Binding and scattering in two-dimensional systems : applications to quantum wires, waveguides, and photonic crystals

Cover......Page 1
Binding and Scattering in Two-Dimensional Systems......Page 4
Preface......Page 6
Contents......Page 8
1.1 The Purpose of This Book......Page 10
1.2 An Overview of the Text......Page 12
2. Bound States in Low-Dimensional Systems......Page 15
2.1 Localized Modes in Constrained Two-Dimensional Systems......Page 17
2.1.1 Bulges and Bound States in Tubes......Page 19
2.1.2 Existence of Bound States in Curved Tubes of Constant Width......Page 23
2.1.3 Bound States in Curved Tubes of Arbitrary Shape......Page 26
2.1.4 Transfer-Matrix Formalism for Curved Tubes......Page 31
2.1.5 Example: One-Dimensional Reduction Applied to the L-Shaped Tube......Page 39
2.2 Bound States in Three.-Dimensional Tubes......Page 41
3.1 Transmission and Reflection in a Long Tube......Page 44
3.1.1 Example: Transmission in the L-Shaped Tube......Page 47
3.2 Transmission and Quantum Probability Flow......Page 54
3.3 Behavior of Electrons in Quantum Heterostructures......Page 61
3.4 Electron Conductance in Quantum Wires......Page 65
3.5 Electron Conductance Through a Straight 2-D Channel......Page 71
4. Waveguide Measurements of the Properties of Curved Tubes......Page 78
4.1 EM Fields in Thin Resonating Cavities......Page 79
4.2 Mapping EM Energy Densities in Waveguide Cavities......Page 80
4.3 Microwave Measurements with Curved Waveguides......Page 82
4.3.1 Confined Mode Studies in Waveguides,......Page 83
4.3.2 Waveguide Experiments Above the Lowest Cutoff Frequency......Page 85
5. Binding and Transmission in Wires and Waveguides......Page 88
5.1 Tube with a Circular Bend......Page 89
5.1.1 Bound States in the Limit of Small Curvature......Page 91
5.1.2 Bound State Properties for a Circular Bend......Page 93
5.2 Tube with a Single Sharp Bend......Page 102
5.2.1 Bound States for Structures with a Sharp Bend......Page 105
5.2.2 Sub-Cutoff Confined Modes in Curved Waveguides......Page 106
5.3 A Tube with a \"T-Stub\"......Page 109
5.3.1 Transmission in Structures with T-Stubs......Page 111
5.4 Structures with Two Coupled Cells......Page 120
5.4.1 Bound States in Systems with Two Coupled Cells......Page 121
5.4.2 Transmission Through a System with Two Coupled Cells......Page 130
5.4.3 Electron Conductance in Double-Bend Quantum Wires......Page 133
6. Two-Dimensional Systems with Finite Periodic Structure......Page 152
6.1 Bound States in Periodic 2-D Systems......Page 153
6.2 Origin of Band Structure in Periodic Systems......Page 161
6.3.1 Transmission in a \"Staircase\" SYstem......Page 164
6.3.2 Transmission in the \"Quantum Dot Superlattice\"......Page 170
6.4 Defects in Quantum Wire \"Crystals\"......Page 180
6.4.1 Trapped Modes in Band Gaps......Page 182
7. Localized Modes in Photonic Crystals......Page 187
7.1 Maxwell\'s Equations in a Dielectric Medium......Page 188
7.1.1 -Band Structure in a Photonic Crystal......Page 190
7.2 \"Waveguides\" in Photonic Crystals......Page 193
7.3 \"Bound States\" in Photonic Crystal Waveguides......Page 195
7.3.1 Bound States in Local Constrictions......Page 196
8. Epilogue......Page 202
A. Comparison of Various Approximate Quantum Wells......Page 203
A.1 Effects of a Diffuse Surface......Page 204
A.2 Potentials of Finite Depth......Page 205
A.3 Effect of Sharp Boundaries on Transmission......Page 206
B. Conducting Sphere on a Grounded Surface......Page 207
References......Page 212
Index......Page 221