Preface ........................................................ xv
Acknowledgments ............................................... xix
About the Author .............................................. xxi
Chapter 1 Electric and Magnetic Fields and Waves ............... 1
1.1 Brief Overview ............................................. 1
1.2 Wave Representation ........................................ 1
1.2.1 Overview ............................................ 1
1.2.2 General Property .................................... 2
1.2.3 Waves by Phasor Representation ...................... 3
1.2.4 Phase Velocity ...................................... 4
1.3 Maxwell's Equations ........................................ 5
1.3.1 Faraday's Law ....................................... 5
1.3.2 Ampere's Law ........................................ 5
1.3.3 Gauss's Law for Electric Field and Charges .......... 7
1.3.4 Gauss's Law for Magnetic Field ...................... 7
1.4 Maxwell Equations in Dielectric Media ...................... 7
1.4.1 Maxwell Equations ................................... 7
1.4.2 Wave Equation ....................................... 9
1.4.3 Boundary Conditions ................................. 9
1.4.4 Reciprocity Theorems ................................ 9
1.5 Current Continuity ........................................ 10
1.6 Lossless ТЕМ Waves ........................................ 11
1.7 Maxwell's Equations in Time-Harmonic and Phasor Forms ..... 14
1.8 Plane Waves ............................................... 14
1.8.1 General Wave Equations ............................. 14
1.8.2 Time-Harmonic Wave Equation ........................ 16
Reference ................................................. 18
Chapter 2 Electrical Transmission Lines ....................... 19
2.1 Model of Time-Harmonic Waves on Transmission Lines ........ 19
2.1.1 Distributed Model of Transmission Lines ............ 19
2.1.2 Time-Harmonic Waves on Transmission Lines .......... 21
2.2 Terminated Transmission Lines ............................. 23
2.2.1 Terminated Line .................................... 23
2.2.2 Reflection Coefficient ............................. 24
2.2.3 Input Line Impedance ............................... 25
2.3 Smith Chart ............................................... 27
2.4 Impedance Matching ................................... 29
2.5 Equipment ............................................ 32
2.5.1 Apparatus ..................................... 32
2.5.2 Experimental Setup ............................ 33
2.5.3 Notes on the Slotted Lines .................... 33
2.5.4 Experiment .................................... 33
2.5.5 Time-Domain Reflectometry ..................... 35
2.6 Concluding Remarks ................................... 37
2.7 Problems ............................................. 38
2.7.1 Problem on TDR Operation on Transmission
and Reflection ................................ 38
2.7.2 Problem on Transmission Line .................. 39
2.7.3 Problem on Slotted Transmission Line
Experiment .................................... 40
2.7.4 Problems on Transmission Lines ................ 40
Reference ................................................. 45
Chapter 3 Antennae ............................................ 47
3.1 Introduction .............................................. 47
3.1.1 Differential Doublet and Dipole Antenna ............ 49
3.1.2 Far Field .......................................... 50
3.1.3 Near Field ......................................... 51
3.1.4 Linear Antenna Current Distribution ................ 51
3.2 Radiating Fields .......................................... 54
3.2.1 Radian Field of Hertzian Antenna ................... 56
3.2.2 Standing Wave Antenna: The Half-Wave Dipole
Antenna ............................................ 57
3.2.3 Monopole Antenna ................................... 58
3.2.4 Traveling Wave Antenna ............................. 60
3.2.5 Omnidirectional Antenna ............................ 61
3.2.6 Horn Waveguide Antenna ............................. 63
3.3 Antenna Figure of Merit ................................... 64
3.4 Experiment ................................................ 66
3.4.1 Background ......................................... 66
3.4.2 Measurement of the Monopole Antenna Admittance ..... 68
3.5 Concluding Remarks ........................................ 69
3.6 Appendix: Metallic Waveguide .............................. 69
3.6.1 Brief Concept ...................................... 69
3.6.2 Experiment on Waveguide ............................ 74
3.7 Problems .................................................. 76
3.7.1 Waveguide Measurements ............................. 76
3.7.2 Antenna Admittance ................................. 76
3.7.3 Waveguide .......................................... 76
References ................................................ 77
Chapter 4 Planar Optical Waveguides ........................... 79
4.1 Introduction .............................................. 79
4.2 Formation of Planar Single-Mode Waveguide Problems ........ 81
4.2.1 TE/TM Wave Equation ................................ 82
4.3 Approximate Analytical Methods of Solution ................ 87
4.3.1 Asymmetrical Waveguides ............................ 88
4.3.2 Symmetrical Waveguides ............................. 99
4.3.3 Concluding Remarks ................................ 121
4.4 Design and Simulations of Planar Optical Waveguides:
Experiments .............................................. 122
4.4.1 Introduction ...................................... 122
4.4.2 Theoretical Background ............................ 122
4.4.3 Simulation of Optical Fields and Propagation in
Slab Optical Waveguide Structures ................. 126
4.5 Appendix A: Exact Analysis of Clad Linear Optical
Waveguides ............................................... 129
4.5.1 Asymmetrical Clad Linear Profile .................. 129
4.5.2 Symmetrical Waveguide ............................. 132
4.6 Appendix B: WKB Method, Turning Points, and Connection
Formulae ................................................. 133
4.6.1 Introduction ...................................... 133
4.6.2 Derivation of the WKB Approximate Solutions ....... 133
4.6.3 Turning Point Corrections ......................... 136
4.6.4 Correction Formulae ............................... 142
4.6.5 Application of Correction Formulae ................ 144
4.7 Problems ................................................. 147
4.7.1 Problem 1 ......................................... 147
4.7.2 Problem 2 ......................................... 148
4.7.3 Problem 3 ......................................... 148
4.7.4 Problem 4 ......................................... 148
References ............................................... 149
Chapter 5 Three-Dimensional Optical Waveguides ............... 153
5.1 Introduction ............................................. 153
5.2 Marcatilli's Method ...................................... 155
5.2.1 Field and Modes Guided in Rectangular Optical
Waveguides ........................................ 156
5.2.2 Dispersion Characteristics ........................ 160
5.3 Effective Index Method ................................... 162
5.3.1 General Considerations ............................ 162
5.3.2 Pseudowaveguide ................................... 165
5.4 Finite Difference Numerical Techniques for 3D
Waveguides ............................................... 166
5.4.1 Nonuniform Grid Semivectorial Polarized Finite
Difference Method for Optical Waveguides with
Arbitrary Index Profile ........................... 167
5.4.2 Ti:LiNb03-Diffused Channel Waveguide .............. 176
5.5 Mode Modeling of Rib Waveguides .......................... 187
5.5.1 Choice of Grid Size ............................... 194
5.5.2 Numerical Results ................................. 195
5.5.3 Higher-Order Modes ................................ 196
5.6 Conclusions .............................................. 198
References ............................................... 200
Chapter 6 Optical Fibers: Single- and Few-Mode Structures
and Guiding Properties ........................................ 203
6.1 Optical Fibers: Circular Optical Waveguides .............. 203
6.1.1 General Aspects ................................... 203
6.1.2 Optical Fiber: General Properties ................. 204
6.1.3 Fundamental Mode of Weakly Guiding Fibers ......... 207
6.1.4 Equivalent Step Index Description ................. 221
6.2 Special Fibers ........................................... 225
6.3 Nonlinear Optical Effects ................................ 227
6.3.1 Nonlinear Self-Phase Modulation Effects ........... 228
6.3.2 Self-Phase Modulation ............................. 228
6.3.3 Cross-Phase Modulation ............................ 229
6.3.4 Stimulated Scattering Effects ..................... 230
6.4 Optical Fiber Manufacturing and Cabling .................. 234
6.5 Concluding Remarks ....................................... 238
6.6 Problems ................................................. 239
6.6.1 Problem 1 ......................................... 239
6.6.2 Problem 2 ......................................... 239
6.6.3 Problem 3 ......................................... 240
6.6.4 Problem 4 ......................................... 240
6.6.5 Problem 5 ......................................... 240
6.6.6 Problem 6 ......................................... 240
6.6.7 Problem 7 ......................................... 241
6.6.8 Problem 8 ......................................... 241
6.6.9 Problem 9 ......................................... 241
6.6.10 Problem 10 ........................................ 242
Appendix 6.1: Technical Specification of Corning
Single-Mode Optical Fibers ............................... 243
References ............................................... 248
Chapter 7 Optical Fiber Operational Parameters ............... 249
7.1 Introductory Remarks ..................................... 249
7.2 Signal Attenuation in Optical Fibers ..................... 250
7.2.1 Intrinsic or Material Attenuation ................. 250
7.2.2 Absorption ........................................ 250
7.2.3 Rayleigh Scattering ............................... 251
7.2.4 Waveguide Loss .................................... 251
7.2.5 Bending Loss ...................................... 251
7.2.6 Microbending Loss ................................. 252
7.2.7 Joint or Splice Loss .............................. 252
7.2.8 Attenuation Coefficient ........................... 253
7.3 Signal Distortion in Optical Fibers ...................... 253
7.3.1 Basics on Group Velocity .......................... 253
7.3.2 Group Velocity Dispersion ......................... 256
7.3.3 Transmission Bit Rate and the Dispersion Factor ... 266
7.3.4 Effects of Mode Hopping ........................... 267
7.4 Advanced Optical Fibers: Dispersion-Shifted,
-Flattened, and -Compensated Optical Fibers .............. 268
7.5 Propagation of Optical Signals in Optical Fiber
Transmission Line: Split-Step Fourier Method ............. 268
7.5.1 Symmetrical Split-Step Fourier Method (SSFM) ...... 269
7.5.2 MATLAB® Program and MATLAB Simulink® Models of
the SSFM .......................................... 270
7.5.3 Remarks ........................................... 277
Appendix 7.1: Program Listings for Design of Standard
Single-Mode Fiber ................................. 278
Appendix 7.2: Program Listings of the Design of Non-
Zero-Dispersion-Shifted Fiber ..................... 280
7.6 Problems ................................................. 281
7.6.1 Problem 1 ......................................... 283
7.6.2 Problem 2 ......................................... 283
7.6.3 Problem 3 ......................................... 283
7.6.4 Problem 4 ......................................... 283
7.6.5 Problem 5 ......................................... 284
7.6.6 Problem 6 ......................................... 284
7.6.7 Problem 7 ......................................... 284
7.6.8 Problem 8 ......................................... 285
7.6.9 Problem 9 ......................................... 285
7.6.10 Problem 10 ........................................ 285
7.6.11 Problem 11 ........................................ 285
7.6.12 Problem 12 ........................................ 286
7.6.13 Problem 13 Fiber Design Mini-Project .............. 286
References ............................................... 291
Chapter 8 Guided Wave Optical Transmission Lines: Transfer
Functions ..................................................... 293
8.1 Transfer Function of Single-Mode Fibers .................. 293
8.1.1 Linear Transfer Function .......................... 293
8.1.2 Single-Mode Optical Fiber Transfer Function:
Simplified Linear and Nonlinear Operating
Regions ........................................... 298
8.1.3 Nonlinear Fiber Transfer Function ................. 306
8.2 Fiber Nonlinearity ....................................... 309
8.2.1 SPM and XPM Effects ............................... 309
8.2.2 Modulation Instability ............................ 310
8.2.3 Effects of Mode Hopping ........................... 311
8.3 Nonlinear Fiber Transfer Functions and Application in
Compensations ............................................ 311
8.3.1 Cascades of Linear and Nonlinear Transfer
Functions in Time and Frequency Domains ........... 313
8.3.2 Volterra Nonli near Transfer Function and
Electronic Compensation ........................... 315
8.3.3 SPM and Intrachannel Nonlinear Effects ............ 316
8.4 Concluding Remarks ....................................... 322
Appendix 8.1: Program Listings of Split-Step Fourier
Method (SSFM) with Nonlinear SPM Effect and
Raman Gain Distribution ........................... 322
Appendix 8.2: Program Listings of an Initialization
File .............................................. 325
References ............................................... 328
Chapter 9 Fourier Guided Wave Optics ......................... 331
Abbreviations ............................................ 331
9.1 Introduction ............................................. 331
9.2 Background: Fourier Transformation ....................... 333
9.2.1 Basic Transform ................................... 333
9.2.2 Optical Circuitry Implementation .................. 334
9.2.3 Optical DFT by Mach-Zehnder Delay
Interferometers (MZDIs) ........................... 339
9.2.4 Fourier Transform Signal Flow and Optical
Implementation .................................... 340
9.2.5 AWG Structure and Characteristics ................. 345
9.3 Guided Wave Wavelet Transformer .......................... 349
9.3.1 Wavelet Transformation and Wavelet Packets ........ 349
9.3.2 Fiber Optic Synthesis ............................. 352
9.3.3 Synthesis Using Multimode Interference Structure .. 355
9.3.4 Remarks ........................................... 357
9.4 Optical Orthogonal Frequency Division Multiplexing ....... 359
9.5 Nyquist Orthogonal Channels for Tbps Optical
Transmission Systems ..................................... 360
9.6 Design of Optical Waveguides for Optical FFT and lFFT .... 363
9 7 Concluding Remarks ....................................... 366
Appendix 9.1 ............................................. 368
References ............................................... 369
Appendix: Vector Analysis ..................................... 371
Index ......................................................... 379
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