光波导模式 : 偏振、耦合与对称

PREFACE xi

ACKNOWLEDGMENTS xiii

Chapter 1 Introduction

1.1 Modes

1.2 Polarization Dependence of Wave Propagation

1.3 Weak-Guidance Approach to Vector Modes

1.4 Group Theory for Waveguides

1.5 Optical Waveguide Modes: A Simple Introduction

1.5.1 Ray Optics Description

1.5.2 Wave Optics Description

1.5.3 Adiabatic Tra itio and Coupling

1.6 Outline and Major Results

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

2.1 Electrically Anisotropic （and Isotropic） Media

2.2 General Wave Equatio for Electrically Anisotropic（and Isotropic） Media

2.3 Tra lational Invariance and Modes

2.4 Wave Equatio for Longitudinally Invariant Media

2.4.1 General Anisotropic Media

2.4.2 Anisotropic Media with z-Aligned Principal Axis

2.4.3 "Diagonal" Anisotropies

2.5 Tra ve e Field Vector Wave Equation for Isotropic Media

2.6 Scalar Wave Equation

2.7 Weak-Guidance Expa ion for Isotropic Media

2.8 Polarization-Dependent Mode Splitting and Field Correctio

2.8.1 Fi t-Order Eigenvalue Correction

2.8.2 Fi t-Order Field and Higher-Order Correctio

2.8.3 Simplificatio Due to Symmetry

2.9 Reciprocity Relatio for Isotropic Media

2.10 Physical Properties of Waveguide Modes

Chapter 3 Circular Isotropic Longitudinally Invariant Fibe

3.1 Summary of Modal Representatio

3.1.1 Scalar and Pseudo-Vector Mode Sets

3.1.2 True Weak-Guidance Vector Mode Set Co tructio Using Pseudo-Modes

3.1.3 Pictorial Representation and Notation Details

3.2 Symmetry Concepts for Circular Fibe : Scalar Mode Fields and Degeneracies

3.2.1 Geometrical Symmetry: C

3.2.2 Scalar Wave Equation Symmetry: CS

3.2.3 Scalar Modes: Basis Functio of Irreps of CSv

3.2.4 Symmetry Tutorial: Scalar Mode Tra formatio

3.3 Vector Mode Field Co truction and Degeneracies via Symmetry

3.3.1 Vector Field

3.3.2 Polarization Vector Symmetry Group: C

3.3.3 Zeroth-Order Vector Wave Equation Symmetry:Cs c

3.3.4 Pseudo-Vector Modes: Basis Functio of Irreps of CSv Cv

3.3.5 Full Vector Wave Equation Symmetry:CSv Cv CLv

3.3.6 True Vector Modes: Qualitative Features via CSv CPvD CIv

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

3.4 Polarization-Dependent Level-Splitting

3.4.1 Fi t-Order Eigenvalue Correctio

3.4.2 Radial Profile-Dependent Polarization Splitting

3.4.3 Special Degeneracies and Shifts for Particular Radial Dependence of Profile

3.4.4 Physical Effects

Chapter 4 Azimuthal Symmetry Breaking

4.1 Principles

4.1.1 Branching Rules

4.1.2 Anticrossing and Mode Form Tra itio

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

4.2.1 Wave Equation Symmetries and Mode-Irrep Association

4.2.2 Mode Splittings

4.2.3 Vector Mode Form Tra formatio for Competing Perturbatio

4.3 CBv Symmetry: Equilateral Triangular Deformatio

4.4 C4v Symmetry: Square Deformatio

4.4.1 Irreps and Branching Rules

4.4.2 Mode Splitting and Tra ition Co equences

4.4.3 Square Fiber Modes and Extra Degeneracies

4.5 Csv Symmetry: Pentagonal Deformatio

4.5.1 Irreps and Branching Rules

4.5.2 Mode Splitting and Tra ition Co equences

4.6 C6 Symmetry: Hexagonal Deformatio

4.6.1 Irreps and Branching Rules

4.6.2 Mode Splitting and Tra ition Co equences

4.7 Level Splitting Quantification and Field Correctio

Chapter 5 Birefringence: Linear, Radial, and Circular

5.1 Linear Birefringence

5.1.1 Wave Equatio : Longitudinal Invariance

5.1.2 Mode Tra itio : Circular Symmetry

5.1.3 Field Component Coupling

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

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

5.2 Radial Birefringence

5.2.1 Wave Equatio : Longitudinal Invariance

5.2.2 Mode Tra itio for Circular Symmetry

5.3 Circular Birefringence

5.3.1 Wave Equation

5.3.2 Symmetry and Mode Splittings

Chapter 6 Multicore Fibe and Multifiber Couple

6.1 Multilightguide Structures with Discrete Rotational Symmetry

6.1.1 Global Cnv Rotation-Reflection Symmetric Structures:Isotropic Materials

6.1.2 Global Cnv Symmetry: Material and Form Birefringence

6.1.3 Global Cn Symmetric Structures

6.2 General Supermode Symmetry Analysis

6.2.1 Propagation Co tant Degeneracies

6.2.2 Basis Functio for General Field Co truction

6.3 Scalar Supermode Fields

6.3.1 Combinatio of Fundamental Individual Core Modes

6.3.2 Combinatio of Other Nondegenerate Individual Core Modes

6.3.3 Combinatio of Degenerate Individual Core Modes

6.4 Vector Supermode Fields

6.4.1 Two Co truction Methods

6.4.2 Isotropic Cores: Fundamental Mode Combination Supermodes

6.4.3 Isotropic Cores: Higher-Order Mode Combination Supermodes

6.4.4 Anisotropic Cores: Discrete Global Radial Birefringence

6.4.5 Other Anisotropic Structures: Global Linear and Circular Birefringence

6.5 General Numerical Solutio and Field Approximation Improvements

6.5.1 SALCs as Basis Functio in General Expa ion

6.5.2 Variational Approach

6.5.3 Approximate SALC Expa io

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

6.5.5 Harmonic Expa io for Step Profile Cores

6.5.6 Example of Physical Interpretation of Harmonic Expa ion for the Supermodes

6.5.7 Modal Expa io

6.5.8 Relation of Modal and Harmonic Expa io to SALC Expa io

6.5.9 Finite Claddings and Cladding Modes

6.6 Propagation Co tant Splitting: Quantification

6.6.1 Scalar Supermode Propagation Co tant Correctio

6.6.2 Vector Supermode Propagation Co tant Correctio

6.7 Power Tra fer Characteristics

6.7.1 Scalar Supermode Beating

6.7.2 Polarization Rotation

Chapter 7 Conclusio and Exte io

7.1 Summary

7.2 Periodic Waveguides

7.3 Symmetry Analysis of Nonlinear Waveguides and Self-Guided Waves

7.4 Developments in the 1990s and Early Twenty-Fi t Century

7.5 Photonic Computer-Aided Design （CAD） Software

7.6 Photonic Crystals and Quasi Crystals

7.7 Microstructured, Photonic Crystal, or Holey Optical Fibe

7.8 Fiber Bragg Gratings

7.8.1 General FBGs for Fiber Mode Conve ion

7.8.2 （Short-Period） Reflection Gratings for Single-Mode Fibe

7.8.3 （Long-Period） Mode Conve ion Tra mission Gratings

7.8.4 Example: LPol--LPn Mode-Converting Tra mission FBGs for Two-Mode Fibe （TMFs）

7.8.5 Example: LPol（--LPo2 Mode-Converting Tra mission FBGs

Appendix Group Representation Theory

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

of Them

A.1.1 Induced Tra formatio on Scalar Functio

A.1.2 Eigenvalue Problems: Invariance and Degeneracies

A.1.3 Group Representatio

A.1.4 Matrix Irreducible Matrix Representatio

A.1.5 Irrep Basis Functio

A.1.6 Notation Conventio

A.2 Rotation-Reflection Groups

A.2.1 Symmetry Operatio and Group Definitio

A.2.2 Irreps for C and Cnv

A.2.3 Irrep Notation

A.3 Reducible Representatio and Branching Rule

Coefficients via Characte

A.3.1 Example Branching Rule for Cv D C2v

A.3.2 Branching Rule Coefficients via Characte

A.4 Clebsch-Gordan Coefficient for Changing Basis

A.5 Vector Field Tra formation

REFERENCES

INDEX

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