Photonic Crystals

by Lourtioz, Jean-michel; Benisty, Henri; Berger, Vincent; Gerard, Jean-Michel; Maystre, Daniel

• ISBN13: 9783540783466
• ISBN10: 3540783466
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-06-01
• Publisher: Springer Verlag

Summary

Just like the periodical crystalline potential in solid-state crystals determines their properties for the conduction of electrons, the periodical structuring of photonic crystals leads to envisioning the possibility of achieving a control of the photon flux in dielectric and metallic materials. The use of photonic crystals as a cage for storing, filtering or guiding light at the wavelength scale thus paves the way to the realisation of optical and optoelectronic devices with ultimate properties and dimensions. This should contribute toward meeting the demands for a greater miniaturisation that the processing of an ever increasing number of data requires.Photonic Crystals intends to provide students and researchers from different fields with the theoretical background needed for modelling photonic crystals and their optical properties, while at the same time presenting the large variety of devices, from optics to microwaves, where photonic crystals have found applications. As such, it aims at building bridges between optics, electromagnetism and solid-state physics.This book was written by six specialists of nanophotonics, and was coordinated by Jean-Michel Lourtioz, head of the Institut d'Électronique Fondamentale in Orsay and coordinator of the French Research Network in Nanophotonics.

Table of Contents

Foreword	p. V
Theoretical Models for Photonic Crystals	p. 1
Introduction to Part 1	p. 3
Models for Infinite Crystals	p. 5
Plane Wave Expansion	p. 5
Maxwell's Equations	p. 5
The Floquet-Bloch Theorem	p. 6
Hermiticity of the Field Operator	p. 10
Simple Examples of Bloch Functions	p. 11
General Plane Wave Method	p. 13
Other Methods for the Calculation of the Photonic Band Gaps of an Infinite Crystal: the KKR Method	p. 21
Photonic Band Diagram	p. 21
The Irreducible Brillouin Zone	p. 22
Band Diagrams of One-Dimensional Crystals	p. 25
Band Diagrams of Two-Dimensional Photonic Crystals	p. 33
Off-Axis Propagation in One and Two-Dimensional Photonic Crystals	p. 40
Band Diagrams of Three-Dimensional Photonic Crystals	p. 41
Infinite Crystals with Defects	p. 43
Point Defects	p. 44
Coupling of Point Defects	p. 50
Supercell Method	p. 52
Methods derived from Tight-Binding Methods in Solid State Physics	p. 53
Extended Defects	p. 54
Semi-Infinite Crystals and Surface Defects	p. 56
Density of States in Photonic Crystals with or without Defects	p. 59
Models for Finite Crystals	p. 65
Transfer, Reflection and Transmission Matrix Formulations	p. 65
Reflection and Transmission Matrices	p. 66
Pendry Method	p. 72
Finite Difference in Time Domain (FDTD) Method	p. 80
Numerical Formulation of Maxwell's Equations	p. 80
Case of an Incident Pulse	p. 84
Absorption Region and Boundary Conditions	p. 86
Practical Implementation and Convergence of the FDTD Method	p. 87
Examples of Results obtained for a Point Source with the FDTD Method	p. 89
Scattering Matrix Method	p. 91
Other Methods: Integral and Differential Methods, Finite Element Method, Effective Medium Theory	p. 100
Numerical Codes available for the Modelling of Photonic Crystals	p. 104
Quasi-Crystals and Archimedean Tilings	p. 107
Photonic Quasi-Crystals	p. 108
Archimedean Tilings	p. 111
From Photonic Quasi-Crystals to the Localization of Light	p. 115
Specific Features of Metallic Structures	p. 121
Bulk Metals: Drude Model, Skin Effect and Metallic Losses	p. 121
Drude Model	p. 123
Low-Frequency Region: Skin Effect and Metallic Losses	p. 124
From the Infrared to the Visible and UV Regions	p. 125
Periodic Metallic Structures at Low Frequencies	p. 126
Plasmon-Like Photonic Band Gap	p. 126
Transmission Spectra of Metallic and Dielectric Photonic Crystals	p. 129
Complete Band Gaps in Metallic Photonic Crystals	p. 131
Structures with Continuous Metallic Elements and Structures with Discontinuous Metallic Elements	p. 132
Periodic Metallic Structures at Optical Frequencies. Idealized Case of a Dispersive Lossless Dielectric	p. 134
Surface Waves	p. 137
Surface Plasmons at a Metal/Dielectric Plane Interface	p. 137
Propagation of Surface Plasmons along a Periodically Modulated Metal/Dielectric Interface and Local Enhancement of the Field	p. 140
Wood's Anomalies: Phenomenological Theory	p. 144
Photonic Band Gaps for the Propagation of Surface Plasmons at Periodically Modulated Metal/Dielectric Interfaces	p. 148
The Photon Sieve	p. 150
Surface Waves in Metals at Radiofrequencies	p. 151
Optical Properties of Photonic Crystals	p. 157
Introduction to Part II. The `Many Facets' of Photonic Crystals	p. 159
Control of Electromagnetic Waves	p. 163
The Photonic Crystal Mirror	p. 163
The Semi-Infinite Photonic Crystal: Mirror or Diffraction Grating?.	p. 163
Specular Reflection at a Semi-Infinite Crystal	p. 166
Finite Photonic Crystals as Semi-Transparent Mirrors	p. 167
Photonic Crystal Waveguides	p. 168
Index Guiding and Photonic Bandgap Guiding	p. 168
Three-Dimensional Photonic Crystal Waveguides	p. 170
Two-Dimensional Photonic Crystal Waveguides	p. 172
Density of States and Multiplicity of Guided Modes	p. 174
Coexistence of Index Guiding and Photonic Bandgap Guiding	p. 178
Resonators	p. 185
Localized Modes. Origin of Losses	p. 185
Density of States	p. 187
Waveguide formed by Coupled Cavities	p. 188
Hybrid Structures with Index Guiding. The Light Line	p. 190
Light Cone of a Uniform Waveguide	p. 190
Fictitious Periodicity	p. 191
True One-Dimensional Periodicity	p. 191
Channel Waveguides in Two-Dimensional Photonic Crystals	p. 195
Refractive Properties of Photonic Crystals and Metamaterials	p. 197
Phase Refractive index, Group Refractive Index and Energy Propagation	p. 197
Phase Velocity and Group Velocity	p. 197
Refractive Indexes and Dispersion Diagrams	p. 201
Effective Phase Index and Group Refractive Index	p. 202
Refraction of Waves at the Interface between a Periodic Medium and a Homogeneous Medium	p. 203
Summary of Refraction Laws in Homogeneous Media	p. 203
Some Well-Known Anisotropic Media: Birefringent Solid-State Crystals	p. 205
Construction of the Waves Transmitted in a Photonic Crystal	p. 206
Superprism and Negative Refraction Effects	p. 207
Superprism Effect	p. 207
Ultra-Refraction and Negative Refraction	p. 208
Metamaterials	p. 210
Simultaneous Control of the Dielectric Permittivity and the Magnetic Permeability	p. 210
Negative Refraction in a Slab of Perfect Left-Handed Material	p. 212
Stigmatism of a Slab of Perfect Left-Handed Material	p. 215
Perfect Lens or Superlens?	p. 217
Fabrication of Negative Refractive Index Metamaterials	p. 218
Electromagnetic Cloaking	p. 221
Confinement of Light in Zero-Dimensional Microcavities	p. 225
Microcavity Sources. Principles and Effects	p. 226
A Classical Effect: the Angular Redistribution of the Spontaneous Emission and the Example of Planar Microcavities	p. 226
Three-Dimensional Optical Confinement in Zero-Dimensional Microcavities	p. 245
Different Types of Zero-Dimensional Microcavities	p. 245
Control of the Spontaneous Emission in Weak Coupling Regime. Some Experimental Results	p. 250
Single-Mode Coupling of the Spontaneous Emission	p. 254
Towards Strong Coupling Regime for Solid State `Artificial Atoms'	p. 256
Nonlinear Optics with Photonic Crystals	p. 261
The Problem of Phase Matching	p. 262
¿(1) Photonic Crystals	p. 265
One-Dimensional ¿(1) Photonic Crystals	p. 265
Two-Dimensional ¿(1) Photonic Crystals	p. 273
¿<2) Photonic Crystals	p. 274
One-Dimensional ¿(2) Photonic Crystals	p. 274
Two-Dimensional ¿(2) Photonic Crystals	p. 277
Photonic Crystals with Third Order Susceptibility	p. 279
Fabrication, Characterization and Applications of Photonic Bandgap Structures	p. 283
Introduction to Part III	p. 285
Planar Integrated Optics	p. 287
Objectives, New Devices and Challenges	p. 287
Fundamentals of Integrated Optics and Introduction of Photonic Crystals	p. 290
Conventional Waveguides	p. 290
Photonic Crystals in Integrated Optics	p. 295
Planar Photonic Crystals in the Substrate Approach	p. 306
DFB and DBR Laser Diode Structures	p. 306
Photonic Crystals, a Strong Perturbation for Guided Modes	p. 307
Choice of the Diameter of the Holes and of the Period of the Crystal	p. 309
Specific Parameters for InP- and GaAs-Based Systems	p. 310
Deep Etching	p. 310
Membrane Waveguide Photonic Crystals	p. 311
Free-Standing Membranes	p. 311
Reported Membranes	p. 314
Macroporous Silicon Photonic Substrates	p. 314
Characterization Methods for Photonic Crystals in Integrated Optics	p. 318
Internal Light Source Method	p. 318
End-Fire Method	p. 321
Wide-Band Transmission-Reflection Spectroscopy	p. 324
Losses of Photonic Crystal Integrated Optical Devices	p. 324
Analysis of Losses in Planar Photonic Crystal Waveguides	p. 324
Measurement of Propagation Losses in Straight Photonic Crystal Channel Waveguides	p. 326
Losses in the Slow-Light Regime	p. 329
Waveguide Bends in Photonic Crystals and Bend Losses	p. 329
Photonic Crystal Resonators and Quality Factors	p. 330
Photonic Crystal Devices and Functions : Recent Developments	p. 333
Classification of devices	p. 333
Coupled Resonators and Waveguides	p. 335
Very high-Q cavities	p. 337
Other Devices and Optical Functions	p. 339
Microsources	p. 345
High-Efficiency Light-Emitting Diodes	p. 345
Solutions for the Extraction of Light without Confinement	p. 345
Enhanced Extraction Efficiency through Planar Confinement	p. 347
Increase of the Extraction Efficiency using Two-Dimensional Photonic Crystals	p. 350
Ridge-Type Waveguide Lasers confined by Photonics Crystals	p. 352
Bulk Photonic Crystal Band Edge Lasers	p. 355
Photonic crystal VCSELs	p. 358
Microcavity Lasers	p. 360
Potential Interest of Single-Photon Sources	p. 364
Photonic Crystal Fibres	p. 371
Another Implementation of Periodic Structures	p. 371
Fabrication of Microstructured Optical Fibres	p. 372
Solid-Core Microstructured Optical Fibres	p. 375
Confinement Losses and Second Mode Transition	p. 375
Attenuation and Bend Loss	p. 378
Chromatic Dispersion Properties	p. 378
Main Applications of Solid-Core Microstructured Optical Fibres	p. 380
True Photonic Crystal Fibres (PCF)	p. 382
Photonic Bandgap Cladding	p. 382
Losses of Photonic Crystal Fibres with Finite Cladding	p. 385
Photonic Crystal Fibres with Optimised Structures	p. 387
Main Applications of Photonic Crystal Fibres	p. 389
Three-Dimensional Structures in Optics	p. 393
Geometrical Configurations proposed for Three-Dimensional Structures	p. 394
Structures with Omnidirectional Photonic Band Gaps	p. 394
Incomplete Band Gap Three-Dimensional Structures	p. 397
Examples of Fabrication Processes and Realizations of Three-Dimensional Photonic Crystals in the Optical Region	p. 399
Complete Band Gap Structures	p. 399
Metallic Three-Dimensional Photonic Crystals in the Optical Region	p. 410
Three-Dimensional Photonic Crystals and Light Emitters	p. 412
Microwave and Terahertz Antennas and Circuits	p. 413
Photonic Crystal Antennas	p. 414
Photonic-Crystal Antenna Substrates	p. 415
Photonic-Crystal Antenna Mirrors	p. 418
Photonic Crystal Antenna Radomes or Superstrates	p. 422
Controllable Structures and Metamaterials	p. 424
Principles and Characteristics of Electrically Controllable Photonic Crystals	p. 424
Electrically Controllable Photonic Crystal Antennas	p. 426
Antennas and Metamaterials	p. 429
Microwave Circuits and Ultra-Compact Photonic Crystals	p. 430
Ultra-Compact Photonic Crystals	p. 430
Microwave Filters and Waveguides realised from Ultra-Compact Photonic Crystals	p. 433
From Microwaves to Terahertz Waves	p. 435
From Microwaves to Optics	p. 436
Impedance Matching of Photonic Waveguides	p. 437
Photonic Crystal THz Imaging System	p. 439
`Microwave Inspired' Nanostructures and Nanodevices	p. 440
Conclusion and Perspectives	p. 443
Appendices	p. 447
Scattering Matrix Method: Determination of the Field for a Finite Two-Dimensional Crystal formed by Dielectric Rods	p. 449
Incident Field	p. 449
Field inside the Rods	p. 449
Field in the Vicinity of a Rod	p. 452
Magneto-Photonic Cystals	p. 459
Stigmatism of a Slab of Perfect Left-Handed Material: Integral for the Total Field	p. 463
References	p. 467
Index	p. 509
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