ISBN: 3-540-66684-2
TITLE: Binding and Scattering in Two-Dimensional Systems
AUTHOR: Londergan, J. Timothy; Carini, John P.; Murdock, David P.
TOC:

1. Introduction 1
1.1 The Purpose of This Book 1
1.2 An Overview of the Text 3
2. Bound States in Low-Dimensional Systems 7
2.1 Localized Modes in Constrained Two-Dimensional Systems 9
2.1.1 Bulges and Bound States in Tubes 11
2.1.2 Existence of Bound States in Curved Tubes of Constant Width 15
2.1.3 Bound States in Curved Tubes of Arbitrary Shape 18
2.1.4 Transfer-Matrix Formalism for Curved Tubes 23
2.1.5 Example: One-Dimensional Reduction Applied to the L-Shaped Tube 31
2.2 Bound States in Three-Dimensional Tubes 33
3. Transmission and Conductance in Tubes 37
3.1 Transmission and Reflection in a Long Tube 37
3.1.1 Example: Transmission in the L-Shaped Tube 40
3.2 Transmission and Quantum Probability Flow 47
3.3 Behavior of Electrons in Quantum Heterostructures 54
3.4 Electron Conductance in Quantum Wires 58
3.4.1 Conductance for a Many-Channel System 61
3.5 Electron Conductance Through a Straight 2-D Channel 64
3.5.1 Qualitative Features of Conductance in a 2-D Channel 66
4. Waveguide Measurements of the Properties of Curved Tubes 71
4.1 EM Fields in Thin Resonating Cavities 72
4.2 Mapping EM Energy Densities in Waveguide Cavities 73
4.3 Microwave Measurements with Curved Waveguides 75
4.3.1 Confined Mode Studies in Waveguides 76
4.3.2 Waveguide Experiments Above the Lowest Cutoff Frequency 78
5. Binding and Transmission in Wires and Waveguides 81
5.1 Tube with a Circular Bend 82
5.1.1 Bound States in the Limit of Small Curvature 84
5.1.2 Bound State Properties for a Circular Bend 86
5.1.3 Transmission in a System with a Circular Bend 91
5.2 Tube with a Single Sharp Bend 95
5.2.1 Bound States for Structures with a Sharp Bend 98
5.2.2 Sub-Cutoff Confined Modes in Curved Waveguides 99
5.3 A Tube with a "T-Stub" 102
5.3.1 Transmission in Structures with T-Stubs 104
5.4 Structures with Two Coupled Cells 113
5.4.1 Bound States in Systems with Two Coupled Cells 114
5.4.2 Transmission Through a System with Two Coupled Cells 123
5.4.3 Electron Conductance in Double-Bend Quantum Wires 126
6. Two-Dimensional Systems with Finite Periodic Structure 145
6.1 Bound States in Periodic 2-D Systems 146
6.2 Origin of Band Structure in Periodic Systems 154
6.3 Transmission and Conductance in Periodic 2-D Systems 157
6.3.1 Transmission in a "Staircase" System 157
6.3.2 Transmission in the "Quantum Dot Superlattice" 163
6.4 Defects in Quantum Wire "Crystals"173
6.4.1 Trapped Modes in Band Gaps 175
7. Localized Modes in Photonic Crystals 181
7.1 Maxwell's Equations in a Dielectric Medium 182
7.1.1 Band Structure in a Photonic Crystal 184
7.2 "Waveguides" in Photonic Crystals 187
7.3 "Bound States" in Photonic Crystal Waveguides189
7.3.1 Bound States in Local Constrictions 190
7.3.2 Bound States in Curved Photonic Band Gap Waveguides 193
8. Epilogue 197
A. Comparison of Various Approximate Quantum Wells 199
A.1 Effects of a Diffuse Surface 200
A.2 Potentials of Finite Depth 201
A.3 Effect of Sharp Boundaries on Transmission 202
B. Conducting Sphere on a Grounded Surface 203
References 209
Index 219
END
