OPTICAL FIBER COMMUNICATIONS SYSTEMS

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1 OPTICAL FIBER COMMUNICATIONS SYSTEMS Theory and Practice with MATLAB and Simulink Models Le Nguyen Binh LftP) CRC Press W* / Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informs business

2 Contents Preface Author List of Abbreviations and Notations xvii xxi xxiii 1. Introduction Historical Perspectives Digital Modulation for Advanced Optical Transmission Systems Demodulation Techniques MATLAB and Simulink Platforms Organization of the Chapters in This Book 8 2. Optical Waveguides: Geometrical and Lightwave-Guiding Properties Introduction Dielectric Slab Optical Waveguides Structure Numerical Aperture Modes of the Symmetric Dielectric Slab Waveguides Wave Equations Optical Guided Modes Even ТЕ Modes Odd ТЕ Modes Graphical Solutions for Guided ТЕ Modes (Even and Odd) Cutoff Properties Optical Fiber: General Properties Geometrical Structures and Index Profiles Step-Index Profile Graded-Index Profile Power Law-Index Profile Gaussian-Index Profile Fundamental Mode of Weakly Guiding Fibers Solutions of the Wave Equation for Step-Index Fiber Cutoff Properties Power Distribution Approximation of Spot Size r 0 of a Step-Index Fiber Equivalent Step-Index Description Definitions of ESI Parameters Accuracy and Limits Examples on ESI Techniques General Method Nonlinear Optical Effects Nonlinear Phase Modulation Effects Self-Phase Modulation Cross-Phase Modulation 34 v

3 vi Contents Stimulated Scattering Effects Stimulated Brillouin Scattering Stimulated Raman Scattering Four-Wave Mixing Optical Fiber Manufacturing and Cabling Concluding Remarks Problems 42 Appendix: Technical Data of Single-Mode Optical Fibers 44 References Optical Fibers: Signal Attenuation and Dispersion Introduction Signal Attenuation in Optical Fibers Intrinsic or Material Attenuation Absorption Rayleigh Scattering Waveguide Loss Bending Loss Microbending Loss Joint or Splice Loss Attenuation Coefficient Signal Distortion in Optical Fibers Basics on Group Velocity Group Velocity Dispersion Material Dispersion Waveguide Dispersion Transfer Function of Single-Mode Fibers Higher-Order Dispersion Transmission Bit Rate and Dispersion Factor Polarization Mode Dispersion Fiber Nonlinearity Advanced Optical Fibers: Dispersion Shifted, Dispersion Flattened, and Dispersion Compensated Effects of Mode Hopping Numerical Solution: Split-Step Fourier Method Symmetrical Split-Step Fourier Method MATLAB Program and MATLAB and Simulink Models of SSFM MATLAB Program MATLAB and Simulink Models Modeling of Polarization Mode Dispersion Optimization of Symmetrical SSFM Optimization of Computational Time Mitigation of Windowing Effect and Waveform Discontinuity Concluding Remarks Problems 87

4 Contents vii Appendix 3.A.1: MATLAB Program of the Design of Optical Fibers A Solution to the Mini-Project Design 91 Appendix 3.A.2: Program Listings of the Design of Standard Single-Mode Fibers 92 Appendix 3.A.3: Program Listings of the Design of Nonzero Dispersion-Shifted Fibers 94 Appendix 3.A.4: Program Listings of the Split-Step Fourier Method with SPM and Raman Gain Distribution 96 Appendix 3.A.5: Program Listings of the Initialization File 98 References Overview of Modeling Techniques for Optical Transmission Systems Using MATLAB and Simulink Overview Optical Transmitter Background of External Optical Modulators Optical Phase Modulator Optical Intensity Modulator Single-Drive MZIM Dual-Drive MZIM Impairments of Optical Fiber Chromatic Dispersion Chromatic Dispersion as a Total of Material Dispersion and Waveguide Dispersion Dispersion Length Polarization Mode Dispersion Fiber Nonlinearity Modeling of Fiber Propagation Symmetrical Split-Step Fourier Method Modeling of Polarization Mode Dispersion Optimization of Symmetrical SSFM Optimization of Computational Time Mitigation of Windowing Effect and Waveform Discontinuity Optical Amplifiers ASE Noise Noise Figure Optical and Electrical Filters Optical Receiver Performance Evaluation Optical Signal-to-Noise Ratio OSNR Penalty Eye Opening Conventional Evaluation Methods Monte Carlo Method Single Gaussian Statistical Method 125

5 Vlll Contents Novel Statistical Methods Multiple Gaussian Distributions Method Generalized Pareto Distribution Method MATLAB and Simulink Modeling Platforms Concluding Remarks 137 References Optical Modulation Introduction Direct Modulation General Introduction Physics of Semiconductor Lasers The Semiconductor p-n Junction for Lasing Lightwaves Optical Gain Spectrum Types of Semiconductor Lasers Fabry-Perot Heterojunction Semiconductor Laser Distributed-Feedback Semiconductor Laser Constricted Mesa Semiconductor Laser Special Semiconductor Laser Source Single-Mode Optical Laser Rate Equations Dynamic Response of Laser Source Frequency Chirp Laser Noises External Modulation Using Optical Modulators Phase Modulators Intensity Modulators Phasor Representation and Transfer Characteristics Bias Control Chirp-Free Optical Modulators Structures of Photonic Modulators Typical Operational Parameters of Optical Intensity Modulators MATLAB and Simulink Models of External Optical Modulators Phase Modulation Model and Intensity Modulation Dense Wavelength Division Multiplexing Optical Multiplexers and Modulators Concluding Remarks 167 Appendix: MATLAB Program for Solving the Laser Rate Equation 167 References Optical Transmitters for Advanced Modulation Format Introduction External Modulation and Advanced Modulation Formats Modulation Formats and Pulse Shaping Generation Phasor Representation Phasor Representation of CSRZ Pulses Phasor Representation of RZ33 Pulses 181

6 Contents ix Differential Phase Shift Keying Background Optical DPSK Transmitter Generation of Modulation Formats Introductory Remarks Amplitude-Modulation ASK-NRZ and ASK-RZ ASK-NRZ and ASK-RZ Pulse Shaping Amplitude-Modulation Carrier-Suppressed RZ Formats Discrete Phase-Modulation NRZ Formats Differential Phase Shift Keying Differential Quadrature Phase Shift Keying NRZ-DPSK RZ-DPSK Generation of M-Ary Amplitude Differential Phase Shift Keying Using One MZIM Continuous Phase Modulation PM-NRZ Formats Linear and Nonlinear MSK Photonic MSK Transmitter Using Two Cascaded Electro-Optic Phase Modulators Configuration of Optical MSK Transmitter Using Mach-Zehnder Intensity Modulators: I-Q Approach Single Sideband Optical Modulators Optical RZ-MSK Multi-Carrier Multiplexing Optical Modulators Spectra of Modulation Formats Concluding Remarks Problems 209 Appendix: Structures of Mach-Zehnder Modulator 214 References Direct Detection Optical Receivers Introduction Optical Receivers in Various Systems Receiver Components Structure Photodiodes p-i-n Photodiodes Avalanche Photodiodes Quantum Efficiency and Responsivity High-Speed Photodetectors Detection and Noises Linear Channel Data Recovery Noises in Photodetectors Receiver Noises Shot Noises Quantum Shot Noise Thermal Noise Noise Calculations 228

7 x Contents 7.5 Performance Calculations for Binary Digital Optical Systems Signals Received Probability Distribution Minimum Average Optical Received Power Fundamental Limit: Direct Detection Equalized Signal Output Photodiode Shot Noise Total Output Noises and Pulse Shape Parameters FET Front-End Optical Receiver BJT Front-End Optical Receiver HEMT-Matched Noise Network Preamplifier Structure Noise Theory and Equivalent Input Noise Current Concluding Remarks Problems 249 Appendix: Noise Equations 251 References Optical Coherent Detection Introduction Coherent Receiver Components Coherent Detection Optical Heterodyne Detection ASK Coherent System PSK Coherent System FSK Coherent System Optical Homodyne Detection Detection and Optical PLL Quantum Limit Detection Linewidth Influences Self-Coherent Detection and Electronic DSP Digital Signal Processing Coherent Optical Receiver Theory of DSP-Assisted Coherent Detection DSP-Based Phase Estimation and Correction of Phase Noise and Nonlinear Effects DSP-Based Forward Phase Estimation Optical Coherent Receivers of QPSK Modulation Format Coherent Receiver Analysis Shot Noise-Limited Receiver Sensitivity Receiver Sensitivity under Nonideal Conditions MATLAB and Simulink Models Phase Detection Mach Zehnder Delay Interferometer Receiver with Coupler re/2 Optical Hybrid Coupler Amplitude Detection Phase Detection Electronic Noise Model of Electronic Preamplifier 293

8 Contents xi 8.8 Concluding Remarks Problems 294 Appendix: я/2 Hybrid Coupler Embedded MATLAB Code 295 References Erbium-Doped Fiber Optical Amplifiers and Simulink Models Introduction Fundamental and Theoretical Issues of EDFAs EDFA Configuration EDFA Operational Principles Pump Wavelength and Absorption Spectrum Pump Mechanism General Amplifier Noises and Gain in Transmission Amplifier Gain Modulation EDFAs in Long-Haul Transmission Systems EDFA Simulation Model Amplifier Parameters EDFA's Dynamic Model EDFA's Steady-State Modeling Principles Population Inversion Factor Amplifier Noises ASE Noise Model Other Noise Sources Simulation Model Simulator Design Outline Simulator Design Process Simulator Requirement Simulator Design Assumptions Further Assumptions EDFA Simulator Using the EDFA Simulator Signal Data Stream Modeling Pump Source Pumping Wavelength Pump Modulation EDF Modeling EDFA's Dynamic Gain Model EDFA's Steady-State Gain Model Population Inversion Factor Modeling Amplifier Noise Modeling Simulink EDFA Simulator: Execution Procedures Amplification in the L Band Multichannel Operation of the EDFA ASE Measurement Pump Wavelength Testing Gain Pump Modulation Effect Samples of the Simulink Simulator Concluding Remarks 337 References 337

9 xii Contents 10. MATLAB and Simulink Modeling of Raman Amplification and Integration in Fiber Transmission Systems Introduction ROA versus Erbium-Doped Fiber Amplifiers Raman Amplification Principles Raman Amplification Coupled Equations Raman and Fiber Propagation under Linear and Nonlinear Fiber Dispersion Propagation Equation Standard Single-Mode Fiber and DCF as Raman Fibers Noise Figure Dispersion Nonlinear Raman Gain/Scattering Schrödinger Equation Fiber Nonlinearities Dispersion Split-Step Fourier Method Gaussian Pulses, Eye Diagrams, and Bit Error Rate Raman Amplification and Gaussian Pulse Propagation Fiber Profiles Gaussian Pulse Propagation Bidirectional Pumping Case Forward-Pumping Case Backward-Pumping Case Back-to-Back Performance Propagation under No Amplification Propagation under Fiber Raman Amplification Optically Amplified Transmission EDFA Amplification and Distributed Raman Amplification over 99 km Fiber (1 km Mismatch) EDFA Distributed Raman Amplification Hybrid Amplification Long-Haul Optically Amplified Transmission Eye Diagram and BER Evaluation under Noise Loading Effects Launched Power versus BER Dispersion Tolerance Remarks Concluding Remarks Problems 376 Appendix: Raman Amplification and Split-Step Fourier Method MATLAB Program 377 References Design of Optical Communication Systems and Simulink Models Introduction Long-Haul Optical Transmission Systems 383

10 Contents xiii Intensity-Modulation Direct-Detection Systems Loss-Limited Optical Communication Systems Dispersion-Limited Optical Communication Systems System Preliminary Design Single-Span Optical Transmission Systems Power Budget Rise-Time/Dispersion Budget Multi-Span Optical Transmission Systems Maximum Transmission Distance of Cascaded Optically Amplified Multi-Span Systems Gaussian Approximation Link Budget Measurement System Margin Measurement Some Notes on the Design of Optical Transmission Systems Allocations of Wavelength Channels Multiwavelength MATLAB and Simulink Models Link Design Process Link Budget Considerations Link Budget Calculations under Linear and Nonlinear Effects Budget System Impairments Power and Time Eyes Dispersion Tolerance due to Wavelength Channels and Nonlinear Effects Dependence on Wavelength Channels and Launched Power Budget Engineering an OADM Transmission Link Problems Simulink Models of Optically Amplified Digital Transmission Systems ASK Modulation Formats Transmission Models Introductory Remarks Components for Advanced Optical Communication System Optical Source Optical Modulators Mach-Zehnder Intensity Modulator Transmission Loss and Dispersion Revisited Nonlinear Effects Signal Propagation Model Nonlinear Schrodinger Propagation Equation Low-Pass Equivalent Model: Linear Operating Region Modulation Formats NRZ or NRZ-ASK RZorRZ-ASK Return-to-Zero Optical Pulses Generation Phasor Representation 430

11 xiv Contents Phasor Representation of CSRZ Pulses Phasor Representation of RZ33 Pulses Differential Phase Shift Keying NRZ-DPSK RZ-DPSK Receiver Simulink Models Bernoulli Binary Generator DFB Laser Mach-Zehnder Interferometric Modulator Pulse Carver Data Modulator Differential Data Encoder Back-to-Back Receiver Eye Diagram Signal Propagation Bit Error Rate DQPSK Modulation Formats Transmission Models DQPSK Optical System Components DQPSK Transmitter DQPSK Receiver MATLAB and Simulink Simulators Spectral Characteristics of Advanced Modulation Formats Partial Responses Duo-Binary Transmission Model Remarks The DBM Formatter Gb/s DB Optical Fiber Transmission Systems Electro-Optic Duo-Binary Transmitter The Duo-Binary Encoder The External Modulator Duo-Binary Transmitters and Precoder Alternative Phase DB Transmitter MSK Transmission Model Introduction Generation of Optical MSK-Modulated Signals Optical MSK Transmitter Using Two Cascaded Electro-Optic Phase Modulators Possibility to Generate Optical M-Ary CPFSK Format Detection of M-Ary CPFSK Modulated Optical Signal Optical MSK Transmitter Using Parallel Mach-Zehnder Intensity Modulators (I-Q Approach) Optical Binary-Amplitude MSK Format Generation Detection Typical Simulation Results Transmission Performance of Linear and Nonlinear Optical MSK Systems 484

12 Contents xv 12.9 Star-QAM Transmission Systems for 100Gb/s Capacity Introductory Remarks Design of 16-QAM Signal Constellation Star 16-QAM DPSK_2-ASK 16-Star-QAM Receiver Sensitivity and Dispersion Tolerance Long-Haul Transmission Concluding Remarks 499 Appendix 12.A: Simulink and Simulation Guidelines A.1 MATLAB and Simulink A.2 Guidelines for Using Simulink Models A.3 MATLAB Files A.3.1 Initialization File 505 References 512 Appendix: A Short Glossary of Terms in Optical Fiber Communications 515 Index 521

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