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E-raamat: Metamaterials Modelling and Design

(Equipe de Nanophotonique, Groupe d'Etude des Semi-Conducteurs UMR-CNRS 5650, Montpellier, France), (Universite du Sud-Toulon-Var, La Garde, France)
  • Formaat: 368 pages
  • Ilmumisaeg: 06-Jul-2017
  • Kirjastus: Pan Stanford Publishing Pte Ltd
  • ISBN-13: 9789814669993
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Metamaterials Modelling and DesignSuurem pilt
  • Formaat: 368 pages
  • Ilmumisaeg: 06-Jul-2017
  • Kirjastus: Pan Stanford Publishing Pte Ltd
  • ISBN-13: 9789814669993
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The domain of metamaterials now covers many area of physics: electromagnetics, acoustics, mechanics, thermics, or even seismology. Huge literature is now available on the subject but the results are scattered. Although many ideas and possible applications have been proposed, which of these will emerge as a viable technology will only unfold with time.

This book covers the fundamental science behind metamaterials, from the physical, mathematical, and numerical points of view, focusing mainly on methods. It concentrates on electromagnetic waves, but would also be useful in studying other types of metamaterials. It presents the structure of Maxwell equations, discusses the homogenization theory in detail, and includes important problems on resonance. It has an entire section devoted to numerical methods (finite elements, Fourier modal methods, scattering theory), which aims to motivate a reader to implement them. The book is not written as a collection of independent chapters but as a textbook with a strong pedagogical flavor.

Preface xi
Section I: Elements Of Electromagnetic Fields In Media
1 General Introduction
3(24)
Didier Felbacq
Andre Nicolet
Frederic Zolla
1.1 Maxwell Equations
3(6)
1.1.1 Potential and Gauge Invariance
7(2)
1.2 Maxwell Equations in the Fourier Domain
9(1)
1.3 Field Created by Sources
10(1)
1.4 Conservation Laws
10(2)
1.5 A Framework with Differential Forms
12(1)
1.6 Dispersion Relations
13(14)
1.6.1 Introduction
13(2)
1.6.2 Causality and Kramers-Kronig Relations
15(6)
1.6.3 Super-Convergence and Sum Rules
21(2)
1.6.4 Dispersion Relations Versus Mixing Laws
23(1)
1.6.5 Group Velocity
24(3)
2 A Review of Natural Materials and Properties in Micro-Waves and Optics
27(34)
Bernard Gil
2.1 Introduction
27(2)
2.2 Metals and Non-Metals
29(2)
2.3 Examples of Band Structures for Monovalent Elemental Metals
31(3)
2.4 Band Structures of Cubic Semiconductors
34(6)
2.5 Semi-Classical Theory of the Dielectric Function in Crystals
40(9)
2.5.1 Intuitive Description
40(2)
2.5.2 Microscopic Theory of the Dielectric Constant
42(2)
2.5.3 Experimental Values of the Spectral Dependence of the Dielectric Constants of Semiconductors and Metals
44(5)
2.6 Excitonic Effects
49(5)
2.7 Influence of Doping and Alloying
54(2)
2.8 Conclusion
56(5)
3 From Microphysics to Mesophysics: Obtaining Effective Properties from Microscopic Behaviors
61(46)
Alexandru Cabuz
3.1 Metamaterials and Scales
63(2)
3.2 Averaging-Time and Space
65(10)
3.2.1 The Spatial Average as Truncation
67(8)
3.3 Polarizability and Susceptibility
75(6)
3.3.1 The Master Equations: Electric and Magnetic
76(5)
3.4 Permittivity and Permeability: Index and Impedance
81(10)
3.4.1 The Negative Index of Refraction
83(8)
3.5 Periodic Media: Structural Nonlocality
91(5)
3.6 Conductors: Free Charge Nonlocality
96(5)
3.6.1 The Hydrodynamic Model
98(3)
3.7 Summary
101(6)
4 Transformation Optics in a Nutshell
107(36)
Andre Nicolet
4.1 Transformation Optics
107(16)
4.1.1 Geometrical Background
108(2)
4.1.2 Change of Coordinates in Maxwell's Equations
110(5)
4.1.3 Geometric Transformation: Equivalent Material Principle
115(3)
4.1.4 Cylindrical Devices
118(5)
4.2 Superlens Illusion
123(6)
4.3 Cylindrical Cloaks of Arbitrary Cross Section
129(3)
4.4 Generalized Cloaking
132(1)
4.5 Numerical Modeling
133(10)
Section II: General Methods: Waves In Periodic Media
5 Propagation in Periodic Media: Bloch Waves and Evanescent Waves
143(28)
Didier Felbacq
Frederic Zolla
5.1 Bloch Wave Theory
143(6)
5.1.1 The Periodic Structure
143(1)
5.1.2 Waves in a Homogeneous Space
144(2)
5.1.3 Bloch Modes
146(3)
5.2 Computation of Band Structures
149(3)
5.2.1 Two-Dimensional Metamaterials
149(3)
5.3 Periodic Waveguides
152(8)
5.3.1 Bloch Modes
152(2)
5.3.2 The Bloch Conditions
154(3)
5.3.3 A Numerical Example
157(3)
5.3.4 Direct Determination of the Periodic Part
160(1)
5.4 Evanescent Waves
160(11)
5.4.1 Introduction
160(1)
5.4.2 Propagating and Non-Propagating Modes
161(4)
5.4.3 Analysis of the Spectrum
165(1)
5.4.3.1 Decomposition of the field
165(1)
5.4.3.2 Cut wavelengths and classification of the conduction bands
166(5)
6 Scattering Problems: Numerical Methods (FEM, Multiple Scattering)
171(40)
Didier Felbacq
Frederic Zolla
Andre Nicolet
6.1 Finite Element Method
171(25)
6.1.1 Introduction
171(2)
6.1.2 Theoretical Developments
173(1)
6.1.2.1 Set up of the problem and notations
173(1)
6.1.2.2 From a diffraction problem to a radiative one with localized sources
176(1)
6.1.2.3 Quasi-periodicity and weak formulation
177(1)
6.1.2.4 Edge or Whitney 1-form second-order elements
178(2)
6.1.3 Energetic Considerations: Diffraction Efficiencies and Losses
180(2)
6.1.4 Accuracy and Convergence
182(1)
6.1.4.1 Classical crossed gratings
182(1)
6.1.4.2 Convergence and computation time
188(3)
6.1.5 Conclusion
191(1)
6.1.6 Electric Vector Field in Multilayered Stack Illuminated by a Plane Wave of Arbitrary Incidence and Polarization
192(4)
6.2 Multiple Scattering
196(15)
6.2.1 Introduction
196(1)
6.2.2 Multiple Scattering for a Finite Collection of Objects
196(1)
6.2.3 Multiple Scattering for a Periodic Collection of Objects
197(1)
6.2.4 Modal Representation for Cylinders
198(1)
6.2.5 Scattering by a Single Object
199(4)
6.2.6 Numerical Implementation
203(8)
Section III: Applications: Effective Properties Of Metamaterials
7 Soft Problems: Nonresonant Dielectric Structures
211(54)
Didier Felbacq
Frederic Zolla
Guy Bouchitte
7.1 A Brief Foray into the Realm of Two-Scale Homogenization
211(7)
7.1.1 Two-Scale Homogenization with One Small Parameter
211(6)
7.1.2 Two-Scale Homogenization with Several Small Parameters
217(1)
7.2 Soft Problems: Theory
218(1)
7.3 Two-Scale Approach to Homogenization
219(8)
7.3.1 Description of the Structure and Methodology
219(2)
7.3.2 Derivation of the Microscopic Equations
221(1)
7.3.2.1 A short account of the two-scale expansion
221(1)
7.3.2.2 The equations at the microscopic scale
222(1)
7.3.3 Derivation of the Homogenized Parameters
223(1)
7.3.3.1 The special case of a one-dimensional grating
225(2)
7.4 Soft Problems: Numerical Examples
227(18)
7.4.1 A Little Vademecum
227(1)
7.4.2 Some Prerequisites for Two-Phase Materials
228(3)
7.4.3 Fictitious Charges Method as Applied to the Annex Problem
231(1)
7.4.3.1 Introduction to the column space V
231(1)
7.4.3.2 The spaces V, Vi, and V2
232(1)
7.4.3.3 Solution to the annex problem
233(1)
7.4.3.4 An example of total family in V1 and V2
234(1)
7.4.3.5 Fine estimation of the uniform bound of the error
235(1)
7.4.4 Closed Formulae for Small Spherical and Cylindrical Scatterers
235(1)
7.4.4.1 Computation of phi1,1 (cylindrical case)
237(1)
7.4.4.2 Computation of phi3,3 (spherical case)
237(1)
7.4.5 Closed Formulae for Foliated and Checkerboard-Like Media
237(7)
7.4.6 Numerical Examples and Comparisons
244(1)
7.4.6.1 Spherical inclusions: comparison with the main mixing laws
244(1)
7.4.6.2 Non-spherical inclusions giving rise to isotropic metamaterials
245(1)
7.5 Soft Problems: Toward Resonance (Metal-Dielectric Mixing)
245(8)
7.6 Tiny Enough to Be Homogeneous?
253(12)
7.6.1 Introduction
253(1)
7.6.2 Lossless Dielectric
254(1)
7.6.2.1 Convergence
254(1)
7.6.2.2 Angular response
255(2)
7.6.3 Metals
257(1)
7.6.3.1 Convergence
257(1)
7.6.3.2 Angular response
258(1)
7.6.3.3 Comparison between the different homogenization approaches
258(7)
8 Stiff Problems: High Contrast Objects
265(26)
Didier Felbacq
Frederic Zolla
Andre Nicolet
Guy Bouchitte
8.1 Introduction: Metallic Metamaterials and Metasurfaces
265(1)
8.2 Infinitely Long Wires
266(8)
8.2.1 Expression of the Scattered Field
267(1)
8.2.2 Asymptotic Analysis of the Scattered Field
268(3)
8.2.3 Asymptotic Form of the Transfer Operator
271(1)
8.2.4 Derivation of the Transfer Matrix and Effective Parameters
272(2)
8.3 Finitely Long Wires: The Bed of Nails
274(17)
8.3.1 Setup of the Problem
274(3)
8.3.2 Numerical Results
277(4)
8.3.3 Domain of Validity
281(10)
9 Resonant Problems
291
Didier Felbacq
Guy Bouchitte
9.1 Introduction
291(1)
9.2 H||: A Two-Scale Approach
292(4)
9.3 Numerical Results
296(2)
9.3.1 Periodic Resonators
296(2)
9.4 E|| Case: Green's Function Approach
298
Section IV: Mathematical Annex
Appendix A: Mathematical Annex 311(34)
Index 345
Didier Felbacq is a full professor at the University of Montpellier, France. He graduated in mathematics and physics from the Ecole Centrale Paris, France, and Aix-Marseille University, France, respectively. He was appointed associate professor at Blaise Pascal University, France, in 1995, where he founded a group devoted to the modeling and simulation of photonic crystals. He then joined University of Montpellier in 2002, where he formed a group devoted to lightmatter interaction in complex media. Dr. Felbacq has been a member of the Institut Universitaire de France (20092014) and has authored and co-authored numerous articles in international peer-reviewed journals. He has also written few books and contributed book chapters in some books. Prof. Felbacq is involved in theoretical and numerical research in close collaboration with experimentalists and his current activities cover electron transport in transistors for terahertz emission and detection, second harmonic emission in photonic crystals, excitons in 2D materials, quantum metamaterials, thermal metamaterials, acoustic metamaterials, and water transport in root systems.
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