1．Introduction

2．Eigenmodes of Photonic Crystals

2.1 Wave Equations and Eigenvalue Problems

2.2 Eigenvalue Problems in Two-Dimensional Crystals

2.3 Scaling Law and Time Reversal Symmetry

2.4 Photonic Band Calculation

2.4.1 Fourier Expansion of Dielectric Functions

2.4.2 Some Examples

2.5 Phase Velocity,Group Velocity,and Energy Velocity

2.6 Calculation of Group Velocity

2.7 Complete Set of Eigenfunctions

2.8 Retarded Green's Function

3．Symmetry of Eigenmodes

3.1 Group Theory for Two-Dimensional Crystals

3.2 Classification of Eigenmodes in the Square Lattice

3.3 Classification of Eigenmodes in the Hexagonal Lattice

3.4 Group Theory for Three-Dimensional Crystals

3.5 Classification of Eigenmodes in the Simple Cubic Lattice

3.6 Classification of Eigenmodes in the fcc Lattice

4．Transmission Spectra

4.1 Light Transmission and Bragg Reflection

4.2 Field Equations

4.2.1 E Polarization

4.2.2 H Polarization

4.3 Fourier Transform of the Dielectric Function

4.3.1 Square Lattice

4.3.2 Hexagonal Lattice

4.4 Some Examples

4.4.1 Square Lattice

4.4.2 Hexagonal Lattice

4.5 Refraction Law for Photonic Crystals

5．Optical Response ofPhotonic Crystals

5.1 Solutions ofInhomogeneous Equations

5.2 Dipole Radiation

5.3 Stimulated Emission

5.4 Sum-Frequency Generation

5.4.1 Three-Dimensional Case

5.4.2 Two-Dimensional Case

5.5 SHG in the Square Lattice

5.6 Free Induction Decay

6．Defect Modes in Photonic Crystals

6.1 General Properties

6.2 Principle of Calculation

6.3 Point Defects in a Square Lattice

6.4 Point Defects in a Hexagonal Lattice

6.5 Line Defects in a Square Lattice

6.6 Dielectric Loss and Quality Factor

7．Band Calculation with Frequency-Dependent Dielectric Constants

7.1 Principle of Calculation

7.2 Modified Plane Waves in Metallic Crystals

7.3 Surface Plasmon Polaritons

7.3.1 Plasmon Polaritons on Flat Surface

7.3.2 Plasmon Resonance on a Metallic Cylinder

7.3.3 Symmetry of Plasmon Polaritons

7.3.4 Plasmon Bands in a Square Lattice

8．Photonic Crystal Slabs

8.1 Eigenmodes of Uniform Slabs

8.2 Symmetry of Eigenmodes

8.3 Photonic Band Structure and Transmission Spectra

8.4 Quality Factor

9．Low-Threshold Lasing Due to Group-Velocity Anomaly

9.1 Enhanced Stimulated Emission

9.2 Lasing Threshold

9.2.1 Analytical Expression

9.2.2 Numerical Estimation

10．Quantum Optics in Photonic Crystals

10.1 Quantization of the Electromagnetic Field

10.2 Quadrature-Phase Squeezing

10.3 Interaction Hamiltonian

10.4 Lamb Shift

11．Superfluorescence

11.1 Brief Description of Superfluorescence

11.2 Two-Level Atoms

11.3 Superfluorescence in Uniform Materials

11.4 Superfluorescence in Photonic Crystals

11.4.1 Small Distribution Volume Limit

11.4.2 Propagation Effect

12．Epilogue

References

Index