PREFACE ACKNOWLEDGMENTS 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 Simplifi cations 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_∞v 3.2.2 Scalar Wave Equation Symmetry:C^S_∞v 3.2.3 Scalar Modes:Basis Functions of Irreps of C^S_∞v 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^P_∞v 3.3.3 Zeroth-Order Vector Wave Equation Symmetry:C^S_∞v⊗C^P_∞v 3.3.4 Pseudo-Vector Modes:Basis Functions of Irreps ofC^S_∞v⊗C^P_∞v 3.3.5 Full Vector Wave Equation Symmetry:C^S_∞v⊗C^P_∞v⊃C^J_∞v 3.3.6 True Vector Modes:Qualitative Features via C^S_∞v⊗C^P_∞v⊃C^J_∞v 3.3.7 True Vector Modes via Pseudo-Modes:Basis Functions of C^S_∞v⊗C^P_∞v⊃C^J_∞v 3.4 Polarization-Dependent Level-Splitting 3.4.1 First-Order Eigenvalue Corrections 3.4.2 Radial Profi le-Dependent Polarization Splitting 3.4.3 Special Degeneracies and Shifts for Particular Radial Dependence of Profi le 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 C_3v Symmetry:Equilateral Triangular Deformations 4.4 _4v 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 C_5v Symmetry:Pentagonal Deformations 4.5.1 Irreps and Branching Rules 4.5.2 Mode Splitting and Transition Consequences 4.6 C_6v Symmetry:Hexagonal Deformations 4.6.1 Irreps and Branching Rules 4.6.2 Mode Splitting and Transition Consequences 4.7 Level Splitting Quantifi cation 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 δ_xy of Isotropic Fiber Vector Modes Dominated by Δ-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 Multifi ber Couplers 6.1 Multilightguide Structures with Discrete Rotational Symmetry 6.1.1 Global C_nv Rotation-Refl ection Symmetric Structures:Isotropic Materials 6.1.2 Global C_nv Symmetry:Material and Form Birefringence 6.1.3 Global C_n 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 Profi le 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:Quantifi cation 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)Refl ection Gratings for Single-Mode Fibers 7.8.3(Long-Period)Mode Conversion Transmission Gratings 7.8.4 Example:LP_01*LP_11 Mode-Converting Transmission FBGs for Two-Mode Fibers(TMFs) 7.8.5 Example:LP_01*LP_02 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-Refl ection Groups A.2.1 Symmetry Operations and Group Defi nitions A.2.2 Irreps for C_∞v and C_nv A.2.3 Irrep Notation A.3 Reducible Representations and Branching Rule Coeffi cients via Characters A.3.1 Example Branching Rule for C_∞v⊃C_2v A.3.2 Branching Rule Coeffi cients via Characters A.4 Clebsch-Gordan Coeffi cient for Changing Basis A.5 Vector Field Transformation REFERENCES INDEX
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