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Preface | p. XI |
Introduction | p. XIII |
Theory | p. 1 |
Structural Periodicity | p. 3 |
Nonperiodic versus Periodic Structures | p. 4 |
Two-dimensional Point Lattices | p. 6 |
Three-dimensional Point Lattices | p. 10 |
Primitive and Nonprimitive Unit Cells | p. 14 |
Mathematical Description of Periodic Structures | p. 16 |
Fourier Series | p. 20 |
Fourier Series for Two-dimensional Periodic Functions | p. 20 |
Fourier Series for Three-dimensional Periodic Functions | p. 23 |
Arbitrary Unit Cells | p. 25 |
Further Reading | p. 26 |
Problems | p. 26 |
Periodic Functions and Structures | p. 29 |
Introduction | p. 30 |
Creating Simple Periodic Functions in Two Dimensions | p. 31 |
The Square Lattice | p. 31 |
The Triangular Lattice | p. 38 |
Creating Simple Periodic Functions in Three Dimensions | p. 41 |
The Simple Cubic Lattice | p. 44 |
The Face-centered-cubic Lattice | p. 47 |
The Body-centered-cubic Lattice | p. 51 |
Combination of Simple Periodic Functions | p. 59 |
Problems | p. 61 |
Interference of Waves and Interference Lithography | p. 63 |
Electromagnetic Waves | p. 64 |
The Wave Equation | p. 65 |
Electromagnetic Plane Waves | p. 68 |
The Transverse Character of Electromagnetic Plane Waves | p. 69 |
Polarization | p. 72 |
Linearly Polarized Electromagnetic Plane Waves | p. 73 |
Circularly Polarized Electromagnetic Plane Waves | p. 74 |
Elliptically Polarized Electromagnetic Plane Waves | p. 75 |
Electromagnetic Energy | p. 75 |
Energy Density and Energy Flux for Electromagnetic Plane Waves | p. 77 |
Time-averaged Values | p. 77 |
Intensity | p. 80 |
Interference of Electromagnetic Plane Waves | p. 81 |
Three-dimensional Interference Patterns | p. 86 |
Interference Lithography | p. 89 |
Photoresist Materials | p. 89 |
The Interference Lithography Technique | p. 92 |
Designing Periodic Structures | p. 93 |
Further Reading | p. 94 |
Problems | p. 94 |
Periodic Structures and Interference Lithography | p. 97 |
The Connection between the Interference of Plane Waves and Fourier Series | p. 98 |
Simple Periodic Structures in Two Dimensions Via Interference Lithography | p. 100 |
Simple Periodic Structures in Three Dimensions Via Interference Lithography | p. 104 |
Further Reading | p. 110 |
Problems | p. 111 |
Experimental | p. 113 |
Fabrication of Periodic Structures | p. 115 |
Introduction | p. 116 |
Light Beams | p. 116 |
Multiple Gratings and the Registration Challenge | p. 118 |
Beam Configuration | p. 119 |
Using Four Beams | p. 119 |
Using a Single Beam (Phase Mask Lithography) | p. 120 |
Pattern Transfer: Material Platforms and Photoresists | p. 122 |
Negative Photoresists | p. 124 |
Positive Photoresists | p. 126 |
Organic-Inorganic Hybrids Resists | p. 128 |
Practical Considerations for Interference Lithography | p. 128 |
Preserving Polarizations and Directions | p. 128 |
Contrast | p. 131 |
Drying | p. 132 |
Shrinkage | p. 133 |
Backfilling - Creating Inverse Periodic Structures | p. 133 |
Volume Fraction Control | p. 134 |
Closing Remarks | p. 135 |
Further Reading | p. 136 |
Applications | p. 139 |
Photonic Crystals | p. 141 |
Introduction | p. 142 |
One-dimensional Photonic Crystals | p. 143 |
Finite Periodic Structures | p. 143 |
Infinite Periodic Structures | p. 147 |
Finite versus Infinite Periodic Structures | p. 150 |
Two-dimensional Photonic Crystals | p. 151 |
Reciprocal Lattices and Brillouin Zones in Two Dimensions | p. 152 |
Band Diagrams and Photonic Band Gaps in Two Dimensions | p. 157 |
Photonic Band Gaps in Two-dimensional Simple Periodic Structures | p. 160 |
Three-dimensional Photonic Crystals | p. 162 |
Reciprocal Lattices and Brillouin Zones in Three Dimensions | p. 164 |
Band Diagrams and Photonic Band Gaps in Three Dimensions | p. 168 |
Photonic Band Gaps in Three-dimensional Simple Periodic Structures | p. 170 |
Further Reading | p. 176 |
Problems | p. 179 |
Photonic Crystals | p. 183 |
Introduction | p. 184 |
Elastic Waves in Homogeneous Solid Materials | p. 184 |
Acoustic Waves in Homogeneous Fluid Materials | p. 187 |
Phononic Crystals | p. 188 |
One-dimensional Phononic Crystals | p. 190 |
Finite Periodic Structures | p. 190 |
Infinite Periodic Structures | p. 194 |
Two-dimensional Phononic Crystals | p. 198 |
Vacuum Cylinders in a Solid Background | p. 198 |
Solid Cylinders in Air | p. 202 |
Phononic Band Gaps in Two-dimensional Simple Periodic Structures | p. 205 |
Three-dimensional Phononic Crystals | p. 207 |
Solid Spheres in a Solid Background Material | p. 208 |
Further Reading | p. 210 |
Problems | p. 213 |
Periodic Cellular Solids | p. 215 |
Introduction | p. 216 |
One-dimensional Hooke's Law | p. 218 |
The Stress Tensor | p. 219 |
The Strain Tensor | p. 221 |
Expansion | p. 225 |
General Deformation | p. 226 |
Resolving a General Deformation as Strain Plus Rotation | p. 227 |
Stress-Strain Relationship: The Generalized Hooke's Law | p. 229 |
The Generalized Hooke's Law in Matrix Notation | p. 230 |
The Elastic Constants of Cubic Crystals | p. 232 |
Young's Modulus and Poisson's Ratio | p. 233 |
The Shear Modulus | p. 235 |
The Bulk Modulus | p. 237 |
Topological Design of Periodic Cellular Solids | p. 238 |
Finite Element Program to Calculate Linear Elastic Mechanical Properties | p. 243 |
Linear Elastic Mechanical Properties of Periodic Cellular Solids | p. 243 |
Twelve-connected Stretch-dominated Periodic Cellular Solids via Interference Lithography | p. 247 |
Fabrication of a Simple Cubic Cellular Solid via Interference Lithography | p. 249 |
Plastic Deformation of Microframes | p. 250 |
Further Reading | p. 252 |
Further Applications | p. 255 |
Controlling the Spontaneous Emission of Light | p. 256 |
Localization of Light: Microcavities and Waveguides | p. 259 |
Simultaneous Localization of Light and Sound in Photonic-Phononic Crystals: Novel Acoustic-Optical Devices | p. 264 |
Negative Refraction and Superlenses | p. 268 |
Multifunctional Periodic Structures: Maximum Transport of Heat and Electricity | p. 272 |
Microfluidics | p. 273 |
Thermoelectric Energy | p. 275 |
Peltier Effect | p. 275 |
Thomson Effect | p. 276 |
Seebeck Effect | p. 277 |
Further Reading | p. 278 |
MATLAB Program to Calculate the Optimal Electric Field Amplitude Vectors for the Interfering Light Beams | p. 281 |
MATLAB Program to Calculate Reflectance versus Frequency for One-dimensional Photonic Crystals | p. 289 |
MATLAB Program to Calculate Reflectance versus Frequency for One-dimensional Phononic Crystals | p. 297 |
Index | p. 305 |
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