Optical properties of photonic crystals / Kazuaki Sakoda.

Format:

Book

Author/Creator:

Sakoda, Kazuaki, 1957-

Series:

Springer series in optical sciences ; v. 80.

Springer series in optical sciences ; v. 80

Language:

English

Subjects (All):

Photons.

Crystal optics.

Physical Description:

xiii, 253 pages : 107 fig., 29 tables ; 25 cm.

Edition:

Second edition.

Place of Publication:

Berlin ; New York : Springer, 2004.

Summary:

This is the first comprehensive textbook on the optical properties of photonic crystals. It deals not only with the properties of the radiation modes inside the crystals but also with their peculiar optical response to external fields. A general theory of linear and nonlinear optical response is developed in a clear and detailed fashion using the Green's function method. The symmetry of the eigenmodes is treated systematically using group theory to show how it affects the optical properties of photonic crystals. Important recent developments such as the enhancement of stimulated emission, second harmonic generation, quadrature-phase squeezing, and low-threshold lasing are also treated in detail and made understandable. Numerical methods are also emphasized. Thus this book provides both an introduction for graduate and undergraduate students and also key information for researchers in this field. This second edition has been updated and includes a new chapter on superfluorescence.

Contents:

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

2.5 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

4.4.1 Square Lattice 91

4.4.2 Hexagonal Lattice 94

4.5 Refraction Law for Photonic Crystals 95

5 Optical Response of Photonic Crystals 99

5.1 Solutions of Inhomogeneous 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.

Notes:

Includes bibliographical references (pages [247]-250) and index.

ISBN:

3540206825 :

OCLC:

56436092