TABLE OF CONTENTS:
Preface ix
Chapter 1: Transfer Matrix 1
1.1 A Scattering Experiment 2
1.2 Scattering Matrix and Transfer Matrix 3
1.3 Transmission and Reflection Amplitudes 10
1.4 Properties of the Transfer Matrix 12
1.5 Supplementary Notes 19
1.6 Problems 24
Chapter 2: Rectangular Potentials 28
2.1 Transfer Matrix 29
2.2 Transmission Coefficient: E > V0 32
2.3 Tunneling: 0 < E < V0 38
2.4 Current Density 42
2.5 Bound States: V0 < E < 0 45
2.6 Inverse Problem for Rectangular Potential 47
2.7 Problems 49
Chapter 3: δ -Function Potential 56
3.1 Single δ-Function Potential 56
3.2 Two δ-Function Repulsive Potentials 60
3.3 Bound States of Double δ-Function Attractive Potentials 62
3.4 N Identical δ-Function Barriers 64
3.5 Supplementary Notes 68
3.6 Problems 69
Chapter 4: Kronig-Penney Model 74
4.1 The Periodic Model 75
4.2 Allowed Energy Bands 76
4.3 The Density of States 81
4.4 Wave Function 83
4.5 Single Impurity 84
4.6 N δ-Function Barriers versus Infinite Kronig-Penney Model 87
4.7 Supplementary Notes 88
4.8 Problems 91
Chapter 5: Tight Binding Model 98
5.1 Periodic Model 100
5.2 The Transfer Matrix 104
5.3 Transmission Coefficient 106
5.4 Single Impurity 107
5.5 Transmission through Impurities 108
5.6 Coupled Pendulum Analogy of the Tight Binding Model 111
5.7 Problems 114
Chapter 6: Tight Binding Models of Crystals 120
6.1 Periodic One-Dimensional System with Two Different Atoms 120
6.2 Periodic Model with Different Distances between Neighboring Atoms 125
6.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 126
6.4 Reduced Zone Scheme 129
6.5 Problems 130
Chapter 7: Disordered Models 137
7.1 Random Tight Binding Model 138
7.2 Random Kronig-Penney Model 150
7.3 Supplementary Notes 159
7.4 Problems 168
Chapter 8: Numerical Solution of the Schrödinger Equation 173
8.1 Numerical Procedure 173
8.2 Accuracy of Numerical Data 174
8.3 Numerical Data for Transmission 177
8.4 Problems 179
Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 181
9.1 Plane Wave at the Interface 181
9.2 Transmission and Reflection Coefficients 184
9.3 Interface between Two Dielectric Materials 189
9.4 Interface between a Dielectric Material and a Metal 190
9.5 Total Transmission 195
9.6 Total Reflection 198
9.7 Problems 200
Chapter 10: Transmission and Reflection Coefficients for a Slab 205
10.1 Transmission and Reflection Amplitudes: TE and TM modes 206
10.2 Dielectric Slab Embedded in Vacuum 209
10.3 Transmission through a Metallic Slab 220
10.4 Problems 223
Chapter 11: Surface Waves 225
11.1 Surface Waves at the Interface between Two Media 226
11.2 Surface Modes on a Slab 233
11.3 Experimental Observation of Surface Waves 237
11.4 Problems 241
Chapter 12: Resonant Tunneling through Double-Layer Structures 243
12.1 Transmission through Two Dielectric Layers 243
12.2 Transmission through Two Metallic Layers 246
12.3 Problems 248
Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 249
13.1 Photonic Crystals: Infinite Periodic Layered Medium 250
13.2 Periodic Arrangement of Dielectric Layers 252
13.3 Band Structure of Photonic Crystals 254
13.4 Coupling to a Finite Photonic Crystal 258
13.5 Layered Dispersive Media 263
13.6 Kronig-Penney Model of a Photonic Crystal 269
13.7 Problems 271
Chapter 14: Effective Parameters 275
14.1 Effective Parameters of a Layered Medium 276
14.2 Retrieval Procedure 279
14.3 Alternating Layers with Negative Permittivity and Negative Permeability 282
14.4 Problem 285
Chapter 15: Wave Propagation in Nonlinear Structures 286
15.1 Single δ-Function Layer of a Nonlinear Dielectric 286
15.2 Nonlinear Kronig-Penney δ-Function Model 290
15.3 Problems 296
Chapter 16: Left-Handed Materials 298
16.1 Electromagnetic Properties of Left-Handed Materials 299
16.2 Transmission through a Slab of Left-Handed Material 303
16.3 Structure of Left-Handed Materials 309
16.4 Problems 317
Appendix A: Matrix Operations 321
A.1 The Determinant and the Trace of the Matrix 321
A.2 Inverse, Transpose, and Unitary Matrices 322
A.3 Eigenvalues and Eigenvectors 324
A.4 Similarity Transformations 324
A.5 Degeneracy 325
Appendix B: Summary of Electrodynamics Formulas 327
B.1 Maxwell's Equations 327
B.2 Wave Equation 330
B.3 Group Velocity and Phase Velocity 331
B.4 Poynting Vector 333
B.5 Boundary Condition at an Interface 334
B.6 Permitivity and Permeability 335
B.7 Metals 337
Bibliography 341
Index 349
