Photonic Crystals: Molding the Flow of Light - Second Edition / Edition 2

by John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade

Overview

Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications.


Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.

• Extensively revised and expanded
• Features improved graphics throughout
• Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding
• Provides an introduction to coupled-mode theory as a powerful tool for device design
• Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.

Product Details

ISBN-13:	9780691124568
Publisher:	Princeton University Press
Publication date:	03/02/2008
Edition description:	Second Edition
Pages:	304
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

John D. Joannopoulos is the Francis Wright Davis Professor of Physics at the Massachusetts Institute of Technology. Steven G. Johnson is assistant professor of applied mathematics at MIT. Joshua N. Winn is assistant professor of physics at MIT. Robert D. Meade is a physicist and former research scientist at MIT. He currently works in equity trading.

Table of Contents

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

What People are Saying About This

Soukoulis

An excellent textbook to be used in physics, chemistry, and engineering. The revised edition of Photonic Crystals fills the gap between the layperson and the expert reader.
— Costas M. Soukoulis, Iowa State University

From the Publisher

"This book is destined to become the classic textbook in the area. It gathers together the fundamental concepts and tools relevant to photonic crystals and presents them with exceptional clarity. I genuinely enjoyed reading it."—Maryanne Large, University of Sydney

"An excellent textbook to be used in physics, chemistry, and engineering. The revised edition of Photonic Crystals fills the gap between the layperson and the expert reader."—Costas M. Soukoulis, Iowa State University

Maryanne Large

This book is destined to become the classic textbook in the area. It gathers together the fundamental concepts and tools relevant to photonic crystals and presents them with exceptional clarity. I genuinely enjoyed reading it.
— Maryanne Large, University of Sydney

Editorial Reviews

"Photonic Crystals is a timely and well-written account of this new field."

Nature

"This book offers elegant full-color illustrations and is superbly produced. This has to be applauded in an era dominated by low-resolution digital images. In summary: Photonics Crystals is a beauty and is highly recommended to photonics, laser, and optical scientist."

Optics Journal

"This text is certainly pitched at a post third-year quantum mechanics, electromagnetism and solid-state physics level in the Australian context and is ideally suited to study at an Honours or a Masters level. [Images freely available from MIT complement this text]. Certainly for all who offer photonics courses, this book should be in your institution's library if not on your shelf."—-John Holdsworth, Australian Physics

From the Publisher

"Photonic Crystals is a timely and well-written account of this new field."

Nature Lib

This text is certainly pitched at a post third-year quantum mechanics, electromagnetism and solid-state physics level in the Australian context and is ideally suited to study at an Honours or a Masters level. [Images freely available from MIT complement this text]. Certainly for all who offer photonics courses, this book should be in your institution's library if not on your shelf.

Australian Physics - John Holdsworth

This text is certainly pitched at a post third-year quantum mechanics, electromagnetism and solid-state physics level in the Australian context and is ideally suited to study at an Honours or a Masters level. [Images freely available from MIT complement this text]. Certainly for all who offer photonics courses, this book should be in your institution's library if not on your shelf.
— John Holdsworth

Australian Physics