Metamaterials and Wave Control Metamaterials and Wave Control Edited by Éric Lheurette Series Editor Pierre-Noël Favennec First published 2013 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc. 27-37 St George’s Road 111 River Street London SW19 4EU Hoboken, NJ 07030 UK USA www.iste.co.uk www.wiley.com © ISTE Ltd 2013 The rights of Éric Lheurette to be identified as the author of this work have been asserted bythem /her/him in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2013947316 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN: 978-1-84821-518-4 Printed and bound in Great Britain by CPI Group (UK) Ltd., Croydon, Surrey CR0 4YY Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Éric LHEURETTE Chapter 1. Overview of Microwave and Optical Metamaterial Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Didier LIPPENS 1.1. Introduction and background . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Omega-type arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1. Dispersion and angular properties . . . . . . . . . . . . . . . . . . 7 1.2.2. Tunable omega-type structure . . . . . . . . . . . . . . . . . . . . 11 1.2.3. Omega-type pattern at millimeter wavelengths . . . . . . . . . . . 14 1.2.4. SRRs at infrared . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3. Transmission lines with series capacitances and shunt inductances . . 17 1.3.1. Tuneable phase shifter for centimeter wavelengths . . . . . . . . . 18 1.3.2. Left-handed transmission lines at tetrahertz frequencies . . . . . . 18 1.4. Fishnet approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4.1. Tunable fishnet for centimeter wavelengths . . . . . . . . . . . . . 21 1.4.2. Terahertz subwavelength holes arrays . . . . . . . . . . . . . . . . 21 1.4.3. Wedge-type devices . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4.4. Fishnet with twisted apertures: chiral device . . . . . . . . . . . . 27 1.5. Full dielectric approach: Mie resonance based devices . . . . . . . . . 28 1.5.1. BST cube technology . . . . . . . . . . . . . . . . . . . . . . . . . 30 1.6. Photonic crystal technology . . . . . . . . . . . . . . . . . . . . . . . . 31 1.6.1. Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.6.2. Flat lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.6.3. Carpet cloaking devices . . . . . . . . . . . . . . . . . . . . . . . . 35 1.7. Conclusion and prospects . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.8. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.9. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 vi Metamaterials and Wave Control Chapter 2. MetaLines: Transmission Line Approach for the Design of Metamaterial Devices . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Bruno SAUVIAC 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.2. Historical concepts of transmission lines and homogenization . . . . . 43 2.2.1. Electrical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.2.2. Homogenization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3. CRLH transmission lines . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.1. MetaLine cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.2. Case with (cid:550) < (cid:550) . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 S p 2.3.3. Case with (cid:550) > (cid:550) . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 S p 2.3.4. Balanced case with (cid:550) = (cid:550) . . . . . . . . . . . . . . . . . . . . . . 49 S p 2.4. Some technical approaches to realize MetaLines . . . . . . . . . . . . . 50 2.4.1. Context. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.4.2. Discrete component approach . . . . . . . . . . . . . . . . . . . . . 51 2.4.3. Distributed or semi-lumped element approach in microstrip technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.4.4. Distributed element approach in coplanar waveguide technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.5. The resonant approach . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.5. Toward tunability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.5.1. The dual-band behavior . . . . . . . . . . . . . . . . . . . . . . . . 59 2.5.2. Mechanical agility . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.5.3. CRLH line controlled with activecomponents . . . . . . . . . . . . 60 2.5.4. Ferroelectric agility . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.5.5. Ferrimagnetic agility . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 3. Metamaterials for Non-Radiative Microwave Functions and Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Divitha SEETHARAMDOO and Bruno SAUVIAC 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2. Metamaterials for non-radiative applications . . . . . . . . . . . . . . . 68 3.2.1. Miniaturization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.2.2. Bandwidth improvement . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2.3. Dual band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2.4. Zeroth-order resonator (ZOR) . . . . . . . . . . . . . . . . . . . . . 73 3.3. Metamaterials for antennas at microwave frequencies . . . . . . . . . . 75 3.3.1. Antenna miniaturization . . . . . . . . . . . . . . . . . . . . . . . . 76 3.3.2. Efficient electrically small antennas with metamaterials . . . . . . 76 3.3.3. Patch antenna miniaturization considering metamaterial substrate . . 78 3.3.4. Miniature metamaterial antennas: numerical and experimental attempts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Table of Contents vii 3.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Chapter 4. Toward New Prospects for Electromagnetic Compatibility . . 87 Divitha SEETHARAMDOO 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.2. Electromagnetic compatibility . . . . . . . . . . . . . . . . . . . . . . . 88 4.2.1. Trends in the transport and telecommunication industries . . . . . 89 4.2.2. EMC challenges induced by recent industrial trends – metamaterials for EMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.3. Electromagnetic shielding – potential of metamaterials . . . . . . . . . 91 4.3.1. Figures of merit for shielding configurations . . . . . . . . . . . . 92 4.3.2. One-dimensional metamaterial shield . . . . . . . . . . . . . . . . 93 4.4. Metamaterials for 3D shielded cavities – application to electromagnetic reverberation chambers . . . . . . . . . . . . . . . . . . . . 95 4.4.1. General case of a 3D shielded cavity . . . . . . . . . . . . . . . . . 95 4.4.2. Concept of subwavelength cavities . . . . . . . . . . . . . . . . . . 96 4.4.3. Design of a metamaterial surface of reflection coefficient with arbitrary phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.4.4. Application of subwavelength metamaterial cavity to reverberation chambers for EMC tests . . . . . . . . . . . . . . . . . . . 102 4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Chapter 5. Dissipative Loss in Resonant Metamaterials . . . . . . . . . . . 111 Philippe TASSIN, Thomas KOSCHNY, and Costas M. SOUKOULIS 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2. What is the best conducting material?. . . . . . . . . . . . . . . . . . . 115 5.3. Optimize the geometry of meta-atoms . . . . . . . . . . . . . . . . . . 122 5.3.1. Increase RLC inductance . . . . . . . . . . . . . . . . . . . . . . . 122 5.3.2. Geometric tailoring of corners and filling fraction . . . . . . . . . 124 5.3.3. Benefits from periodicity effects . . . . . . . . . . . . . . . . . . . 124 5.3.4. Suppress internal resonant currents in strongly coupled fishnets . . . 125 5.4. Use gain to offset the impact of dissipative loss . . . . . . . . . . . . . 126 5.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.4.2. Self-consistent simulations of loss compensation in metamaterials . . 127 5.4.3. Experimental evidence for loss compensation in metamaterials . . . 128 5.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Chapter 6. Transformation Optics and Antennas . . . . . . . . . . . . . . . 133 André de LUSTRAC, Shah Nawaz BUROKUR and Paul-Henri TICHIT 6.1. Transformation optics . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.1.1. Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.1.2. First example: waveguide taper . . . . . . . . . . . . . . . . . . . . 137 viii Metamaterials and Wave Control 6.2. Applications to antennas . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.2.1. Directive antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.2.2. Isotropic antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.3. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.4. Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Chapter 7. Metamaterials for Control of Surface Electromagnetic and Liquid Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Sébastien GUENNEAU, Mohamed FARHAT, Muamer KADIC, Stefan ENOCH and Romain QUIDANT 7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.1.1. Prehistory of acoustic metamaterials . . . . . . . . . . . . . . . . . 163 7.1.2. Correspondences between electromagneticand acoustic metamaterials via locally resonant models . . . . . . . . . . . . . . . . . . 166 7.2. Acoustic cloaking for liquid surface waves . . . . . . . . . . . . . . . . 168 7.2.1. From Navier–Stokes to Helmholtz . . . . . . . . . . . . . . . . . . 169 7.2.2. Effective anisotropic shear viscosity through homogenization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 7.2.3. Numerical analysis of LSW cloaking . . . . . . . . . . . . . . . . . 173 7.2.4. Experimental measurements of LSW cloaking . . . . . . . . . . . . 175 7.3. Optical cloaking for surface plasmon polaritons . . . . . . . . . . . . . 177 7.3.1. Introduction to surface plasmon polaritons . . . . . . . . . . . . . . 177 7.3.2. From transformational optics to plasmonics . . . . . . . . . . . . . 181 7.3.3. Numerical analysis of plasmonic cloaking . . . . . . . . . . . . . . 183 7.3.4. Experimental measurements of plasmonic cloaking . . . . . . . . . 187 7.4. Concluding remarks on LSW and SPP cloaking . . . . . . . . . . . . . 190 7.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Chapter 8. Classical Analog of Electromagnetically Induced Transparency . 195 Philippe TASSIN, Thomas KOSCHNY and Costas M. SOUKOULIS 8.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 8.2. Design of EIT metamaterials . . . . . . . . . . . . . . . . . . . . . . . . 198 8.3. A simple model for EIT metamaterials – and electromagnetically induced absorption . . . . . . . . . . . . . . . . . . . . 203 8.3.1. The two-oscillator model . . . . . . . . . . . . . . . . . . . . . . . . 203 8.3.2. The radiating two-oscillator model . . . . . . . . . . . . . . . . . . 205 8.4. Electromagnetically induced absorption . . . . . . . . . . . . . . . . . . 207 8.5. EIT metamaterials for sensors . . . . . . . . . . . . . . . . . . . . . . . 209 8.6. EIT metamaterials for nonlinear and tunable operation . . . . . . . . . 211 8.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217