布莱克等编著的《光波导模式——偏振、耦合与对称（影印版）》是一本利用群论分析光学波导模式结构的专著。全书共7章。第1章回顾了光学波导的一般概念，对群论在光学波导模式结构理论分析中的作用做了简单介绍。在第2章中，介绍了各向异性媒质构成的光学波导的电磁理论，并针对纵向不变的光纤结构，给出了弱导近似下的标量波动方程和全矢量波动方程及其各阶微扰形式。第3章针对各向同性媒质构成的圆对称光纤，利用群论分别分析了由弱导近似下的波动方程、零阶微扰形式的矢量方程和全矢量方程求解出的光纤模式结构。第4章讨论了光学波导结构对称性破缺情况下波导模式的群论分析方法和模式结构特点。第5章讨论了波导中的各种双折射形式及其与波导对称性的关系。第6章介绍了多波导组合结构及其分立的旋转对称分析。第7章是全书的总结，讨论了非线性波导、光子晶体和光子准晶、光子晶体光纤和光纤光栅等复杂波导结构的特点和模式分析结构要点。书的最后给出了书中应用的群论基本概念和结论。

布莱克等编著的《光波导模式——偏振、耦合与对称（影印版）》是一本关于波导模式对称性分析的学术专著。在简要介绍传统导波光学内容的基础上，重点以光波导弱导微扰理论和群论作为理论分析手段，对单模和少模光波导，特别是单芯和多芯光纤的波导模式结构和分类进行了系统的介绍，并讨论了模式对称性分析方法对周期结构、非线性波导和光子晶体等复杂波导结构的应用。

《光波导模式——偏振、耦合与对称（影印版）》的理论描述简洁，适合于具有较好的电磁理论基础，并对导波光学理论和群论有一定了解的科研人员阅读参考。

PREFACE xi

ACKNOWLEDGMENTS  xiii

Chapter 1 Introduction 1

 1.1 Modes 1

 1.2 Polarization Dependence of Wave Propagation 3

 1.3 Weak-Guidance Approach to Vector Modes 4

 1.4 Group Theory for Waveguides 5

 1.5 Optical Waveguide Modes: A Simple Introduction

1.5.1 Ray Optics Description 7

1.5.2 Wave Optics Description 9

1.5.3 Adiabatic Transitions and Coupling 14

 1.6 Outline and Major Results 16

Chapter 2 Electromagnetic Theory for Anisotropic Media and Weak Guidance for Longitudinally Invariant Fibers 19

 2.1 Electrically Anisotropic (and Isotropic) Media 19

 2.2 General Wave Equations for Electrically Anisotropic(and Isotropic) Media 22

 2.3 Translational Invariance and Modes 24

 2.4 Wave Equations for Longitudinally Invariant Media 25

2.4.1 General Anisotropic Media 25

2.4.2 Anisotropic Media with z-Aligned Principal Axis 25

2.4.3 "Diagonal" Anisotropies 26

 2.5 Transverse Field Vector Wave Equation for Isotropic Media 27

 2.6 Scalar Wave Equation 27

 2.7 Weak-Guidance Expansion for Isotropic Media 28

 2.8 Polarization-Dependent Mode Splitting and Field Corrections 30

2.8.1 First-Order Eigenvalue Correction 30

2.8.2 First-Order Field and Higher-Order Corrections 31

2.8.3 Simplifications Due to Symmetry 31

 2.9 Reciprocity Relations for Isotropic Media 32

 2.10 Physical Properties of Waveguide Modes 32

Chapter 3 Circular Isotropic Longitudinally Invariant Fibers 35

 3.1 Summary of Modal Representations 35

3.1.1 Scalar and Pseudo-Vector Mode Sets 36

3.1.2 True Weak-Guidance Vector Mode Set Constructions Using Pseudo-Modes 36

3.1.3 Pictorial Representation and Notation Details 36

 3.2 Symmetry Concepts for Circular Fibers: Scalar Mode Fields and Degeneracies 42

3.2.1 Geometrical Symmetry: C 46

3.2.2 Scalar Wave Equation Symmetry: CS 46

3.2.3 Scalar Modes: Basis Functions of Irreps of CSv 47

3.2.4 Symmetry Tutorial: Scalar Mode Transformations 48

 3.3 Vector Mode Field Construction and Degeneracies via Symmetry 50

3.3.1 Vector Field 51

3.3.2 Polarization Vector Symmetry Group: C 52

3.3.3 Zeroth-Order Vector Wave Equation Symmetry:Cs c 52

3.3.4 Pseudo-Vector Modes: Basis Functions of Irreps of CSv Cv 54

3.3.5 Full Vector Wave Equation Symmetry:CSv Cv CLv 55

3.3.6 True Vector Modes: Qualitative Features via CSv CPvD CIv 56

3.3.7 True Vector Modes via Pseudo-Modes: Basis Functions ofCSv Cv CIv 58

 3.4 Polarization-Dependent Level-Splitting 59

3.4.1 First-Order Eigenvalue Corrections 59

3.4.2 Radial Profile-Dependent Polarization Splitting 60

3.4.3 Special Degeneracies and Shifts for Particular Radial Dependence of Profile 63

3.4.4 Physical Effects 64

Chapter 4 Azimuthal Symmetry Breaking 67

 4.1 Principles 67

4.1.1 Branching Rules 67

4.1.2 Anticrossing and Mode Form Transitions 68

 4.2 C2v Symmetry: Elliptical (or Rectangular) Guides:Illustration of Method 68

4.2.1 Wave Equation Symmetries and Mode-Irrep Association 68

4.2.2 Mode Splittings 69

4.2.3 Vector Mode Form Transformations for Competing Perturbations 72

 4.3 CBv Symmetry: Equilateral Triangular Deformations 72

 4.4 C4v Symmetry: Square Deformations 75

4.4.1 Irreps and Branching Rules 75

4.4.2 Mode Splitting and Transition Consequences 75

4.4.3 Square Fiber Modes and Extra Degeneracies 77

 4.5 Csv Symmetry: Pentagonal Deformations 77

4.5.1 Irreps and Branching Rules 77

4.5.2 Mode Splitting and Transition Consequences 78

 4.6 C6 Symmetry: Hexagonal Deformations 80

4.6.1 Irreps and Branching Rules 80

4.6.2 Mode Splitting and Transition Consequences 80

 4.7 Level Splitting Quantification and Field Corrections 82

Chapter 5 Birefringence: Linear, Radial, and Circular 83

 5.1 Linear Birefringence 83

5.1.1 Wave Equations: Longitudinal Invariance 83

5.1.2 Mode Transitions: Circular Symmetry 85

5.1.3 Field Component Coupling 87

5.1.4 Splitting by xy of lsotropic Fiber Vector Modes Dominated by a-Splitting 88

5.1.5 Correspondence between Isotropic "True" Modes and Birefringent LP Modes 89

 5.2 Radial Birefringence 89

5.2.1 Wave Equations: Longitudinal Invariance 89

5.2.2 Mode Transitions for Circular Symmetry 91

 5.3 Circular Birefringence 91

5.3.1 Wave Equation 93

5.3.2 Symmetry and Mode Splittings 93

Chapter 6 Multicore Fibers and Multifiber Couplers 97

 6.1 Multilightguide Structures with Discrete Rotational Symmetry 97

6.1.1 Global Cnv Rotation-Reflection Symmetric Structures:Isotropic Materials 98

6.1.2 Global Cnv Symmetry: Material and Form Birefringence 99

6.1.3 Global Cn Symmetric Structures 99

 6.2 General Supermode Symmetry Analysis 101

6.2.1 Propagation Constant Degeneracies 101

6.2.2 Basis Functions for General Field Construction 104

 6.3 Scalar Supermode Fields 107

6.3.1 Combinations of Fundamental Individual Core Modes 107

6.3.2 Combinations of Other Nondegenerate Individual Core Modes 108

6.3.3 Combinations of Degenerate Individual Core Modes 108

 6.4 Vector Supermode Fields 109

6.4.1 Two Construction Methods 109

6.4.2 Isotropic Cores: Fundamental Mode Combination Supermodes 113

6.4.3 Isotropic Cores: Higher-Order Mode Combination Supermodes 116

6.4.4 Anisotropic Cores: Discrete Global Radial Birefringence 119

6.4.5 Other Anisotropic Structures: Global Linear and Circular Birefringence 121

 6.5 General Numerical Solutions and Field Approximation Improvements 121

6.5.1 SALCs as Basis Functions in General Expansion 121

6.5.2 Variational Approach 122

6.5.3 Approximate SALC Expansions 122

6.5.4 SALC = Supermode Field with Numerical Evaluation of Sector Field Function 123

6.5.5 Harmonic Expansions for Step Profile Cores 124

6.5.6 Example of Physical Interpretation of Harmonic Expansion for the Supermodes 125

6.5.7 Modal Expansions 126

6.5.8 Relation of Modal and Harmonic Expansions to SALC Expansions 126

6.5.9 Finite Claddings and Cladding Modes 127

 6.6 Propagation Constant Splitting: Quantification 127

6.6.1 Scalar Supermode Propagation Constant Corrections 127

6.6.2 Vector Supermode Propagation Constant Corrections 130

 6.7 Power Transfer Characteristics 131

6.7.1 Scalar Supermode Beating 131

6.7.2 Polarization Rotation 133

Chapter 7 Conclusions and Extensions 137

 7.1 Summary 137

 7.2 Periodic Waveguides 138

 7.3 Symmetry Analysis of Nonlinear Waveguides and Self-Guided Waves 139

 7.4 Developments in the 1990s and Early Twenty-First Century 140

 7.5 Photonic Computer-Aided Design (CAD) Software 141

 7.6 Photonic Crystals and Quasi Crystals 142

 7.7 Microstructured, Photonic Crystal, or Holey Optical Fibers 143

 7.8 Fiber Bragg Gratings 144

7.8.1 General FBGs for Fiber Mode Conversion 144

7.8.2 (Short-Period) Reflection Gratings for Single-Mode Fibers 145

7.8.3 (Long-Period) Mode Conversion Transmission Gratings 146

7.8.4 Example: LPol--LPn Mode-Converting Transmission FBGs for Two-Mode Fibers (TMFs) 146

7.8.5 Example: LPol(--LPo2 Mode-Converting Transmission FBGs 148

Appendix Group Representation Theory 151

A.1 Preliminaries: Notation, Groups, and Matrix Representations

of Them 152

A.1.1 Induced Transformations on Scalar Functions 153

A.1.2 Eigenvalue Problems: Invariance and Degeneracies 154

A.1.3 Group Representations 155

A.1.4 Matrix Irreducible Matrix Representations 155

A.1.5 Irrep Basis Functions 155

A.1.6 Notation Conventions 155

 A.2 Rotation-Reflection Groups 156

A.2.1 Symmetry Operations and Group Definitions 156

A.2.2 Irreps for C and Cnv 156

A.2.3 Irrep Notation 160

 A.3 Reducible Representations and Branching Rule

Coefficients via Characters 160

A.3.1 Example Branching Rule for Cv D C2v 161

A.3.2 Branching Rule Coefficients via Characters 161

 A.4 Clebsch-Gordan Coefficient for Changing Basis 164

 A.5 Vector Field Transformation 165

REFERENCES 167

INDEX 179