Bibliographic record and links to related information available from the Library of Congress catalog

Information from electronic data provided by the publisher. May be incomplete or contain other coding.

Preface to the Second Edition xiii

Preface to the First Edition xv

Chapter 1: Introduction 1

Controlling the Properties of Materials 1

Photonic Crystals 2

An Overview of the Text 3

Chapter 2: Electromagnetism in Mixed Dielectric Media 6

The Macroscopic Maxwell Equations 6

Electromagnetism as an Eigenvalue Problem 10

General Properties of the Harmonic Modes 12

Electromagnetic Energy and the Variational Principle 14

Magnetic vs. Electric Fields 16

The Effect of Small Perturbations 17

Scaling Properties of the Maxwell Equations 20

Discrete vs. Continuous Frequency Ranges 21

Electrodynamics and Quantum Mechanics Compared 22

Further Reading 24

Chapter 3: Symmetries and Solid-State Electromagnetism 25

Using Symmetries to Classify Electromagnetic Modes 25

Continuous Translational Symmetry 27

Index guiding 30

Discrete Translational Symmetry 32

Photonic Band Structures 35

Rotational Symmetry and the Irreducible Brillouin Zone 36

Mirror Symmetry and the Separation of Modes 37

Time-Reversal Invariance 39

Bloch-Wave Propagation Velocity 40

Electrodynamics vs. Quantum Mechanics Again 42

Further Reading 43

Chapter 4: The Multilayer Film: A One-Dimensional Photonic Crystal 44

The Multilayer Film 44

The Physical Origin of Photonic Band Gaps 46

The Size of the Band Gap 49

Evanescent Modes in Photonic Band Gaps 52

Off-Axis Propagation 54

Localized Modes at Defects 58

Surface States 60

Omnidirectional Multilayer Mirrrors 61

Further Reading 65

Chapter 5: Two-Dimensional Photonic Crystals 66

Two-Dimensional Bloch States 66

A Square Lattice of Dielectric Columns 68

A Square Lattice of Dielectric Veins 72

A Complete Band Gap for All Polarizations 74

Out-of-Plane Propagation 75

Localization of Light by Point Defects 78

Point defects in a larger gap 83

Linear Defects and Waveguides 86

Surface States 89

Further Reading 92

Chapter 6: Three-Dimensional Photonic Crystals 94

Three-Dimensional Lattices 94

Crystals with Complete Band Gaps 96

Spheres in a diamond lattice 97

Yablonovite 99

The woodpile crystal 100

Inverse opals 103

A stack of two-dimensional crystals 105

Localization at a Point Defect 109

Experimental defect modes in Yablonovite 113

Localization at a Linear Defect 114

Localization at the Surface 116

Further Reading 121

Chapter 7: Periodic Dielectric Waveguides 122

Overview 122

A Two-Dimensional Model 123

Periodic Dielectric Waveguides in Three Dimensions 127

Symmetry and Polarization 127

Point Defects in Periodic Dielectric Waveguides 130

Quality Factors of Lossy Cavities 131

Further Reading 134

Chapter 8: Photonic-Crystal Slabs 135

Rod and Hole Slabs 135

Polarization and Slab Thickness 137

Linear Defects in Slabs 139

Reduced-radius rods 139

Removed holes 142

Substrates, dispersion, and loss 144

Point Defects in Slabs 147

Mechanisms for High Q with Incomplete Gaps 149

Delocalization 149

Cancellation 151

Further Reading 155

Chapter 9: Photonic-Crystal Fibers 156

Mechanisms of Confinement 156

Index-Guiding Photonic-Crystal Fibers 158

Endlessly single-mode fibers 161

The scalar limit and LP modes 163

Enhancement of nonlinear effects 166

Band-Gap Guidance in Holey Fibers 169

Origin of the band gap in holey fibres 169

Guided modes in a hollow core 172

Bragg Fibers 175

Analysis of cylindrical fibers 176

Band gaps of Bragg fibers 178

Guided modes of Bragg fibers 180

Losses in Hollow-Core Fibers 182

Cladding losses 183

Inter-modal coupling 187

Further Reading 189

Chapter 10: Designing Photonic Crystals for Applications 190

Overview 190

A Mirror, a Waveguide, and a Cavity 191

Designing a mirror 191

Designing a waveguide 193

Designing a cavity 195

A Narrow-Band Filter 196

Temporal Coupled-Mode Theory 198

The temporal coupled-mode equations 199

The filter transmission 202

A Waveguide Bend 203

A Waveguide Splitter 206

A Three-Dimensional Filter with Losses 208

Resonant Absorption and Radiation 212

Nonlinear Filters and Bistability 214

Some Other Possibilities 218

Reflection, Refraction, and Diffraction 221

Reflection 222

Refraction and isofrequency diagrams 223

Unusual refraction and diffraction effects 225

Further Reading 228

Epilogue 228

A Comparisons with Quantum Mechanics 229

B The Reciprocal Lattice and the Brillouin Zone 233

The Reciprocal Lattice 233

Constructing the Reciprocal Lattice Vectors 234

The Brillouin Zone 235

Two-Dimensional Lattices 236

Three-Dimensional Lattices 238

Miller Indices 239

C Atlas of Band Gaps 242

A Guided Tour of Two-Dimensional Gaps 243

Three-Dimensional Gaps 251

D Computational Photonics 252

Generalities 253

Frequency-Domain Eigenproblems 255

Frequency-Domain Responses 258

Time-Domain Simulations 259

A Planewave Eigensolver 261

Further Reading and Free Software 263

Bibliography 265

Index 283

Library of Congress subject headings for this publication:

Photons.

Crystal optics.