Binding and Scattering in Two-Dimensional Systems

by Londergan, J. Timothy; Beiglbock, W.; Beig, R.; Ehlers, J.; Frisch, U.; Hepp, K.; Kippenhahn, R.

• ISBN13: 9783540666844
• ISBN10: 3540666842
• Format: Hardcover
• Copyright: 1999-12-01
• Publisher: Springer Verlag

Summary

This monograph is accessible to anyone with an undergraduate background in quantum mechanics, electromagnetism and some solid state physics. It describes in detail the properties of particles and fields in quasi-two-dimensional systems used to approximate realistic quantum heterostructures. Here the authors treat wires, i.e. they assume an infinite hardwall potential for the system. They discuss bound states, the properties of transmission and reflection, conductance, etc. It is shown that the simple models developed in this book in detail are capable of understanding even complex physical phenomena. The methods are applied to optical states in photonic crystals, and similarities and differences between those and electronic states in quantum heterostructures and electromagnetic fields in waveguides are discussed.

Table of Contents

Introduction	1	(7)
The Purpose of This Book	1	(2)
An Overview of the Text	3	(4)
Bound States in Low-Dimensional Systems	7	(30)
Localized Modes in Constrained Two-Dimensional Systems	9	(24)
Bulges and Bound States in Tubes	11	(4)
Existence of Bound States in Curved Tubes of Constant Width	15	(3)
Bound States in Curved Tubes of Arbitrary Shape	18	(5)
Transfer-Matrix Formalism for Curved Tubes	23	(8)
Example: One-Dimensional Reduction Applied to the L-Shaped Tube	31	(2)
Bound States in Three-Dimensional Tubes	33	(4)
Transmission and Conductance in Tubes	37	(34)
Transmission and Reflection in a Long Tube	37	(10)
Example: Transmission in the L-Shaped Tube	40	(7)
Transmission and Quantum Probability Flow	47	(7)
Behavior of Electrons in Quantum Heterostructures	54	(4)
Electron Conductance in Quantum Wires	58	(6)
Conductance for a Many-Channel System	61	(3)
Electron Conductance Through a Straight 2-D Channel	64	(7)
Qualitative Features of Conductance in a 2-D Channel	66	(5)
Waveguide Measurements of the Properties of Curved Tubes	71	(10)
EM Fields in Thin Resonating Cavities	72	(1)
Mapping EM Energy Densities in Waveguide Cavities	73	(2)
Microwave Measurements with Curved Waveguides	75	(6)
Confined Mode Studies in Waveguides	76	(2)
Waveguide Experiments Above the Lowest Cutoff Frequency	78	(3)
Binding and Transmission in Wires and Waveguides	81	(64)
Tube with a Circular Bend	82	(13)
Bound States in the Limit of Small Curvature	84	(2)
Bound State Properties for a Circular Bend	86	(5)
Transmission in a System with a Circular Bend	91	(4)
Tube with a Single Sharp Bend	95	(7)
Bound States for Structures with a Sharp Bend	98	(1)
Sub-Cutoff Confined Modes in Curved Waveguides	99	(3)
A Tube with a ``T-Stub''	102	(11)
Transmission in Structures with T-Stubs	104	(9)
Structures with Two Coupled Cells	113	(32)
Bound States in Systems with Two Coupled Cells	114	(9)
Transmission Through a System with Two Coupled Cells	123	(3)
Electron Conductance in Double-Bend Quantum Wires	126	(19)
Two-Dimensional Systems with Finite Periodic Structure	145	(36)
Bound States in Periodic 2-D Systems	146	(8)
Origin of Band Structure in Periodic Systems	154	(3)
Transmission and Conductance in Periodic 2-D Systems	157	(16)
Transmission in a ``Staircase'' System	157	(6)
Transmission in the ``Quantum Dot Superlattice''	163	(10)
Defects in Quantum Wire ``Crystals''	173	(8)
Trapped Modes in Band Gaps	175	(6)
Localized Modes in Photonic Crystals	181	(16)
Maxwell's Equations in a Dielectric Medium	182	(5)
Band Structure in a Photonic Crystal	184	(3)
``Waveguides'' in Photonic Crystals	187	(2)
``Bound States'' in Photonic Crystal Waveguides	189	(8)
Bound States in Local Constrictions	190	(3)
Bound States in Curved Photonic Band Gap Waveguides	193	(4)
Epilogue	197	(2)
A. Comparison of Various Approximate Quantum Wells	199	(4)
A.1 Effects of a Diffuse Surface	200	(1)
A.2 Potentials of Finite Depth	201	(1)
A.3 Effect of Sharp Boundaries on Transmission	202	(1)
B. Conducting Sphere on a Grounded Surface	203	(6)
References	209	(10)
Index	219