Photonic crystals : theory, applications and fabrication

This book presents in detail the fundamental theoretical background necessary to understand the unique optical phenomena arising from the crystalline nature of photonic-crystal structures and their application across a range of disciplines. Organized to take readers from basic concepts to more advanced topics, the book covers:

Preliminary concepts of electromagnetic waves and periodic media

Numerical methods for analyzing photonic-crystal structures

Devices and applications based on photonic bandgaps

Engineering photonic-crystal dispersion properties

Fabrication of two- and three-dimensional photonic crystals

The authors assume an elementary knowledge of electromagnetism, vector calculus, Fourier analysis, and complex number analysis. Therefore, the book is appropriate for advanced undergraduate students in physics, applied physics, optics, electronics, and chemical and electrical engineering, as well as graduate students and researchers in these fields.

Author Notes

Dennis W. Prather, PhD, is a Professor in the Department of Electrical and Computer Engineering at the University of Delaware, where he leads the Laboratory for Nanoscale and Integrated Photonic Systems. Professor Prather is a Fellow of SPIE and OSA.

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

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