Wave Propagation: From Electrons to Photonic Crystals and Left-Handed Materials

Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 10
1 Transfer Matrix......Page 16
1.1 A Scattering Experiment......Page 17
1.2 Scattering Matrix and Transfer Matrix......Page 18
1.3 Transmission and Reflection Amplitudes......Page 25
1.4 Properties of the Transfer Matrix......Page 27
1.5 Supplementary Notes......Page 34
1.6 Problems......Page 39
2 Rectangular Potentials......Page 43
2.1 Transfer Matrix......Page 44
2.2 Transmission Coefficient: E > V[sub(0)]......Page 47
2.3 Tunneling: 0 < E < V[sub(0)]......Page 53
2.4 Current Density......Page 57
2.5 Bound States: V[sub(0)] < E <0......Page 60
2.6 Inverse Problem for Rectangular Potential......Page 62
2.7 Problems......Page 64
3.1 Single δ-Function Potential......Page 71
3.2 Two δ-Function Repulsive Potentials......Page 75
3.3 Bound States of Double δ-Function Attractive Potentials......Page 77
3.4 N Identical δ-Function Barriers......Page 79
3.5 Supplementary Notes......Page 83
3.6 Problems......Page 84
4 Kronig-Penney Model......Page 89
4.1 The Periodic Model......Page 90
4.2 Allowed Energy Bands......Page 91
4.3 The Density of States......Page 96
4.4 Wave Function......Page 98
4.5 Single Impurity......Page 99
4.6 N δ-Function Barriers versus Infinite Kronig-Penney Model......Page 102
4.7 Supplementary Notes......Page 103
4.8 Problems......Page 106
5 Tight Binding Model......Page 113
5.1 Periodic Model......Page 115
5.2 The Transfer Matrix......Page 119
5.3 Transmission Coefficient......Page 121
5.4 Single Impurity......Page 122
5.5 Transmission through Impurities......Page 123
5.6 Coupled Pendulum Analogy of the Tight Binding Model......Page 126
5.7 Problems......Page 129
6.1 Periodic One-Dimensional System with Two Different Atoms......Page 135
6.2 Periodic Model with Different Distances between Neighboring Atoms......Page 140
6.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a......Page 141
6.4 Reduced Zone Scheme......Page 144
6.5 Problems......Page 145
7 Disordered Models......Page 152
7.1 Random Tight Binding Model......Page 153
7.2 Random Kronig-Penney Model......Page 165
7.3 Supplementary Notes......Page 174
7.4 Problems......Page 183
8.1 Numerical Procedure......Page 188
8.2 Accuracy of Numerical Data......Page 189
8.3 Numerical Data for Transmission......Page 192
8.4 Problems......Page 194
9.1 Plane Wave at the Interface......Page 196
9.2 Transmission and Reflection Coefficients......Page 199
9.3 Interface between Two Dielectric Materials......Page 204
9.4 Interface between a Dielectric Material and a Metal......Page 205
9.5 Total Transmission......Page 210
9.6 Total Reflection......Page 213
9.7 Problems......Page 215
10 Transmission and Reflection Coefficients for a Slab......Page 220
10.1 Transmission and Reflection Amplitudes: TE and TM modes......Page 221
10.2 Dielectric Slab Embedded in Vacuum......Page 224
10.3 Transmission through a Metallic Slab......Page 235
10.4 Problems......Page 238
11 Surface Waves......Page 240
11.1 Surface Waves at the Interface between Two Media......Page 241
11.2 Surface Modes on a Slab......Page 248
11.3 Experimental Observation of Surface Waves......Page 252
11.4 Problems......Page 256
12.1 Transmission through Two Dielectric Layers......Page 258
12.2 Transmission through Two Metallic Layers......Page 261
12.3 Problems......Page 263
13 Layered Electromagnetic Medium: Photonic Crystals......Page 264
13.1 Photonic Crystals: Infinite Periodic Layered Medium......Page 265
13.2 Periodic Arrangement of Dielectric Layers......Page 267
13.3 Band Structure of Photonic Crystals......Page 269
13.4 Coupling to a Finite Photonic Crystal......Page 273
13.5 Layered Dispersive Media......Page 278
13.6 Kronig-Penney Model of a Photonic Crystal......Page 284
13.7 Problems......Page 286
14 Effective Parameters......Page 290
14.1 Effective Parameters of a Layered Medium......Page 291
14.2 Retrieval Procedure......Page 294
14.3 Alternating Layers with Negative Permittivity and Negative Permeability......Page 297
14.4 Problem......Page 300
15.1 Single δ-Function Layer of a Nonlinear Dielectric......Page 301
15.2 Nonlinear Kronig-Penney δ-Function Model......Page 305
15.3 Problems......Page 311
16 Left-Handed Materials......Page 313
16.1 Electromagnetic Properties of Left-Handed Materials......Page 314
16.2 Transmission through a Slab of Left-Handed Material......Page 318
16.3 Structure of Left-Handed Materials......Page 324
16.4 Problems......Page 332
A.1 The Determinant and the Trace of the Matrix......Page 336
A.2 Inverse, Transpose, and Unitary Matrices......Page 337
A.4 Similarity Transformations......Page 339
A.5 Degeneracy......Page 340
B.1 Maxwell’s Equations......Page 342
B.2 Wave Equation......Page 345
B.3 Group Velocity and Phase Velocity......Page 346
B.4 Poynting Vector......Page 348
B.5 Boundary Condition at an Interface......Page 349
B.6 Permitivity and Permeability......Page 350
B.7 Metals......Page 352
Bibliography......Page 356
E......Page 364
L......Page 365
S......Page 366
W......Page 367