Theory and phenomena of metamaterials

Cover......Page 1
Theory and Phenomena of Metamaterials......Page 2
Dedication......Page 4
Contents......Page 5
Foreword......Page 9
Preface......Page 10
References......Page 11
Editor......Page 12
Advisory Board......Page 13
Contributors......Page 15
Part I: General Concepts......Page 19
1.1 Introduction......Page 20
1.2.1 Artificial Dielectrics......Page 22
1.2.3 Artificial Plasma......Page 23
1.2.4 Backward Waves in Bulk Media......Page 25
1.3.1 Negative Refraction and Subwavelength Resolution......Page 27
1.3.2 Transmission-Line Networks......Page 32
1.4 Conclusions......Page 33
References......Page 34
2.1 Introduction......Page 37
2.2.1 Preliminary Remarks......Page 38
2.2.2 On Material Parameters of Media with Strong Spatial Dispersion......Page 39
2.2.3 Locality and Nonlocality......Page 41
2.3.1 Definition of Weak Spatial Dispersion......Page 43
2.3.2 Polarization Current in Media with Weak Spatial Dispersion......Page 44
2.3.3 Electric and Magnetic Polarization Currents......Page 45
2.3.4 Noncovariant Form of Material Equations of Media with WSD......Page 46
2.3.5 Material Equations Covariant in the First Order of WSD......Page 49
2.3.6 Material Equations Covariant in the Second Order of WSD......Page 51
2.3.7 Special Cases of Material Equations in Media with WSD......Page 52
2.4 What the Theory of WSD Reveals for MTM......Page 53
2.5 An Alternative Approach to the Description of WSD......Page 56
2.6.1 Energy Density......Page 58
2.6.2.1 Causal Dispersion......Page 59
2.6.2.2 The Sign of the Imaginary Part of Effective Parameters......Page 62
2.6.3 Concluding Remarks......Page 63
References......Page 64
3.1 Introduction......Page 67
3.2 Symmetry of Maxwell’s Equations......Page 68
3.3.2 Symmetry of Electromagnetic Sources......Page 69
3.3.3 Curie’s Principle of Symmetry Superposition......Page 70
3.4.1 Time-Reversal Symmetry......Page 71
3.4.3 Bidirectionality......Page 72
3.5.1 Different Forms of the Constitutive Relations......Page 73
3.5.2 Calculation of the Constitutive Tensors and Some of Their Properties......Page 74
3.6.1 Symmetry Description of 2D Magnetic Crystal with Square Lattice......Page 76
3.6.2 Group of Symmetry of the Wave Vector......Page 78
3.6.3 Lifting of Degeneracy by dc Magnetic Field......Page 80
Appendix A: Elements of Group Theory and Theory of Representations......Page 81
Appendix B: Notations of Elements of Symmetry, Symmetry Operations, and Point Groups......Page 82
Appendix C: Brief Description of Magnetic Groups......Page 83
References......Page 84
4.1 Introduction......Page 86
4.2 Field and Medium Equations......Page 87
4.3.1 Perfect Electromagnetic Conductor......Page 88
4.3.2 Q-Media......Page 89
4.3.3 Generalized Q-Media......Page 90
4.3.4 IB-Media......Page 91
4.3.5 Self-Dual Media......Page 94
4.3.5.2 AB Media......Page 95
4.3.5.3 Fields......Page 96
4.A.2 Products......Page 97
4.A.3 Dyadics......Page 98
4.A.4 Products of Dyadics......Page 99
4.A.5 Identities......Page 100
References......Page 101
Part II: Modeling Principles of Metamaterials......Page 102
5.1 Introduction......Page 104
5.2 Equivalence Principle......Page 105
5.3.1 Spatial Domain......Page 107
5.3.1.1 Basis and Testing Functions......Page 108
5.3.1.2 The Integral Equations and Discretization......Page 109
5.3.1.3 Periodic Structures......Page 111
5.3.2 Spectral Domain......Page 112
5.3.2.1 Periodic Arrangements......Page 115
5.4 Green’s Functions for Periodic Structures......Page 116
5.5.1 Arrays of Spheres, Using Subdomain Basis Functions......Page 120
5.5.2 Arrays of Apertures, Using Entire-Domain Basis Functions......Page 121
5.6 Eigenmode Analysis......Page 123
5.8.1 Fast Multipole Methods......Page 124
5.8.3 Macro Basis Functions Approach......Page 125
References......Page 127
6.2 FDTD Fundamentals......Page 135
6.3 Periodic FDTD Method for Waveguide Designs......Page 138
6.4 Periodic FDTD Method for Scattering Analysis......Page 140
6.4.2 Oblique Incidence: Sine–Cosine Method......Page 142
6.4.3 Oblique Incidence: Split-Field Method......Page 144
6.5.1 Basic Concept of the Unified Spectral FDTD Method......Page 146
6.5.2 Implementation Issues......Page 148
6.6 Finite Source on Periodic Structure......Page 149
6.6.1 ASM–FDTD Theory......Page 151
6.6.2 ASM–FDTD Algorithm Properties......Page 152
6.6.3 Numerical Examples......Page 154
References......Page 157
7.2 Static Electric Response of a Simple Scatterer......Page 160
7.3 Other Inclusion Shapes......Page 165
7.3.1 Regular Polyhedra......Page 166
7.3.3 Semisphere......Page 167
7.3.4 Double Sphere......Page 168
References......Page 169
8.1 Introduction......Page 172
8.2 Single Dipole Formulation for Modeling Collections of Spherical Nanoparticles......Page 174
8.2.1 Polarizability Expressions for a Spherical Nanoparticle......Page 176
8.2.3 Calculation of the Induced Dipole Moments of Nanoparticles......Page 179
8.3.1 Quasiperiodic Excitation of Periodic Arrangements of Nanoparticles......Page 180
8.3.2 Periodic Arrangements of Nanoparticles Excited by a Single Dipole Source......Page 181
8.4.1 Modes......Page 182
8.4.2 Transmission......Page 183
References......Page 186
9.1 Introduction......Page 189
9.3 Clausius–Mossotti and Maxwell Garnett Formulas......Page 190
9.4 Ellipsoids and Multiphase Mixtures......Page 192
9.5.1 Bruggeman Mixing Rule......Page 197
9.5.3 Unified Mixing Rule......Page 198
9.5.4 Other Mixing Rules......Page 199
References......Page 200
10.1 Introduction......Page 202
10.2 Macroscopic Electromagnetism and Constitutive Relations in Local Media......Page 203
10.3 Homogenization of Nonlocal Media......Page 205
10.3.1 Constitutive Relations in Nonlocal Media......Page 206
10.3.2 Fields with Floquet Variation......Page 207
10.3.4 Plane Wave Solutions......Page 210
10.3.5 Symmetries of the Dielectric Function......Page 211
10.4 Dielectric Function of a Lattice of Electric Dipoles......Page 212
10.5.1 Regularized Formulation......Page 215
10.5.2 Integral Equation Solution......Page 217
10.5.3 Application to Wire Media......Page 218
10.6.1 Relation between the Local and Nonlocal Effective Parameters......Page 220
10.6.2 Spatial Dispersion Effects of First and Second Order......Page 221
10.6.3 Characterization of Materials with Negative Parameters......Page 224
10.7 The Problem of Additional Boundary Conditions......Page 226
10.7.1 Additional Boundary Conditions for Wire Media......Page 227
References......Page 230
11.1 Introduction......Page 234
11.2 Bloch Material Parameters Impedance: Lorentz Material Parameters and Wave Impedance......Page 236
11.3 Direct Retrieval of Effective Material Parameters......Page 238
11.4 Bloch Lattices......Page 240
11.5 Nonlocality of Bloch’s Material Parameters......Page 241
11.6 How to Distinguish Bloch Lattices?......Page 243
11.7 Extraction of Lorentz’s Material Parameters......Page 247
11.8 Discussion......Page 249
References......Page 251
12.1 Introduction......Page 253
12.2 Quasiperiodic Fields in Periodic Structures......Page 255
12.3.1 Calculation of the Field......Page 256
12.4 Field Produced by a Single Source in the Presence of a Periodic Medium: The Array Scanning Method......Page 259
12.4.1 Fourier Transform of Aperture Field via the Array Scanning Method......Page 261
12.4.2 Numerical Considerations......Page 262
12.5 Relation between the ASM and the Plane-Wave Superposition Method......Page 263
12.6.1 Total Field Representation......Page 265
12.6.2 Leaky and Bound Modes......Page 267
12.7 Examples of Field Species in a PAM Excited by a Single Source......Page 269
12.8 Conclusions......Page 272
Appendix A: Spectral Singularities......Page 273
References......Page 275
13.1 Introduction......Page 279
13.2 Background......Page 280
13.3 Grounded Metamaterial Slabs: Structure Description......Page 281
13.4 Grounded Metamaterial Slabs: Surface Waves......Page 282
13.4.2 TM Surface Waves......Page 283
13.4.3 Surface-Wave Suppression in Grounded DNG Slabs......Page 284
13.4.5 Nonradiative Dielectric Waveguides......Page 288
13.5 Grounded Metamaterial Slabs: Leaky Waves......Page 291
References......Page 296
Part III: Artificial Magnetics and Dielectrics, Negative Index Media......Page 298
14.1 Introduction......Page 300
14.2 RF Metamaterials Design......Page 301
14.2.1 Dielectrics......Page 302
14.2.3 Spiral Resonators......Page 303
14.2.5 Swiss Rolls......Page 304
14.3.1 Permeability......Page 306
14.3.2 Propagation......Page 307
14.3.3 Transmission......Page 308
14.3.4 Numerical modeling......Page 309
14.3.5.1 The Square Prism......Page 310
14.3.5.2 The Hexagonal Prism......Page 311
14.3.6 Discussion......Page 312
14.4.1 Flux Guiding—Initial Demonstration......Page 314
14.4.2 Flux Guiding—High-Performance Material......Page 316
14.4.3 RF Focusing......Page 318
14.4.4 Discussion......Page 319
14.5.1 RF Endoscope/Faceplate......Page 320
14.5.2 Yoke......Page 321
14.5.4 Flux Compressor......Page 323
References......Page 324
15.1 Introduction......Page 328
15.2.1 Plasma Frequency for Wire Media......Page 330
15.2.2 Spatial Dispersion......Page 331
15.2.3 Inconsistence of the Local Model......Page 334
15.2.4 Nonlocal Model for a Periodic Array of є-Negative Rods......Page 335
15.3.1 Modes in the yz-Plane......Page 337
15.3.2 Evanescent Modes......Page 338
15.3.3 Propagation in the z-Direction......Page 340
15.3.4 Group Velocity and Poynting Vector in DWM......Page 342
15.4 Eigenmodes in a Waveguide Filled with Wire Medium......Page 343
15.5.1 Coupling Reduction in Antenna Arrays......Page 346
15.5.2 Antenna Lenses and Other Applications......Page 348
15.6 Conclusion......Page 349
References......Page 350
16.1 Introduction......Page 353
16.2 Nonbianisotropic SRR......Page 354
16.3 Other SRR Configurations with Inversion Symmetry......Page 357
16.4 Bianisotropic Effects in SRRs......Page 358
16.5 Chirality in SRRs......Page 361
16.7 Complementary SRRs......Page 362
16.8 SRR Behavior at Infrared and Optical Frequencies......Page 364
16.9 Synthesis of Metamaterials and Other Applications of SRRs......Page 367
References......Page 368
17.1 Introduction......Page 371
17.2.1 Electric Response of the SRRs and Its Role in the Electric Response of LHMs......Page 374
17.2.2 Bianisotropy of SRR and Its Influence on the LH Behavior......Page 376
17.3 Two-Dimensional and Three-Dimensional Left-Handed Materials from SRRs and Wires......Page 377
17.4 Effects of Periodicity in the Homogeneous Effective Medium Retrieved Parameters in SRRs and Wire Metamaterials......Page 378
17.5 SRRs and Wire Metamaterials toward Optical Regime......Page 379
17.6 Slab Pairs and Slab-Pair-Based Left-Handed Materials......Page 381
17.7 Left-Handed Behavior from Slab Pairs and Wires—The Fishnet Design......Page 382
17.7.1 The Fishnet Design......Page 383
17.8 Slab-Pair-Based Systems toward Optical Regime......Page 384
17.9 Conclusions......Page 385
References......Page 386
18.1 Introduction......Page 389
18.2 Left-Handed Metamaterial......Page 390
18.3 Negative Refraction......Page 392
18.4 Subwavelength Imaging......Page 393
Acknowledgments......Page 394
References......Page 395
19.1 Introduction......Page 396
19.2 Background......Page 397
19.3 From SRR and Wire Media to Planar Metamaterials: Short-Strip Pairs and Related Structures......Page 398
19.4 Negative Refractive Index Behavior from Loaded Strip Pairs: The Dogbone-Pair Design......Page 401
19.4.2 Phenomena Involved in Dogbone Pairs......Page 402
19.4.3 Approximate Transmission Line Model for Magnetic Resonances......Page 406
Accuracy and Limitations of the TL Model......Page 409
19.4.4 Transverse Equivalent Circuit Network......Page 410
19.4.5 Backward-Wave Propagation in Media Formed by Stacked Dogbone Particle Layers......Page 412
19.5 Planar 2D Isotropic Negative Refractive Index Metamaterial......Page 413
19.5.1 The Jerusalem-Cross-Pair Design......Page 415
Effective Material Parameters......Page 416
Modal Dispersion Analyses......Page 418
19.5.4 Left-Handed Transmission in Tripole-Pair Media......Page 421
19.6 Plasmonic Nanopairs and Nanoclusters......Page 423
19.6.1 Resonance Modes of a Pair of Tightly Coupled Metallic Nanospheres......Page 426
19.6.2 Quasistatic Resonance Modes of Two Coupled Metallic Nanospheres......Page 429
19.6.3 Array of Pairs of Tightly Coupled Nanospheres......Page 431
19.6.4 Effective Magnetic Permeability for a Two Coupled Nanosphere System......Page 432
19.6.5 Electromagnetic Modes of Four Coupled Metallic Nanospheres......Page 433
19.6.6 Array of Four Tightly Coupled Nanospheres......Page 434
References......Page 439
20.1 Introduction......Page 443
20.2 Physical Realization of Metamorphism through Babinet Complementarity......Page 446
20.3 Realization and Design of a Two-State Metamorphic Material......Page 447
20.4 Realization and Design of a Three-State Metamorphic Material......Page 450
20.5 Metamaterial Characterization of Photonic Crystals and Their Metamorphic States Their Metamorphic States......Page 451
20.6 Power Balance, Loss, and Usefulness of the Resonant Effective Description......Page 454
References......Page 460
21.1 Introduction......Page 463
21.2 Two-Dimensional and Three-Dimensional Isotropic Metamaterials Formed by an Array of Cubic Cells with Metallic Planar Inclusions......Page 464
21.3 TL-Based Metamaterials......Page 469
21.4 Two-Dimensional Structure of DNG Metamaterial Based on Resonant Inclusions......Page 472
21.5.1 Symmetry of the Bispherical DNG Structure......Page 474
21.5.2 DNG Medium Composed of Magnetodielectric Spherical Inclusions......Page 476
21.5.3 DNG Medium Composed of Dielectric Spheres with Different Radii (Garnet–Maxwell Mixing Rule)......Page 477
21.5.4 DNG Medium Composed of Dielectric Spheres with Different Radii (Electromagnetic Wave Diffraction Model)......Page 480
21.6 Effective Permittivity and Permeability of the Bispherical Lattice......Page 481
21.6.1 Electric and Magnetic Dipole Moments of Spherical Resonators......Page 482
21.6.2 Comparison of the Effective Permittivity and Permeability Obtained with Different Models......Page 483
21.6.3 Results of the Full-Wave Analysis......Page 484
21.6.4 Results of the Experiment......Page 486
21.6.5 Influence of Distribution of Size and Permittivity of Spherical Particles on DNG Characteristics......Page 488
21.6.6 Isotropic Medium of Coupled Dielectric Spherical Resonators......Page 490
21.7 Metamaterials for Optical Range......Page 491
References......Page 492
22.1 Introduction......Page 495
22.2.1 One-Dimensional Metamaterials......Page 496
22.2.1.1 Implementation of Dispersion Models......Page 497
22.2.2 Scattering Matrix Representation of Metamaterial Cells......Page 500
22.3 Two-Dimensional Metamaterials......Page 501
22.4 Three-Dimensional Scalar Isotropic Metamaterials......Page 502
22.5 Three-Dimensional Vectorial Isotropic Metamaterial Based on the Rotated TLM Method......Page 505
22.5.1 Dispersion Behavior......Page 507
22.5.2 Physical Realization of the Rotated TLM Metamaterial......Page 508
22.5.4 Signal Propagation through the Cell......Page 509
22.5.5 Experimental Verification......Page 510
22.6.1.1 Rotated TLM Unit Cell......Page 512
22.6.1.3 Kron’s Unit Cell......Page 515
22.6.2 Topology-Invariant Planarization......Page 516
22.6.2.2 Scalar 3D Metamaterial in Series Configuration......Page 517
References......Page 521
23.1 Introduction......Page 525
23.2 Nanocircuit Elements at IR and Optical Frequencies......Page 527
23.3 Negative Permeability and DNG Metamaterials at IR and Optical Frequencies......Page 530
23.4 Optical Nanotransmission Lines as One-Dimensional and Two-Dimensional Photonic Metamaterials with Positive or Negative Index of Refraction......Page 537
23.5 Three-Dimensional Optical Negative-Index Metamaterials......Page 545
23.6 Conclusions......Page 550
References......Page 551
Part IV: Artificial Chiral, Bianisotropic Media, and Quasicrystals......Page 553
24.1 Introduction......Page 554
24.2 Fundamentals of NIM......Page 555
24.3.1 Isotropic Chiral Materials......Page 557
24.3.2 Gyrotropic Chiral Materials......Page 562
24.3.2.1 Chiroplasma......Page 564
24.3.2.2 Generalized Gyrotropy......Page 565
24.3.3.1 Brewster Angles and Chirality Effects in Semi-Infinite Chiral Nihility......Page 572
24.3.3.2 Constraints and Conditions of Isotropic/Gyrotropic Chiral Nihility......Page 576
24.3.4 Bianisotropic Routes......Page 581
References......Page 583
25.1 Introduction......Page 589
25.2 Backward Waves in Chiral Media......Page 590
25.3 Chiral Materials with the Effective Refraction Index n=-1......Page 591
25.4 Using Bianisotropic Effects......Page 592
References......Page 593
26.1 Introduction......Page 595
26.2 Classes of Bianisotropic Media......Page 596
26.3 PEMC Medium......Page 598
References......Page 600
27.1 Introduction and Background......Page 602
27.2.2 Aperiodic Tilings......Page 603
27.2.3 Generation Algorithms......Page 605
27.2.4 Order vs. Symmetry......Page 606
27.4 Compact Review of Results and Applications Available in the Literature......Page 607
27.5.1 Geometry......Page 609
27.5.2 Bandgap Properties......Page 610
27.5.3 Localized Modes......Page 611
27.6 Examples of Planar PQCs......Page 614
References......Page 618
Part V: Transmission-Line- Based Metamaterials......Page 626
28.1.1 Artificial Dielectrics and Metamaterials......Page 627
28.1.3 Negative Refraction......Page 628
28.1.4 Focusing......Page 629
28.1.5 Transmission-Line-Based Artificial Dielectric Realizations......Page 630
28.2 Transmission-Line Theory of LH Media......Page 631
28.2.1 Transmission-Line Network Topologies......Page 632
28.2.2 The Conventional (Low-Pass) RH Topology......Page 633
28.2.3 The Dual (High-Pass) LH Topology......Page 634
28.3.1 Determination of Permittivity......Page 635
28.3.2 Determination of Permeability......Page 636
28.3.4 Negative Permittivity......Page 638
28.3.5 Positive Permeability......Page 639
28.3.5.1 Case 1: Inductive Loop......Page 640
28.3.6.1 Case 3: Capacitively Loaded Inductive Loop......Page 641
28.4.1 The Recipe for Broadband, Low-Loss Left-Handedness......Page 642
28.4.2 Free-Space Coupling to a Transmission-Line-Based Metamaterial......Page 646
28.4.2.1 Case 1: Decoupled System......Page 647
28.4.2.2 Case 2: General Coupled System......Page 648
28.4.2.3 Case 3: Isolated L–C Resonator Limit......Page 649
28.5 Periodically Loaded Transmission-Line Metamaterials......Page 650
28.5.1 Dispersion Characteristics......Page 653
28.5.2 The Effective Medium Limit: Determining the Effective Permittivity and Permeability......Page 654
28.5.3 Closure of the Stopband......Page 656
28.5.4 Equivalent Unit Cell in the Effective Medium Limit......Page 657
28.6 Conclusion......Page 658
References......Page 659
29.1 Introduction......Page 662
29.1.2 Equivalent Circuit Model for TE and TM Modes in Rectangular Waveguides......Page 663
29.2.1 Equivalent Circuit Model......Page 664
29.2.3 Asymptotic Boundary Conditions......Page 666
29.2.4 Green’s Function Approach......Page 667
29.2.4.1 Development of Green’s Functions......Page 668
29.2.4.2.1 Probe Excitation......Page 669
29.3.1 Experimental Verification......Page 670
29.3.2 Dispersion Characteristics for Dominant Mode......Page 671
29.3.3 Parametric Studies and Bandwidth Control......Page 674
29.3.5 Asymptotic Boundary Conditions......Page 677
29.3.6 Complete Dispersion Diagram for Transverse Wave Number......Page 678
29.3.7 Input Impedance of a Probe Exciting the Metaguide......Page 681
29.3.8 Waveguide Discontinuities and Transitions......Page 683
References......Page 684
Part VI Artificial Surfaces......Page 686
30.1 Introduction to Frequency Selective Surface and Electromagnetic Bandgap Structures......Page 687
30.2 Two-Dimensional Planar Metallodielectric Arrays and Frequency-Selective Surface......Page 689
30.3 Array Analysis......Page 690
30.4.1 Modal Field Representation......Page 692
30.5.1 Fields at Different Interfaces......Page 695
30.5.2 Electric Field Integral Equation......Page 698
30.6 Method of Moments......Page 699
30.7 Reflection and Transmission Coefficients......Page 700
30.8 Propagation along the Surface (x–y Plane)......Page 701
30.9 Direct and Reciprocal Lattices in Two Dimensions......Page 702
30.9.1 Irreducible Brillouin Zone and the Array Element......Page 706
30.10 Planar 2D EBG Using a Dipole Conducting Array......Page 707
30.11 Dipole Array Results and Discussion......Page 709
30.12 Dipole Dimension D= 10 mm, L= 7.5 mm......Page 710
30.13 Dipole Dimension D= 8 mm, L= 6 mm......Page 712
References......Page 713
31.1 Introduction......Page 716
31.2.1 Electromagnetic Bandgap Surfaces......Page 717
31.2.1.1 Leaky and Surface Waves......Page 718
31.2.1.2.1 Brillouin Zone and Irreducible Brillouin Zone......Page 719
31.2.1.3 Experimental Testing of EBG......Page 721
31.2.2.1 Reflection from an HIS......Page 723
31.2.2.2 Experimental Testing of AMC......Page 725
31.2.3.1 Reflection Properties......Page 727
31.2.3.2 Band Structure......Page 728
31.2.3.3 Measured Performance......Page 729
31.2.4 Uniplanar HIS......Page 730
31.3.1 Doubly Periodic Metallic Arrays (FSS)......Page 731
31.3.2 Resonant Cavity Model for AMC Operation......Page 732
31.3.3.1 Free-Standing Doubly Periodic Array of Metallic Elements......Page 734
31.3.3.2 FSS in Proximity to a Ground Plane......Page 735
31.3.3.3 AMC and EBG Operation......Page 737
31.4.1.1 Analytical Models: Incident Plane Wave (AMC)......Page 738
31.4.1.1.2 Array of Printed Jerusalem Crosses......Page 740
31.4.1.2 Analytical Models: Surface waves (EBG)......Page 742
31.4.1.2.1 Model I......Page 743
31.4.1.2.2 Model II......Page 744
31.4.1.2.3 SurfaceWaves in Square Patch and Jerusalem Cross Arrays......Page 745
31.4.2 Semianalytical Methods......Page 747
31.5 Performance Characteristics......Page 749
31.5.1.1.2 Electromagnetic Bandgap Characteristics......Page 750
31.5.1.1.3 Emerging Trends......Page 751
31.5.2 AMC Bandwidth......Page 753
31.5.3 AMC Angular Stability......Page 754
31.5.4.1 Miniaturized MEBG Structures......Page 757
31.5.4.1.1 Close Coupling......Page 758
31.5.4.1.2 Complex Elements......Page 760
31.5.4.1.3 AMC Responses......Page 761
References......Page 764
Part VII: Tunable and Nonlinear Metamaterials......Page 768
32.1.1 Why Have Tunable Surfaces?......Page 769
32.2.2 Mechanical Tuning......Page 770
32.2.3 PIN Diodes......Page 772
32.2.4 Varactor Diodes......Page 774
32.2.5 Microelectromechanical Systems......Page 776
32.2.6 Photonic Control of FSS......Page 780
References......Page 783
33.1 Introduction......Page 786
33.2.1 Spontaneous Polarization......Page 788
33.2.2 Second-Order Phase Transition......Page 792
33.2.3 Incipient Ferroelectrics......Page 793
33.2.4 Dielectric Response of a Ferroelectric Sample......Page 794
33.2.4.1 Dielectric Response in Ferroelectric and Paraelectric States......Page 796
33.2.4.2 Stationary (dc) Ferroelectric Polarization......Page 797
33.2.5.2 Temperature of the Maximum Dielectric Permittivity......Page 799
33.3.1 Size Effect......Page 800
33.3.1.1 Correlation of the Ferroelectric Polarization......Page 802
33.3.1.2 Boundary Conditions for Dynamic Polarization on the Interface between Ferroelectric Layer and Electrodes......Page 805
33.3.1.3 Effective Dielectric Constant of a Thin-Film Sample......Page 807
33.3.2.1 Primary Model of the “Dead Layer”......Page 808
33.3.2.2 Real (Nondefected) Nature of the “Dead Layer”......Page 810
33.4.1.1 Eigenfrequency of the Ferroelectric Mode of Crystal Lattice Oscillation......Page 812
33.4.1.2 Complex Dielectric Permittivity of a Ferroelectric Material......Page 813
33.4.2.1 Multiphonon Scattering of the Ferroelectric Soft Mode......Page 814
33.4.3.1 Contribution of Charged Defects......Page 815
33.5 Ferroelectrics in Tuneable Metamaterials......Page 816
33.5.1 Tuneable Metasurface Based on Ferroelectric Tuneable Capacitors......Page 818
33.5.2 Composite Right/Left-Handed Transmission Line......Page 820
33.5.3 Tuneable Zero-Order Resonator on CRLH TL......Page 822
33.5.4 Phase Shifter on CRLH TL......Page 823
References......Page 825
34.1 Introduction......Page 829
34.2.1 Formulation of the Problem......Page 832
34.2.2 Analytical Approaches......Page 838
34.2.2.1 Plane Wave Approach......Page 839
34.2.2.2 Transfer Matrix Technique......Page 840
34.2.2.3 Effective Medium Approximation......Page 841
34.2.2.4 Method of Tensorial Green’s Functions......Page 842
34.2.2.5 SWM Approach......Page 844
34.2.3 Spin-Wave Normal Mode Expansion Technique......Page 847
34.2.4 General Dispersion Relation......Page 851
34.2.5 Approximate Dispersion Relation......Page 854
34.3 Periodic Structures as Metamaterials: Band Theory of Infinite Film Stack......Page 857
34.4 Dispersion Properties of Spin Waves in Thin Films and Multilayered Structures......Page 862
34.4.1.1 Perpendicular Magnetization......Page 863
34.4.1.2 In-Plane Magnetization......Page 865
34.4.1.4 Surface Anisotropies......Page 866
34.4.2.1 Influence of the Dipole Interlayer Interaction......Page 867
34.4.2.2 Influence of the Exchange Interaction......Page 871
34.4.3 Magnetic/Magnetic Multilayered Structures......Page 874
34.5 Planar Patterned Metamaterials......Page 876
34.5.1 Direct Space Green’s Function......Page 877
34.5.2 Coupled Standing-Wave Modes on a Multilayer Stripe......Page 878
34.5.3 Role of the Interlayer Exchange Interaction......Page 881
34.5.4 Formation of Collective Modes and Brillouin Zones......Page 882
34.5.5 Microwave Properties of Planar Patterned Metamaterials......Page 885
References......Page 886
35.2 Providing Nonlinearity......Page 894
35.3.1 Macroscopic Description of Metamaterials: Basic Principles......Page 896
35.3.2 Split Ring with In-Series Nonlinear Insertion......Page 897
35.3.3 Quadratic Magnetic Susceptibility......Page 898
35.3.4 Practical Estimates for Low Nonlinearity......Page 902
35.4.1 Frequency Conversion......Page 903
35.4.2 Nonlinear Wave Propagation, Multistability, and Solitons......Page 906
35.4.4 Tuning and Switching......Page 908
35.5 Concluding Remarks......Page 909
References......Page 910
36.2 Magnetic Coupling between Resonant Elements......Page 913
36.3.1 Dispersion for One-Dimensional Arrays......Page 915
36.3.3 Dispersion for Two- and Three-Dimensional Lattices: Negative Refraction......Page 918
36.3.4 Coupled Arrays......Page 919
36.3.5 Experimental Verification......Page 920
36.4.1 Impedance Matrix......Page 921
36.4.2 Boundary Conditions: Terminal Impedances......Page 922
36.5 Interaction with Electromagnetic Waves......Page 923
References......Page 925