Preface to the Second Edition
Preface to the First Edition
1 Introduction
Controlling the Properties of Materials
Photonic Crystals
An Overview of the Text
2 Electromagnetism in Mixed Dielectric Media
The Macroscopic Maxwell Equations
Electromagnetism as an Eigenvalue Problem
General Properties of the Harmonic Modes
Electromagnetic Energy and the Variational Principle
Magnetic vs. Electric Fields
The Effect of Small Perturbations
Scaling Properties of the Maxwell Equations
Discrete vs, Continuous Frequency Ranges
Electrodynamics and Quantum Mechanics Compared
Further Reading
3 Symmetries and Solid-State Electromagnetism
Using Symmetries to Classify Electromagnetic Modes
Continuous Translational Symmetry
Index guiding
Discrete Translational Symmetry
Photonic Band Structures
Rotational Symmetry and the lrreducible Brillouin Zone
Mirror Symmetry and the Separation of Modes
Time-Reversal Invariance
Bloch-Wave Propagation Velocity
Electrodynamics vs. Quantum Mechanics Again
Further Reading
4 The Multilayer Film: A One-Dimensional Photonic
Crystal
the Muttilayer Film
The Physical Origin of Photonic Band Gaps
The Size of the Band Gap
Evanescent Modes in Photonic Band Gaps
Off-Axis Propagation
Localized Modes at Defects
Surface States
Omnidirectional Multilayer Mirrrors
Further Reading
5 Two-Dimensional Photonic Crystals
Two-Dimensional Bloch States
A Square Lattice of Dielectric Columns
A Square Lattice of Dielectric Veins
A Complete Band Gap for All Polarizations
Out-of-Plane Propagation
Localization of Light by Point Defects
Point defects ln a larger gap
Linear Defects and Waveguides
Surface States
Further Reading
6 Three-Dimensional Photonic Crystals
Three-Dimensional Lattices
Crystals with Complete Band Gaps
Spheres ln a diamond lattice
Yablonovite
the woodpile crystal
lnverse opals
A stack of two-dimensional crystals
Localization at a Point Defect
Experimental defect modes in Yablonovite
Localization at a Linear Defect
Localization at the Surface
Further Reading
7 Periodic Dielectric Waveguides
Overview
A Two-Dimensional Model
Periodic Dielectric Waveguides in Three Dimensions
Symmetry and Polarization
Point Defects in Periodic Dielectric Waveguides
Quality Factors of Lossy Cavities
Further Reading
8 Photonic-Crystal Slabs
Rod and Hole Slabs
Polarization and Slab Thickness
Linear Defects in Slabs
Reduced-radius rods
Removed holes
Substrates, dispersion, and loss
Point Defects in Slabs
Mechanisms for High Q with Incomplete Gaps
Delocalizafion
Cancellation
Further Reading
9 Photonic-Crystal Fibers
Mechanisms of Confinement
Index-Guiding Photonic-Crystal Fibers
Endlessly single-mode fibers
The scalar limit and LP modes
Enhancement of nonlinear effects
Band-Gap Guidance in Holey Fibers
Origin of the band gap in holey fibres
Guided modes in a hollow core
Bragg Fibers
Analysis of cylindrical fibers
Band gaps of Bragg fibers
Guided modes of Bragg fibers
Losses in Hollow-Core Fibers
Cladding losses
Inter-modal coupling
Further Reading
10 Designing Photonic Crystals for Applications
Overview
A Mirror, a Waveguide, and a Cavity
Designing a mirror
Designing a waveguide
Designing a cavity
A Narrow-Band Filter
Temporal Coupled-Mode Theory
The temporal coupled-mode equations
The filter transmission
A Waveguide Bend
A Waveguide Splitter
A Three-Dimensional Filter with Losses
Resonant Absorption and Radiation
Nonlinear Filters and Bistability
Some Other Possibilities
Reflection, Refraction, and Diffraction
Reflection
Refraction and isofrequency diagrams
Unusual refraction and diffraction effects
Further Reading
Epilogue
A Comparisons with Quantum Mechanics
B The Reciprocal Lattice and the Brillouin Zone
The Reciprocal Lattice
Constructing the Reciprocal Lattice Vectors
The Brillouin Zone
Two-Dimensional Lattices
Three-Dimensional Lattices
Miller Indices
C Atlas of Band Gaps
A Guided Tour of Two-Dimensional Gaps
Three-Dimensional Gaps
D Computational Photonics
Generalities
Frequency-Domain Eigenproblems
Frequency-Domain Responses
Time-Domain Simulations
A Planewave Eigensolver
Further Reading and Free Software
Bibliography
Index
