Preface ........................................................ ix
Chapter 1. Introduction ........................................ 1
1.1 Historical Overview ........................................ 3
1.2 Analogy Between Photonic and Semiconductor Crystals ........ 6
1.3 Analyzing Photonic-Bandgap Structures ...................... 8
References ..................................................... 11
Chapter 2. Preliminary Concepts of Electromagnetic Waves and
Periodic Media ..................................... 17
2.1 Electromagnetic Waves ..................................... 17
2.1.1 Maxwell's Equations in Linear, Homogeneous Media ... 18
2.1.2 Electromagnetic Waves .............................. 21
2.1.3 Optical Waves ...................................... 23
2.1.4 Guided Waves ....................................... 28
2.1.5 Group Velocity in Homogeneous Media ................ 37
2.2 Periodic Media ............................................ 38
2.2.1 Real-Space Lattices, Lattice Vectors ............... 39
2.2.2 Reciprocal Lattice and Brillouin Zone .............. 47
2.3 Waves in Periodic Media ................................... 49
2.3.1 Wave Equation in Periodic Dielectric Structures .... 49
2.3.2 Group Velocity in Periodic Media ................... 55
2.3.3 Dispersion Surfaces and Band Diagrams .............. 57
References ..................................................... 60
Chapter 3. Numerical Methods .................................. 63
3.1 Overview .................................................. 63
3.2 Plane-Wave Expansion Method ............................... 65
3.2.1 Preliminaries ...................................... 65
3.2.2 One-Dimensional Plane-Wave Expansion Method ........ 66
3.2.3 Two-Dimensional Plane-Wave Expansion Method ........ 72
3.2.4 Three-Dimensional Plane-Wave Expansion Method ...... 84
3.2.5 Practical Considerations in the Implementation
of the Plane-Wave Expansion Method ................. 87
3.2.6 Photonic-Crystal Slab by Plane-Wave Expansion
Method ............................................. 90
3.2.7 Revised Plane-Wave Method for Dispersive
Material and its Application to Band-Structure
Calculations of Photonic-Crystal Slabs ............ 102
3.3 Finite-Difference Time-Domain (FDTD) Method .............. 108
3.3.1 Central-Difference Expressions of Maxwell's
Equations ......................................... 109
3.3.2 Two-Dimensional FDTD Method ....................... 110
3.3.3 Three-Dimensional FDTD Method ..................... 112
3.3.4 Numerical Stability and Dispersion ................ 114
3.3.5 Simulating Transient and Steady-State System
Response .......................................... 116
3.3.6 Absorbing Boundary Conditions ..................... 118
3.3.7 FDTD for Photonic Crystals ........................ 122
References .................................................... 125
Chapter 4. Devices and Applications Based on Photonic
Bandgaps .......................................... 133
4.1 Introduction ............................................. 133
4.2 Point Defects ............................................ 134
4.2.1 Numerical Analysis of Point Defects ............... 134
4.2.2 Design Criteria for Photonic-Crystal Cavities ..... 137
4.3 Line Defects ............................................. 139
4.3.1 Photonic-Crystal Line Defects for Waveguiding ..... 140
4.3.2 Line Defects in Photonic-Crystal Slabs ............ 144
4.3.3 Extracting Dispersion Properties Using a
Single-Frequency Source ........................... 147
4.4 Applications that Use Strong Confinement in PhC .......... 150
4.4.1 Waveguide Bends ................................... 150
4.4.2 Zero-Cross-Talk Waveguide Crossing ................ 154
4.4.3 Narrow-Band Beam Splitter ......................... 156
4.4.4 Air-Bridge Microcavity ............................ 157
4.4.5 Channel-Drop Filters in Photonic Crystals ......... 159
4.4.6 Optical Spectrometer .............................. 160
4.4.7 Hybrid Photonic-Crystal Structures ................ 163
4.4.8 Electrically and Thermally Tunable Photonic
Crystals .......................................... 168
4.4.9 Photonic-Crystal Optical Networks ................. 169
4.4.10 Coupled Photonic-Crystal Waveguides ............... 171
4.4.11 Other Applications of Photonic Bandgap ............ 188
References .................................................... 189
Chapter 5. Engineering Photonic-Crystal Dispersion
Properties ........................................ 197
5.1 Introduction ............................................. 197
5.2 Dispersion in Photonic Crystals .......................... 198
5.3 Superprism Effect ........................................ 201
5.4 Self-Collimation ......................................... 205
5.4.1 Experimental Demonstration of Self-Collimation .... 208
5.4.2 Self-Guiding Heterolattice ........................ 211
5.4.3 Redirecting Light in Self-Collimating PhCs ........ 214
5.4.4 Beam Splitting in Self-Collimating PhC ............ 217
5.4.5 Optical Analog-to-Digital Converter ............... 224
5.4.6 Self-Collimation in Three-Dimensional Photonic
Crystals .......................................... 231
5.4.7 Experimental Verification of 3D Self-
Collimation ....................................... 239
5.5 Left-Handed Behavior and Negative Refraction ............. 245
5.5.1 3D Subwavelength Imaging by a Photonic-Crystal
Flat Lens ......................................... 247
5.6 Superprism, Negative Refraction and Self-Collimation ..... 254
5.7 Summary .................................................. 259
References .................................................... 259
Chapter 6. Fabrication ....................................... 263
6.1 Two-Dimensional Photonic Crystals ........................ 263
6.1.1 Fabrication of Planar Photonic Crystals ........... 266
6.1.2 Fabrication of 2D Photonic Crystals ............... 269
6.2 Three-Dimensional Photonic Crystals: Micromachining ...... 274
6.2.1 Layer-by-Layer Fabrication ........................ 274
6.2.2 Woodpile Photonic Crystals ........................ 281
6.2.3 Autocloning Technique ............................. 297
6.2.4 Glancing Angle Deposition (GLAD) .................. 307
6.2.5 Macroporous Silicon ............................... 313
6.2.6 Realizing Yablonovite for Near Infrared with
Chemically Assisted Ion-Beam Etching .............. 323
6.2.7 Sculpting Bulk Silicon with Reactive Plasma ....... 327
6.3 Three-Dimensional Photonic Crystals: Holographic
Lithography .............................................. 333
6.3.1 Interference of Coherent Waves .................... 334
6.3.2 Patterning PhCs with Interference Lithography ..... 336
6.3.3 Engineering the Interference Pattern .............. 336
6.3.4 Holographic Fabrication Methods for 3D PhCs ....... 341
6.3.5 Summary ........................................... 349
6.4 Three-Dimensional Photonic Crystals: Multiphoton
Polymerization ........................................... 350
6.4.1 Stereolithography/Laser Rapid Prototyping to
Fabricate Arbitrary 3D Structures ................. 350
6.4.2 Multiphoton Absorption ............................ 350
6.4.3 PhC Fabrication Using Multiphoton Absorption ...... 356
6.5 Three-Dimensional Photonic Crystals: Self-Assembly ....... 358
6.5.1 Monodisperse Colloidal Suspensions ................ 359
6.5.2 Colloidal Crystallization ......................... 362
6.5.3 Self-Assembly Methods ............................. 364
References .................................................... 369
Index ......................................................... 383
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