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Electromagnetic Surface Waves This page is intentionally left blank Electromagnetic Surface Waves A Modern Perspective John A. Polo, Jr. Department of Physics and Technology Edinboro University of Pennsylvania, Edinboro, PA, USA Tom G. Mackay School of Mathematics University of Edinburgh, Edinburgh, UK Akhlesh Lakhtakia Department of Engineering Science and Mechanics The Pennsylvania State University, University Park, PA, USA AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Elsevier 225 Wyman Street, Waltham, MA 02451, USA 32 Jamestown Road, London NW1 7BY First edition Copyright © 2013 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-397024-4 For information on all Elsevier publications visit our website at store.elsevier.com This book has been manufactured using Print On Demand technology. Each copy is produced to order and is limited to black ink. The online version of this book will show color figures where appropriate. To His mother, Eunice Polo (1928–2002) —John A. Polo, Jr. His father, William Mackay (1927–2012). —Tom G. Mackay His students who have accompanied him on old and new paths —Akhlesh Lakhtakia This page is intentionally left blank Contents Preface xiii List of Acronyms and Principal Symbols xvii 1 Surface Waves 1 1.1 Introduction 1 1.2 A Brief History 2 1.3 Simple SPP Wave 6 1.3.1 Canonical Boundary-Value Problem 6 1.3.2 Practical Configurations 10 1.3.2.1 Prism-Coupled Configurations 10 1.3.2.2 Grating-Coupled Configuration 13 1.3.2.3 Waveguide-Coupled Configurations 14 1.4 Dielectric Materials 15 1.4.1 Solid Crystals 15 1.4.2 Particulate Composite Materials 16 1.4.3 Nanoengineered Materials 16 1.4.3.1 Columnar Thin Films 17 1.4.3.2 Sculptured Thin Films 19 1.4.3.3 Photonic Crystals 21 1.4.3.4 Rugate Filters 23 1.4.4 Liquid Crystals 24 1.4.5 Reusch Piles 25 1.5 Negative-Phase-Velocity Materials 26 1.6 Bianisotropic Materials 27 1.7 Taxonomy of Electromagnetic Surface Waves 27 1.7.1 SPP Waves 27 1.7.2 Dyakonov Waves 30 1.7.3 Tamm Waves 31 1.7.4 Dyakonov-Tamm Waves 32 1.7.5 Emerging Types of Surface Waves 32 1.8 Applications 33 1.8.1 SPP Waves 33 1.8.2 Other Surface Waves 35 1.8.3 STFs for Optical Sensing 36 viii Contents 2 Surface-Plasmon-Polariton Waves I 37 2.1 Introduction 37 2.2 Canonical Boundary-Value Problem 37 2.2.1 Geometry 38 2.2.2 Field Representation 38 2.2.3 Linear Polarization States 41 2.2.4 Boundary Conditions 41 2.2.5 Amplitude Vectors 42 2.2.6 Time-Averaged Poynting Vector 43 2.2.7 Wavenumbers 43 2.2.8 Phase Speed and Characteristic Lengths 44 2.2.9 Characteristics of Simple SPP Waves 45 2.2.10 Fano Wave 46 2.2.11 Zenneck Wave 48 2.3 Optical Excitation of Simple SPP Waves 48 2.3.1 Turbadar-Kretschmann-Raether Configuration 50 2.3.1.1 Boundary-Value Problem 52 2.3.1.2 p-Polarized Incident Plane Wave 53 2.3.1.3 s-Polarized Incident Plane Wave 56 2.3.1.4 Illustrative Results 58 2.3.1.5 SPR-Based Prism-Coupled Sensing 59 2.3.1.6 Fiber-Optic Coupling 60 2.3.2 Turbadar-Otto Configuration 61 2.3.3 Sarid Configuration 63 2.3.4 Grating-Coupled Configuration 66 2.3.4.1 Incident Plane Wave 67 2.3.4.2 Reflected and Transmitted Field Phasors 68 2.3.4.3 Linear Reflectances and Transmittances 69 2.3.4.4 Rigorous Coupled-Wave Approach 69 2.3.4.5 Stable RCWA Algorithm 75 2.3.4.6 Excitation of an SPP Wave 77 2.3.4.7 Illustrative Results 78 2.3.5 Waveguide-Coupled Configuration 79 2.4 Nonlinear Dielectric Materials 79 3 General Theory of Surface-Wave Propagation 81 3.1 Introduction 81 3.2 Bianisotropic Materials 81 3.2.1 Maxwell Postulates 82 3.2.2 Linear Constitutive Relations 83 3.2.3 Periodic Nonhomogeneity 84 3.2.4 Homogeneous Bianisotropic Materials 84 3.3 Propagation in a Homogeneous Bianisotropic Material 85 Contents ix 3.3.1 Matrix Ordinary Differential Equation 85 3.3.2 Eigenmodes 88 3.4 Propagation in a Periodically Nonhomogeneous Bianisotropic Material 90 3.4.1 Matrix Ordinary Differential Equation 90 3.4.2 Eigenmodes 93 3.5 Canonical Boundary-Value Problem 94 3.5.1 Dispersion Equation 94 3.5.2 Computational Matters 97 3.6 Modified Canonical Boundary-Value Problem 98 3.7 Prism-Coupled Configuration 101 3.7.1 Incident, Reflected, and Transmitted Plane Waves 102 3.7.2 Solution of Boundary-Value Problem 104 3.7.3 Linear Reflectances and Transmittances 106 3.7.4 Circular Reflectances and Transmittances 107 3.8 Grating-Coupled Configuration 108 3.8.1 Incident Plane Wave 110 3.8.2 Reflected and Transmitted Field Phasors 111 3.8.3 Linear Reflectances and Transmittances 112 3.8.4 Circular Reflectances and Transmittances 113 3.8.5 Rigorous Coupled-Wave Approach 114 3.8.6 Stable RCWA Algorithm 122 3.8.7 Excitation of a Surface Wave 125 4 Dyakonov Waves 127 4.1 Introduction 127 4.2 Interface of an Anisotropic Material and an Isotropic Material 128 4.2.1 Interface of a Uniaxial Material and an Isotropic Material 128 4.2.1.1 Optic Axis in Interface Plane 128 4.2.1.2 Optic Axis not in Interface Plane 135 4.2.2 Interface of a Biaxial Material and an Isotropic Material 136 4.2.2.1 Optic Ray Axes in Interface Plane 136 4.2.2.2 Optic Ray Axes not in Interface Plane 137 4.3 Interface of Two Anisotropic Materials 138 4.3.1 Interface of Two Uniaxial Materials 138 4.3.1.1 Optic Axes in Interface Plane 138 4.3.1.2 Optic Axes not in Interface Plane 143 4.3.2 Interface of Two Biaxial Materials 144 4.3.2.1 Optic Ray Axes in Interface Plane 144 4.3.2.2 Optic Ray Axes not in Interface Plane 145 4.4 Nanostructured Materials 145 4.4.1 Liquid Crystals 146