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

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Overview

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 crystals, negative index materials, and surface plasmons. Problem sets aid students working through the subject for the first time.

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Editorial Reviews

Zentralblatt MATH Database
The book can be recommended to everyone who is going to enter the field of wave propagation.
— Aleksander Pankov
Zentralblatt MATH

The book can be recommended to everyone who is going to enter the field of wave propagation.
— Aleksander Pankov
Choice - M. Coplan
In this excellent volume, physicists Marko? and Soukoulis treat a wide range of physical phenomenon with a single unifying mathematical matrix method.
Zentralblatt MATH - Aleksander Pankov
The book can be recommended to everyone who is going to enter the field of wave propagation.
Mathematical Reviews - David H. Delphenich
This book is conceptually well-organized and concisely focused in its applications. It also has numerous illustrative problems to give the reader experience with using the techniques. It will undoubtedly emerge as a standard upper-divison undergraduate/graduate text for the teaching of the subject.
Annalen der Physik - Ulrich Eckern
I strongly recommend this volume for undergraduate students, graduate students, and researchers alike. It is very carefully prepared and offers insights into numerous aspects of wave propagation, from standard problems of quantum theory to topics of today's research. In particular, the graphical supplements allow for an easy comprehension of the theoretical considerations. For students, the book is a profitable amendment to standard treatises on quantum theory, electrodynamics, and solid state physics. Researchers will enjoy the succinct presentation of a variety of topics from a unified point of view, and, last but not least, professors will be able to extract new ideas (and some exercises) for their lectures from this remarkable volume.
From the Publisher

"In this excellent volume, physicists Markoš and Soukoulis treat a wide range of physical phenomenon with a single unifying mathematical matrix method."--M. Coplan, Choice

"The book can be recommended to everyone who is going to enter the field of wave propagation."--Aleksander Pankov, Zentralblatt MATH

"This book is conceptually well-organized and concisely focused in its applications. It also has numerous illustrative problems to give the reader experience with using the techniques. It will undoubtedly emerge as a standard upper-divison undergraduate/graduate text for the teaching of the subject."--David H. Delphenich, Mathematical Reviews

"I strongly recommend this volume for undergraduate students, graduate students, and researchers alike. It is very carefully prepared and offers insights into numerous aspects of wave propagation, from standard problems of quantum theory to topics of today's research. In particular, the graphical supplements allow for an easy comprehension of the theoretical considerations. For students, the book is a profitable amendment to standard treatises on quantum theory, electrodynamics, and solid state physics. Researchers will enjoy the succinct presentation of a variety of topics from a unified point of view, and, last but not least, professors will be able to extract new ideas (and some exercises) for their lectures from this remarkable volume."--Ulrich Eckern, Annalen der Physik

Choice
In this excellent volume, physicists Marko? and Soukoulis treat a wide range of physical phenomenon with a single unifying mathematical matrix method.
— M. Coplan
Mathematical Reviews
This book is conceptually well-organized and concisely focused in its applications. It also has numerous illustrative problems to give the reader experience with using the techniques. It will undoubtedly emerge as a standard upper-divison undergraduate/graduate text for the teaching of the subject.
— David H. Delphenich
Annalen der Physik
I strongly recommend this volume for undergraduate students, graduate students, and researchers alike. It is very carefully prepared and offers insights into numerous aspects of wave propagation, from standard problems of quantum theory to topics of today's research. In particular, the graphical supplements allow for an easy comprehension of the theoretical considerations. For students, the book is a profitable amendment to standard treatises on quantum theory, electrodynamics, and solid state physics. Researchers will enjoy the succinct presentation of a variety of topics from a unified point of view, and, last but not least, professors will be able to extract new ideas (and some exercises) for their lectures from this remarkable volume.
— Ulrich Eckern
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Product Details

  • ISBN-13: 9780691130033
  • Publisher: Princeton University Press
  • Publication date: 4/1/2008
  • Pages: 376
  • Product dimensions: 7.00 (w) x 10.00 (h) x 1.05 (d)

Meet the Author

Peter Markos is a researcher at the Institute of Physics at the Slovak Academy of Sciences. Costas M. Soukoulis is Distinguished Professor of Physics at Iowa State University and senior physicist at Ames Laboratory. His books include "Photonic Band Gap Materials" and "Photonic Crystals and Light Localization in the Twenty-First Century".

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Table of Contents

Preface ix

Chapter 1: Transfer Matrix 1
1.1 A Scattering Experiment 2
1.2 Scattering Matrix and Transfer Matrix 3
1.3 Transmission and Reflection Amplitudes 10
1.4 Properties of the Transfer Matrix 12
1.5 Supplementary Notes 19
1.6 Problems 24

Chapter 2: Rectangular Potentials 28
2.1 Transfer Matrix 29
2.2 Transmission Coefficient: E > V0 32
2.3 Tunneling: 0 < E < V0 38
2.4 Current Density 42
2.5 Bound States: V0 < E < 0 45
2.6 Inverse Problem for Rectangular Potential 47
2.7 Problems 49

Chapter 3: δ -Function Potential 56
3.1 Single δ-Function Potential 56
3.2 Two δ-Function Repulsive Potentials 60
3.3 Bound States of Double δ-Function Attractive Potentials 62
3.4 N Identical δ-Function Barriers 64
3.5 Supplementary Notes 68
3.6 Problems 69

Chapter 4: Kronig-Penney Model 74
4.1 The Periodic Model 75
4.2 Allowed Energy Bands 76
4.3 The Density of States 81
4.4 Wave Function 83
4.5 Single Impurity 84
4.6 N δ-Function Barriers versus Infinite Kronig-Penney Model 87
4.7 Supplementary Notes 88
4.8 Problems 91

Chapter 5: Tight Binding Model 98
5.1 Periodic Model 100
5.2 The Transfer Matrix 104
5.3 Transmission Coefficient 106
5.4 Single Impurity 107
5.5 Transmission through Impurities 108
5.6 Coupled Pendulum Analogy of the Tight Binding Model 111
5.7 Problems 114

Chapter 6: Tight Binding Models of Crystals 120
6.1 Periodic One-Dimensional System with Two Different Atoms 120
6.2 Periodic Model with Different Distances between Neighboring Atoms 125
6.3 Periodic One-dimensional System with Two Different Atoms and Spatial Period l = 4a 126
6.4 Reduced Zone Scheme 129
6.5 Problems 130

Chapter 7: Disordered Models 137
7.1 Random Tight Binding Model 138
7.2 Random Kronig-Penney Model 150
7.3 Supplementary Notes 159
7.4 Problems 168

Chapter 8: Numerical Solution of the Schrödinger Equation 173
8.1 Numerical Procedure 173
8.2 Accuracy of Numerical Data 174
8.3 Numerical Data for Transmission 177
8.4 Problems 179

Chapter 9: Transmission and Reflection of Plane Electromagnetic Waves on an Interface 181
9.1 Plane Wave at the Interface 181
9.2 Transmission and Reflection Coefficients 184
9.3 Interface between Two Dielectric Materials 189
9.4 Interface between a Dielectric Material and a Metal 190
9.5 Total Transmission 195
9.6 Total Reflection 198
9.7 Problems 200

Chapter 10: Transmission and Reflection Coefficients for a Slab 205
10.1 Transmission and Reflection Amplitudes: TE and TM modes 206
10.2 Dielectric Slab Embedded in Vacuum 209
10.3 Transmission through a Metallic Slab 220
10.4 Problems 223

Chapter 11: Surface Waves 225
11.1 Surface Waves at the Interface between Two Media 226
11.2 Surface Modes on a Slab 233
11.3 Experimental Observation of Surface Waves 237
11.4 Problems 241

Chapter 12: Resonant Tunneling through Double-Layer Structures 243
12.1 Transmission through Two Dielectric Layers 243
12.2 Transmission through Two Metallic Layers 246
12.3 Problems 248

Chapter 13: Layered Electromagnetic Medium: Photonic Crystals 249
13.1 Photonic Crystals: Infinite Periodic Layered Medium 250
13.2 Periodic Arrangement of Dielectric Layers 252
13.3 Band Structure of Photonic Crystals 254
13.4 Coupling to a Finite Photonic Crystal 258
13.5 Layered Dispersive Media 263
13.6 Kronig-Penney Model of a Photonic Crystal 269
13.7 Problems 271

Chapter 14: Effective Parameters 275
14.1 Effective Parameters of a Layered Medium 276
14.2 Retrieval Procedure 279
14.3 Alternating Layers with Negative Permittivity and Negative Permeability 282
14.4 Problem 285

Chapter 15: Wave Propagation in Nonlinear Structures 286
15.1 Single δ-Function Layer of a Nonlinear Dielectric 286
15.2 Nonlinear Kronig-Penney δ-Function Model 290
15.3 Problems 296

Chapter 16: Left-Handed Materials 298
16.1 Electromagnetic Properties of Left-Handed Materials 299
16.2 Transmission through a Slab of Left-Handed Material 303
16.3 Structure of Left-Handed Materials 309
16.4 Problems 317

Appendix A: Matrix Operations 321
A.1 The Determinant and the Trace of the Matrix 321
A.2 Inverse, Transpose, and Unitary Matrices 322
A.3 Eigenvalues and Eigenvectors 324
A.4 Similarity Transformations 324
A.5 Degeneracy 325
Appendix B: Summary of Electrodynamics Formulas 327
B.1 Maxwell's Equations 327
B.2 Wave Equation 330
B.3 Group Velocity and Phase Velocity 331
B.4 Poynting Vector 333
B.5 Boundary Condition at an Interface 334
B.6 Permitivity and Permeability 335
B.7 Metals 337

Bibliography 341
Index 349

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