| Preface |
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xi | |
| Acknowledgments |
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xiii | |
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1 | (18) |
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1 | (2) |
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Polarization Dependence of Wave Propagation |
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3 | (1) |
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Weak-Guidance Approach to Vector Modes |
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4 | (1) |
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Group Theory for Waveguides |
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5 | (2) |
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Optical Waveguide Modes: A Simple Introduction |
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7 | (9) |
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7 | (2) |
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9 | (5) |
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Adiabatic Transitions and Coupling |
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14 | (2) |
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Outline and Major Results |
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16 | (3) |
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Electromagnetic Theory for Anisotropic Media and Weak Guidance for Longitudinally Invariant Fibers |
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19 | (16) |
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Electrically Anisotropic (and Isotropic) Media |
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19 | (3) |
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General Wave Equations for Electrically Anisotropic (and Isotropic) Media |
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22 | (2) |
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Translational Invariance and Modes |
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24 | (1) |
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Wave Equations for Longitudinally Invariant Media |
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25 | (2) |
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General Anisotropic Media |
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25 | (1) |
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Anisotropic Media with z-Aligned Principal Axis |
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25 | (1) |
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``Diagonal'' Anisotropies |
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26 | (1) |
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Transverse Field Vector Wave Equation for Isotropic Media |
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27 | (1) |
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27 | (1) |
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Weak-Guidance Expansion for Isotropic Media |
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28 | (2) |
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Polarization-Dependent Mode Splitting and Field Corrections |
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30 | (2) |
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First-Order Eigenvalue Correction |
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30 | (1) |
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First-Order Field and Higher-Order Corrections |
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31 | (1) |
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Simplificatins Due to Symmetry |
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31 | (1) |
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Reciprocity Relations for Isotropic Media |
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32 | (1) |
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Physical Properties of Waveguide Modes |
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32 | (3) |
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Circular Isotropic Longitudinally Invariant Fibers |
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35 | (32) |
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Summary of Modal Representations |
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35 | (7) |
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Scalar and Pseudo-Vector Mode Sets |
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36 | (1) |
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True Weak-Guidance Vector Mode Set Constructions Using Pseudo-Modes |
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36 | (1) |
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Pictorial Representation and Notation Details |
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36 | (6) |
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Symmetry Concepts for Circular Fibers: Scalar Mode Fields and Degeneracies |
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42 | (8) |
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Geometrical Symmetry: C∞v |
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46 | (1) |
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Scalar Wave Equation Symmetry: Cs∞v |
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46 | (1) |
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Scalar Modes: Basis Functions of Irreps of Cs∞v |
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47 | (1) |
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Symmetry Tutorial: Scalar Mode Transformations |
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48 | (2) |
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Vector Mode Field Construction and Degeneracies via Symmetry |
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50 | (9) |
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51 | (1) |
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Polarization Vector Symmetry Group: Cp∞v |
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52 | (1) |
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Zeroth-Order Vector Wave Equation Symmetry: Cs∞v ⊗ Cp∞v |
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52 | (2) |
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Pseudo-Vector Modes: Basis Functions of Irreps of Cs∞V ⊗ Cp∞V |
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54 | (1) |
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Full Vector Wave Equation Symmetry: Cs∞V ⊗ Cp∞V ⊃ CJ∞v |
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55 | (1) |
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True Vector Modes: Qualitative Features via CS∞V ⊗ CP∞V ⊃ CJ∞V |
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56 | (2) |
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True Vector Modes via Pseudo-Modes: Basis Functions of CS∞V ⊗ CP∞V ⊃ CJ∞V |
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58 | (1) |
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Polarization-Dependent Level-Splitting |
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59 | (8) |
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First-Order Eigenvalue Corrections |
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59 | (1) |
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Radial Profile-Dependent Polarization Splitting |
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60 | (3) |
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Special Degeneracies and Shifts for Particular Radial Dependence of Profile |
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63 | (1) |
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64 | (3) |
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Azimuthal Symmetry Breaking |
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67 | (16) |
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67 | (1) |
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67 | (1) |
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Anticrossing and Mode Form Transitions |
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68 | (1) |
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C2v Symmetry: Elliptical (or Rectangular) Guides: Illustration of Method |
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68 | (4) |
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Wave Equation Symmetries and Mode-Irrep Association |
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68 | (1) |
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69 | (3) |
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Vector Mode Form Transformations for Competing Perturbations |
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72 | (1) |
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C3v Symmetry: Equilateral Triangular Deformations |
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72 | (3) |
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C4v Symmetry: Square Deformations |
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75 | (2) |
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Irreps and Branching Rules |
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75 | (1) |
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Mode Splitting and Transition Consequences |
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75 | (2) |
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Square Fiber Modes and Extra Degeneracies |
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77 | (1) |
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C5v Symmetry: Pentagonal Deformations |
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77 | (3) |
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Irreps and Branching Rules |
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77 | (1) |
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Mode Splitting and Transition Consequences |
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78 | (2) |
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C6v Symmetry: Hexagonal Deformations |
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80 | (2) |
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Irreps and Branching Rules |
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80 | (1) |
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Mode Splitting and Transition Consequences |
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80 | (2) |
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Level Splitting Quantification and Field Corrections |
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82 | (1) |
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Birefringence: Linear, Radial, and Circular |
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83 | (14) |
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83 | (6) |
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Wave Equations: Longitudinal Invariance |
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83 | (2) |
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Mode Transitions: Circular Symmetry |
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85 | (2) |
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87 | (1) |
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Splitting by δxy of Isotropic Fiber Vector Modes Dominated by Δ-Splitting |
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88 | (1) |
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Correspondence between Isotropic ``True'' Modes and Birefringent LP Modes |
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89 | (1) |
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89 | (2) |
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Wave Equations: Longitudinal Invariance |
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89 | (2) |
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Mode Transitions for Circular Symmetry |
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91 | (1) |
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91 | (6) |
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93 | (1) |
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Symmetry and Mode Splittings |
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93 | (4) |
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Multicore Fibers and Multifiber Couplers |
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97 | (40) |
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Multilightguide Structures with Discrete Rotational Symmetry |
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97 | (4) |
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Global Cnv Rotation-Reflection Symmetric Structures: Isotropic Materials |
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98 | (1) |
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Global Cnv Symmetry: Material and Form Birefringence |
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99 | (1) |
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Global Cn Symmetric Structures |
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99 | (2) |
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General Supermode Symmetry Analysis |
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101 | (6) |
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Propagation Constant Degeneracies |
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101 | (3) |
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Basis Functions for General Field Construction |
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104 | (3) |
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107 | (2) |
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Combinations of Fundamental Individual Core Modes |
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107 | (1) |
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Combinations of Other Nondegenerate Individual Core Modes |
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108 | (1) |
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Combinations of Degenerate Individual Core Modes |
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108 | (1) |
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109 | (12) |
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109 | (4) |
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Isotropic Cores: Fundamental Mode Combination Supermodes |
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113 | (3) |
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Isotropic Cores: Higher-Order Mode Combination Supermodes |
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116 | (3) |
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Anisotropic Cores: Discrete Global Radial Birefringence |
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119 | (2) |
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Other Anisotropic Structures: Global Linear and Circular Birefringence |
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121 | (1) |
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General Numerical Solutions and Field Approximation Improvements |
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121 | (6) |
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SALCs as Basis Functions in General Expansion |
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121 | (1) |
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122 | (1) |
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Approximate SALC Expansions |
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122 | (1) |
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SALC = Supermode Field with Numerical Evaluation of Sector Field Function |
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123 | (1) |
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Harmonic Expansions for Step Profile Cores |
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124 | (1) |
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Example of Physical Interpretation of Harmonic Expansion for the Supermodes |
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125 | (1) |
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126 | (1) |
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Relation of Modal and Harmonic Expansions to SALC Expansions |
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126 | (1) |
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Finite Claddings and Cladding Modes |
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127 | (1) |
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Propagation Constant Splitting: Quantification |
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127 | (4) |
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Scalar Supermode Propagation Constant Corrections |
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127 | (3) |
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Vector Supermode Propagation Constant Corrections |
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130 | (1) |
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Power Transfer Characteristics |
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131 | (6) |
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131 | (2) |
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133 | (4) |
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Conclusions and Extensions |
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137 | (14) |
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137 | (1) |
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138 | (1) |
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Symmetry Analysis of Nonlinear Waveguides and Self-Guided Waves |
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139 | (1) |
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Developments in the 1990s and Early Twenty-First Century |
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140 | (1) |
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Photonic Computer-Aided Design (CAD) Software |
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141 | (1) |
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Photonic Crystals and Quasi Crystals |
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142 | (1) |
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Microstructured, Photonic Crystal, or Holey Optical Fibers |
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143 | (1) |
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144 | (7) |
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General FBGs for Fiber Mode Conversion |
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144 | (1) |
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(Short-Period) Reflection Gratings for Single-Mode Fibers |
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145 | (1) |
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(Long-Period) Mode Conversion Transmission Gratings |
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146 | (1) |
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Example: LP01↔LP11 Mode-Converting Transmission FBGs for Two-Mode Fibers (TMFs) |
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146 | (2) |
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Example: LP01↔LP02 Mode-Converting Transmission FBGs |
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148 | (3) |
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Appendix Group Representation Theory |
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151 | (16) |
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Preliminaries: Notation, Groups, and Matrix Representations of Them |
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152 | (4) |
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Induced Transformations on Scalar Functions |
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153 | (1) |
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Eigenvalue Problems: Invariance and Degeneracies |
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154 | (1) |
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155 | (1) |
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Matrix Irreducible Matrix Representations |
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155 | (1) |
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155 | (1) |
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155 | (1) |
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Rotation-Reflection Groups |
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156 | (4) |
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Symmetry Operations and Group Definitions |
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156 | (1) |
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156 | (4) |
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160 | (1) |
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Reducible Representations and Branching Rule Coefficients via Characters |
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160 | (4) |
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Example Branching Rule for C∞v ⊃ C2v |
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161 | (1) |
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Branching Rule Coefficients via Characters |
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161 | (3) |
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Clebsch-Gordan Coefficient for Changing Basis |
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164 | (1) |
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Vector Field Transformation |
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165 | (2) |
| References |
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167 | (12) |
| Index |
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179 | |
Lisainfo e-raamatute kohta