1．Introduction 1
2．Eigenmodes of Photonic Crystals 13
2.1 Wave Equations and Eigenvalue Problems 13
2.2 Eigenvalue Problems in Two-Dimensional Crystals 19
2.3 Scaling Law and Time Reversal Symmetry 21
2.4 Photonic Band Calculation 23
2.4.1 Fourier Expansion of Dielectric Functions 23
2.4.2 Some Examples 26
2.5 Phase Velocity,Group Velocity,and Energy Velocity 30
2.6 Calculation of Group Velocity 32
2.7 Complete Set of Eigenfunctions 34
2.8 Retarded Green's Function 39
3．Symmetry of Eigenmodes 43
3.1 Group Theory for Two-Dimensional Crystals 43
3.2 Classification of Eigenmodes in the Square Lattice 55
3.3 Classification of Eigenmodes in the Hexagonal Lattice 57
3.4 Group Theory for Three-Dimensional Crystals 62
3.5 Classification of Eigenmodes in the Simple Cubic Lattice 65
3.6 Classification of Eigenmodes in the fcc Lattice 75
4．Transmission Spectra 81
4.1 Light Transmission and Bragg Reflection 81
4.2 Field Equations 83
4.2.1 E Polarization 83
4.2.2 H Polarization 85
4.3 Fourier Transform of the Dielectric Function 87
4.3.1 Square Lattice 87
4.3.2 Hexagonal Lattice 89
4.4 Some Examples 91
4.4.1 Square Lattice 91
4.4.2 Hexagonal Lattice 94
4.5 Refraction Law for Photonic Crystals 95
5．Optical Response ofPhotonic Crystals 99
5.1 Solutions ofInhomogeneous Equations 99
5.2 Dipole Radiation 102
5.3 Stimulated Emission 105
5.4 Sum-Frequency Generation 109
5.4.1 Three-Dimensional Case 109
5.4.2 Two-Dimensional Case 112
5.5 SHG in the Square Lattice 116
5.6 Free Induction Decay 121
6．Defect Modes in Photonic Crystals 125
6.1 General Properties 125
6.2 Principle of Calculation 128
6.3 Point Defects in a Square Lattice 131
6.4 Point Defects in a Hexagonal Lattice 136
6.5 Line Defects in a Square Lattice 142
6.6 Dielectric Loss and Quality Factor 146
7．Band Calculation with Frequency-Dependent Dielectric Constants 151
7.1 Principle of Calculation 151
7.2 Modified Plane Waves in Metallic Crystals 154
7.3 Surface Plasmon Polaritons 161
7.3.1 Plasmon Polaritons on Flat Surface 162
7.3.2 Plasmon Resonance on a Metallic Cylinder 165
7.3.3 Symmetry of Plasmon Polaritons 169
7.3.4 Plasmon Bands in a Square Lattice 170
8．Photonic Crystal Slabs 175
8.1 Eigenmodes of Uniform Slabs 175
8.2 Symmetry of Eigenmodes 179
8.3 Photonic Band Structure and Transmission Spectra 181
8.4 Quality Factor 183
9．Low-Threshold Lasing Due to Group-Velocity Anomaly 187
9.1 Enhanced Stimulated Emission 187
9.2 Lasing Threshold 191
9.2.1 Analytical Expression 192
9.2.2 Numerical Estimation 193
10．Quantum Optics in Photonic Crystals 199
10.1 Quantization of the Electromagnetic Field 199
10.2 Quadrature-Phase Squeezing 201
10.3 Interaction Hamiltonian 205
10.4 Lamb Shift 206
11．Superfluorescence 211
11.1 Brief Description of Superfluorescence 211
11.2 Two-Level Atoms 213
11.3 Superfluorescence in Uniform Materials 217
11.4 Superfluorescence in Photonic Crystals 224
11.4.1 Small Distribution Volume Limit 224
11.4.2 Propagation Effect 235
12．Epilogue 243
References 247
Index 251