Okamoto, Katsunari

Fundamentals of Optical Waveguides/ Katsunari Okamoto - 2nd ed. - Amsterdam: Elsevier, 2006. - xvi, 561p.

1 Wave Theory of Optical Waveguides 1
1.1 Waveguide Structure 1
1.2 Formation of Guided Modes 2
1.3 Maxwell's Equations 7
1.4 Propagating Power 10
2 Planar Optical Waveguides 13
2.1 Slab Waveguides 13
2.1.1 Derivation of Basic Equations 13
2.1.2 Dispersion Equations for TE and TM Modes 16
2.1.3 Computation of Propagation Constant 19
2.1.4 Electric Field Distribution 22
2.1.5 Dispersion Equation for TM Mode 25
2.2 Rectangular Waveguides 27
2.2.1 Basic Equations 27
2.2.2 Dispersion Equations for and Modes 29
2.2.3 Kumar's Method 31
2.2.4 Effective Index Method 37
2.3 Radiation Field from Waveguide 41
2.3.1 Fresnel and Fraunhofer Regions 41
2.3.2 Radiation Pattern of Gaussian Beam 43
2.4 Multimode Interference(MMI)Device 46
3 Optical Fibers 57
3.1 Basic Equations 57
3.2 Wave Theory of Step-index Fibers 58
3.2.1 TE Modes 58
3.2.2 TM Modes 62
3.2.3 Hybrid Modes 63
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Contents
3.3 Optical Power Carried by Each Mode 67
3.3.1 TE Modes 68
3.3.2 TM Modes 69
3.3.3 Hybrid Modes 70
3.4 Linearly Polarized(LP) Modes 71
3.4.1 Unified Dispersion Equation for LP Modes 71
3.4.2 Dispersion Characteristics of LP Modes 75
3.4.3 Propagating Power of LP Modes 78
3.5 Fundamental HE,, Mode 80
3.6 Dispersion Characteristics of Step-index Fibers 83
3.6.1 Signal Distortion Caused by Group Velocity Dispersion 83
3.6.2 Mechanisms Causing Dispersion 88
3.6.3 Derivation of Delay-time Formula 92
3.6.4 Chromatic Dispersion 96
3.6.5 Zero-dispersion Wavelength 102
3.7 Wave Theory of Graded-index Fibers 103
3.7.1 Basic Equations and Mode Concepts in
Graded-index Fibers 103
3.7.2 Analysis of Graded-index Fibers by the WKB Method 108
3.7.3 Dispersion Characteristics of Graded-index Fibers 113
3.8 Relation Between Di.spersion and Transmission Capacity 117
3.8.1 Multimode Fiber 119
3.8.2 Single-mode Fiber 119
3.9 Birefringent Optical Fibers 120
3.9.1 Two Orthogonally-polarized Modes in Nominally
Single-mode Fibers 120
3.9.2 Derivation of Basic Equations 123
3.9.3 Elliptical-core Fibers 126
3.9.4 Modal Birefringence 127
3.9.5 Polarization Mode Dispersion 130
3.10 Dispersion Control in Single-Mode Optical Fibers 134
3.10.1 Dispersion Compensating Fibers 134
3.10.2 Dispersion-shifted Fibers 135
3.10.3 Dispersion Flattened Fibers 139
3.10.4 Broadly Dispersion Compensating Fibers 142
3.11 Photonic Crystal Fibers 144
Coupled Mode Theory 159
4.1 Derivation of Coupled Mode Equations Based
on Perturbation Theory 159
4.2 Codirectional Couplers 166Contents
IX
4.3 Contradirectional Coupling in Comigaied Waveguides 169
4.3.1 Transmission and Reflection Characteristics in
Uniform Gratings 169
4.3.2 Phase-shift Grating I75
4.4 Derivation of Coupling Coefficients I77
4.4.1 Coupling Coefficients for Slab Waveguides 177
4.4.2 Coupling Coefficients for Rectangular Waveguides 178
4.4.3 Derivation of Coupling Coefficients Based on Mode
Interference 1go
4.4.4 Coupling Coefficients for Optical Fibers 183
4.4.5 Coupling Coefficients for Corrugated Waveguides 187
4.5 Optical Waveguide Devices using Directional Couplers 195
4.5.1 Mach-Zehnder Interferometers I95
4.5.2 Ring Resonators I97
4.5.3 Bistable Devices 200
4.6 Fiber Bragg Gratings 203
5 Nonlinear Optical Effects in Optical Fibers 209
5.1 Figure of Merit for Nonlinear Effects 209
5.2 Optical Kerr Effect 211
5.2.1 Self-phase Modulation 211
5.2.2 Nonlinear Schrodinger Equation 213
5.3 Optical Solitons 217
5.3.1 Fundamental and Higher-Order Solitons 217
5.3.2 Fiber Loss Compensation by Optical Amplification 223
5.3.3 Modulational Instability 225
5.3.4 Dark Solitons 229
5.4 Optical Pulse Compression 230
5.5 Light Scattering in Isotropic Media 233
5.5.1 Vibration of One-Dimensional Lattice 233
5.5.2 Selection Rules for Light Scattering by Phonons 236
5.6 Stimulated Raman Scattering 240
5.7 Stimulated Brillouin Scattering 243
5.8 Second-Harmonic Generation 246
5.9 Erbium-doped Fiber Amplifier 250
5.10 Four-wave Mixing in Optical Fiber 252
5 Finite Element Method 261
6.1 Introduction 261
6.2 Finite Element Method Analysis of Slab Waveguides 262
6.2.1 Variational Formulation 262
6.2.2 Discretization of the Functional 264Cotttciits
6.2.3 Dispersion Equation Based on the Stationar>' Condition 266
6.2.4 Dispersion Characteristics of Graded-index
Slab Waveguides 269
6.3 Finite Element Method Analysis of Optical Fibers 273
6.3.1 Variational Formulation 273
6.3.2 Discretization of the Functional 275
6.3.3 Dispersion Equation Ba.sed on the Stationary Condition 275
6.3.4 Single-mode Conditions of Graded-index Fibers 277
6.3.5 Variational Expression for the Delay Time 279
6.4 Finite Element Method Analysis of Rectangular Waveguides 284
6.4.1 Vector and Scalar Analyses 284
6.4.2 Variational Formulation and Discretization into Finite
Number of Elements 284
6.4.3 Dispersion Equation Based on the Stationary' Condition 289
6.5 Stress Analysis of Optical Waveguides 298
6.5.1 Energy Principle 298
6.5.2 Plane Strain and Plane Stress 301
6.5.3 Basic Equations for Di.splacement,
Strain and Stress 301
6.5.4 Formulation of the Total Potential Energy 303
6.5.5 Solution of the Problem by the Stationary Condition 308
6.5.6 Combination of Finite-Element Waveguide and
Stress Analysis 309
6.6 Semi-Vector FEM Analysis of High-Index Contrast
Waveguides 315
6.6.1 E-field Formulation 316
6.6.2 H-field Formulation 317
6.6.3 Steady State Mode Analysis 318
Beam Propagation Method 329
7.1 Basic Equations for Beam Propagation Method Based on the EFT 329
7.1.1 Wave Propagation in Optical Waveguides 329
7.1.2 Pulse Propagation in Optical Fibers 331
7.2 FFTBPM Analysis of Optical Wave Propagation 332
7.2.1 Formal Solution Using Operators 332
7.2.2 Concrete Numerical Procedures Using Split-step
Fourier Algorithm 334
7.3 FFTBPM Analysis of Optical Pulse Propagation 336
7.4 Di.screte Fourier Transform 339
7.5 Fast Fourier Transform 346
7.6 Formulation of Numerical Procedures Using Discrete
Fourier Transform 348Contents
XI
7.7 Application.s of FFTBPM 35O
7.8 Finite Difference Method Analysi.s of Planar Optical
Waveguides 354
7.8.1 Derivation of Basic Equations 364
7.8.2 Tran.sparent Boundary Conditions 366
7.8.3 Solution of Tri-diagonal Equations 368
7.9 FDMBPM Analysis of Rectangular Waveguides 370
7.10 FDMBPM Analysis of Optical Pulse Propagation 373
7.11 Semi-Vector FDMBPM Analysis of High-Index
Contrast Waveguides 377
7.11.1 Quasi-TE Modes 373
7.11.2 Quasi-TM Modes 3gO
7.11.3 Polarization Splitter Using Silicon-on-Insulator
(SO!)Waveguide 382
7.12 Finite Difference Time Domain(FDTD)Method 383
8 Staircase Concatenation Method 399
8.1 Staircase Approximation of Waveguide Boundary 399
8.2 Amplitudes and Phases Between the Connecting Interfaces 403
8.3 Wavelength Division Multiplexing Couplers 408
8.4 Wavelength-flattened Couplers 408
9 Planar Lightwave Circuits 417
9.1 Waveguide Fabrication 41g
9.2 N X N Star Coupler 419
9.3 Arrayed-waveguide Grating 423
9.3.1 Principle of Operation and Fundamental
Characteristics 423
9.3.2 Analytical Treatment of AWG Demultiplexing
Properties 42g
9.3.3 Waveguide Layout of AWG 434
9.3.4 Gaussian Spectral Response AWG 436
9.3.5 Polarization Dependence of Pass Wavelength 439
9.3.6 Vernier Technique for the Center Wavelength
Adjustment 442
9.4 Crosstalk and Dispersion^Characteristics of AWGs 443
9.4.1 Crosstalk of AWGs 443
9.4.2 Dispersion Characteristics of AWGs 448
9.5 Functional AWGs 453
9.5.1 Flat Spectral Response AWG 458
9.5.2 Loss Reduction in AWG 473
9.5.3 Unequal Channel Spacing AWG 476Xll
Contents
9.5.4 Variable Bandwidth AWG 478
9.5.5 Unilorm-loss and Cyclic-frequency(ULCF)AWG 479
9.5.6 Alhermal (Temperature Insensitive) AWG 484
9.5.7 Multiwaveiength Simultaneous Monitoring Device
Using AWG 490
9.5.8 Pha.se Error Compensation of AWG 495
9.5.9 Tandem AWG Configuration 499
9.6 Reconfigurabie Optical Add/Drop Multiplexer(ROADM) 500
9.7 N X N Matrix Switches 505
9.8 Lattice-form Programmable Dispersion Equalizers 508
9.9 Temporal Pulse Waveform Shapers 511
9.10 Coherent Optical Transversal Filters 515
9.1 1 Optical Label Recognition Circuit for Photonic Label
Switch Router
9.12 Polarization Mode Dispersion Compensator 522
9.13 Hybrid Integration Technology Using PLC Platforms 524
10 Several Important Theorems and Formulas 535
10.1 Gauss's Theorem ^55
10.2 Green's Theorem ^59
10.3 Stokes' Theorem ^40
10.4 Integral Theorem of Helmholtz and Kirchhoff 545
10.5 Fre.snel-Kirchhoff Diffraction Formula 547
10.6 Formulas for Vector Analysis 551
10.7 Formulas in Cylindrical and Spherical Coordinates 553
10.7.1 Cylindrical Coordinates 553
10.7.2 Spherical Coordinates 554

ISBN: 9780125250962

Dewey Class. No.: 621.38275 / OKA/F