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

Preface     ix
Transfer Matrix     1
A Scattering Experiment     2
Scattering Matrix and Transfer Matrix     3
Transmission and Reflection Amplitudes     10
Properties of the Transfer Matrix     12
Supplementary Notes     19
Problems     24
Rectangular Potentials     28
Transfer Matrix     29
Transmission Coefficient: E > V[subscript 0]     32
Tunneling: 0 < E < V[subscript 0]     38
Current Density     42
Bound States: V[subscript 0] < E < 0     45
Inverse Problem for Rectangular Potential     47
Problems     49
[Delta]-Function Potential     56
Single [Delta]-Function Potential     56
Two [Delta]-Function Repulsive Potentials     60
Bound States of Double [Delta]-Function Attractive Potentials     62
N Identical [Delta]-Function Barriers     64
Supplementary Notes     68
Problems     69
Kronig-Penney Model     74
The Periodic Model     75
Allowed Energy Bands     76
The Density of States     81
Wave Function     83
Single Impurity     84
N [Delta]-Function Barriers versus Infinite Kronig-Penney Model     87
Supplementary Notes     88
Problems     91
Tight Binding Model     98
Periodic Model     100
The Transfer Matrix     104
Transmission Coefficient     106
Single Impurity     107
Transmission through Impurities     108
Coupled Pendulum Analogy of the Tight Binding Model     111
Problems     114
Tight Binding Models of Crystals     120
Periodic One-Dimensional System with Two Different Atoms     120
Periodic Model with Different Distances between Neighboring Atoms     125
Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a     126
Reduced Zone Scheme     129
Problems     130
Disordered Models     137
Random Tight Binding Model     138
Random Kronig-Penney Model     150
Supplementary Notes     159
Problems     168
Numerical Solution of the Schrodinger Equation     173
Numerical Procedure     173
Accuracy of Numerical Data     174
Numerical Data for Transmission     177
Problems     179
Transmission and Reflection of Plane Electromagnetic Waves on an Interface     181
Plane Wave at the Interface     181
Transmission and Reflection Coefficients     184
Interface between Two Dielectric Materials     189
Interface between a Dielectric Material and a Metal     190
Total Transmission     195
Total Reflection     198
Problems     200
Transmission and Reflection Coefficients for a Slab     205
Transmission and Reflection Amplitudes: TE and TM modes     206
Dielectric Slab Embedded in Vacuum     209
Transmission through a Metallic Slab     220
Problems     223
Surface Waves     225
Surface Waves at the Interface between Two Media     226
Surface Modes on a Slab     233
Experimental Observation of Surface Waves     237
Problems     241
Resonant Tunneling through Double-Layer Structures     243
Transmission through Two Dielectric Layers     243
Transmission through Two Metallic Layers     246
Problems     248
Layered Electromagnetic Medium: Photonic Crystals      249
Photonic Crystals: Infinite Periodic Layered Medium     250
Periodic Arrangement of Dielectric Layers     252
Band Structure of Photonic Crystals     254
Coupling to a Finite Photonic Crystal     258
Layered Dispersive Media     263
Kronig-Penney Model of a Photonic Crystal     269
Problems     271
Effective Parameters     275
Effective Parameters of a Layered Medium     276
Retrieval Procedure     279
Alternating Layers with Negative Permittivity and Negative Permeability     282
Problem     285
Wave Propagation in Nonlinear Structures     286
Single [Delta]-Function Layer of a Nonlinear Dielectric     286
Nonlinear Kronig-Penney [Delta]-Function Model     290
Problems     296
Left-Handed Materials     298
Electromagnetic Properties of Left-Handed Materials     299
Transmission through a Slab of Left-Handed Material     303
Structure of Left-Handed Materials     309
Problems     317
Matrix Operations     321
The Determinant and the Trace of the Matrix     321
Inverse, Transpose, and Unitary Matrices     322
Eigenvalues and Eigenvectors     324
Similarity Transformations     324
Degeneracy     325
Summary of Electrodynamics Formulas     327
Maxwell's Equations     327
Wave Equation     330
Group Velocity and Phase Velocity     331
Poynting Vector     333
Boundary Condition at an Interface     334
Permitivity and Permeability     335
Metals     337
Bibliography     341
Index     349