM on the DOP in 1- and 2-channel systems have been demonstrated [178,180-181], However, the XPM effect on the DOP in the absence of PMD has not been studied as the number of channels, channel spacing, and modulation format varies. In addition, the effect of XPM on the half-bit-rate frequency component (one oftenused PMD monitoring parameter) is not clear. In this section, we statistically investigate DOP and half-bit-rate frequency component degradation due to XPM-induced depolarization for 10-Gbit/s RZ and NRZ signals using a recirculating fiber loop in the absence of PMD [182]. The loop consists of 80 km SMF, 16 km DCF, and 2 EDFAs (480 km). We realized the statistical behavior of XPM on the DOP and half-bit-rate frequency power by uniformly changing the SOP of each channel relative to each other at the transmitter. We show that the variation of these two parameters depends on the total optical input power, the number of channels, the modulation format, and the channel spacing. As the total optical power increases, the DOP and RF power decreases in NRZ and RZ 256 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. systems (in the absence of PMD). Our results show that by increasing the number of channels the effect of XPM on the monitoring parameters decreases for the same input power. This is due to the fact that although the number of channels increases, the total optical power is divided between more channels, and the increased total bandwidth results in an increase of the walkoff effect (and corresponding reduction in XPM effects) between edge channels. For example, our simulation results show that when the number of channels increases from 2 to 8, the variation of the 10% tail of the half-bit-rate frequency component power and DOP decrease from 4(3.8) to 1.5(0.5) and 28%(31%) to 10%(8%), respectively, for 10-Gbit/s NRZ(RZ) signals (total input optical power =15 dBm) [182], Moreover, the simulation results show that the variation of RZ signal monitoring parameters is less than NRZ. In addition, when the channel spacing increases from 50 GHz to 100 GHz in 2-channel NRZ system, the 10% tail of DOP and RF power decreases 3.5 dB and 11%, respectively [182]. 4,10,1 XPM Induced DOP and RF Power Degradation in WDM System In a WDM system, the SOP of a modulated signal is a function of frequency and the SOPs of the various intra-channel optical frequency components are parallel to each other at the transmitter, as shown in Fig. 4.78. The SOPs of different channels need not be parallel. An XPM changes the phase of the signal in the time domain and this phase depends on the data streams on the other channels, the walkoff between any two channels, and their optical power. This phase evolution in time domain can be explained as a nonlinear polarization evolution in the frequency domain as XPM 257 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. rotates the SOP’s of different intra-channel optical frequency components and degrades the signal’s DOP, even when there is no PMD in the link (for low walkoff between the WDM channels, i.e. when the dispersion is low). In addition, this depolarization effect distorts the detected data spectrum and causes a variation in the half-bit-rate frequency component, making these two monitoring parameters unreliable for PMD monitoring. Moreover, since XPM makes the signal’s SOP pattern dependent, this nonlinear evolution happens on a nanosecond time scale and makes PMD monitoring and compensation difficult. Polarized Optical Spectrum “ J - 1 “ V 1 Depolarized A1 a2 Spectrums j k Jfflk SST', ’l > O B f F £ p 1 \ ™ 1 Depolarization Effect 4 . J L H NO PMD *S— Half Bit rate Frequency Fading •f <V 2 R f/2 Bectricai Spectrum_______________________________________________Bectricai Spectrum Fig. 4.78. Concept o f XPM-induced DOP and half-bit-rate frequency power degradation. 4.10.2 Simulation Details In this section, the effect of XPM-induced depolarization is studied using a recirculating fiber loop. Our setup for these simulations is shown in Fig. 4.79. The loop consists of 80 km SMF, 16 km DCF and 2 EDFAs (480 km). Data is modulated on 2 channels and is cycled through the loop 5 times. We filter out the 1550 nm channel using a 20-GHz optical filter and measure the DOP (using a polarimeter) and the RF power fading at the half-bit-rate frequency (using a detector and a 5-GHz 258 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. electrical bandpass filter). The power entering the SMF in the loop is varied between 5 dBm and 15 dBm in steps of 5 dBm by adjusting the output power of the EDFA in the loop. It should also be noted that we fixed the input optical power to the DCF to -3 dBm to more accurately emulate a real optical link. The simulation is repeated for the case of 4 and 8 channels. Results were obtained for both RZ and NRZ signals. 100 samples were taken for each simulation and the PC before the multiplexer were uniformly varied between -90° to +90° to realize a real transmission system where the SOPs of adjacent channels are unrelated. The fiber specifications are listed in the inset table in Fig. 4.79. 10 G bit/s NRZ & RZ BPF 5 GHz SMF. 80 km P olarim eter OBPF t ^ j PD % 0 fC c y o -i5 > DCF, 16 km Q -3 EDFA J 20 GHz RF Pow er M eter SMF DCF D @ 1550 nm , ps/nm 16 -80 S, ps/nm 2 /km 0.08 -0 .2 1 Loss, dB /km 0 . 2 0 . 6 Effective Area, pm2 80 30 n ,x l 0 2 i\ mVW 2 . 6 4 Fig. 4.79. Simulated optical transmission system. 4.10.3 Simulation Results We conducted our simulation with input optical powers to the SMF of 5, 10, and 15 dBm in the dispersion compensated transmission link. We use NRZ and RZ signals and demonstrate the effect of the fiber nonlinear effects on the DOP and the half-bit- rate frequency RF power (after detection). The effect of XPM on the DOP and RF power of a 10-Gbit/s NRZ signal for 5, 10, and 15 dBm SMF input power in the loop is shown in Fig. 4.80(a) and (b). 259 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fig. 4.80(c) and (d) illustrate the DOP and half-bit-rate frequency fading results for a 10-Gbit/s RZ signal with the same input power levels. 1 0.95 0.90 Q . 0.85 Q 0.80 0.75 0.70 0.65 1 0.95 0.90 0.85 0.80 0.75 0.70 0.65 / 1 1 1 V ......... L 5 d B m \ NRZ f--------- 10 dBm \ \ 10 Gb/s \ : 4 Channels 9.99 90 50 10 1 0.1 Percentage (a ) C Q - 1 S * - -2 fl) 5 2* -5 5 dBm 10 dBm 15 dBm 10 Gb/s 4 Channels J.99 90 50 10 1 0.1 P ercentage (b ) \ RZ 0 S' - 1 "X.s RZ : — 5 d B n \ ■ o «™ ™ - 5 dBm ----------10 dBm w -2 --------- 10 dBm £ . . . . . . . . 15 dBm O - 3 a. 10 Gb/s & - 10 Gb/s 4 C hannels 4 Channels 99.99 90 50 10 1 0.1 P ercentage (C) 99.99 90 50 10 1 0.1 P ercentage (d) Fig. 4.80. Variation of (a,c) DOP and (b,d) RF power at half-bit-rate frequency for 10-Gbit/s (a,b) NRZ and (c,d) RZ signals for different total input powers, respectively. The x-axis shows the percentage of samples. To have a reference to compare the change in the DOP and the half-bit-rate frequency power, we note that, theoretically, for a link with instantaneous DGD of 50 ps (when the signal is aligned at 45° relative to the PSPs of the fiber), the half-bit- rate frequency power decreases by ~3dB(~3dB) and the DOP drops to ~75%(~0%) for an NRZ(RZ) signal. In this case, due to the effects of XPM, even though this link has zero PMD, the 10% tail of DOP drops to 78% (85%) and the 10% tail of half-bit- rate RF power drops by ~3 dB (-1.4 dB) for an NRZ (RZ) signal in the case of 15 dBm input power to the SMF and 4-channel system. These changes can result in significant errors by a PMD monitor that uses these signals for feedback control. It is 260 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. clear from the results shown in Fig. 4.80 that the variation of the DOP and the half- bit-rate frequency for RZ data channels is less than that for NRZ channels. This may be due to the fact that the narrowband 20-GHz optical filter in the monitoring tap line filters out the higher-ffequency RZ components and thus reduces the effect of depolarization due to XPM. Fig. 4.81 shows the variation of the 10% tail of the DOP and RF power for the RZ and NRZ modulation formats with respect to the number of channels. When the number of channels decreases the RF power variation always increases for a fixed total input power to the SMF in the loop. It is also seen that increasing the number of channels results in similar variation for both RZ and NRZ signals. Note that the RF power and DOP variation are reduced if the total input power to the SMF is reduced. This reduction in RF powe and DOP variation is due to reduced XPM effects as the power per channel is decreased (as the total SMF input power is constant). a 3 u ( 0 > k 2 I £ 1 O' 0 • 15 dBm, NRZ - ® o 15 dBm.RZ <A ■ 10 dBm, NRZ ^ □ 10 dBm, RZ . w 0.4 • 15 dBm, NRZ O 15 dBm, RZ ■ 10 dBm, NRZ 10 dBm, RZ 2 4 6 8 10 # of Channels 2 4 6 8 10 # o f C h an n els (a ) (b) Fig. 4.81. Variation o f the 10% tail o f the (a) half-bit-rate frequency RF power and (b) DOP as the number of channels is varied. Fig. 4.82 shows the effect of channel spacing on the DOP and RF power for two 10-Gbit/s NRZ WDM channels at 15 dBm power input to the SMF in the loop. 261 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This figure shows that the effect of XPM on the RF power and the DOP becomes more pronounced as the channel spacing is reduced. For example the 10% tail of DOP (RF power) due to XPM changes from 82%(-0.4 dB) to 70%(-4 dB) when the channel spacing changes from 100 GHz to 50 GHz. This results from the increased effects of nonlinearities as the channels are spaced more closely. m -1 2 - r-2 a > 5 O -3 Q . q E ■ * -5 i \ 15 dBm 15 dBm \ 0.95 0.90 \ \ a : ---------100 GHZ*, ----- — 50 GHZ \ ft- 0.85 O Q 0.80 --------- 100 GHZ ^ --------- 50 GHZ \ : 0.75 10 Gb/s NRZ V “ — 0.70 10 G b/s NRZ % 2 Channels 0.65 2 C hannels 90 50 10 1 0.1 P e rc e n ta g e 99.99 90 50 10 1 0.1 9 9 P e rc e n ta g e (a ) (b ) Fig. 4.82. (a) Half-bit-rate frequency power and (b) DOP variation for different channel spacing for two 10-Gbit/s NRZ channels. 262 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5 Component DGD Measurement As systems become more complex and bit-rates rise, the quality of signals can be significantly affected by polarization-based effects from fiber and in-line components such as demultiplexers, optical filters, and modulators. Vendors regularly demand from optical component manufacturers that the DGD introduced by a device is guaranteed to be below a certain value. A key step in the post-manufacturing process is the painstaking measurement of all components for their compliance to a specification value. Moreover, the characterization of optical fiber and/or PMD emulators requires not only knowing DGD (i.e., first-order PMD) but also the value of higher-order PMD. For this reason it is imperative to be able to accurately measure the PMD of devices and components within a network. Typically, manufacturers measure the DGD of a component by sweeping the wavelength of a tunable laser, passing the light through a 3-state polarization synthesizer and then the DUT, and use a polarization analyzer to do JME analysis, MMM analysis, or PSA to measure DGD [192-193,195]. This method is accurate but is rather complex to implement and is dependent on the linewidth of the tunable laser and the frequency tuning steps in the process of measuring the DGD. Other techniques that have been demonstrated for measuring a component’s DGD include: (i) time domain measurements (the 263 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. interferometic and optical pulse method) [188] and (ii) using FWM products using a probe signal and a variable wavelength signal [189-190], However, it remains a laudable goal to reduce the time and complexity in testing components for DGD and for higher-order PMD after manufacturing. In this chapter, i demonstrate two techniques for measuring component DGD using: (i) polarized limited-bandwidth ASE noise and monitoring the DOP [236-237] and (ii) polarized fixed optical frequency components and monitoring the DOP [239], 5.1 M easuring Component DGD Using Polarized Lim ited Bandwidth ASE Noise and M onitoring the DOP Recently, a technique for monitoring the PMD vector using polarized ASE noise and sweeping a narrowband optical filter over the ASE spectrum at the receiver was demonstrated [239]. This technique was used to estimate an output SOP and could be used to measure DGD. However, this technique requires a PMD analyzer, sweeping a narrowband filter to get frequency-resolved polarization information, and a polarization switch. In this section, i demonstrate a straightforward technique for accurately measuring the DGD of any optical component [234-237]. This method involves: (i) using an inexpensive broadband ASE source, (ii) filtering and polarizing its output, (iii) scrambling and passing it through the DUT, (iv) measuring DOP of the received optical spectrum, and (v) relating the maximum and minimum DOP to DGD and second-order PMD directly. In addition, we show that the DOP of polarized ASE 264 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. noise after passing through a DUT depends on its DGD and the characteristics (shape, bandwidth) of the optical filter used in the second step. This technique is simple, can measure first- and second-order PMD, and can act as both a high- resolution, low-measurement-range monitor to a lower-resolution, high- measurement-range monitor by changing the optical filter. 5.1.1 Theory of Measuring the DOP of a Spectrum-Shaped ASE Source A diagram of the proposed measurement technique is shown in Fig. 5.1. When a filtered, then polarized, ASE signal is launched at a 45° angle with respect to the PSPs of a DUT, different optical frequency components rotate relative to the central frequency component of the spectrum and the signal becomes depolarized due to DGD. Polarized ASE spectrum De-polarized ASE spectrum due to DGO ASE S ource DUT w/ DGD Polarimeter Optical filter Polarizer Polarization scrambler or PC Fig. 5.1. The DGD of a DUT depolarizes the spectrum of filtered-and-polarized ASE noise. By measuring the DOP of this depolarized signal an accurate DGD estimate can be obtained. I derive the relationship between the DGD of a DUT and the minimum DOP of a filtered and polarized ASE noise source after passing through the DUT, resulting in the following equation [236-237]: D O P (dgd) = F - ‘{ \ H ( f ) \ 2} (5.1.1) 265 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where H(f ) is the filter transfer function and F 1 is the inverse Fourier transform operator. The minimum DOP can always be attained by tuning a PC located prior to the DUT (or by scrambling the SOPs of the filtered/polarized ASE signal at the transmitter). The filter function depends on the type of filter used in the system. Two common optical filters are the Gaussian filter and the FPF filter. As the FPF filter is a periodic filter, for measuring DGD, we place a Gaussian filter after the FPF filter to select only one of the filter peaks. When a Gaussian filter is used and its filter function placed in equation (5.1.1), it becomes [237] D O P (dgd) = expC (7tBWdgd)2 ) (5.1.2) 4 In 2 where BW is the 3-dB filter bandwidth. This equation demonstrates the relationship between the minimum DOP, the Gaussian filter bandwidth, and the DGD of the DUT, as well as the relationship between filter bandwidth, the sensitivity and DGD measurement range of this technique. When either the bandwidth or DGD is very large, the exponent is large and the minimum DOP goes to zero. If the filter bandwidth is large, it takes very little DGD to null the minimum DOP, resulting in a high-resolution measurement of the DGD, but a low measurement range. This corresponds to an almost complete depolarization of the ASE signal with a small amount of DGD. If instead a narrow filter bandwidth is chosen, ( B W is small), it takes a corresponding increase in DGD to null the minimum DOP, resulting in a wide measurement range, but lower- resolution. This DGD-bandwidth relationship makes this technique very flexible as a 266 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DGD measurement tool, allowing for high-resolution measurements of small DGD values (such as in-line optical components) as well as wide measurement ranges for high-DGD applications (such as PMD emulators). Fig. 5.2(a) shows the theoretical minimum DOP as a function of DGD when the bandwidth of a Gaussian optical filter is varied. When a 30-GHz filter is used, there is a very steep slope to the minimum DOP curve, resulting in a high-resolution measurement, but the measurement range is only -30 ps. When a 10-GHz filter is used, the slope is shallower, but the measurement range is more than doubled (-100 ps). In addition, by using a FPF filter in series with a Gaussian filter, the equation (5.1.1) instead becomes [237] * = c o + U If DOHnhi!}-- ------- - .---------------- - ---------------------- <5.1.3) where R and FSR are the reflectivity and the free spectral range of the FPF filter, respectively, and each h(x) function is an exponential of the type described in (5.1.2) where x replaces the dgd of (5.1.2). While (5.1.2) DOP result is more complex than (5.1.2), it is comprised of exponential expressions similar to (5.1.2), and the resulting relationship between the DGD, FPF filter bandwidth, and minimum DOP is similar to that described above (inverse relationship between the resolution and sensitivity of the DGD measurement). Fig. 5.2(b) shows the theoretical minimum DOP as a function of DGD as the bandwidth of a FPF filter is varied. A 30-GHz filter results in a high-resolution measurement with a ~40-ps range, while decreasing the 267 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. bandwidth to 10 GHz results in a measurement range of >90 ps with a corresponding decrease in resolution. T heory T heory A \ \ B W = 5GHz 10GHz \ \G a u s s ia n 10GHz \ 20GHz*. 30GHz 30GHz DGD ( p s ) D G D ( p s ) (a) (b) Fig. 5.2. Theoretical results showing the relationship between minimum DOP, DGD, and filter bandwidth when (a) a Gaussian filter and (b) a FPF filter is used with our measurement technique. Wider filter bandwidths result in higher sensitivity but lower measurement ranges. 5.1.2 DGD Measurement Using a Band limited ASE Source Fig. 5.3(a) and (b) show the simulation results for minimum DOP versus DGD for different filter shapes and bandwidths when the SOPs of the filtered/polarized ASE noise are uniformly scrambled over the Poincare sphere at 20 kHz. Fig. 5.3(a) and (b) shows the simulated results when a Gaussian filter and a FPF filter are used, respectively. These simulation results match almost exactly with the theoretical results we derived (shown in Fig. 5.2). Fig. 5.3(c) shows the effect of the order of the Gaussian filter on the DGD/minimum DOP relationship. Increasing the order of the optical filter increases the DGD measurement range resulting in a corresponding decrease in resolution, an effect which is much more significant as the filter bandwidth decreases. 268 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sim ulation BW Sim ulation FPF ,10GHz G au ssian 10GHz \ 20G H z‘. 30GHzV .20GHz — __ 30GHz 1st order- 2n d order- 3rt order \ 5 GHz 0.6 a. O Q 0.4 30 GHz 0.2 4 0 60 DGD (ps) 8 0 1 0 0 0 2 0 40 60 8 0 1 0 0 0 20 4 0 60 80 100 DGD (ps) DGD (ps) (a) (b) (c) Fig. 5.3. Simulation results showing the relationship between minimum DOP, DGD, and filter bandwidth when (a) a Gaussian filter and (b) a FPF filter is used with our measurement technique, (c) The effects o f the Gaussian filter order on the monitoring range and sensitivity of this DGD measurement technique. To demonstrate the proposed technique, we used different lengths (between 1 and 40 meters) of PANDA PM fiber and applied three differenr filter profiles: (i) a Gaussian filter with a bandwidth of -35 GHz, (ii) a FPF filter with a bandwidth of -8 GHz in series with a Gaussian filter, and (iii) two FPF filters in series, one with a bandwidth of -8 GHz ( FSR = 750GHz) and the other with a bandwidth of -9 GHz ( FSR = 750GHz ). The broadband ASE source was filtered using these filter techniques. The spectrum-shaped ASE source passed through a polarizer in order to (i) be able to measure the depolarization effects due to the DGD of the PANDA fiber and (ii) cancel the effects of the PDL and PMD of the optical filters used. The resulting polarized ASE signal passed through the DUT (in this case, PANDA fiber), and into a polarimeter. By adjusting the PC (or by using polarization scrambling), the minimum DOP was found. I then used a standard Jones matrix method for measuring DGD (using a tunable laser and PMD analyzer) and plotted the minimum DOP versus the Jones matrix DGD values. Fig. 5.4(a)-(c) show the results for the 269 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. three filtering techniques - (i) using the 3 5-GHz Gaussian filter, (ii) using a single -8-GHz FPF filter, and (iii) using the two cascaded FPF filters. In each case, the DGD values that our minimum DOP values correspond are match closely with the theoretical and simulation results, proving that our measurement technique is a simple, flexible, and accurate way to measure the DGD of in-line components, and allowing for high-resolution measurements or large measurement ranges by tuning the bandwidth of an optical filter. O Experimental • — Simulation — Theory ° \ °\ °\ \ BW * 0.28 nm O Experimental — Simulation Theory BW * 0.06 nm 1 0.8 0.6 0 .4 0.2 0 5 ^ ... .............. o "S ' O Experimental -----Simulation O ' * X b > \ S o S \ s BW « 0.04 nm 0 2 0 40 60 80 100 0 20 4 0 60 80 10 0 0 20 4 0 6 0 80 100 DGD (ps) DGD (ps) DGD (ps) (a) (b) (c) Fig. 5.4. Experimental, simulated, and theoretical results when our measurement technique is applied using a (a) ~35-GHz Gaussian filter, (b) an ~8-GHz FPF filter, and (c) two cascaded FPF filters with an effective bandwidth o f ~5 GHz. In each case our technique matches up well with the theoretical and simulated results. 5.1.3 Effects of Higher-Order PMD on DGD Measurement While in-line components typically do not have significant amounts of second-order PMD, when measuring the DGD of PMD emulators and/or fiber spans the higher- order PMD can cause some measurement error, as shown in Fig. 5.5(a). However, our technique can also be adapted to measure second-order PMD as well as DGD by using the maximum DOP. When the second-order PMD (|/2f f l|) is equal to zero, the maximum DOP is always equal to one. In the presence of second-order PMD, the 270 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. maximum DOP decreases depending on the DGD and second-order PMD value. Using the minimum and maximum DOP, one can estimate DGD and second-order PMD. The theoretical relationship between DGD, second-order PMD (when PCD, one part of second-order PMD, is zero), and maximum DOP is shown in Fig. 5.5(b). Experimental results are shown in Fig. 5.5(c) when the proposed technique is used to measure the second-order PMD of an all-order PMD emulator [62], This figure demonstrates that the maximum DOP decreases as the second-order PMD increases. This trend can be used to effectively measure the second-order PMD (PCD+depolarization rate) of a DUT. In addition, switching between two different filters can allow accurate and independent measurement of DGD, PCD, and the depolarization rate. 0.8 8 0.6 £ 3 .§ 0.4 c S 0.2 BW * 0.06 nm 100 DGD (ps) DGD = 25 ps DGD = 50 ps \ \ O 0.8 PCD = 0 BW * 0.06 nm BW » 0.06 nm (a) 0 800 1600 2400 3200 4000 I OJ P S 2 (b) 0 300 600 900 1200 1500 I OJ P S 2 (C) Fig. 5.5. (a) The measurement o f DGD using minimum DOP is affected by higher-order PMD, (b) in the presence o f second-order PMD, the maximum DOP is not equal to one - maximum DOP can then be used to measure second-order-PMD, and (c) experimental data showing a relationship between second-order PMD and the maximum DOP allowing application o f this technique to second-order PMD measurement. 271 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2. M easuring Component DGD Using Polarized Fixed Optical Frequency Components and M onitoring the DOP In this section, i propose four methods to accurately measure the DGD of any optical component based on measuring the DGD depolarization effect on polarized frequency components from a limited bandwidth optical source [239]. We measure the minimum DOP after transmission of a test signal through a DUT and relate the minimum DOP to the DGD of the DUT. The four test signals that we use are (i) a DSB subcarrier tone generated via high-modulation-depth, (ii) a SSB subcarrier tone generated using ECSF [168,233], (iii) two polarized laser sources, and (iv) a filtered ASE noise source. These methods are simple and can be used to measure DGD over a wavelength range by changing the carrier frequency, laser wavelengths, or filter center frequency. In addition, these techniques can be used to measure the DGD of a device with a narrow transmission bandwidth. Moreover, these methods offer great freedom in selecting the DGD measurement range and sensitivity. In addition, these techniques can be used to determine the PSPs of the DUT by measuring the ellipsoid of the output SOPs on the Poincare sphere and noting that the major axis points in the direction of the PSPs. 5.2.1 DGD Measurement Concept and Setup A conceptual diagram and experimental setup for our DGD measurement methods is shown in Fig. 5.6 for the (i) DSB subcarrier tone, (ii) SSB subcarrier tone, (iii) dual laser source, and (iv) ASE noise methods. 272 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We generate the test signal and send it through a polarization scrambler running at 20 kHz (in our simulations) or use a PC to align the test signal at a 45° angle (in Jones space) with respect to the PSPs of the DUT (in our experiments). The DGD of the DUT causes the frequency components of the test signal to depolarize with respect to each other by an angle of rfdgd (in Jones space), where Af refers to the spacing between any two arbitrary frequency components within the test signal. This results in a reduction of the DOP of the test signal. The signal is then passed to a polarimeter to measure the minimum DOP, which we show is correlated to the DGD of the DUT. In each of our four measurement methods, we will use this simple setup to obtain the minimum DOP of our test signal after transmission through the DUT and thus measure its DGD. LD M ethod 1 “ 3 dB 3 P - L X t - L ( a ) /, /„+ /. ' % f \ J . (a) /,+/. / > > 1 Polarizer Fast Slow axis Polarization scrambler or PC P olarim eter o. O a M ethod 3 DGD DUT/w DGD Polarizer L D t AX AX l d 2 Polarized Spectrum Polarizer ASE Source Polarizer m k p Wm Ilk ASE , /Bill 111) * \ w . V _________ ✓ Fig. 5.6. Diagram of four propose methods for DGD measurement using (a) a DSB subcarrier tone, (b) an SSB subcarrier tone generated using ECSF, (c) two polarized laser sources, and (d) a single polarized and filtered ASE noise source. 273 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2.2 DGD Measurement for Different Limited-Bandwidth Optical Sources 5.2.2.1 Subcarrier Tone-Based DGD Measurement The first two methods for DGD measurement involve the use of subcarrier tones. We take advantage of the fact that as the subcarrier tone frequency is determined when generating the test signal, the rotation (in Jones space) of the sideband(s) with respect to the carrier is known (n*f * D G D ). We previously demonstrated that the DOP of subcarrier tone is not highly sensitive to DGD and its sensitivity is modulation depth dependent [232]. The proposed DGD measurement techniques using subcarrier tones address this sensitivity issue via the use of a high modulation depth DSB tone or ECSF of an SSB tone [168,233]. The first method uses a high modulation depth DSB tone to increase the minimum DOP sensitivity to DGD. The relationship between the minimum DOP and first-order PMD in a system using a finite linewidth source has been previously reported [206-208], Applying the expression for the optical spectrum of a subcarrier tone to the equation derived in [208], we obtain DOP ( dgd ) = n V 2 ran J n ( )cos(2m f dgd) 2 s n = " ~ c o ____ n = + c o o T tm X J 2n ( ^ f ) n ~ -oo (5.2.1) 2V where m is the modulation depth ( — ^ ), f s is the subcarrier tone frequency, y is the power splitting ratio between the two PSPs, and Jn is a Bessel function of order 274 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. n . For an optical subcarrier signal, due to the high optical power of the carrier compared to the sidebands (a result of the low modulation depth), even in the worst possible depolarization case (when the optical carrier and sidebands are orthogonal to each other, in Jones space, d g d = — ), the measured minimum DOP change is 2f, negligible. As the modulation depth increases, the first-order Bessel functions in (5.2.1) become comparable in magnitude to the zero-order Bessel function and an increase in minimum DOP variation to DGD is observed. By increasing the modulation depth when generating the test signal, we bring each of the two sidebands optical power to ~3 dB down from the carrier optical power. At this power level, the square of the zero-order Bessel function is equal to twice the square of the first-order Bessel function, resulting in much higher DOP sensitivity to DGD. We tested this method using a 6.75-GHz subcarrier tone on a 1531.4 nm carrier. Fig. 5.6(a) shows the generation of this subcarrier tone, while Fig. 5.7(a) shows the optical power spectrum of this test signal. We measured the spectrum using an OSA with -l-G H z resolution. We then launched this signal at 45° relative to the PSPs of various lengths of PANDA PM-fiber (from 1 to 40 meters) which we used as DUTs, and measured the resulting DOP using a polarimeter, the results of which are shown in Fig. 5.7(b). The maximum measurement range is -75 ps with a DOP dynamic range of 1 to ~0. 275 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.7 6.75 G H z 1531.42 1531.17 1531.67 0.8 a. 06 o Q 0.4 0.2 f = 6.75 GHz 100 40 60 DGD (ps) (b) Fig. 5.7. (a) Optical spectrum of a 6.75-GHz DSB subcarrier tone by increasing the modulation depth until each sideband’s optical power was 3 dB less than that o f the carrier and (b) experimental results for minimum DOP vs. DGD for this subcarrier tone. The second method uses an SSB subcarrier tone for DGD measurement. Using an optical filter centered at or near the optical sideband of a DSB signal such that the carrier is on the edge of the filter, we can equalize the power levels of the optical carrier and optical sideband, which we call ECSF [168,233]. This also removes the other sideband, resulting in an SSB signal. This test signal generation is shown in Fig. 5.6(b). We then launched this signal at 45° relative to the PSPs of the PM fibers described above and measured the resulting DOP using a polarimeter. In this case, the resulting minimum DOP after transmission through the DUT is [168,233] D O P ( d g d ) = n i T j 2n ( ~ ) n = “ oo H (nfs - f 0 ) 2 cos( 2 n n f^ d g d ) " l r J 2n (^ j) n - — oo H ( n f - f J s 2 (5.2.2) where H(f) is the optical filter transfer function, and f0 is the frequency offset of the filter from the optical carrier. 276 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. We tested this DGD measurement technique using a 20-GHz ECSF-generated SSB subcarrier tone signal. Fig. 5.8(a) and (b) show the generated DSB signal prior to ECSF and SSB signal after ECSF using a FPF filter with an 8-GHz bandwidth and an FSR of 750 GHz, respectively. Fig. 5.8(c) shows the DGD measurement results - prior to ECSF SSB generation, the minimum DOP of the 30% modulation depth test signal is fairly insensitive to DGD. However, after ECSF, the minimum DOP varies from 1 to ~0 as the DGD varies from 0 to 25 ps. The maximum DGD measurement range using both of these subcarrier-tone-based techniques is 2f, W/o ECSF fc-20 GHz Q. C D O £ -30 -40 1531 1531.2 1531.4 1531.6 1531.8 W/ ECSF m=30% f„ f-+20 GHz f^-20 GHz . 2 f j -30 4-1 W a, o O C l ^ -40 X (nm) (a ) 1531 1531.2 1531.4 1531.6 1531.8 Mnm) (b) W/o ECSF, 0.8 0.6 Q . o Q 0.4 W/ ECSF 0.2 m * 30% f5= 20GHz 100 40 60 DGD (p s) (c) Fig. 5.8. (a) Optical spectrum o f a 20-GHz, 30% modulation depth DSB subacrreir tone prior to ECSF, (b) optical spectrum of the same signal after ECSF, and (c) minimum DOP vs. DGD curves before and after ECSF. 277 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S.2.2.2 Dual Laser Source-Based DGD Measurement An alternate method for measuring component DGD is through the use of two known, polarized and fixed laser sources. The DGD of the DUT depolarizes the two sources and rotates the frequency components with respect to each other by an amount equal to n * f * DGD (in Jones space) when the signals are launched at a 45° with respect to the PSPs of the DUT, and where A f is the frequency spacing between the two laser sources. The setup used to generate the test signal is shown in Fig. 5.6(c), showing the two laser sources, a coupler or beam combiner, and a polarizer to ensure both begin at an identical polarization. After the polarizer, both wavelengths should have the same optical power to ensure best results. We launched at 45° (in Jones space) with respect to the PSPs of our varying PM fiber (DUTs discussed above) and measured the minimum DOP of the combined two sources. This minimum DOP as a result of DGD depolarization effects can be expressed by DOP (d g d ) ncAAdgd cos(---------------) A 2 0 (5.2.3) where A0 is either of the laser wavelengths and AA is the wavelength spacing between the two laser sources. The simulation results showing the relationship between the minimum DOP, the DGD of the DUT, and the spacing between the two laser sources are shown in Fig. 5.9(a) for spacings of 0.08, 0.16, and 1.0 nm, while some experimental and 278 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. simulation results with laser spacings of 0.054 and 0.086 nm are shown in Fig. 5.9(b). Note the good agreement between the simulation and experimental results. In addition, the maximum DGD measurement range is equal to X, -, thus, ( 2 * c * A X ) by changing the wavelength spacing between the two laser sources, the sensitivity and maximum measurement range can be changed. = 0.08 n m Simulation o 0 -6 \ I \ I 1 I AX, = 0.16 nm 1 1 I I ^AX = 1 nm 5 10 15 20 25 DGD (ps) (a ) . AX = 0.054 n m 0.8 0.6 .E 0.4 0.2 AX = 0.086Vim, 100 40 60 DGD (ps) (b) Fig. 5.9. (a) Simulation results of minimum DOP vs. DGD for our dual laser source DGD measurement technique for varying laser spacings. The greater the laser spacing, the lower the measurements range but the greater the DOP sensitivity to DGD. (b) Simulation and experimental results for minimum DOP vs. DGD for two laser spacings. 5.2.3 Discussion We applied these three techniques (high modulation depth DSB tone, dual laser source, and ASE noise) as well as the conventional JME method to measure the DGD of three different spools of fiber - first, a 1 km spool of highly nonlinear (HNL) fiber, second, a 500 meter spool of HNL fiber from a different manufacturer, and third, a 4 km spool of DSF. The results of the DGD measurement are shown in Table 5.1. Note the good agreement between our methods and the established JME 279 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. method. The slight inaccuracy in the ASE noise measurement was due to the slightly off-Gaussian profile of the filter that we used. ASE noise (BW = 1.5 nm) Dual laser source (Spacing: 0.873 nm, 2.27 nm) DSB tone (fs = 20 GHz) JME DOP DGD (ps) DOP DGD (ps) DOP DGD (ps) DGD (ps) HNL#1 (1 km) 0.22 3.45 0.33 3.6 0.95 3.5 4 HNL#2 (0.5 km) 0.82 1.25 0.56 1 .1 0.994 1 1.5 DSF (4 km) 0.96 0.55 0.92 0.45 1 ? 0.6 Table 5.1. Results for three of our DGD measurement techniques (20-GHz DSB subcarrier tone, ASE noise using a 1.5 nm Gaussian filter, and dual laser source with 0.873 (for the first measurement) and 2.27 nm (for the rest) spacing) along with conventional JME measurement results when measuring the DGD o f three different spools o f fiber - one 1 km spool o f HNL fiber, a different 500 m spool of HNL fiber, and one 4 km spool ofDSF. The “?” entry refers to a DOP that is approximately 1 and thus the DGD cannot be measured. Since these methods are polarimetric techniques, it is less sensitive to fiber leads moving and multi-path-reflection in comparison to non-polarimetric methods (e.g. interferometry and fixed analyzer methods). Through the use of fast polarization scrambling (~20KHz) and monitoring the instantaneous DOP using a polarimeter, these methods can measure DGD on a millisecond time scale and there is no need for complicated control circuits either at the transmitter or receiver - this is a significant advance over traditional JME, MMM, or MPS methods that require either the launch of two (or three) polarization states at two optical frequencies or four controlled predetermined polarization states. We believe that ASE method is the simplest and most flexible available method for measuring DGD. 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Fading channel equalization and video traffic classification using nonlinear signal processing techniques

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Contributions to image and video coding for reliable and secure communications

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Dynamic radio resource management for 2G and 3G wireless systems

Asset Metadata

Creator Motaghian Nezam, Seyed Mohammad Reza (author)

Core Title Chromatic and polarization mode dispersion monitoring for equalization in optical fiber communication systems

Contributor Digitized by ProQuest (provenance)

School Graduate School

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, electronics and electrical,OAI-PMH Harvest

Language English

Advisor Willner, Alan E. (committee chair), Gagliardi, Robert (committee member), Goo, Edward (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-411035

Unique identifier UC11340308

Identifier 3145249.pdf (filename),usctheses-c16-411035 (legacy record id)

Legacy Identifier 3145249.pdf

Dmrecord 411035

Document Type Dissertation

Rights Motaghian Nezam, Seyed Mohammad Reza

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA