Photonic Crystals (eBook)

Foreword 5
The Analogy between Electronic Waves and Electromagnetic Waves 5
Photonic Bandgap Materials or Photonic Crystals? 6
Basic One, Two and Three-Dimensional Structures 8
Objectives of this Book 11
Table of Contents 13
Part I Theoretical Models for Photonic Crystals 20
Introduction to Part I 21
1 Models for Infinite Crystals 23
1.1 Plane Wave Expansion 23
1.2 Other Methods for the Calculation of the Photonic Band Gaps of an Infinite Crystal: the KKR Method 39
1.3 Photonic Band Diagram 39
1.4 Infinite Crystals with Defects 61
2 Models for Finite Crystals 83
2.1 Transfer, Reflection and Transmission Matrix Formulations 83
2.2 Finite Difference in Time Domain (FDTD) Method 98
2.3 Scattering Matrix Method 109
2.4 Other Methods: Integral and Differential Methods, Finite Element Method, Effective Medium Theory 118
2.5 Numerical Codes available for the Modelling of Photonic Crystals 122
3 Quasi-Crystals and Archimedean Tilings 125
3.1 Photonic Quasi-Crystals 126
3.2 Archimedean Tilings 129
3.3 From Photonic Quasi-Crystals to the Localization of Light 133
4 Specific Features of Metallic Structures 139
4.1 Bulk Metals: Drude Model, Skin Effect and Metallic Losses 139
4.2 Periodic Metallic Structures at Low Frequencies 144
4.3 Periodic Metallic Structures at Optical Frequencies. Idealized Case of a Dispersive Lossless Dielectric 152
4.4 Surface Waves 155
Part II Optical Properties of Photonic Crystals 175
5 Control of Electromagnetic Waves 180
5.1 The Photonic Crystal Mirror 180
5.2 Photonic Crystal Waveguides 185
5.3 Resonators 202
5.4 Hybrid Structures with Index Guiding. The Light Line 207
6 Refractive Properties of Photonic Crystals and Metamaterials 215
6.1 Phase Refractive index, Group Refractive Index and Energy Propagation 215
6.3 Superprism and Negative Refraction Effects 225
7 Confinement of Light in Zero-Dimensional Microcavities 243
7.1 Microcavity Sources. Principles and Effects 244
7.2 Three-Dimensional Optical Confinement in Zero- Dimensional Microcavities 263
8 Nonlinear Optics with Photonic Crystals 279
8.1 The Problem of Phase Matching 280
8.2 (1) Photonic Crystals 283
8.3. (2) Photonic Crystals 292
8.4 Photonic Crystals with Third Order Susceptibility 297
Part III Fabrication, Characterization and Applications of Photonic Bandgap Structures 302
Introduction to Part III 304
9 Planar Integrated Optics 305
9.1 Objectives, New Devices and Challenges 305
9.2 Fundamentals of Integrated Optics and Introduction of Photonic Crystals 308
9.3 Planar Photonic Crystals in the Substrate Approach 324
9.4 Membrane Waveguide Photonic Crystals 329
9.5 Macroporous Silicon Photonic Substrates 332
9.6 Characterization Methods for Photonic Crystals in Integrated Optics 336
9.7 Losses of Photonic Crystal Integrated Optical Devices 342
9.8 Photonic Crystal Devices and Functions : Recent Developments 351
10 Microsources 363
10.1 High-Efficiency Light-Emitting Diodes 363
10.2 Ridge-Type Waveguide Lasers confined by Photonics Crystals 370
10.3 Bulk Photonic Crystal Band Edge Lasers 374
10.4 Photonic crystal VCSELs 376
10.5 Microcavity Lasers 378
10.6 Potential Interest of Single-Photon Sources 382
11 Photonic Crystal Fibres 389
11.1 Another Implementation of Periodic Structures 389
11.2 Fabrication of Microstructured Optical Fibres 390
11.3 Solid-Core Microstructured Optical Fibres 393
12 Three-Dimensional Structures in Optics 411
12.1 Geometrical Configurations proposed for Three- Dimensional Structures 412
12.2 Examples of Fabrication Processes and Realizations of Three-Dimensional Photonic Crystals in the Optical Region 417
12.3 Metallic Three-Dimensional Photonic Crystals in the Optical Region 428
12.4 Three-Dimensional Photonic Crystals and Light Emitters 430
13 Microwave and Terahertz Antennas and Circuits 431
13.1 Photonic Crystal Antennas 432
13.2 Controllable Structures and Metamaterials 442
13.3 Microwave Circuits and Ultra-Compact Photonic Crystals 448
13.4 From Microwaves to Terahertz Waves 453
13.5 From Microwaves to Optics 454
Conclusion and Perspectives 461
Appendix A. Scattering Matrix Method: Determination of the Field for a Finite Two- Dimensional Crystal formed by Dielectric Rods 467
Appendix B. Magneto-Photonic Crystals 477
Appendix C. Stigmatism of a Slab of Perfect Left- Handed Material: Integral for the Total Field 481
References 485
Index 527