YOUJI KOTSUKA, PHD, is a professor emeritus of Telecommunication Engineering at Tokai University, Tokyo, and a visiting professor at Harvard University, Cambridge, from 1995 to 1996. He has served as chair of the committees on Biological Effect of EM-waves and Medical Application and Measurement Technic in the Institute of Electrical Engineering Japan (IEE). He is a chair of the Japan Technical Committee on EMC in the Institute of Electronics, Information and Communication Engineers (IEICE). He is also a chair in IEEE-EMC, Japan Chapter. He is a co-editor of the November 2000 special issue on Medical Applications and Biological Effect of RF/ Microwaves, part of IEEE Transactions on Microwave Theory and Techniques. He has authored and co-authored books such as EMC Handbook and the Wiley title RF/Microwave Interaction with Biological Tissues.

Preface xi

1 Fundamentals of Electromagnetic Wave Absorbers 1

1.1 Introduction to Electromagnetic-Wave Absorbers 2

1.2 Fundamentals of Absorber Characteristics 3

1.3 Classifications of Absorbers 4

1.3.1 Classifications by Appearance 4

1.3.1.1 Single-layer-type Absorber 4

1.3.1.2 Quarter-wavelength-type Absorber 7

1.3.1.3 Multilayered Absorber 7

1.3.1.4 Jaumann Absorber 7

1.3.1.5 Sawtooth-shape Absorber 7

1.3.1.6 Pyramidal Wave Absorber 7

1.3.1.7 Absorbers by Artificial Materials and Special Materials 8

1.3.2 Classifications of Material 8

1.3.2.1 Conductive Absorber Material 8

1.3.2.2 Dielectric Absorber Material 8

1.3.2.3 Magnetic Absorber Material 8

1.3.2.4 Metamaterial 8

1.3.3 Classifications by Configuration Forms 9

1.3.3.1 Classification from Layered Numbers 9

1.3.4 Classifications by Frequency Characteristics 10

1.3.4.1 Narrowband-type Absorber 10

1.3.4.2 Broadband-type Absorber 10

1.3.4.3 Ultra-wideband-type Absorber 11

1.4 Application Examples of Wave Absorbers 11

References 13

2 Fundamental Theory of EM-Wave Absorbers 17

2.1 Transmission Line Theory 17

2.1.1 Transmission Line Equation 18

2.1.2 Reflection Coefficient 23

2.1.2.1 Reflection Coefficient at Load Terminal End 23

2.1.2.2 Reflection Coefficient on Transmission Line 24

2.1.2.3 Reflection Coefficient and Standing-Wave Ratio 25

2.1.3 Transmission Line with Loss 26

2.1.4 Reflection Coefficient in Transmission Line with Loss 27

2.2 Smith Chart 28

2.2.1 Principle of Smith Chart 28

2.2.2 Admittance Chart 34

2.2.3 Examples of Smith Chart Application 35

2.2.3.1 Impedance of Transmission Line with Short-circuit Termination 35

2.2.3.2 Matching Method with a Single Movable Stub 36

2.2.3.3 Matching Method Using Fixed Multiple Stubs 38

2.3 Fundamentals of Electromagnetic Wave Analysis 40

2.3.1 Derivation of Maxwell’s Equations 40

2.3.1.1 Maxwell’s First Electromagnetic Equation 41

2.3.1.2 Maxwell’s Second Electromagnetic Equation 43

2.3.2 Wave Equations 45

2.3.3 Reflection from Perfect Conductor in Normal Incidence 47

2.3.4 Reflection and Transmission in Two Medium Interfaces 50

2.3.4.1 Normal Incidence Cases 50

2.3.4.2 Oblique Incidence 53

2.3.5 Theory of Multiple Reflections 59

2.3.5.1 Reflection and Transmission Coefficients 59

2.A Appendix 62

2.A.1 Appendix to Section 2.3.2 (1) 62

References 63

3 Methods of Absorber Analysis 65

3.1 Normal Incidence to Single-layer Flat Absorber 65

3.2 Oblique Incidence to Single-layer Flat Absorber 68

3.3 Characteristics of the Multilayered Absorber 71

3.3.1 Normal Incidence Case 71

3.3.2 Case of Oblique Incidence 73

3.3.2.1 Case of the TE Wave 73

3.3.2.2 Case of the TM Wave 73

3.4 Case of Multiple Reflected and Scattered Waves 74

3.4.1 Standing Wave Ratio in Beat Generation 78

3.A Appendix 80

3.A.1 Appendix to Section 3.4.1 (1) 80

References 82

4 Basic Theory of Computer Analysis 83

4.1 FDTD Analysis Method 84

4.1.1 Basis of FDTD 84

4.1.2 Methods of Time and Space Difference 86

4.1.3 Relationship of Time Arrangement of the Electromagnetic Field 87

4.1.4 Relationship of Spatial Arrangement of the Electromagnetic Field 89

4.1.5 General Expressions of FDTD Analysis 91

4.1.6 Absorbing Boundary Conditions 95

4.1.7 Analysis Model and Boundary Conditions 95

4.1.7.1 Behavior of the Periodic Boundary 97

4.1.7.2 Behavior of the PLM Absorbing Boundary 98

4.1.7.3 Behaviors at Variable Cell Size 99

4.1.7.4 Convergence by Configuration Dimensions and Number of Cells 101

4.2 Finite Element Method 102

4.2.1 Foundation of the Finite Element Method 102

4.2.1.1 Outline of the Finite Element Method 102

4.2.1.2 History of FEM 102

4.2.1.3 Variational Method as FEM Foundation 102

4.2.1.4 Relationship Between Functional and Laplace Equation 104

4.2.2 Summary of Analytical Procedures 105

4.2.3 Example of Electrostatic Field Analysis 106

4.2.4 Application of Electrostatic Field Analysis 112

4.3 Three-Dimensional Electric Current Potential Method 112

4.3.1 Outline of the Electric Current Vector Potential Method 112

4.3.2 Basic Equation and Auxiliary Equation 113

4.3.3 Formulations of the Basic and Auxiliary Equations 116

4.3.4 Derivation of the Approximate Potential Function 118

4.3.5 Discretization of the Basic Equation 122

4.3.5.1 The First Term on the Right Side of Eq. (4.110) 122

4.3.5.2 x Component in the First Term of the Basic Equation (4.110) 124

4.3.5.3 y Component in the First Term of Basic Equation (4.110) 125

4.3.5.4 z Component in the First Term of the Basic Equation (4.110) 125

4.3.5.5 The Second Term on the Right Side of Eq. (4.110) 125

4.3.5.6 x Component of the Second Term on the Right Side of the Basic Equation (4.110) 126

4.3.5.7 The First Term of x Component in Eq. (4.133) 126

4.3.5.8 The Second Term of the x Component in Eq. (4.133) 126

4.3.5.9 The Third Term of the x Component in Eq. (4.133) 127

4.3.6 Discretization of the Auxiliary Equation 128

4.3.6.1 x Component in Eq. (4.144) 129

4.3.7 General Potential Equation in Elements 130

4.3.8 Example of the Analytical Model 132

4.3.9 Unnecessary Current Absorber Analysis 134

4.A Appendix 139

4.A.1 Appendix to Section 4.3.4 (1) 139

4.A.2 Appendix to Section 4.3.5 (1) 142

4.A.3 Appendix to Section 4.3.5 (2) 143

References 143

5 Fundamental EM-Wave Absorber Materials 145

5.1 Carbon Graphite 145

5.2 Ferrite 148

5.2.1 Soft Magnetic Material 148

5.2.2 Spinel-type Magnetic Oxide 149

5.2.2.1 Crystal Structure of Oxide 149

5.2.2.2 Crystal Structure of Ferrite 151

5.3 Hexagonal Ferrite 152

References 154

6 Theory of Special Mediums 155

6.1 Chiral Medium 156

6.1.1 Electromagnetic Fields in Chiral Medium 158

6.1.2 Electromagnetic-Field Reflection by Chiral Medium 160

6.2 Theory of Magnetized Ferrite 166

6.2.1 Foundation of Equation of Magnetization Motion 167

6.2.2 Tensor Susceptibility 170

6.2.2.1 Lossless Medium Case 170

6.2.2.2 Loss Medium Case 174

6.3 MW-Propagation of Circular Waveguide with Ferrite 179

6.3.1 Derivation of Fundamental Equations 179

6.3.2 Derivation of Electromagnetic-Field Components 182

6.3.3 Circular Waveguide with Ferrite 185

6.3.3.1 Ferrite Fully Filled Case 185

6.3.3.2 Ferrite Partially Filled Case 186

6.3.4 Coaxial Waveguide with Ferrite 188

6.4 Metamaterial 192

6.4.1 Metamaterial Outlines 192

6.4.2 Metamaterial Theories 195

6.4.2.1 Left-Handed and Right-Handed Systems 195

6.4.2.2 Conversion from Material to Transmission Line Concept 196

6.4.3 Negative Permittivity and Permeability 198

6.4.4 Negative Refractive Index Medium 202

6.4.5 Metamaterial as a Medium 204

6.4.6 Metamaterial Absorber 205

6.A Appendix 206

6.A.1 Appendix to Section 6.1.2 (1) 206

6.A.2 Appendix to Section 6.2.2 (1) 207

6.A.3 Appendix to Section 6.2.2 (2) 208

6.A.4 Appendix to Section 6.3.1 (1) 209

6.A.5 Appendix to Section 6.3.1 (2) 210

6.A.6 Appendix to Section 6.3.1 (3) 212

References 213

7 Measurement Methods on EM-Wave Absorbers 217

7.1 Material Constant Measurement Methods 217

7.1.1 Standing-Wave Method 218

7.1.1.1 Case of Using Waveguide 218

7.1.1.2 Method of Using Coaxial Waveguides 221

7.1.2 Cavity Resonator Method 225

7.1.2.1 Method of Micro-sample Insertion 225

7.1.2.2 Complex Permittivity Measurement 230

7.1.2.3 Complex Permeability Measurement 233

7.2 Measurement of EM-Wave Absorption Characteristics 235

7.2.1 Method of Using TEM Mode Transmission Line 235

7.2.1.1 Coaxial Waveguide Method 236

7.2.1.2 Strip Line Method 237

7.2.1.3 TEM Cell Method 238

7.2.2 Waveguide Method 239

7.2.3 Space Standing-Wave Method 240

7.A Appendix 242

7.A.1 Appendix to Section 7.1.2 (1) 242

7.A.2 Appendix to Section 7.1.2 (2) 243

7.A.3 Appendix to Section 7.1.2 (3) 243

7.A.4 Appendix to Section 7.1.2 (4) 244

References 244

8 Configuration Examples of the EM-wave Absorber 247

8.1 Quarter-wave-Type Absorber 247

8.2 Single-Layer-Type Absorber 252

8.2.1 Ferrite Absorber 252

8.3 Two-Layered Absorber 253

8.4 Applications as Building Material 255

8.4.1 TV Ghost Prevention Measures 255

8.4.2 Ferrite Core-Embedded PC Board 258

8.5 Low-Reflective Shield Building Materials 260

References 262

9 Absorber Characteristic Control by Equivalent Transformation Method of Material Constants 265

9.1 Basic Concepts and Means 265

9.2 Examples of ETMMC Absorbers 266

9.2.1 Microchip Integrated -type Absorber 266

9.2.2 Absorber with Small Holes 269

9.2.2.1 Effect of Square Hole Size 271

9.2.2.2 Effect of Adjacent Hole Space 272

9.2.2.3 Relation of Absorber Thickness and Hole Dimensions 272

9.2.3 Absorber with Square Conductive Elements 274

9.2.3.1 Effect of Conductor Dimensions 276

9.2.3.2 Input Admittance Characteristics 279

9.2.4 Absorber with Line-Shaped Conductive Elements 281

9.2.4.1 Lattice Type 282

9.2.4.2 Cross Type 283

9.2.4.3 Square Conductive Line Frame 284

9.2.4.4 Double-Layered PCLF Type 288

9.2.5 Absorber Based on Integrated Circuit Concept 291

9.2.5.1 Configuration of Absorber 291

9.2.5.2 Space Experiment Characteristic 295

References 296

10 Autonomous Controllable-Type Absorber 299

10.1 Autonomous Control-type Metamaterial 299

10.2 Configurations of the ACMM Absorber 301

10.3 The Main Point as the Technical Breakthrough 302

10.4 Characteristics as the EM-Wave Absorber 304

10.4.1 Complicated Wiring Problems 305

10.4.2 Controlling the Problem of Absorber Characteristics 305

10.4.3 Stability of Wave Absorption Characteristics 306

10.4.4 Oblique Incidence Characteristics 306

10.4.5 Controllability of Frequency Characteristic 308

10.4.6 Broadband Characteristic 308

10.5 Input Impedance Characteristic 311

10.6 Examples of Application Fields 313

References 314

Index 317

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