Table Of ContentO F
PTICAL IBER
C
OMMUNICATIONS
S
YSTEMS
Theory and Practice with
MATLAB® and Simulink® Models
Le Nguyen Binh
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To the memory of my father
To my mother
To Phuong and Lam
Contents
Preface ..........................................................................................................................................xvii
Author ...........................................................................................................................................xxi
List of Abbreviations and Notations ......................................................................................xxiii
1. Introduction .............................................................................................................................1
1.1 Historical Perspectives .................................................................................................1
1.2 Digital Modulation for Advanced Optical Transmission Systems ........................4
1.3 Demodulation Techniques ...........................................................................................7
1.4 MATLAB® and Simulink® Platforms .........................................................................8
1.5 Organization of the Chapters in This Book ..............................................................8
2. Optical Waveguides: Geometrical and Lightwave-Guiding Properties ...................11
2.1 Introduction .................................................................................................................11
2.2 Dielectric Slab Optical Waveguides .........................................................................12
2.2.1 Structure ..........................................................................................................13
2.2.2 Numerical Aperture ......................................................................................13
2.2.3 Modes of the Symmetric Dielectric Slab Waveguides ..............................14
2.2.3.1 Wave Equations ..............................................................................15
2.2.4 Optical Guided Modes ..................................................................................16
2.2.4.1 Even TE Modes ...............................................................................17
2.2.4.2 Odd TE Modes ................................................................................17
2.2.4.3 Graphical Solutions for Guided TE Modes (Even and
Odd) ..................................................................................................18
2.2.5 Cutoff Properties ............................................................................................18
2.3 Optical Fiber: General Properties .............................................................................19
2.3.1 Geometrical Structures and Index Profi les ................................................19
2.3.1.1 Step-Index Profi le ...........................................................................19
2.3.1.2 Graded-Index Profi le ......................................................................20
2.3.1.3 Power Law–Index Profi le ..............................................................21
2.3.1.4 Gaussian-Index Profi le ..................................................................21
2.3.2 Fundamental Mode of Weakly Guiding Fibers .........................................21
2.3.2.1 Solutions of the Wave Equation for Step-Index Fiber ...............22
2.3.3 Cutoff Properties ............................................................................................26
2.4 Power Distribution ......................................................................................................27
2.4.1 Approximation of Spot Size r of a Step-Index Fiber ................................29
0
2.4.2 Equivalent Step–Index Description .............................................................29
2.4.2.1 Defi nitions of ESI Parameters .......................................................30
2.4.2.2 Accuracy and Limits ......................................................................31
2.4.2.3 Examples on ESI Techniques ........................................................31
2.4.2.4 General Method ..............................................................................32
2.5 Nonlinear Optical Effects ..........................................................................................33
2.5.1 Nonlinear Phase Modulation Effects ..........................................................33
2.5.1.1 Self-Phase Modulation ...................................................................33
2.5.1.2 Cross-Phase Modulation ...............................................................34
v
vi Contents
2.5.2 Stimulated Scattering Effects .......................................................................35
2.5.2.1 Stimulated Brillouin Scattering ....................................................36
2.5.2.2 Stimulated Raman Scattering .......................................................37
2.5.3 Four-Wave Mixing .........................................................................................38
2.6 Optical Fiber Manufacturing and Cabling ..............................................................39
2.7 Concluding Remarks ..................................................................................................40
2.8 Problems .......................................................................................................................42
Appendix: Technical Data of Single-Mode Optical Fibers ...............................................44
References ...............................................................................................................................57
3. Optical Fibers: Signal Attenuation and Dispersion ......................................................59
3.1 Introduction .................................................................................................................59
3.2 Signal Attenuation in Optical Fibers ........................................................................60
3.2.1 Intrinsic or Material Attenuation ................................................................60
3.2.2 Absorption ......................................................................................................61
3.2.3 Rayleigh Scattering ........................................................................................61
3.2.4 Waveguide Loss .............................................................................................61
3.2.5 Bending Loss ..................................................................................................61
3.2.6 Microbending Loss ........................................................................................61
3.2.7 Joint or Splice Loss .........................................................................................62
3.2.8 Attenuation Coeffi cient .................................................................................63
3.3 Signal Distortion in Optical Fibers ...........................................................................63
3.3.1 Basics on Group Velocity ..............................................................................63
3.3.2 Group Velocity Dispersion ...........................................................................65
3.3.2.1 Material Dispersion........................................................................65
3.3.2.2 Waveguide Dispersion...................................................................67
3.4 Transfer Function of Single-Mode Fibers ................................................................70
3.4.1 Higher-Order Dispersion .............................................................................70
3.4.2 Transmission Bit Rate and Dispersion Factor ............................................72
3.4.3 Polarization Mode Dispersion .....................................................................73
3.4.4 Fiber Nonlinearity .........................................................................................76
3.5 Advanced Optical Fibers: Dispersion Shifted, Dispersion Flattened,
and Dispersion Compensated ...................................................................................78
3.6 Effects of Mode Hopping ...........................................................................................79
3.7 Numerical Solution: Split-Step Fourier Method .....................................................80
3.7.1 Symmetrical Split-Step Fourier Method .....................................................80
3.7.2 MATLAB® Program and MATLAB® and Simulink® Models of
SSFM ................................................................................................................81
3.7.2.1 MATLAB® Program .......................................................................81
3.7.2.2 MATLAB® and Simulink® Models ..............................................84
3.7.3 Modeling of Polarization Mode Dispersion ...............................................84
3.7.4 Optimization of Symmetrical SSFM ...........................................................85
3.7.4.1 Optimization of Computational Time.........................................85
3.7.4.2 Mitigation of Windowing Effect and Waveform
Discontinuity ..................................................................................86
3.8 Concluding Remarks ..................................................................................................87
3.9 Problems .......................................................................................................................87
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 .............................................................................................................................100
4. Overview of Modeling Techniques for Optical Transmission Systems
Using MATLAB® and Simulink® ....................................................................................103
4.1 Overview ....................................................................................................................103
4.2 Optical Transmitter ...................................................................................................105
4.2.1 Background of External Optical Modulators...........................................106
4.2.2 Optical Phase Modulator ............................................................................106
4.2.3 Optical Intensity Modulator .......................................................................107
4.2.3.1 Single-Drive MZIM ......................................................................107
4.2.3.2 Dual-Drive MZIM ........................................................................108
4.3 Impairments of Optical Fiber ..................................................................................109
4.3.1 Chromatic Dispersion .................................................................................109
4.3.2 Chromatic Dispersion as a Total of Material Dispersion
and Waveguide Dispersion ........................................................................110
4.3.3 Dispersion Length .......................................................................................112
4.3.4 Polarization Mode Dispersion ...................................................................113
4.3.5 Fiber Nonlinearity .......................................................................................114
4.4 Modeling of Fiber Propagation ...............................................................................115
4.4.1 Symmetrical Split-Step Fourier Method ...................................................115
4.4.2 Modeling of Polarization Mode Dispersion .............................................117
4.4.3 Optimization of Symmetrical SSFM .........................................................118
4.4.3.1 Optimization of Computational Time.......................................118
4.4.3.2 Mitigation of Windowing Effect and Waveform
Discontinuity ................................................................................118
4.5 Optical Amplifi ers ....................................................................................................118
4.5.1 ASE Noise .....................................................................................................118
4.5.2 Noise Figure .................................................................................................119
4.5.3 Optical and Electrical Filters ......................................................................119
4.6 Optical Receiver ........................................................................................................120
4.7 Performance Evaluation ...........................................................................................122
4.7.1 Optical Signal-to-Noise Ratio ....................................................................123
4.7.2 OSNR Penalty ...............................................................................................123
4.7.3 Eye Opening .................................................................................................123
4.7.4 Conventional Evaluation Methods ............................................................124
4.7.4.1 Monte Carlo Method ....................................................................124
4.7.4.2 Single Gaussian Statistical Method ...........................................125
viii Contents
4.7.5 Novel Statistical Methods ...........................................................................126
4.7.5.1 Multiple Gaussian Distributions Method .................................126
4.7.5.2 Generalized Pareto Distribution Method .................................128
4.8 MATLAB® and Simulink® Modeling Platforms ...................................................130
4.9 Concluding Remarks ................................................................................................137
References .............................................................................................................................138
5. Optical Modulation ............................................................................................................141
5.1 Introduction ...............................................................................................................141
5.2 Direct Modulation .....................................................................................................142
5.2.1 General Introduction ...................................................................................142
5.2.2 Physics of Semiconductor Lasers ...............................................................143
5.2.2.1 The Semiconductor p–n Junction for Lasing Lightwaves .......143
5.2.2.2 Optical Gain Spectrum ................................................................144
5.2.2.3 Types of Semiconductor Lasers ..................................................145
5.2.2.4 Fabry–Perot Heterojunction Semiconductor Laser .................145
5.2.2.5 Distributed-Feedback Semiconductor Laser ............................146
5.2.2.6 Constricted Mesa Semiconductor Laser ...................................147
5.2.2.7 Special Semiconductor Laser Source .........................................148
5.2.2.8 Single-Mode Optical Laser Rate Equations ..............................148
5.2.2.9 Dynamic Response of Laser Source ..........................................150
5.2.2.10 Frequency Chirp...........................................................................151
5.2.2.11 Laser Noises ..................................................................................152
5.3 External Modulation Using Optical Modulators..................................................156
5.3.1 Phase Modulators ........................................................................................157
5.3.2 Intensity Modulators ...................................................................................157
5.3.3 Phasor Representation and Transfer Characteristics .............................158
5.4 Bias Control ................................................................................................................160
5.4.1 Chirp-Free Optical Modulators .................................................................160
5.4.1.1 Structures of Photonic Modulators ............................................161
5.4.2 Typical Operational Parameters of Optical Intensity Modulators ...163
5.4.3 MATLAB® and Simulink® Models of External Optical
Modulators ..................................................................................................163
5.4.3.1 Phase Modulation Model and Intensity Modulation ..............163
5.4.3.2 Dense Wavelength Division Multiplexing Optical
Multiplexers and Modulators .....................................................164
5.5 Concluding Remarks ................................................................................................167
Appendix: MATLAB® Program for Solving the Laser Rate Equation .........................167
References .............................................................................................................................169
6. Optical Transmitters for Advanced Modulation Format ...........................................171
6.1 Introduction ...............................................................................................................171
6.2 External Modulation and Advanced Modulation Formats ................................172
6.2.1 Modulation Formats and Pulse Shaping ..................................................177
6.2.1.1 Generation .....................................................................................177
6.2.1.2 Phasor Representation .................................................................179
6.2.1.3 Phasor Representation of CSRZ Pulses .....................................180
6.2.1.4 Phasor Representation of RZ33 Pulses .....................................181
Contents ix
6.2.2 Differential Phase Shift Keying .................................................................182
6.2.2.1 Background ...................................................................................182
6.2.2.2 Optical DPSK Transmitter ..........................................................183
6.3 Generation of Modulation Formats ........................................................................184
6.3.1 Introductory Remarks .................................................................................184
6.3.2 Amplitude-Modulation ASK-NRZ and ASK-RZ .....................................185
6.3.2.1 ASK-NRZ and ASK-RZ Pulse Shaping .....................................185
6.3.2.2 Amplitude-Modulation Carrier-Suppressed RZ Formats ...187
6.3.3 Discrete Phase-Modulation NRZ Formats ...............................................187
6.3.3.1 Differential Phase Shift Keying .................................................187
6.3.3.2 Differential Quadrature Phase Shift Keying ...........................188
6.3.3.3 NRZ-DPSK ....................................................................................188
6.3.3.4 RZ-DPSK ........................................................................................188
6.3.3.5 Generation of M-Ary Amplitude Differential Phase
Shift Keying Using One MZIM ..................................................189
6.3.3.6 Continuous Phase Modulation PM-NRZ Formats ..................191
6.3.3.7 Linear and Nonlinear MSK ........................................................192
6.3.4 Photonic MSK Transmitter Using Two Cascaded Electro-Optic
Phase Modulators ........................................................................................195
6.3.4.1 Confi guration of Optical MSK Transmitter Using
Mach–Zehnder Intensity Modulators: I–Q Approach ............197
6.3.4.2 Single Sideband Optical Modulators .........................................198
6.3.4.3 Optical RZ-MSK ...........................................................................198
6.3.5 Multi-Carrier Multiplexing Optical Modulators .....................................199
6.3.6 Spectra of Modulation Formats .................................................................202
6.4 Concluding Remarks ................................................................................................208
6.5 Problems .....................................................................................................................209
Appendix: Structures of Mach–Zehnder Modulator ......................................................214
References .............................................................................................................................215
7. Direct Detection Optical Receivers ................................................................................219
7.1 Introduction ...............................................................................................................219
7.2 Optical Receivers in Various Systems ....................................................................220
7.3 Receiver Components ...............................................................................................220
7.3.1 Structure ........................................................................................................220
7.3.2 Photodiodes ..................................................................................................222
7.3.2.1 p-i-n Photodiodes .........................................................................222
7.3.2.2 Avalanche Photodiodes ...............................................................222
7.3.2.3 Quantum Effi ciency and Responsivity .....................................223
7.3.2.4 High-Speed Photodetectors ........................................................224
7.4 Detection and Noises ................................................................................................224
7.4.1 Linear Channel .............................................................................................225
7.4.2 Data Recovery ...............................................................................................225
7.4.3 Noises in Photodetectors ............................................................................225
7.4.4 Receiver Noises ............................................................................................226
7.4.4.1 Shot Noises ....................................................................................227
7.4.4.2 Quantum Shot Noise ...................................................................228
7.4.4.3 Thermal Noise ..............................................................................228
7.4.5 Noise Calculations .......................................................................................228
