Digital Optical Communications Le Nguyen Binh CRC Press Taylor &. Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business
Contents Preface Acknowledgments Author Abbreviations xix xxi xxiii xxv Chapter 1 Introduction 1 1.1 Digital Optical Communications and Transmission Systems: Challenging Issues 1 1.2 Enabling Technologies 3 1.2.1 Modulation Formats and Generation of Optical Signals 3 1.2.1.1 Binary Level 3 1.2.1.2 Binary and Multi-level 5 1.2.1.3 In-phase and Quadrature Phase Channels 6 1.2.1.4 External Optical Modulation 6 1.2.2 Advanced Modulation Formats 8 1.2.3 Incoherent Optical Receivers 8 1.2.4 Coherent Optical Receivers 9 1.2.5 Transmission of Ultra-short Pulse Sequence 9 1.2.6 Electronic Equalization 10 1.2.6.1 Feed Forward Equalizer 10 1.2.6.2 Decision Feedback Equalization 11 1.2.6.3 Minimum Mean Square Error Equalization 11 1.2.6.4 Placement of Equalizers 11 1.2.6.5 MLSE Electronic Equalizers 11 1.2.7 Ultra-short Pulse Transmission 11 1.3 Organization of Book Chapters 12 References 14 Chapter 2 Photonic Transmitters 19 2.1 Optical Modulators 19 2.1.1 Phase Modulators 19 2.1.2 Intensity Modulators 20 2.1.2.1 Phasor Representation and Transfer Characteristics 20 2.1.2.2 Bias Control 22 2.1.2.3 Chirp-free Optical Modulators 22 2.1.3 Structures of Photonic Modulators 24 2.1.4 Typical Operational Parameters 24 2.2 Return-to-Zero Optical Pulses 24 2.2.1 Generation 24 2.2.2 Phasor Representation 27 2.2.2.1 Phasor Representation of CSRZ Pulses 28 2.2.2.2 Phasor Representation of RZ33 Pulses 28 vii
viii Contents 2.3 Differential Phase Shift Keying 30 2.3.1 Background 30 2.3.2 Optical DPSK Transmitter 31 2.4 Generation of Modulation Formats 32 2.4.1 Amplitude-modulation OOK-RZ Formats 32 2.4.2 Amplitude-modulation Carrier-Suppressed RZ (CSRZ) Formats 34 2.4.3 Discrete Phase-modulation NRZ Formats 34 2.4.3.1 Differential Phase Shift Keying (DPSK) 34 2.4.3.2 Differential Quadrature Phase Shift Keying (DQPSK) 35 2.4.3.3 NRZ-DPSK 35 2.4.3.4 RZ-DPSK 35 2.4.3.5 Generation of M-ary Amplitude Differential Phase Shift Keying (M-ary ADPSK) Using One MZIM 35 2.4.4 Continuous Phase-modulation PM-NRZ Formats 38 2.4.4.1 Linear and Non-linear MSK 39 2.4.4.2 MSK as a Special Case of Continuous Phase FSK (CPFSK) 40 2.4.4.3 MSK as Offset Differential Quadrature Phase Shift Keying (ODQPSK)... 41 2.4.4.4 Configuration of Photonic MSK Transmitter Using Two Cascaded Electro-optic Phase Modulators 42 2.4.4.5 Configuration of Optical MSK Transmitter Using Mach-Zehnder Intensity Modulators: I-Q Approach 43 2.4.5 Single Side Band (SSB) Optical Modulators 43 2.4.5.1 Operating Principles 43 2.4.5.2 Optical RZ-MSK 45 2.4.6 Multi-carrier Multiplexing (MCM) Optical Modulators 47 2.4.7 Spectra of Modulation Formats 51 2.5 Spectral Characteristics of Digital Modulation Formats 51 2.6 Remarks 54 References 62 Chapter 3 Optical Receivers and Transmission Performances 65 3.1 Inroduction 65 3.2 Digital Optical Receivers 67 3.2.1 Photonic and Electronic Noise 67 3.2.1.1 Electronic Noise of Receiver 67 3.2.1.2 Shot Noises 67 3.2.1.3 Biasing Current Shot Noises 67 3.2.1.4 Quantum Shot Noise 68 3.2.1.5 Thermal Noise 68 3.2.1.6 ASE Noise of Optical Amplifier 68 3.2.1.7 Optical Amplifier Noise Figure 68 3.2.1.8 Electronic Beating Noise 69 3.2.1.9 Accumulated ASE Noise in Cascaded Optical Amplifiers 69 3.3 Performance Evaluation of Binary Amplitude Modulation Format 70 3.3.1 Received Signals 70 3.3.1.1 Case 1: OFF or a Transmitted "0" is Received 71 3.3.1.2 Case 2: ON Transmitted "1" Received 71 3.3.2 Probability Distribution Functions 72
Contents ix 3.3.3 Receiver Sensitivity 73 3.3.4 Optical Signal-to-Noise Ratio and Noise Impact 75 3.3.4.1 OSNR 75 3.3.4.2 Determination of the Impact of Noise 76 3.4 Quantum Limit of Optical Receivers under Different Modulation Formats 76 3.4.1 Direct Detection 77 3.4.2 Coherent Detection 79 3.4.3 Coherent Detection with Matched Filter 79 3.4.3.1 Coherent ASK Systems 80 3.4.3.2 Coherent Phase and Frequency Shift Keying Systems 80 3.5 Binary Coherent Optical Receiver 84 3.6 Non-coherent Detection for Optical DPSK and MSK 86 3.6.1 Photonic Balanced Receiver 86 3.6.2 Optical Frequency Discrimination Receiver (OFDR) 86 3.7 Transmission Impairments 87 3.7.1 Chromatic Dispersion (CD) 87 3.7.2 Chromatic Linear Dispersion 88 3.7.3 Polarization Mode Dispersion (PMD) 91 3.7.4 Fiber Non-linearity 92 3.8 MATLAB Simulink Simulator for Optical Communications Systems 92 3.8.1 Fiber Propagation Model 93 3.8.1.1 Non-linear Schroedinger Equation (NLSE) 93 3.8.1.2 Symmetrical Split-Step Fourier Method 93 3.8.1.3 Modeling of Polarization Mode Dispersion (PMD) 94 3.8.1.4 Optimizing the Symmetrical SSFM 95 3.8.1.5 Fiber Propagation in Linear Domain 95 3.8.2 Non-linear Effects via Fiber Propagation Model 95 3.8.2.1 SPM Effects 95 3.8.2.2 XPM Effects 97 3.8.2.3 FWM Effects 98 3.8.2.4 SRS Effects 99 3.8.2.5 SBS Effects 101 3.9 Performance Evaluation 102 3.9.1 BER from Monte Carlo Method 102 3.9.2 BER and Q-factor from Probability Distribution Functions 102 3.9.3 Histogram Approximation 103 3.9.4 Optical Signal-to-Noise Ratio (OSNR) 103 3.9.5 Eye Opening Penalty (EOP) 104 3.9.6 Statistical Evaluation Techniques 104 3.9.6.1 Multi-Gaussian Distributions (MGD) via Expectation Maximization (EM) Theorem 105 3.9.6.2 Selection of Number of Gaussian Distributions for MGD Fitting 106 3.9.6.3 Selection of Threshold for GPD Fitting 108 3.9.6.4 Validation of Novel Statistical Methods 109 3.9.7 Novel BER Statistical Techniques 114 3.9.7.1 Multi-Gaussian Distributions (MGD) and Expectation Maximization (EM) Theorem 114 3.10 Effects of Source Linewidth 115 3.11 Remarks 117
x Contents 3.12 Appendices 118 3.12.1 Sellmeir's Coefficients for Different Core Materials 118 3.12.2 Total Equivalent Electronic Noises 118 3.13 Problems Chapter 3 119 References 128 Chapter 4 Coherent Photonic Transmission 131 4.1 Coherent Detection. 131 4.1.1 Optical Heterodyne Detection 133 4.1.1.1 ASK Coherent System 135 4.1.1.2 Envelop Detection 135 4.1.1.3 Synchronous Detection 137 4.1.2 PSK Coherent System 137 4.1.2.1 Differential Detection 138 4.1.3 Optical Homodyne Detection 138 4.1.4 FSK Coherent System 139 4.2 Coherent and Non-coherent Photonic Transmission Technologies 140 4.2.1 Integrated Optics 140 4.2.2 Optical Source and Modulation 140 4.2.2.1 Demands on Laser Linewidth 140 4.2.2.2 Differential Detection 141 4.2.2.3 CPFSK Differential Detection 141 4.2.2.4 Balanced Receiver 142 4.2.2.5 Phase Diversity Receiver 143 4.2.2.6 Channel-Selective Receiver 143 4.3 Photonic Filters and Phase Comparators 146 4.3.1 Transmission Characteristics 147 4.4 Coherent Phase and Differential Phase Shift Keying 148 4.5 Fiber Propagation and Non-linearities 152 4.5.1 Linear Dispersion: Analytical Approach 152 4.5.1.1 Signal Propagation and the Governing NLSE Equation 152 4.5.1.2 Fiber Transfer Function 153 4.5.1.3 Pulse Shapes 154 4.5.2 Non-linear Impairments 157 4.5.3 Non-linear Phase Noise 157 4.6 Optical Multi-level Modulation: General Theory 160 4.6.1 Optical Multilevel Modulation: General Theory 161 4.6.2 Multi-phase and Amplitude Format Optical Transmitters 162 4.7. Coherent OFDM 163 4.7.1 Principles 163 4.7.2 Experimental Implementation of Coherent Detection 165 4.8 Remarks 167 References 168 Chapter 5 Differential Phase Shift Keying Photonic Systems 171 5.1 Introduction 171 5.2 Optical DPSK Modulation and Formats 172
Contents xi 5.2.1 Generation of Return-to-Zero Pulses 172 5.2.2 Phasor Representation 175 5.2.3 Phasor Representation of CS-RZ Pulses 175 5.2.4 Phasor Representation of RZ33 Pulses 176 5.2.5 Discrete Phase Modulation (DPSK) 178 5.2.5.1 Principles of DPSK and Theoretical Treatment of DPSK and DQPSK Transmission 178 5.2.5.2 Optical DPSK Transmitter 179 5.2.6 DPSK Balanced Receiver 179 5.3 DPSK Transmission Experiment 181 5.3.1 Components and Operational Characteristics 181 5.3.2 Spectra of Modulation Formats 181 5.3.3 Dispersion Tolerance of Optical DPSK Formats 182 5.3.4 Optical Filtering Effects 184 5.3.5 Performance of CSRZ-DPSK over a Dispersion Managed Optical Transmission Link 185 5.3.6 Mutual Impact of Adjacent 10 G and 40 G DWDM Channels 186 5.4 DQPSK Modulation Format 186 5.4.1 DQPSK 187 5.4.2 Offset DQPSK Modulation Format 194 5.4.2.1 Influence of the Minimum Symbol Distance on the Receiver Sensitivity 196 5.4.2.2 Influence of Self Homodyne Detection on the Receiver Sensitivity 197 5.4.3 MATLAB Simulink Model 197 5.4.3.1 The Simulink Model 197 5.4.3.2 Eye Diagrams 197 5.5 Comparisons of Different Formats and ASK and DPSK 200 5.5.1 BER and Receiver Sensitivity 200 5.5.1.1 RZ ASK and NRZ ASK 200 5.5.1.2 RZ DPSK and NRZ DQPSK 202 5.5.1.3 RZ ASK and NRZ DQPSK 202 5.5.2 Dispersion Tolerance 204 5.5.3 Polarization Mode Dispersion Tolerance 205 5.5.4 Robustness Towards Non-linear Effects 205 5.5.4.1 Robustness Towards SPM 205 5.5.4.2 Robustness Towards XPM 206 5.5.4.3 Robustness Towards FWM 207 5.5.4.4 Robustness Towards SRS 207 5.5.4.5 Robustness Towards SBS 208 5.6 Remarks 209 References 209 Appendix: MATLAB Simulink Model for DQPSK Optical System 211 Chapter 6 Continuous Phase Modulation Format Optical Systems 215 6.1 Introduction 215 6.2 Generation of Optical MSK Modulated Signals 217 6.2.1 Optical MSK Transmitter Using Two Cascaded Electro-Optic Phase Modulators 217 6.3 Detection of M-ary CPFSK Modulated Optical Signal 219
xii Contents 6.3.1 Optical MSK Transmitter Using Parallel I-Q Mach-Zehnder Intensity Modulators 221 6.3.1.1 Linear MSK 221 6.3.1.2 Weakly Non-linear MSK 221 6.3.1.3 Strongly Non-linear MSK 223 6.3.2 Optical MSK Receivers 224 6.4 Optical Binary-Amplitude MSK Format 225 6.4.1 Generation 225 6.5 Optical Minimum Shift Keying 226 6.6 Numerical Results and Discussions 228 6.6.1 Transmission Performance of Linear and Non-linear Optical MSK Systems 229 6.6.2 Transmission Performance of Binary Amplitude Optical MSK Systems 232 6.7 Remarks 234 References 235 Chapter 7 Multi-level Amplitude and Phase Shift Keying Optical Transmission 237 7.1 Introduction 237 7.2 Amplitude and Differential Phase Modulation 239 7.2.1 ASK Modulation 239 7.2.1.1 NRZ-ASK Modulation 239 7.2.1.2 RZ-ASK Modulation 239 7.2.1.3 CSRZ-ASK Modulation 239 7.2.1.4 Differential Phase Modulation 241 7.2.2 Comparison of Different Optical Modulation Formats 249 7.2.3 Multilevel Optical Transmitter 249 7.2.4 Single Dual-Drive MZIM Transmitter for MADPSK 252 7.3 MADPSK Optical Transmission 254 7.3.1 Performance Evaluation 255 7.3.2 Implementation of MADPSK Transmission Models 257 7.3.2.1 System Modeling 257 7.3.3 Transmitter Model 258 7.3.4 Receiver Model 258 7.3.5 Transmission Fiber and Dispersion Compensation Fiber Model 258 7.4 Transmission Performance 258 7.4.1 Signal Spectrum, Signal Constellation and Eye Diagram 258 7.4.2 BER Evaluation 260 7.4.2.1 ASK Sub-System Error Probability 261 7.4.3 DQPSK Sub-System Error Probability Evaluation 262 7.4.4 MADPSK System BER Evaluation 265 7.4.5 Chromatic Dispersion Tolerance 266 7.4.6 Critical Issues 268 7.4.6.1 Noise Mechanism and Noise Effect on MADPSK 270 7.4.6.2 Transmission Fiber Impairments 271 7.4.6.3 Non-linear Effects on MADPSK 272 7.4.6.4 Offset Detection 272 7.5 Star 16-QAM Optical Transmission 274 7.5.1 Introduction 275 7.5.2 Design of 16-QAM Signal Constellation 277
Contents xiii 7.5.2.1 Signal Constellation 277 7.5.2.2 Optimum RR for Star Constellation 278 7.5.3 Detection Methods 280 7.5.3.1 Direct Detection 280 7.5.3.2 Coherent Detection 281 7.5.3.3 Homodyne Receiver 281 7.5.3.4 Heterodyne Receiver 281 7.5.3.5 Intradyne Receiver 281 7.5.4 Star 16-QAM Format 282 7.5.4.1 Transmitter Design 282 7.5.4.2 Receiver for 16-star QAM 284 7.5.4.3 Coherent Detection Receiver without Phase Estimation 284 7.5.4.4 Coherent Detection Receiver with Phase Estimation 286 7.5.4.5 Direct Detection Receiver 287 7.6 Coherent Receiver without Phase Estimation 288 7.6.1 Linear Channel 288 7.6.2 Non-linear Effects 291 7.7 Remarks 293 7.8 Other Multilevel and Multi-subcarrier Modulation Formats for 100Gb/s Ethernet Transmission 293 7.8.1 Remarks on Multilevel Modulation 294 7.8.2 Optical Orthogonal Frequency Division Multiplexing (oofdm) [27] 295 7.8.3 100 Gb/s 8-DPSK_2-ASK 16-Star QAM 296 7.8.3.1 Introduction 296 7.8.3.2 Configuration of 8-DPSK _ 2-ASK Optical Transmitter 296 7.8.3.3 Configuration of 8-DPSK _ 2-ASK Detection Scheme 298 7.8.3.4 Transmission Performance of 100Gb/s 8-DPSK_2-ASK Scheme 299 7.9 Concluding Remarks 300 7.9.1 Offset MADPSK Modulation 303 7.9.2 Multi-level Amplitude-minimum Shift Keying (MAMSK) Modulation 303 7.9.3 Star QAM Coherent Detection 303 References 304 Chapter 8 Frequency Discrimination Receiver for Optical MSK 307 8.1 Operational Principles of ONFDR 307 8.2 Receiver Modeling 309 8.3 Receiver Design 312 8.3.1 Bandwidth of the Optical Filter 312 8.3.2 Center Frequency of the Optical Filter 313 8.3.3 Selection of Optimal Values of Optical Delay Line 316 8.4 Selection of Optimum Bandwidth and Center Frequency of Optical Frequency Discrimination Filters 314 8.5 Receiver Performance 316 8.5.1 Numerical Results Validating Receiver Design 316 8.6 Robustness to Chromatic Dispersion of ONFDR 317 8.6.1 40-Gb/s Transmission 317 8.6.2 Dispersion Tolerance 319 8.6.3 10-Gb/s Transmission 321
XIV Contents 8.6.4 Robustness to Polarization Mode Dispersion (PMD) of ONFDR 321 8.6.5 Resilience to Non-linearity (SPM) of ONFDR 321 8.6.6 Transmission Limits of OFDR-based Optical MSK Systems 322 8.7 Dual-level Optical Minimum Shift Keying (MSK) 324 8.7.1 Generation Scheme 324 8.7.2 Incoherent Detection Technique 326 8.7.3 Optical Power Spectrum 326 8.7.4 Receiver Sensitivity 326 8.7.5 Remarks 328 8.8 Remarks 329 References 329 Chapter 9 Partial Responses and Single-sideband Modulation Formats 331 9.1 Partial Responses: Duo-Binary Modulation Formats 331 9.1.1 Introduction 331 9.1.2 The DBM Formatter 332 9.1.3 40-Gb/s DB Optical Fiber Transmission Systems 333 9.1.4 Electro-Optic Duo-Binary Transmitter 335 9.1.5 The DuoB Encoder 336 9.1.6 The External Modulator 336 9.1.7 DuoB Transmitters and Pre-Coder 339 9.1.8 Alternative Phase DB Transmitter 339 9.1.9 Fiber Propagation 339 9.2 Duo-Binary Direct Detection Receiver 343 9.3 System Transmission and Performance 345 9.3.1 The DB Encoder 346 9.3.2 The Transmitter 347 9.3.3 Transmission Performance 350 9.3.4 Alternating Phase and Variable Pulse Width DuoB: Experimental Setup and Transmission Performance 354 9.3.4.1 Transmission Setup 354 9.3.4.2 Test-bed for Variable Pulse Width Alternating Phase Duo-Binary Modulation Optical Transmission 356 9.3.5 Remarks 365 9.4 DWDM VSB Modulation-format Optical Transmission 365 9.4.1 Transmission System 366 9.4.2 VSB Filtering and DWDM Channels 368 9.4.3 Transmission Dispersion and Compensation Fibers 369 9.4.4 Transmission Performance 372 9.4.4.1 Effects of Channel Spacing on ß-Factor 373 9.4.4.2 Effects of GVD on ß-factor 374 9.4.4.3 Effects of Filter Pass-band on the ß-Factor 374 9.5 Single Side Band Modulation 378 9.5.1 Hubert Transform SSB MZ Modulator Simulation 378 9.5.2 SSB Demodulator Simulation 379 9.6 Concluding Remarks 379 References 379
Contents xv Chapter 10 Temporal Lens and Adaptive Electronic/Photonic Equalization 381 10.1 Introduction 381 10.2 Space-Time Duality and Equalization 382 10.2.1 Space-Time Duality 383 10.2.1.1 Paraxial Diffraction 383 10.2.1.2 The Governing Non-linear Schrödinger (NLS) Equation 384 10.2.1.3 Diffractive and Dispersive Phases 384 10.2.1.4 Spatial Lens 385 10.2.1.5 Time Lens 386 10.2.1.6 Temporal Imaging 386 10.2.1.7 Electro-optic Phase Modulator as a Time Lens 387 10.2.2 Equalization in Transmission System 389 10.2.2.1 Equalization with Sinusoidal Driven-Voltage Phase Modulator 390 10.2.2.2 Equalization with Parabolic Driven-Voltage Phase Modulator 391 10.3 Simulation of Transmission and Equalization 392 10.3.1 Single Pulse Transmission 392 10.3.1.1 Equalization of Second Order Dispersion 392 10.3.1.2 Equalization of Third-Order Dispersion 395 10.3.2 Pulse Train Transmission 396 10.3.2.1 Second-Order Dispersion 396 10.3.2.2 Equalization of Third-Order Dispersion 399 10.3.3 Equalization of Timing Jitter and Polarization-Mode Dispersion 399 10.4 Equalization in 160-Gb/s Transmission Systems 400 10.4.1 System Overview 400 10.4.1.1 System Configurations 400 10.4.1.2 Experimental Setup 402 10.4.2 Simulation Model Overview 403 10.4.2.1 System Overview 403 10.4.2.2 Transmitter Block 404 10.4.2.3 Transmission Link 404 10.4.2.4 De-multiplexer 406 10.4.2.5 Equalizer System 407 10.4.2.6 Errors Calculation 410 10.4.3 Simulation Results 412 10.4.3.1 Single Pulse Transmission 412 10.4.3.2 160-Gb/s Transmission and Equalization 414 10.5 Conclusions 420 References 421 Chapter 11 Electronic Signal Processing in Optical Transmission Systems 425 11.1 Introduction 425 11.2 Electronic Digital Processing Equalization 428 11.3 System Representation of Equalized Transfer Function 431 11.3.1 Generic Equalization Formulation 431 11.3.1.1 Signal Representation and Channel Pure Phase Distortion 431
xvi Contents 11.3.1.2 Equalizers at Receiver 432 11.3.1.3 Equalizers at the Transmitter 441 11.3.1.4 Equalization Shared Between Receiver and Transmitter 443 11.3.1.5 Performance of FFE and DFE 444 11.3.2 Impulse and Step Responses of the Single Mode Optical Fiber 444 11.4 Electrical Linear Double Sampling Equalizers for Duobinary Modulation Formats for Optical Transmission 446 11.5 Non-linear MLSE Equalizers for MSK Optical Transmission Systems 452 11.5.1 Non-linear MLSE 453 11.5.2 Trellis Structure and Viterbi Algorithm 453 11.5.2.1 Trellis Structure 454 11.5.2.2 Viterbi Algorithm 454 11.5.3 Optical Fiber as a Finite State Machine 454 11.5.3.1 Construction of State Trellis Structure 455 11.6 MLSE Equalizer for Optical MSK Systems 455 11.6.1 Configuration of MLSE Equalizer in OFDR 455 11.6.2 MLSE Equalizer with Vitertic Algorithm 455 11.6.3 MLSE Equalizer with Reduced-State Template Matching 457 11.7 MLSE Scheme Performance 459 11.7.1 Performance of MLSE Schemes in 40 Gb/s Transmission 459 11.7.2 Transmission of 10Gb/s Optical MSK Signals Over 1472 km SSMF Uncompensated Optical Link 460 11.7.3 Performance Limits of Viterbi-MLSE Equalizers 461 11.7.4 Viterbi-MLSE Equalizers for PMD Mitigation 465 11.7.5 On the Uncertainty and Transmission Limitation of Equalization Process 469 11.8 Uncertainty in Optical Signal Transmission 470 11.8.1 Uncertainty in ASK Modulation Optical Receiver without Equalization 470 11.8.2 Uncertainty in MSK Optical Receiver with Equalization 471 11.9 Electronic Dispersion Compensation of Modulation Formats 472 11.10 Conclusions 477 References 478 Chapter 12 Optical Soliton Transmission 481 12.1 Introduction 481 12.2 Fundamentals of Non-linear Propagation Theory 481 12.3 Numerical Approach 483 12.3.1 Beam Propagation Method 483 12.3.2 Analytical Approach Inverse Scattering Method 483 12.3.2.1 Soliton N= 1 by Inverse Scattering 485 12.3.2.2 Soliton N= 2 by Inverse Scattering 485 12.4 Fundamental and Higher Order Solitons 486 12.4.1 Soliton Evolution for N= 1, 2, 3, 4 and 5 486 12.4.2 Soliton Breakdown 488 12.5 Interaction of Fundamental Solitons 488 12.5.1 Two Solitons Interaction with Different Pulse Separation 488 12.5.2 Two Solitons Interaction with Different Relative Amplitude 488 12.5.3 Two Solitons Interaction under Different Relative Phase 490 12.5.4 Three Soliton Interaction with Different Relative Phase 490 12.5.5 Three Solitons Interaction with Different Relative Phase and r= 1.5 490
Contents xvii 12.6 Soliton Pulse Transmission Systems and Inverse Scattering Method 492 12.6.1 Inverse Scattering Method Revisited 493 12.6.2 N-Solitons Solution (Explicit Formula) 501 12.6.3 Special Case A =N 503 12.6.4 N-Soliton Solutions (Asymptotic Form as x -> ± ) 504 12.6.5 Bound States and Multiple Eigenvalues 506 12.7 Interaction between Two Solitons in an Optical Fiber 506 12.7.1 Soliton Pair with Initial Identical Phases 507 12.7.2 Soliton Pair with Initial Equal Amplitudes 507 12.7.3 Soliton Pair with Initial Unequal Amplitudes 507 12.7.4 Design Strategy 508 12.8 Generations of Solitons 510 12.8.1 Generation of Bound-Solitons in Actively Phase Modulation Mode-Locked Fiber Ring Resonators 510 12.8.1.1 Introduction 510 12.8.1.2 Formation of Bound States in a FM Mode-Locked Fiber Laser 510 12.8.1.3 Experimental Setup and Results 512 12.8.1.4 Simulation of Dynamics of Bound States in a FM Mode-locked Fiber Laser 515 12.8.2 Active Harmonic Mode-Locked Fiber Laser for Soliton Generation 522 12.8.2.1 Experiment Setup 522 12.8.2.2 Tunable Wavelength Harmonic Mode-locked Pulses 524 12.8.2.3 Measurement of the Fundamental Frequency 526 12.8.2.4 Effect of the Modulation Frequency 526 12.8.2.5 Effect of the Modulation Depth/Index 527 12.8.2.6 Effect of Fiber Ring Length 527 12.8.2.7 Effect of Pump Power 530 12.9 Remarks 530 References 531 Chapter 13 OFDM Optical Transmission Systems 533 13.1 Introduction 533 13.1.1 Principles of oofdm 533 13.1.1.1 OFDM as a Multi-carrier Modulation Format 537 13.1.2 FFT and IFFT Based OFDM Principles 539 13.2 Optical OFDM Transmission Systems 539 13.2.1 Impacts on Non-linear Modulation Effects on Optical OFDM 541 13.2.2 Dispersion Tolerance 542 13.2.3 Resilience to PMD Effects 543 13.3 OFDM and DQPSK Formats for 100 Gb/s Ethernet 543 13.4 Concluding Remarks 544 References 544 Chapter 14 Comparison of Modulations Formats for Long-Haul Optically Amplified Transmission Systems and Networks 547 14.1 Identification of Modulation Features for Combating Impairment Effects 547 14.1.1 Binary Digital Optical Signals 547
XVIII Contents 14.1.2 M-ary Digital Optical Signals 548 14.1.3 Multi Sub-carrier Digital Optical Signals 548 14.1.4 Modulation Formats and Electronic Equalization 548 14.2 Amplitude, Phase and Frequency Modulation Formats 549 14.2.1 ASK and DPSK & DPSK and DQPSK 549 14.2.1.1 Dispersion Sensitivity of Different Modulation Formats of ASK and DPSK 549 14.2.2 NRZ-ASK and NRZ DPSK 549 14.2.3 RZ-ASK and RZ-DPSK 551 14.2.4 CSRZ ASK and CSRZ-DPSK 551 14.2.5 ASK and DPSK Spectra 552 14.2.6 ASK and DPSK in Long-Haul Transmission 554 14.2.7 Non-linear Effects in ASK and DPSK in Long-Haul Transmission 554 14.2.7.1 Performance of DWDM RZ-DPSK and CSRZ-DPSK 554 14.2.7.2 Non-linear Effects on CSRZ-DPSK and RZ-DPSK 554 14.2.7.3 Non-linear Effects on CSRZ-ASK and RZ-ASK 556 14.2.8 Continuous Phase Versus Discrete Phase Shift Keying 557 14.2.9 Multi Sub-carrier Versus Single/Dual Carrier Modulation 557 14.2.10 Multi-level Versus Binary or IQ Modulation 559 14.2.11 Single Sideband and Partial Response Modulation 560 14.3 Modulation Formats and All-optical Networking 561 14.3.1 Advanced Modulation Formats in Long-Haul Transmission Systems 561 14.3.2 Advanced Modulation Formats in All-optical Networks 561 14.4 Hybrid 40 Gb/s over 10 Gb/s Optical Networks: 328 km SSMF+DCF for 320 km Tx: Impact of Adjacent 10 G/40 G channels 562 14.5 Ultra-fast Optical Networks 563 14.5.1 OTDM Networking 563 References 564 Chapter 15 Index 567