光波導(dǎo)模式

內(nèi)容概要

光波導(dǎo)模式——偏振、耦合與對稱（英文版）是一本關(guān)于波導(dǎo)模式對稱性分析的學(xué)術(shù)專著。在簡要介紹傳統(tǒng)導(dǎo)波光學(xué)內(nèi)容的基礎(chǔ)上，重點(diǎn)以光波導(dǎo)弱導(dǎo)微擾理論和群論作為理論分析手段，對單模和少模光波導(dǎo)，特別是單芯和多芯光纖的波導(dǎo)模式結(jié)構(gòu)和分類進(jìn)行了系統(tǒng)的介紹，并討論了模式對稱性分析方法對周期結(jié)構(gòu)、非線性波導(dǎo)和光子晶體等復(fù)雜波導(dǎo)結(jié)構(gòu)的應(yīng)用。
光波導(dǎo)模式——偏振、耦合與對稱（英文版）的理論描述簡潔，適合于具有較好的電磁理論基礎(chǔ)，并對導(dǎo)波光學(xué)理論和群論有一定了解的科研人員閱讀參考。

作者簡介

Richard J. Black博士是光波導(dǎo)模式、光纖傳感技術(shù)、結(jié)構(gòu)健康監(jiān)測領(lǐng)域的權(quán)威專家。他在光電子學(xué)方面擁有多年的學(xué)術(shù)界和工業(yè)界經(jīng)驗(yàn)，合作出版了250多種出版物和官方技術(shù)報(bào)告。他是OSA和ASM International的終身會(huì)員、IEEE高級(jí)會(huì)員，同時(shí)還是多家技術(shù)公司的創(chuàng)始人和首席科學(xué)家。
Langis Gagnon博士是蒙特利爾計(jì)算技術(shù)研究中心（CRIM）視覺與成像方向的首席研究員和團(tuán)隊(duì)負(fù)責(zé)人，同時(shí)也是拉瓦爾大學(xué)計(jì)算機(jī)與電氣工程學(xué)院的兼職教授。他在光學(xué)、圖像處理、模式識(shí)別、基于數(shù)學(xué)的非線性光學(xué)建模等方面已發(fā)表150多篇論文。他是SPIE、ACM、IEEE、AIA 和IASTED的會(huì)員。

書籍目錄

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 Transitions and Coupling
1.6 Outline and Major Results
Chapter 2 Electromagnetic Theory for Anisotropic Media and Weak
Guidance for Longitudinally Invariant Fibers
2.1 Electrically Anisotropic (and Isotropic) Media
2.2 General Wave Equations for Electrically Anisotropic(and
Isotropic) Media
2.3 Translational Invariance and Modes
2.4 Wave Equations 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 Transverse Field Vector Wave Equation for Isotropic Media
2.6 Scalar Wave Equation
2.7 Weak-Guidance Expansion for Isotropic Media
2.8 Polarization-Dependent Mode Splitting and Field
Corrections
2.8.1 First-Order Eigenvalue Correction
2.8.2 First-Order Field and Higher-Order Corrections
2.8.3 Simplifications Due to Symmetry
2.9 Reciprocity Relations for Isotropic Media
2.10 Physical Properties of Waveguide Modes
Chapter 3 Circular Isotropic Longitudinally Invariant Fibers
3.1 Summary of Modal Representations
3.1.1 Scalar and Pseudo-Vector Mode Sets
3.1.2 True Weak-Guidance Vector Mode Set Constructions Using
Pseudo-Modes
3.1.3 Pictorial Representation and Notation Details
3.2 Symmetry Concepts for Circular Fibers: 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 Functions of Irreps of CSv
3.2.4 Symmetry Tutorial: Scalar Mode Transformations
3.3 Vector Mode Field Construction 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 Functions 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 Functions ofCSv Cv
CIv
3.4 Polarization-Dependent Level-Splitting
3.4.1 First-Order Eigenvalue Corrections
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 Transitions
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 Transformations for Competing
Perturbations
4.3 CBv Symmetry: Equilateral Triangular Deformations
4.4 C4v Symmetry: Square Deformations
4.4.1 Irreps and Branching Rules
4.4.2 Mode Splitting and Transition Consequences
4.4.3 Square Fiber Modes and Extra Degeneracies
4.5 Csv Symmetry: Pentagonal Deformations
4.5.1 Irreps and Branching Rules
4.5.2 Mode Splitting and Transition Consequences
4.6 C6 Symmetry: Hexagonal Deformations
4.6.1 Irreps and Branching Rules
4.6.2 Mode Splitting and Transition Consequences
4.7 Level Splitting Quantification and Field Corrections
Chapter 5 Birefringence: Linear, Radial, and Circular
5.1 Linear Birefringence
5.1.1 Wave Equations: Longitudinal Invariance
5.1.2 Mode Transitions: 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 Equations: Longitudinal Invariance
5.2.2 Mode Transitions for Circular Symmetry
5.3 Circular Birefringence
5.3.1 Wave Equation
5.3.2 Symmetry and Mode Splittings
Chapter 6 Multicore Fibers and Multifiber Couplers
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 Constant Degeneracies
6.2.2 Basis Functions for General Field Construction
6.3 Scalar Supermode Fields
6.3.1 Combinations of Fundamental Individual Core Modes
6.3.2 Combinations of Other Nondegenerate Individual Core
Modes
6.3.3 Combinations of Degenerate Individual Core Modes
6.4 Vector Supermode Fields
6.4.1 Two Construction 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 Solutions and Field Approximation
Improvements
6.5.1 SALCs as Basis Functions in General Expansion
6.5.2 Variational Approach
6.5.3 Approximate SALC Expansions
6.5.4 SALC = Supermode Field with Numerical Evaluation of Sector
Field Function
6.5.5 Harmonic Expansions for Step Profile Cores
6.5.6 Example of Physical Interpretation of Harmonic Expansion for
the Supermodes
6.5.7 Modal Expansions
6.5.8 Relation of Modal and Harmonic Expansions to SALC
Expansions
6.5.9 Finite Claddings and Cladding Modes
6.6 Propagation Constant Splitting: Quantification
6.6.1 Scalar Supermode Propagation Constant Corrections
6.6.2 Vector Supermode Propagation Constant Corrections
6.7 Power Transfer Characteristics
6.7.1 Scalar Supermode Beating
6.7.2 Polarization Rotation
Chapter 7 Conclusions and Extensions
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-First Century
7.5 Photonic Computer-Aided Design (CAD) Software
7.6 Photonic Crystals and Quasi Crystals
7.7 Microstructured, Photonic Crystal, or Holey Optical
Fibers
7.8 Fiber Bragg Gratings
7.8.1 General FBGs for Fiber Mode Conversion
7.8.2 (Short-Period) Reflection Gratings for Single-Mode
Fibers
7.8.3 (Long-Period) Mode Conversion Transmission Gratings
7.8.4 Example: LPol--LPn Mode-Converting Transmission FBGs for
Two-Mode Fibers (TMFs)
7.8.5 Example: LPol(--LPo2 Mode-Converting Transmission FBGs
Appendix Group Representation Theory
A.1 Preliminaries: Notation, Groups, and Matrix
Representations
of Them
A.1.1 Induced Transformations on Scalar Functions
A.1.2 Eigenvalue Problems: Invariance and Degeneracies
A.1.3 Group Representations
A.1.4 Matrix Irreducible Matrix Representations
A.1.5 Irrep Basis Functions
A.1.6 Notation Conventions
A.2 Rotation-Reflection Groups
A.2.1 Symmetry Operations and Group Definitions
A.2.2 Irreps for C and Cnv
A.2.3 Irrep Notation
A.3 Reducible Representations and Branching Rule
Coefficients via Characters
A.3.1 Example Branching Rule for Cv D C2v
A.3.2 Branching Rule Coefficients via Characters
A.4 Clebsch-Gordan Coefficient for Changing Basis
A.5 Vector Field Transformation
REFERENCES
INDEX

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