Electromagnetic Metamaterials Transmission Line Theory and Microwave Applications.pdf

ELECTROMAGNETIC

METAMATERIALS:

TRANSMISSION LINE

THEORY AND

MICROWAVE

APPLICATIONS

The Engineering Approach

CHRISTOPHE CALOZ

Ecole Polytechnique de Montreal

TATSUO ITOH

University of California at Los Angeles

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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

2005048976

Printed in the United States of America.

10987654321

To Dominique, Maxime, and Raphael

Christophe

CONTENTS

Preface

xiii

Acknowledgments

Acronyms

xvii

1 Introduction 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

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-Hanchen Effect, 50

2.10 Reversal of Convergence and Divergence in Convex and Concave

Lenses, 51

2.11 Subwavelength Diffraction, 53

References, 57

3TLTheoryofMTMs

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

133

4.1 Eigenvalue Problem, 134

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

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