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Preface to the Second Edition xiii Preface to the First Edition xvChapter 1: Introduction 1 Controlling the Properties of Materials 1Photonic Crystals 2 An Overview of the Text 3 Chapter 2:Electromagnetism in Mixed Dielectric Media 6 The Macroscopic MaxwellEquations 6 Electromagnetism as an Eigenvalue Problem 10 General Propertiesof the Harmonic Modes 12 Electromagnetic Energy and the VariationalPrinciple 14 Magnetic vs. Electric Fields 16 The Effect of SmallPerturbations 17 Scaling Properties of the Maxwell Equations 20 Discretevs. Continuous Frequency Ranges 21 Electrodynamics and Quantum MechanicsCompared 22 Further Reading 24 Chapter 3: Symmetries and Solid-StateElectromagnetism 25 Using Symmetries to Classify Electromagnetic Modes 25Continuous Translational Symmetry 27 Index guiding 30 DiscreteTranslational Symmetry 32 Photonic Band Structures 35 Rotational Symmetryand the Irreducible Brillouin Zone 36 Mirror Symmetry and the Separation ofModes 37 Time-Reversal Invariance 39 Bloch-Wave Propagation Velocity 40Electrodynamics vs. Quantum Mechanics Again 42 Further Reading 43Chapter 4: The Multilayer Film: A One-Dimensional Photonic Crystal 44 TheMultilayer Film 44 The Physical Origin of Photonic Band Gaps 46 The Size ofthe Band Gap 49 Evanescent Modes in Photonic Band Gaps 52 Off-AxisPropagation 54 Localized Modes at Defects 58 Surface States 60Omnidirectional Multilayer Mirrrors 61 Further Reading 65 Chapter 5:Two-Dimensional Photonic Crystals 66 Two-Dimensional Bloch States 66 ASquare Lattice of Dielectric Columns 68 A Square Lattice of Dielectric Veins72 A Complete Band Gap for All Polarizations 74 Out-of-Plane Propagation 75Localization of Light by Point Defects 78 Point defects in a larger gap 83Linear Defects and Waveguides 86 Surface States 89 Further Reading 92Chapter 6: Three-Dimensional Photonic Crystals 94 Three-Dimensional Lattices94 Crystals with Complete Band Gaps 96 Spheres in a diamond lattice 97Yablonovite 99 The woodpile crystal 100 Inverse opals 103 A stack oftwo-dimensional crystals 105 Localization at a Point Defect 109Experimental defect modes in Yablonovite 113 Localization at a Linear Defect114 Localization at the Surface 116 Further Reading 121 Chapter 7:Periodic Dielectric Waveguides 122 Overview 122 A Two-Dimensional Model 123Periodic Dielectric Waveguides in Three Dimensions 127 Symmetry andPolarization 127 Point Defects in Periodic Dielectric Waveguides 130Quality Factors of Lossy Cavities 131 Further Reading 134 Chapter 8:Photonic-Crystal Slabs 135 Rod and Hole Slabs 135 Polarization and SlabThickness 137 Linear Defects in Slabs 139 Reduced-radius rods 139 Removedholes 142 Substrates, dispersion, and loss 144 Point Defects in Slabs 147Mechanisms for High Q with Incomplete Gaps 149 Delocalization 149Cancellation 151 Further Reading 155 Chapter 9: Photonic-Crystal Fibers156 Mechanisms of Confinement 156 Index-Guiding Photonic-Crystal Fibers 158Endlessly single-mode fibers 161 The scalar limit and LP modes 163Enhancement of nonlinear effects 166 Band-Gap Guidance in Holey Fibers 169Origin of the band gap in holey fibres 169 Guided modes in a hollow core 172Bragg Fibers 175 Analysis of cylindrical fibers 176 Band gaps of Braggfibers 178 Guided modes of Bragg fibers 180 Losses in Hollow-Core Fibers182 Cladding losses 183 Inter-modal coupling 187 Further Reading 189Chapter 10: Designing Photonic Crystals for Applications 190 Overview 190 AMirror, a Waveguide, and a Cavity 191 Designing a mirror 191 Designing awaveguide 193 Designing a cavity 195 A Narrow-Band Filter 196 TemporalCoupled-Mode Theory 198 The temporal coupled-mode equations 199 The filtertransmission 202 A Waveguide Bend 203 A Waveguide Splitter 206 AThree-Dimensional Filter with Losses 208 Resonant Absorption and Radiation212 Nonlinear Filters and Bistability 214 Some Other Possibilities 218Reflection, Refraction, and Diffraction 221 Reflection 222 Refraction andisofrequency diagrams 223 Unusual refraction and diffraction effects 225Further Reading 228 Epilogue 228 A Comparisons with Quantum Mechanics229 B The Reciprocal Lattice and the Brillouin Zone 233 The ReciprocalLattice 233 Constructing the Reciprocal Lattice Vectors 234 The BrillouinZone 235 Two-Dimensional Lattices 236 Three-Dimensional Lattices 238Miller Indices 239 C Atlas of Band Gaps 242 A Guided Tour ofTwo-Dimensional Gaps 243 Three-Dimensional Gaps 251 D ComputationalPhotonics 252 Generalities 253 Frequency-Domain Eigenproblems 255Frequency-Domain Responses 258 Time-Domain Simulations 259 A PlanewaveEigensolver 261 Further Reading and Free Software 263 Bibliography 265Index 283