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ELECTROMAGNETIC METAMATERIALS

ELECTROMAGNETIC METAMATERIALS: TRANSMISSION LINE THEORY AND MICROWAVE APPLICATIONS The Engineering Approach CHRISTOPHE CALOZ ´Ecole Polytechnique de Montr´eal TATSUO ITOH University of California at Los Angeles A JOHN WILEY & SONS, INC., PUBLICATION

Copyright  2006 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and speciﬁcally disclaim any implied warranties of merchantability or ﬁtness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of proﬁt or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Caloz, Christophe, 1969- Electromagnetic metamaterials : transmission line theory and microwave applications : the engineering approach / Christophe Caloz, Tatsuo Itoh. p.cm. “Wiley-Interscience publication.” Includes bibliographical references and index. ISBN-10: 0-471-66985-7 (alk.paper) ISBN-13: 978-0-471-66985-2 (alk.paper) 1. Magnetic materials. 2. Nanostructured materials. 3. Microwave transmission lines. I. Itoh, Tatsuo. II. Title. TK454.4.M3C36 2006 620.1 18—dc22 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 2005048976

To Dominique, Maxime, and Rapha¨el Christophe

CONTENTS Preface Acknowledgments Acronyms 1 Introduction xiii xv xvii 1 1.1 Deﬁnition of Metamaterials (MTMs) and Left-Handed (LH) MTMs, 1 1.2 Theoretical Speculation by Viktor Veselago, 3 1.3 Experimental Demonstration of Left-Handedness, 4 1.4 Further Numerical and Experimental Conﬁrmations, 9 1.5 “Conventional” Backward Waves and Novelty of LH MTMs, 10 1.6 Terminology, 12 1.7 Transmission Line (TL) Approach, 12 1.8 Composite Right/Left-Handed (CRLH) MTMs, 16 1.9 MTMs and Photonic Band-Gap (PBG) Structures, 17 1.10 Historical “Germs” of MTMs, 20 References, 22 2 Fundamentals of LH MTMs 2.1 Left-Handedness from Maxwell’s Equations, 28 2.2 Entropy Conditions in Dispersive Media, 33 2.3 Boundary Conditions, 38 27 vii

viii CONTENTS 2.4 Reversal of Doppler Effect, 39 2.5 Reversal of Vavilov- ˘Cerenkov Radiation, 41 2.6 Reversal of Snell’s Law: Negative Refraction, 43 2.7 Focusing by a “Flat LH Lens”, 46 2.8 Fresnel Coefﬁcients, 48 2.9 Reversal of Goos-H¨anchen Effect, 50 2.10 Reversal of Convergence and Divergence in Convex and Concave Lenses, 51 2.11 Subwavelength Diffraction, 53 References, 57 3 TL Theory of MTMs 59 3.1 Ideal Homogeneous CRLH TLs, 59 3.1.1 Fundamental TL Characteristics, 60 3.1.2 Equivalent MTM Constitutive Parameters, 67 3.1.3 Balanced and Unbalanced Resonances, 70 3.1.4 Lossy Case, 74 3.2 LC Network Implementation, 79 3.2.1 Principle, 79 3.2.2 Difference with Conventional Filters, 83 3.2.3 Transmission Matrix Analysis, 85 3.2.4 Input Impedance, 100 3.2.5 Cutoff Frequencies, 103 3.2.6 Analytical Dispersion Relation, 106 3.2.7 Bloch Impedance, 113 3.2.8 Effect of Finite Size in the Presence of Imperfect Matching, 115 3.3 Real Distributed 1D CRLH Structures, 119 3.3.1 General Design Guidelines, 120 3.3.2 Microstrip Implementation, 122 3.3.3 Parameters Extraction, 124 3.4 Experimental Transmission Characteristics, 127 3.5 Conversion from Transmission Line to Constitutive Parameters, 131 References, 131 4 Two-Dimensional MTMs 4.1 Eigenvalue Problem, 134 133 4.1.1 General Matrix System, 134 4.1.2 CRLH Particularization, 138 4.1.3 Lattice Choice, Symmetry Points, Brillouin Zone, and 2D Dispersion Representations, 139 4.2 Driven Problem by the Transmission Matrix Method (TMM), 143 4.2.1 Principle of the TMM, 144 4.2.2 Scattering Parameters, 145

CONTENTS ix 4.2.3 Voltage and Current Distributions, 147 4.2.4 Interest and Limitations of the TMM, 154 4.3 Transmission Line Matrix (TLM) Modeling Method, 154 4.3.1 TLM Modeling of the Unloaded TL Host Network, 155 4.3.2 TLM Modeling of the Loaded TL Host Network (CRLH), 158 4.3.3 Relationship between Material Properties and the TLM Model Parameters, 159 4.3.4 Suitability of the TLM Approach for MTMs, 161 4.4 Negative Refractive Index (NRI) Effects, 162 4.4.1 Negative Phase Velocity, 162 4.4.2 Negative Refraction, 163 4.4.3 Negative Focusing, 165 4.4.4 RH-LH Interface Surface Plasmons, 167 4.4.5 Reﬂectors with Unusual Properties, 169 4.5 Distributed 2D Structures, 170 4.5.1 Description of Possible Structures, 171 4.5.2 Dispersion and Propagation Characteristics, 173 4.5.3 Parameter Extraction, 178 4.5.4 Distributed Implementation of the NRI Slab, 183 References, 190 5 Guided-Wave Applications 5.1 Dual-Band Components, 193 192 5.1.1 Dual-Band Property of CRLH TLs, 193 5.1.2 Quarter-Wavelength TL and Stubs, 197 5.1.3 Passive Component Examples: Quadrature Hybrid and Wilkinson Power Divider, 201 5.1.3.1 Quadrature Hybrid, 201 5.1.3.2 Wilkinson Power Divider, 202 5.1.4 Nonlinear Component Example: Quadrature Subharmonically Pumped Mixer, 205 5.2 Enhanced-Bandwidth Components, 210 5.2.1 Principle of Bandwidth Enhancement, 211 5.2.2 Rat-Race Coupler Example, 215 5.3 Super-compact Multilayer “Vertical” TL, 217 5.3.1 “Vertical” TL Architecture, 219 5.3.2 TL Performances, 221 5.3.3 Diplexer Example, 225 5.4 Tight Edge-Coupled Coupled-Line Couplers (CLCs), 227 5.4.1 Generalities on Coupled-Line Couplers, 228 5.4.1.1 TEM and Quasi-TEM Symmetric Coupled-Line Structures with Small Interspacing: Impedance Coupling (IC), 228 5.4.1.2 Non-TEM Symmetric Coupled-Line Structures with Relatively Large Spacing: Phase Coupling (PC), 232

x CONTENTS 5.4.1.3 Summary on Symmetric Coupled-Line Structures, 233 5.4.1.4 Asymmetric Coupled-Line Structures, 234 5.4.1.5 Advantages of MTM Couplers, 235 5.4.2 Symmetric Impedance Coupler, 235 5.4.3 Asymmetric Phase Coupler, 245 5.5 Negative and Zeroth-Order Resonator, 249 5.5.1 Principle, 249 5.5.2 LC Network Implementation, 251 5.5.3 Zeroth-Order Resonator Characteristics, 253 5.5.4 Circuit Theory Veriﬁcation, 256 5.5.5 Microstrip Realization, 258 References, 259 6 Radiated-Wave Applications 261 6.1 Fundamental Aspects of Leaky-Wave Structures, 262 6.1.1 Principle of Leakage Radiation, 262 6.1.2 Uniform and Periodic Leaky-Wave Structures, 266 6.1.2.1 Uniform LW Structures, 266 6.1.2.2 Periodic LW Structures, 268 6.1.3 Metamaterial Leaky-Wave Structures, 269 6.2 Backﬁre-to-Endﬁre (BE) Leaky-Wave (LW) Antenna, 270 6.3 Electronically Scanned BE LW Antenna, 275 6.3.1 Electronic Scanning Principle, 276 6.3.2 Electronic Beamwidth Control Principle, 277 6.3.3 Analysis of the Structure and Results, 279 6.4 Reﬂecto-Directive Systems, 282 6.4.1 Passive Retro-Directive Reﬂector, 283 6.4.2 Arbitrary-Angle Frequency Tuned Reﬂector, 286 6.4.3 Arbitrary-Angle Electronically Tuned Reﬂector, 287 6.5 Two-Dimensional Structures, 290 6.5.1 Two-Dimensional LW Radiation, 290 6.5.2 Conical-Beam Antenna, 292 6.5.3 Full-Space Scanning Antenna, 296 6.6 Zeroth Order Resonating Antenna, 297 6.7 Dual-Band CRLH-TL Resonating Ring Antenna, 300 6.8 Focusing Radiative “Meta-Interfaces”, 304 6.8.1 Heterodyne Phased Array, 305 6.8.2 Nonuniform Leaky-Wave Radiator, 310 References, 313 7 The Future of MTMs 316 7.1 “Real-Artiﬁcial” Materials: the Challenge of Homogenization, 316 7.2 Quasi-Optical NRI Lenses and Devices, 319 7.3 Three-Dimensional Isotropic LH MTMs, 323

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