Photonic Crystals, Theory, Applications and Fabrication

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.

• Chapter 1. Introduction 11.1 Historical Overview 31.2 Analogy Between Photonic and Semiconductor Crystals 61.3 Analyzing Photonic-Bandgap Structures 8References 11Chapter 2. Preliminary Concepts of Electromagnetic Waves and Periodic Media 172.1 Electromagnetic Waves 172.1.1 Maxwell’s Equations in Linear, Homogeneous Media 182.1.2 Electromagnetic Waves 212.1.3 Optical Waves 232.1.4 Guided Waves 282.1.5 Group Velocity in Homogeneous Media 372.2 Periodic Media 382.2.1 Real-Space Lattices, Lattice Vectors 392.2.2 Reciprocal Lattice and Brillouin Zone 472.3 Waves in Periodic Media 492.3.1 Wave Equation in Periodic Dielectric Structures 492.3.2 Group Velocity in Periodic Media 552.3.3 Dispersion Surfaces and Band Diagrams 57References 60Chapter 3. Numerical Methods 633.1 Overview 633.2 Plane-Wave Expansion Method 653.2.1 Preliminaries 653.2.2 One-Dimensional Plane-Wave Expansion Method 663.2.3 Two-Dimensional Plane-Wave Expansion Method 723.2.4 Three-Dimensional Plane-Wave Expansion Method 843.2.5 Practical Considerations in the Implementation of the Plane-Wave Expansion Method 873.2.6 Photonic-Crystal Slab by Plane-Wave Expansion Method 903.2.7 Revised Plane-Wave Method for Dispersive Material and its Application to Band-Structure Calculations of Photonic-Crystal Slabs 1023.3 Finite-Difference Time-Domain (FDTD) Method 1083.3.1 Central-Difference Expressions of Maxwell’s Equations 1093.3.2 Two-Dimensional FDTD Method 1103.3.3 Three-Dimensional FDTD Method 1123.3.4 Numerical Stability and Dispersion 1143.3.5 Simulating Transient and Steady-State System Response 1163.3.6 Absorbing Boundary Conditions 1183.3.7 FDTD for Photonic Crystals 122References 125Chapter 4. Devices and Applications Based on Photonic Bandgaps 1334.1 Introduction 1334.2 Point Defects 1344.2.1 Numerical Analysis of Point Defects 1344.2.2 Design Criteria for Photonic-Crystal Cavities 1374.3 Line Defects 1394.3.1 Photonic-Crystal Line Defects for Waveguiding 1404.3.2 Line Defects in Photonic-Crystal Slabs 1444.3.3 Extracting Dispersion Properties Using a Single-Frequency Source 1474.4 Applications that Use Strong Confinement in PhC 1504.4.1 Waveguide Bends 1504.4.2 Zero-Cross-Talk Waveguide Crossing 1544.4.3 Narrow-Band Beam Splitter 1564.4.4 Air-Bridge Microcavity 1574.4.5 Channel-Drop Filters in Photonic Crystals 1594.4.6 Optical Spectrometer 1604.4.7 Hybrid Photonic-Crystal Structures 1634.4.8 Electrically and Thermally Tunable Photonic Crystals 1684.4.9 Photonic-Crystal Optical Networks 1694.4.10 Coupled Photonic-Crystal Waveguides 1714.4.11 Other Applications of Photonic Bandgap 188References 189Chapter 5. Engineering Photonic-Crystal Dispersion Properties 1975.1 Introduction 1975.2 Dispersion in Photonic Crystals 1985.3 Superprism Effect 2015.4 Self-Collimation 2055.4.1 Experimental Demonstration of Self-Collimation 2085.4.2 Self-Guiding Heterolattice 2115.4.3 Redirecting Light in Self-Collimating PhCs 2145.4.4 Beam Splitting in Self-Collimating PhC 2175.4.5 Optical Analog-to-Digital Converter 2245.4.6 Self-Collimation in Three-Dimensional Photonic Crystals 2315.4.7 Experimental Verification of 3D Self-Collimation 2395.5 Left-Handed Behavior and Negative Refraction 2455.5.1 3D Subwavelength Imaging by a Photonic-Crystal Flat Lens 2475.6 Superprism, Negative Refraction and Self-Collimation 2545.7 Summary 259References 259Chapter 6. Fabrication 2636.1 Two-Dimensional Photonic Crystals 2636.1.1 Fabrication of Planar Photonic Crystals 2666.1.2 Fabrication of 2D Photonic Crystals 2696.2 Three-Dimensional Photonic Crystals: Micromachining 2746.2.1 Layer-by-Layer Fabrication 2746.2.2 Woodpile Photonic Crystals 2816.2.3 Autocloning Technique 2976.2.4 Glancing Angle Deposition (GLAD) 3076.2.5 Macroporous Silicon 3136.2.6 Realizing Yablonovite for Near Infrared with Chemically Assisted Ion-Beam Etching 3236.2.7 Sculpting Bulk Silicon with Reactive Plasma 3276.3 Three-Dimensional Photonic Crystals: Holographic Lithography 3336.3.1 Interference of Coherent Waves 3346.3.2 Patterning PhCs with Interference Lithography 3366.3.3 Engineering the Interference Pattern 3366.3.4 Holographic Fabrication Methods for 3D PhCs 3416.3.5 Summary 3496.4 Three-Dimensional Photonic Crystals: Multiphoton Polymerization 3506.4.1 Stereolithography/Laser Rapid Prototyping to Fabricate Arbitrary 3D Structures 3506.4.2 Multiphoton Absorption 3506.4.3 PhC Fabrication Using Multiphoton Absorption 3566.5 Three-Dimensional Photonic Crystals: Self-Assembly 3586.5.1 Monodisperse Colloidal Suspensions 3596.5.2 Colloidal Crystallization 3626.5.3 Self-Assembly Methods 364References 369Index 383