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

Publication subTitle ：From Electrons to Photonic Crystals and Left-Handed Materials

Author： Markos Peter;Soukoulis Costas M.;;

Publisher： Princeton University Press‎

Publication year： 2008

E-ISBN: 9781400835676

P-ISBN(Paperback): 9780691130033

Subject： O347.4 stress wave

Keyword：物理学,电工技术

Language： ENG

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Description

This textbook offers the first unified treatment of wave propagation in electronic and electromagnetic systems and introduces readers to the essentials of the transfer matrix method, a powerful analytical tool that can be used to model and study an array of problems pertaining to wave propagation in electrons and photons. It is aimed at graduate and advanced undergraduate students in physics, materials science, electrical and computer engineering, and mathematics, and is ideal for researchers in photonic crystals, negative index materials, left-handed materials, plasmonics, nonlinear effects, and optics.

Peter Markos and Costas Soukoulis begin by establishing the analogy between wave propagation in electronic systems and electromagnetic media and then show how the transfer matrix can be easily applied to any type of wave propagation, such as electromagnetic, acoustic, and elastic waves. The transfer matrix approach of the tight-binding model allows readers to understand its implementation quickly and all the concepts of solid-state physics are clearly introduced. Markos and Soukoulis then build the discussion of such topics as random systems and localized and delocalized modes around the transfer matrix, bringing remarkable clarity to the subject. Total internal reflection, Brewster angles, evanescent waves, surface waves, and resonant tunneling in left-handed materials are introduced and treated in detail, as are important new developments like photonic

Chapter

1.1 A Scattering Experiment

1.2 Scattering Matrix and Transfer Matrix

1.3 Transmission and Reflection Amplitudes

1.4 Properties of the Transfer Matrix

1.5 Supplementary Notes

1.6 Problems

2 Rectangular Potentials

2.1 Transfer Matrix

2.2 Transmission Coefficient: E > V[sub(0)]

2.3 Tunneling: 0 < E < V[sub(0)]

2.4 Current Density

2.5 Bound States: V[sub(0)] < E <0

2.6 Inverse Problem for Rectangular Potential

2.7 Problems

3 δ-Function Potential

3.1 Single δ-Function Potential

3.2 Two δ-Function Repulsive Potentials

3.3 Bound States of Double δ-Function Attractive Potentials

3.4 N Identical δ-Function Barriers

3.5 Supplementary Notes

3.6 Problems

4 Kronig-Penney Model

4.1 The Periodic Model

4.2 Allowed Energy Bands

4.3 The Density of States

4.4 Wave Function

4.5 Single Impurity

4.6 N δ-Function Barriers versus Infinite Kronig-Penney Model

4.7 Supplementary Notes

4.8 Problems

5 Tight Binding Model

5.1 Periodic Model

5.2 The Transfer Matrix

5.3 Transmission Coefficient

5.4 Single Impurity

5.5 Transmission through Impurities

5.6 Coupled Pendulum Analogy of the Tight Binding Model

5.7 Problems

6 Tight Binding Models of Crystals

6.1 Periodic One-Dimensional System with Two Different Atoms

6.2 Periodic Model with Different Distances between Neighboring Atoms

6.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a

6.4 Reduced Zone Scheme

6.5 Problems

7 Disordered Models

7.1 Random Tight Binding Model

7.2 Random Kronig-Penney Model

7.3 Supplementary Notes

7.4 Problems

8 Numerical Solution of the Schrödinger Equation

8.1 Numerical Procedure

8.2 Accuracy of Numerical Data

8.3 Numerical Data for Transmission

8.4 Problems

9 Transmission and Reflection of Plane Electromagnetic Waves on an Interface

9.1 Plane Wave at the Interface

9.2 Transmission and Reflection Coefficients

9.3 Interface between Two Dielectric Materials

9.4 Interface between a Dielectric Material and a Metal

9.5 Total Transmission

9.6 Total Reflection

9.7 Problems

10 Transmission and Reflection Coefficients for a Slab

10.1 Transmission and Reflection Amplitudes: TE and TM modes

10.2 Dielectric Slab Embedded in Vacuum

10.3 Transmission through a Metallic Slab

10.4 Problems

11 Surface Waves

11.1 Surface Waves at the Interface between Two Media

11.2 Surface Modes on a Slab

11.3 Experimental Observation of Surface Waves

11.4 Problems

12 Resonant Tunneling through Double-Layer Structures

12.1 Transmission through Two Dielectric Layers

12.2 Transmission through Two Metallic Layers

12.3 Problems

13 Layered Electromagnetic Medium: Photonic Crystals

13.1 Photonic Crystals: Infinite Periodic Layered Medium

13.2 Periodic Arrangement of Dielectric Layers

13.3 Band Structure of Photonic Crystals

13.4 Coupling to a Finite Photonic Crystal

13.5 Layered Dispersive Media

13.6 Kronig-Penney Model of a Photonic Crystal

13.7 Problems

14 Effective Parameters

14.1 Effective Parameters of a Layered Medium

14.2 Retrieval Procedure

14.3 Alternating Layers with Negative Permittivity and Negative Permeability

14.4 Problem

15 Wave Propagation in Nonlinear Structures

15.1 Single δ-Function Layer of a Nonlinear Dielectric

15.2 Nonlinear Kronig-Penney δ-Function Model

15.3 Problems

16 Left-Handed Materials

16.1 Electromagnetic Properties of Left-Handed Materials

16.2 Transmission through a Slab of Left-Handed Material

16.3 Structure of Left-Handed Materials

16.4 Problems

Appendix A: Matrix Operations

A.1 The Determinant and the Trace of the Matrix

A.2 Inverse, Transpose, and Unitary Matrices

A.3 Eigenvalues and Eigenvectors

A.4 Similarity Transformations

A.5 Degeneracy

Appendix B: Summary of Electrodynamics Formulas

B.1 Maxwell’s Equations

B.2 Wave Equation

B.3 Group Velocity and Phase Velocity

B.4 Poynting Vector

B.5 Boundary Condition at an Interface

B.6 Permitivity and Permeability

B.7 Metals

Bibliography

Index

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