Metamaterials with Negative Parameters Theory, Design, and Microwave Applications

RICARDO MARQUES FERRAN MARTIN MARIO SOROLLA

B I C E N T E N N I A U

B I C E N T E N N I A L

WILEY-INTERSCIENCE A JOHN WILEY & SONS. INC.. PUBLICATION

Contents

Preface xii i

Acknowledgments xvii

1 The Electrodynamics of Left-Handed Media 1

1.1 Introduction 1 1.2 Wave Propagation in Left-Handed Media 2 1.3 Energy Density and Group Velocity 4 1.4 Negative Refraction 6 1.5 Fermat Principle 9 1.6 Other Effects in Left-Handed Media 9

1.6.1 Inverse Doppler Effect 10 1.6.2 Backward Cerenkov Radiation 10 1.6.3 Negative Goos-Hänchen Shift 12

1.7 Waves at Interfaces 13 1.7.1 Transmission and Reflection Coefficients 13 1.7.2 Surface Waves 15

1.8 Waves Through Left-Handed Slabs 16 1.8.1 Transmission and Reflection Coefficients 17 1.8.2 Guided Waves 17 1.8.3 Backward Leaky and Complex Waves 19

1.9 Slabs with e/e0—+ —1 and JX/JXQ^ —1 20 1.9.1 Phase Compensation and Amplification of

Evanescent Modes 20 1.9.2 Perfect Tunneling 21 1.9.3 The Perfect Lens 25 1.9.4 The Perfect Lens as a Tunneling/

Matching Device 29 1.10 Losses and Dispersion 32

viii CONTENTS

1.11 Indefinite Media 34 Problems 35 References 37

2 Synthesis of Bulk Metamaterials 43

2.1 Introduction 43 2.2 Scaling Plasmas at Microwave Frequencies 44

2.2.1 Metallic Waveguides and Plates as One- and Two-Dimensional Plasmas 44

2.2.2 Wire Media 47 2.2.3 Spatial Dispersion in Wire Media 49

2.3 Synthesis of Negative Magnetic Permeability 51 2.3.1 Analysis of the Edge-Coupled SRR 52 2.3.2 Other SRR Designs 59

2.3.2.1 The Broadside-Coupled SRR 60 2.3.2.2 The Nonbianisotropic SRR 62 2.3.2.3 The Double-Split SRR 62 2.3.2.4 Spirals 62

2.3.3 Constitutive Relationships for Bulk SRR Metamaterials 65 2.3.4 Higher-Order Resonances in SRRs 70 2.3.5 Isotropie SRRs 73 2.3.6 Scaling Down SRRs to Infrared and Optical Frequencies 75

2.4 SRR-Based Left-Handed Metamaterials 80 2.4.1 One-Dimensional SRR-Based Left-Handed

Metamaterials 81 2.4.2 Two-Dimensional and Three-Dimensional SRR-Based

Left-Handed Metamaterials 85 2.4.3 On the Application of the Continuous-Medium Approach to

Discrete SRR-Based Left-Handed Metamaterials 87 2.4.4 The Superposition Hypothesis 88 2.4.5 On the Numerical Accuracy of the Developed Model for

SRR-Based Metamaterials 90

2.5 Other Approaches to Bulk Metamaterial Design 91 2.5.1 Ferrite Metamaterials 92 2.5.2 Chiral Metamaterials 97 2.5.3 Other Proposais 102

Appendix 107 Problems 109 References 114

3 Synthesis of Metamaterials in Planar Technology 119

3.1 Introduction 119 3.2 The Dual (Backward) Transmission Line Concept 120

CONTENTS ix

3.3 Practical Implementation of Backward Transmission Lines 128 3.4 Two-Dimensional (2D) Planar Metamaterials 131 3.5 Design of Left-Handed Transmission Lines by Means of

SRRs: The Resonant Type Approach 135 3.5.1 Effective Negative Permeability Transmission Lines 136 3.5.2 Left-Handed Transmission Lines in Microstrip and

CPW Technologies 139 3.5.3 Size Reduction 144

3.6 Equivalent Circuit Models for SRRs Coupled to Conventional Transmission Lines 146 3.6.1 Dispersion Diagrams 151 3.6.2 Implications of the Model 151

3.7 Duality and Complementary Split Ring Resonators (CSRRs) 155 3.7.1 Electromagnetic Properties of CSRRs 156 3.7.2 Numerical Calculation and Experimental Validation 160

3.8 Synthesis of Metamaterial Transmission Lines by Using CSRRs 163 3.8.1 Negative Permittivity and Left-Handed Transmission Lines 163 3.8.2 Equivalent Circuit Models for CSRR-Loaded

Transmission Lines 166 3.8.3 Parameter Extraction 170 3.8.4 Effects of Cell Geometry on Frequency Response 172

3.9 Comparison between the Circuit Models of Resonant-Type and Dual Left-Handed Lines 175

Problems 180 References 182

4 Microwave Applications of Metamaterial Concepts 187

4.1 Introduction 187 4.2 Filters and Diplexers 188

4.2.1 Stopband Filters 189 4.2.2 Planar Filters with Improved Stopband 193 4.2.3 Narrow Bandpass Filter and Diplexer Design 198

4.2.3.1 Bandpass Filters Based on Altemate Right-/Left-Handed (ARLH) Sections Implemented by Means of SRRs 199

4.2.3.2 Bandpass Filters and Diplexers Based on Alternate Right-/Left-Handed (ARLH) Sections Implemented by Means of CSRRs 203

4.2.4 CSRR-Based Bandpass Filters with Controllable Characteristics 207 4.2.4.1 Bandpass Filters Based on the Hybrid Approach:

Design Methodology and Illustrative Examples 208

x CONTENTS

4.2.4.2 Other CSRR-Based Filters Implemented by Means of Right-Handed Sections 218

4.2.5 Highpass Filters and Ultrawide Bandpass Filters (UWBPFs) Implemented by Means of Resonant-Type Balanced CRLH Metamaterial Transmission Lines 225

4.2.6 Tunable Filters Based on Varactor-Loaded Split Rings Resonators (VLSRRs) 227 4.2.6.1 Topology of the VLSRR and Equivalent-Circuit

Model ' 228 4.2.6.2 Validation of fhe Model 230 4.2.6.3 Some Illustrative Results: Tunable Notch

Filters and Stopband Filters 230 4.3 Synthesis of Metamaterial Transmission Lines with Controllable

Characteristics and Applications 233

4.3.1 Miniaturization of Microwave Components 234 4.3.2 Compact Broadband Devices 236 4.3.3 Dual-Band Components 244 4.3.4 Coupled-Line Couplers 246

4.4 Antenna Applications 252 Problems 258 References 260

5 Advanced and Related Topics 267

5.1 Introduction 267 5.2 SRR- and CSRR-Based Admittance Surfaces 268

5.2.1 Babinet Principle for a Single Split Ring Resonator 268 5.2.2 Surface Admittance Approach for SRR Planar

Arrays 270 5.2.3 Babinet Principle for CSRR Planar Arrays 272 5.2.4 Behavior at Normal Incidence 273 5.2.5 Behavior at General Incidence 274

5.3 Magneto- and Electro-Inductive Waves 278

5.3.1 The Magneto-Inductive Wave Equation 279 5.3.2 Magneto-Inductive Surfaces 282 5.3.3 Electro-Inductive Waves in CSRR Arrays 284 5.3.4 Applications of Magneto- and Electro-Inductive Waves 285

5.4 Subdiffraction Imaging Devices 287

5.4.1 Some Universal Features of Subdiffraction Imaging Devices 288

5.4.2 Imaging in the Quasielectrostatic Limit: Role of Surface Plasmons 292

5.4.3 Imaging in the Quasimagnetostatic Limit: Role of Magnetostatic Surface Waves 295

CONTENTS xi

5.4.4 Imaging by Resonant Impedance Surfaces: Magneto-Inductive Lenses 299

5.4.5 Canalization Devices 302 Problems 304 References 305

Index 309