Waves in gradient metamaterials

339 Pages·2013·5.035 MB·English

by  A B Shvart︠s︡burg, A A Maradudin

Waves in Gradient
Metamaterials
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Waves in Gradient
Metamaterials
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Alexander B Shvartsburg
Russian Academy of Sciences, Russia
Alexei A Maradudin
The University of California, Irvine, USA
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
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Published by
World Scientific Publishing Co. Pte. Ltd.
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
WAVES IN GRADIENT METAMATERIALS
Copyright © 2013 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN 978-981-4436-95-3
In-house Editor: Song Yu
Typeset by Stallion Press
Email: [email protected]
Printed in Singapore
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To the memory of a dear friend and colleague,
Tamara Aleksandrovna Leskova
v
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CONTENTS
1. Introduction 1
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 12
2. Non-local Dispersion of Heterogeneous Dielectrics 15
2.1. Giant Heterogeneity-Induced Dispersion of Gradient
Photonic Barriers . . . . . . . . . . . . . . . . . . . 18
2.2. Reflectance and Transmittance of Subwavelength
Gradient Photonic Barriers: Generalized Fresnel
Formulae . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3. Non-Fresnel Reflectance of Unharmonic Periodic
Gradient Structures . . . . . . . . . . . . . . . . . . 28
Comments and Conclusions to Chapter 2 . . . . . . . . . 38
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 41
3. Gradient Photonic Barriers: Generalizations
of the Fundamental Model 43
3.1. Effects of the Steepness of the Refractive Index
Profile near the Barrier Boundaries on Reflectance
Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2. Asymmetric Photonic Barriers . . . . . . . . . . . . 47
3.3. Inverse Functions and Parametric Presentations
— New Ways to Model the Photonic Barriers . . . 55
Comments and Conclusions to Chapter 3 . . . . . . . . . 63
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 65
vii
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viii Waves in Gradient Metamaterials
4. Resonant Tunneling of Light Through Gradient
Dielectric Nanobarriers 67
4.1. Transparency Windows for Evanescent
Modes: Amplitude — Phase Spectra of
Transmitted Waves . . . . . . . . . . . . . . . . . . 73
4.2. Energy Transfer in Gradient Media
by Evanescent Waves . . . . . . . . . . . . . . . . . 78
4.3. Weakly Attenuated Tunneling of Radiation
Through a Subwavelength Slit, Confined
by Curvilinear Surfaces . . . . . . . . . . . . . . . . 82
Comments and Conclusions to Chapter 4 . . . . . . . . . 91
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 92
5. Interaction of Electromagnetic Waves with
Continuously Structured Dielectrics 93
5.1. Reflectance/Transmittance Spectra of Lossy
Gradient Nanostructures . . . . . . . . . . . . . . . 97
5.2. Interplay of Natural and Artificial Dispersion
in Gradient Coatings . . . . . . . . . . . . . . . . . 100
5.3. EM Radiation in Gradient Superlattices . . . . . . 109
Comments and Conclusions to Chapter 5 . . . . . . . . . 117
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 119
6. Polarization Phenomena in Gradient Nanophotonics 121
6.1. Wideangle Broadband Antireflection Coatings . . . 124
6.2. Polarization-Dependent Tunneling of Light
in Gradient Optics . . . . . . . . . . . . . . . . . . 133
6.3. Reflectionless Tunneling and Goos–H¨anchen
Effect in Gradient Metamaterials . . . . . . . . . . 140
Comments and Conclusions to Chapter 6 . . . . . . . . . 147
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 150
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Contents ix
7. Gradient Optics of Guided and Surface
Electromagnetic Waves 151
7.1. Narrow-Banded Spectra of S-polarized Guided
Electromagnetic Waves on the Surface of a Gradient
Medium: Heterogeneity-Induced Dispersion . . . . 153
7.1.1. 0 <ω < Ωc . . . . . . . . . . . . . . . . . . 159
7.1.2. ω > Ωc . . . . . . . . . . . . . . . . . . . . . 164
7.2. Surface Electromagnetic Waves on a Curvilinear
Interface: Geometrical Dispersion . . . . . . . . . . 165
7.3. Surface Electromagnetic Waves on Rough Surfaces:
Roughness-Induced Dispersion . . . . . . . . . . . . 177
7.3.1. Periodically corrugated surfaces . . . . . . . 182
7.3.2. A randomly rough surface . . . . . . . . . . 187
Comments and Conclusions to Chapter 7 . . . . . . . . . 197
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 199
8. Non-local Acoustic Dispersion of Gradient Solid Layers 203
8.1. Gradient Acoustic Barrier with Variable Density:
Reflectance/Transmittance Spectra of Longitudinal
Sound Waves . . . . . . . . . . . . . . . . . . . . . 207
8.2. Heterogeneous Elastic Layers: “Auxiliary Barrier”
Method . . . . . . . . . . . . . . . . . . . . . . . . 210
8.3. Double Acoustic Barriers: Combined Effects
of Gradient Elasticity and Density . . . . . . . . . 217
Comments and Conclusions to Chapter 8 . . . . . . . . . 224
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . 225
9. Shear Acoustic Waves in Gradient Elastic Solids 227
9.1. Strings with Variable Density . . . . . . . . . . . . 229
9.2. Torsional Oscillations of a Graded Elastic Rod . . . 234
9.3. Tunneling of Acoustic Waves Through a Gradient
Solid Layer . . . . . . . . . . . . . . . . . . . . . . 243