Artificial metamaterials have made a huge splash in antenna, microwave, and optics engineering thanks to their extraordinary electromagnetic properties. And now, modeling their unique characteristics and behaviors in electromagnetic systems just got easier. This one-stop resource gives engineers powerful finite-difference time-domain (FDTD) techniques for modeling metamaterials, complete with applications and time-saving sample FDTD scripts. This comprehensive volume provides how-to guidance in a wide range of areas that are critical to antenna design, from computing dispersion diagrams and verifying left-handedness...to characterizing the interface of metamaterial slabs. The book also reviews electromagnetic metamaterial basics and FDTD essentials, providing the foundation needed to fully understand the material.
Author(s): Yang Hao, Raj Mittra
Edition: 1
Year: 2008
Language: English
Pages: 379
FDTD Modeling of Metamaterials: Theory and Applications......Page 2
Contents......Page 6
Preface......Page 12
Acknowledgments......Page 14
1.1 What Are Electromagnetic Metamaterials?......Page 16
1.2 A Historical Overview of Electromagntic Metamaterials......Page 17
1.2.1 Artificial Dielectrics......Page 19
1.2.3 Bianisotropic Composites......Page 23
1.2.4 Double-Negative and Indefinite Media......Page 24
1.2.5 Photonic and Electromagnetic Crystals......Page 26
1.3 Numerical Modeling of Electromagnetic Metamaterials......Page 30
1.4 Layout of the Book......Page 32
References......Page 33
2.2.1 Translational Symmetry......Page 40
2.2.2 Bloch’s Theorem and Periodic Boundary Condition (PBC)......Page 42
2.2.3 Brillouin Zone......Page 44
2.2.4 Dispersion Diagram and EBG......Page 45
2.3.1 The Generalized Rayleigh’s Identity Method and the Korringa-Kohn-Rostoker (KKR) Method......Page 48
2.3.2 Plane-Wave Expansion Method......Page 50
2.3.3 The Transfer-Matrix Method......Page 51
2.3.4 The Finite-Difference Time-Domain (FDTD) Method......Page 54
2.4.1 In-Phase Reflection......Page 56
2.4.2 Suppression of Surface Waves......Page 60
2.4.3 EBGs Operating in Defect Modes......Page 61
2.4.4 Subwavelength Imaging from the Passband of the EBGs......Page 72
References......Page 76
3.2.1 Maxwell’s Equations......Page 82
3.2.2 Yee’s Orthogonal Mesh......Page 84
3.2.3 Time Domain Discretization: The Leapfrog Scheme and the CourantStability Condition (CFL Condition)......Page 85
3.3.1 Subgridding Mesh......Page 87
3.3.2 Nonorthogonal Mesh......Page 90
3.3.3 Hybrid FDTD Meshes......Page 91
3.4.1 Mur’s Absorbing Boundary Conditions (ABCs)......Page 93
3.4.2 Perfect Matched Layers (PMLs)......Page 95
3.4.3 Periodic Boundary Condition (PBC)......Page 96
3.5 Bandgap Calculation......Page 98
3.5.2 Dispersion Diagram Calculation......Page 99
3.5.3 Transmission and Reflection Coefficient Calculation......Page 100
3.6 Summary......Page 102
References......Page 103
4.2.1 Physical Model of EBG Structures......Page 106
4.2.2 Mesh Generation and Simulation Parameters in FDTD Modeling......Page 108
4.2.3 Simulation Results of Infinite EBGs Using the Conformal and Yee’s FDTD......Page 109
4.3.1 FDTD Model and Simulation Results......Page 117
4.4.1 Introduction......Page 120
4.4.2 Design and Modeling of Woodpile EBG......Page 123
4.4.3 A Millimeter-Wave EBG Antenna Based on a Woodpile Structure......Page 130
4.4.4 Experimental Results......Page 132
References......Page 136
5.2 Effective Medium Theory and Left-Handed Metamaterials......Page 138
5.2.1 A Composite Medium of Metallic Wires and Split Ring Resonators......Page 139
5.2.2 Isotropic Three-Dimensional Left-Handed Metamaterials......Page 140
5.2.3 Left-Handed Metamaterials Using Simple Short Wire Pairs......Page 141
5.3.1 Imaging by a Perfect LHM Lens......Page 142
5.3.2 Transmission Line Structures of Left-Handed Metamaterials......Page 143
5.3.3 Directive Electromagnetic Scattering by an Infinite Conducting CylinderCoated with LHMs......Page 157
5.3.4 Negative Index Materials (NIM) for Selective Angular Separation ofMicrowave by Polarization......Page 159
References......Page 160
6.1 Introduction......Page 162
6.2 The Effective Medium of Left-Handed Materials (LHMs)......Page 163
6.3.1 Two-Dimensional Dispersive FDTD with Auxiliary Differential Equations(ADEs)......Page 171
6.3.2 Phase Compensation Through Layered LHM Structures......Page 175
6.3.3 Conjugate Dielectric and Metamaterial Slab as Radomes......Page 176
6.3.4 Numerical Results......Page 178
References......Page 184
7.1 Introduction......Page 188
7.2.2 Scattering Parameters Measurements Obtained from the PBC/FDTD Code......Page 189
7.2.3 Phase Data Inside the DNG Slab......Page 190
7.3.1 Review of the Inversion Approach......Page 197
7.3.2 Retrieval of the Effective Material Parameters from the Numerical S-Parameters Obtained from FDTD Simulations of Metamaterials......Page 201
7.4 EM Response of a Finite Artificial-DNG Slab with Localized Beam Illumination......Page 223
7.4.2 FDTD Model......Page 224
7.4.3 Total Transmission and Reflection Power UnderGaussian Beam Illumination......Page 225
7.4.4 EM Response of the Artificial-DNG Slab at Normal Incidence with Ey Polarization......Page 228
7.4.5 EM Response of the Artificial-DNG Slab at Oblique TMz IncidenceComing from (q = 150◦, f = 90◦) with Hx Polarization......Page 234
7.4.6 EM Response of the Artificial-DNG Slab at Oblique TEz Incidence Comingfromq = 150◦, f = 0◦ with Ey Polarization......Page 238
7.4.7 EM Response of a Finite Artificial-DNG Slab Excited by Small Dipole......Page 241
7.5 Figure-of-Merit (FOM) Analysis......Page 243
7.5.1 Loss and Bandwidth of Metamaterials with Different Electrical Sizes and Particle Densities......Page 244
7.5.2 Figure-of-Merit Analysis by Numerical Experiments......Page 247
7.6 Conclusions......Page 250
References......Page 251
8.1 Introduction......Page 254
8.2 Dispersive FDTD Modeling of LHMs with Spatial Averaging at the Boundaries......Page 256
8.2.1 The (E, D, H, B) Scheme......Page 257
8.2.2 The (E, J, H, M) Scheme......Page 259
8.2.3 The Spatial Averaging Methods......Page 260
8.3 Numerical Implementation......Page 265
8.4 Effects of Material Parameters on the Accuracy of Numerical Simulation......Page 270
8.5 Effects of Switching Time......Page 273
8.6 Effects of Transverse Dimensions on Image Quality......Page 275
8.7 Modeling of Subwavelength Imaging......Page 277
References......Page 279
9.1 Introduction......Page 282
9.2 Spatial Dispersion in the Wire Medium......Page 284
9.3 Spatially Dispersive FDTD Formulations......Page 285
9.4 Stability and Numerical Dispersion Analysis......Page 289
9.5 Perfectly Matched Layer for Wire Medium Slabs......Page 294
9.6 Numerical Thickness of Wire Medium Slabs......Page 297
9.7 Two-Dimensional FDTD Simulations......Page 301
9.8 Three-Dimensional FDTD Simulations......Page 309
9.9 Experimental Verifications......Page 312
9.10 Internal Imaging by Wire Medium Slabs......Page 314
9.11 Conclusions......Page 318
References......Page 319
10.2.1 Introduction......Page 322
10.2.2 FDTD Modeling of the Silver-Dielectric Layered Structure......Page 325
10.2.3 Numerical Results and Discussions......Page 326
10.3.1 Introduction......Page 331
10.3.3 Simulation......Page 332
10.4 FDTD Study of Guided Modes in Nanoplasmonic Waveguides......Page 336
10.4.1 Conformal Dispersive FDTD Method Using Effective Permittivities (EPs)......Page 337
10.5 FDTD Calculation of Dispersion Diagrams......Page 341
10.5.1 Wave Propagation in Plasmonic Waveguides Formed by Finite Numberof Elements......Page 346
10.6 FDTD Modeling of Electromagnetic Cloaking Structures......Page 348
10.6.1 Dispersive FDTD Modeling of the Cloaking Structure......Page 350
10.6.2 Numerical Results and Discussion......Page 356
References......Page 361
11.2 Overview of Advantages and Disadvantages of the FDTD Method in Modeling Metamaterials......Page 368
11.3 Overview of Metamaterial Applications and Final Remarks......Page 369
11.3.1 Small Antennas Enclosed by an ENG Shell......Page 372
11.3.2 Focusing and Superlensing Effects......Page 376
11.3.4 Electromagnetic Cloaks......Page 385
References......Page 386
List of Abbreviations......Page 388
About the Authors......Page 390
Index......Page 392
