[Matériaux d’indice négatif : à la frontière de l’électromagnétisme macroscopique]
Les notions de réfraction négative et d’indice négatif, imaginées par V. Veselago il y a plus de 50 ans, ont semblé au-delà des frontières de l’électromagnétisme macroscopique et sont restées purement formelles pendant 30 ans, jusqu’aux travaux de J. Pendry à la fin des années 1990. Depuis lors, les matériaux à indice négatif et les métamatériaux ont montré des propriétés extraordinaires et des effets spectaculaires qui ont mis à l’épreuve le domaine de validité de l’électromagnétisme macroscopique. Dans cet article, plusieurs de ces propriétés et phénomènes sont passés en revue. Tout d’abord, les mécanismes sous-jacents aux indices négatifs et à la réfraction négative sont brièvement présentés. Ensuite, il est montré que le cadre des équations de Maxwell harmoniques en temps ne peut pas décrire le comportement des ondes électromagnétiques dans les situations de la lentille plate et du réflecteur en coin parfaits en raison de la présence de spectre essentiel à la fréquence où l’indice prend la valeur . Plus généralement, il est montré que de simples structures en coin remplies d’une permittivité dispersive en fréquence ont un intervalle entier de spectre essentiel associé à un analogue du phénomène de « trou noir ». Enfin, des arguments sont fournis pour soutenir que, dans les milieux passifs, la partie imaginaire de la perméabilité magnétique peut prendre des valeurs positives et négatives. Ces arguments reposent notamment sur l’expression exacte, pour toutes les fréquences et tous les vecteurs d’onde, du tenseur de permittivité effective avec dispersion spatiale d’une structure multicouche.
The notions of negative refraction and negative index, introduced by V. Veselago more than 50 years ago, have appeared beyond the frontiers of macroscopic electromagnetism and purely formal during 30 years, until the work of J. Pendry in the late 1990s. Since then, the negative index materials and the metamaterials displayed extraordinary properties and spectacular effects which have tested the domain of validity of macroscopic electromagnetism. In this article, several of these properties and phenomena are reviewed. First, mechanisms underlying the negative index and negative refraction are briefly presented. Then, it is shown that the frame of the time-harmonic Maxwell’s equations cannot describe the behavior of electromagnetic waves in the situations of the perfect flat lens and corner reflector due to the presence of essential spectrum at the perfect index frequency. More generally, it is shown that simple corner structures filled with frequency dispersive permittivity have a whole interval of essential spectrum associated with an analog of “black hole” phenomenon. Finally, arguments are provided to support that, in passive media, the imaginary part of the magnetic permeability can take positive and negative values. These arguments are notably based on the exact expression, for all frequency and wave vector, of the spatially-dispersive effective permittivity tensor of a multilayered structure.
Mot clés : Indice négatif, Métamatériaux, Dispersion en fréquence, Mode de coin, Dispersion spatiale, Passivité, Perméabilité
Boris Gralak 1
@article{CRPHYS_2020__21_4-5_343_0, author = {Boris Gralak}, title = {Negative index materials: at the frontier of macroscopic electromagnetism}, journal = {Comptes Rendus. Physique}, pages = {343--366}, publisher = {Acad\'emie des sciences, Paris}, volume = {21}, number = {4-5}, year = {2020}, doi = {10.5802/crphys.29}, language = {en}, }
Boris Gralak. Negative index materials: at the frontier of macroscopic electromagnetism. Comptes Rendus. Physique, Volume 21 (2020) no. 4-5, pp. 343-366. doi : 10.5802/crphys.29. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.29/
[1] The electrodynamics of substances with simultaneously negative values of and , Sov. Phys. Usp., Volume 10 (1968), p. 509 | DOI
[2] Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microw. Theory Tech., Volume 47 (1999), p. 2075 | DOI
[3] Electrodynamics of Continuous Media, Courses of Theoretical Physics, vol. 8, Robert Maxwell, M. C., 1984
[4] A variational approach to the theory of the effective magnetic permeability of multiphase materials, J. Appl. Phys., Volume 33 (1962), p. 3125 | DOI | Zbl
[5] The dielectric constant of a composite material—a problem in classical physics, Phys. Rep., Volume 43 (1978), p. 377 | DOI | MR
[6] Bounds on the complex dielectric constant of a composite material, Appl. Phys. Lett., Volume 37 (1980), p. 300 | DOI
[7] Bounds on the complex permittivity of a two-component composite material, J. Appl. Phys., Volume 52 (1981), p. 5286 | DOI
[8] Bounds on the electromagnetic, elastic, and other properties of two-component composites, Phys. Rev. Lett., Volume 46 (1981), p. 542 | DOI
[9] The Theory of Composites, Cambridge University Press, Cambridge, 2002 | Zbl
[10] Asymptotic Analysis for Periodic Structures, American Mathematical Society Chelsea Publishing, Providence, RI, 2011 | DOI
[11] Extremely low frequency plasmons in metallic mesostructures, Phys. Rev. Lett., Volume 76 (1996), p. 4773 | DOI
[12] Low frequency plasmons in thin-wire structures, J. Phys.: Condens. Matter., Volume 10 (1998), p. 4785
[13] Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett., Volume 84 (2000), p. 4184 | DOI
[14] Experimental verification of a negative index of refraction, Science, Volume 292 (2001), p. 77 | DOI
[15] Electromagnetic metamaterials, Proc. SPIE, Complex Mediums II: Beyond Linear Isotropic Dielectr (A. Lakhtakia; W. S. Weiglhofer; I. J. Hodgkinson, eds.), SPIE, San Diego, CA, USA, 2001, 4467 pages
[16] Inhibited spontaneous emission in solid-state physics and electronics, Phys. Rev. Lett., Volume 58 (1987), 002059 | DOI
[17] Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett., Volume 58 (1987), 002486
[18] Anomalous refractive properties of photonic crystals, J. Opt. Soc. Am. A, Volume 17 (2000), p. 1012 | DOI
[19] Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap, Phys. Rev. B, Volume 62 (2000), 10696 | DOI
[20] Electromagnetic propagation in birefringent layered media, J. Opt. Soc. Am., Volume 69 (1979), 000742 | MR
[21] Superprism effects and EBG antenna applications, Metamaterials: Physics and Engineering Explorations, Chapter 10 (N. Engheta; R. W. Ziolkowski, eds.), John Wiley and Sons, Hoboken, NJ, USA
[22] Electromagnetic waves in photonic crystals: laws of dispersion, causality and analytical properties, Compendium of Electromagnetic Analysis — From Electrostatics to Photonics, Volume 4: Optics and Photonics I, Chapter 4, World Scientific, Hackensack, NJ, USA, 2020 (Editor-in-chief I. Tsukerman) | DOI
[23] Negative refraction by photonic crystals, Nature, Volume 423 (2003), p. 604 | DOI
[24] Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators, IEEE Trans. Antennas Propag., Volume 51 (2003), 002582
[25] Material parameters of metamaterials (a review), Opt. Spectrosc., Volume 107 (2009), 000726
[26] On an extension of the method of two-scale convergence and its applications, Sb. Math., Volume 191 (2000), p. 973 | DOI | Zbl
[27] Homogenization near resonances and artificial magnetism from dielectrics, C. R. Math., Volume 339 (2004), p. 377 | DOI | MR | Zbl
[28] Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients, Phys. Rev. B, Volume 65 (2002), 195104
[29] Local constitutive parameters of metamaterials from an effective-medium perspective, Phys. Rev. B, Volume 75 (2007), 195111
[30] Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters, Phys. Rev. B, Volume 75 (2007), 115104
[31] Generalized lorentz-lorenz formulas for microstructured materials, Phys. Rev. B, Volume 76 (2007), 245117
[32] First-principles homogenization theory for periodic metamaterials, Phys. Rev. B, Volume 84 (2011), 075153
[33] Classical Electrodynamics, Whiley, New York, 1998 | Zbl
[34] Artificial dispersion via high-order homogenization: magnetoelectric coupling and magnetism from dielectric layers, Proc. R. Soc. A, Volume 469 (2013), 20130240 | MR | Zbl
[35] Spatial dispersion and negative refraction of light, Usp. Phys. Nauk. (UFN), Volume 176 (2006), 001051
[36] High-frequency homogenization for periodic media, Proc. R. Soc. A, Volume 466 (2010), 002341 | MR | Zbl
[37] High-frequency homogenization for checkerboard structures: defect modes, ultrarefraction, and all-angle negative refraction, J. Opt. Soc. Am. A, Volume 28 (2011), 001032
[38] Boundary conditions for interfaces of electromagnetic crystals and the generalized ewald-oseen extinction principle, Phys. Rev. B, Volume 73 (2006), 045102
[39] Additional boundary condition for the wire medium, IEEE Trans. Antennas Propag., Volume 54 (2006), 001766 | DOI | MR | Zbl
[40] Validity of the effective-medium approximation of photonic crystals, Phys. Rev. B, Volume 77 (2008), 235445 | DOI
[41] Appropriate truncation for photonic crystals, J. Mod. Opt., Volume 55 (2008), 001759 | DOI | Zbl
[42] On electromagnetic characterization and homogenization of nanostructured metamaterials, J. Opt., Volume 13 (2011), 103001
[43] Homogenization of Maxwell’s equations in periodic composites: Boundary effects and dispersion relations, Phys. Rev. E, Volume 85 (2012), 066603
[44] Current-driven homogenization and effective medium parameters for finite samples, Phys. Rev. B, Volume 88 (2013), 125131
[45] Classical and non-classical effective medium theories: New perspectives, Phys. Lett. A, Volume 381 (2017), 001635 | DOI | MR
[46] Taming spatial dispersion in wire metamaterial, J. Phys.: Condens. Matter., Volume 20 (2008), 295222
[47] Spatial dispersion in negative-index composite metamaterials, Phys. Rev. A, Volume 77 (2008), 013807
[48] Can the imaginary part of permeability be negative?, Phys. Rev. E, Volume 78 (2008), 026608
[49] Poynting vector, heating rate, and stored energy in structured materials: A first-principles derivation, Phys. Rev. B, Volume 80 (2009), 235120
[50] Restoring the physical meaning of metamaterial constitutive parameters, Phys. Rev. B, Volume 83 (2011), 081102(R)
[51] Examining the validity of Kramers–Kronig relations for the magnetic permeability, Phys. Rev. B, Volume 83 (2011), 165119
[52] Causality relations in the homogenization of metamaterials, Phys. Rev. B, Volume 84 (2011), 054305
[53] Causality and passivity properties of effective parameters of electromagnetic multilayered structures, Phys. Rev. B, Volume 88 (2013), 165104
[54] Negative refraction makes a perfect lens, Phys. Rev. Lett., Volume 85 (2000), pp. 3966-3969 | DOI
[55] Controlling electromagnetic fields, Science, Volume 312 (2006), p. 1780 | DOI | MR | Zbl
[56] Metamaterial electromagnetic cloak at microwave frequencies, Science, Volume 314 (2006), p. 977
[57] Optical conformal mapping, Science, Volume 312 (2006), p. 1777 | DOI | MR
[58] Bounds on Herglotz functions and fundamental limits of broadband passive quasistatic cloaking, J. Math. Phys., Volume 58 (2017), 071504 | DOI | MR | Zbl
[59] Analytic properties of the electromagnetic Green’s function, J. Math. Phys., Volume 58 (2017), 071501 | DOI | MR | Zbl
[60] Comment on “Negative refraction makes a perfect lens”, Phys. Rev. Lett., Volume 87 (2001), 249701
[61] Some problems with negative refraction, Phys. Rev. Lett., Volume 87 (2001), 249703
[62] Left-handed materials do not make a perfect lens, Phys. Rev. Lett., Volume 88 (2002), 207403 | DOI
[63] Problem of image superresolution with a negative-refractive-index slab, J. Opt. Soc. Am. A, Volume 21 (2004), 000491 | DOI
[64] Perfect lenses made with left-handed materials: Alice’s mirror?, J. Opt. Soc. Am. A, Volume 21 (2004), p. 122 | DOI
[65] Criterion for negative refraction with low optical losses from a fundamental principle of causality, Phys. Rev. Lett., Volume 98 (2007), 177404 | DOI
[66] Wave refraction in negative-index media: Always positive and very inhomogeneous, Phys. Rev. Lett., Volume 88 (2002), 187401
[67] Macroscopic Maxwell’s equations and negative index materials, J. Math. Phys., Volume 51 (2010), 052902 | DOI | MR | Zbl
[68] Light propagation in composite materials with gain layers, Phys.-Usp., Volume 55 (2012), 001080
[69] Fourier–Laplace analysis and instabilities of a gainy slab, J. Opt. Soc. Am. B, Volume 32 (2015), 001947
[70] Fourier theory of linear gain media, Phys. Rev. A, Volume 91 (2018), 043826 | MR
[71] Linear absorptive dielectric, Phys. Rev. A, Volume 57 (1998), 004818
[72] Spectral properties of absorptive photonic crystals, Contemporary Mathematics (Waves in Periodic and Random Media), Volume 339, American Mathematical Society, Providence, RI, 2003, 1 pages | DOI | MR | Zbl
[73] Mathematical models for dispersive electromagnetic waves: an overview, Comput. Math. Appl., Volume 74 (2017), 002792 | DOI | MR | Zbl
[74] Equivalence of the Langevin and auxiliary-field quantization methods for absorbing dielectrics, Phys. Rev. A, Volume 63 (2001), 043806
[75] Singularity of the dyadic Green’s function for heterogeneous dielectrics, Phys. Rev. E, Volume 75 (2007), 056601
[76] Spectral theory of time dispersive and dissipative systems, J. Stat. Phys., Volume 118 (2005), 000199 | DOI | MR | Zbl
[77] Frequency dispersion limits resolution in veselago lens, Progr. Electromagn. Res. B, Volume 19 (2010), p. 233 | DOI
[78] Negative index materials and time-harmonic electromagnetic field, C. R. Phys., Volume 13 (2012), 000786 | DOI
[79] Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part I: Generalized Fourier transform, Commun. Partial Differ. Equ., Volume 42 (2017), 001707 | DOI | MR | Zbl
[80] Perfect corner reflector, Opt. Lett., Volume 30 (2005), 001204 | DOI
[81] Negative refraction in 2d checkerboards related by mirror anti-symmetry and 3d corner lenses, New J. Phys., Volume 7 (2005), 000164 | DOI
[82] Cloaking and imaging effects in plasmonic checkerboards of negative and and dielectric photonic crystal checkerboards, Photon. Nanostruct.-Fundam. Appl., Volume 10 (2007), 000083
[83] Transfer matrix method for point sources radiating in classes of negative refractive index materials with 2n-fold antisymmetry, Waves Random Complex Media, Volume 17 (2007), 000581 | DOI | MR | Zbl
[84] T-coercivity for scalar interface problems between dielectrics and metamaterials, J. Math. Mod. Num. Anal., Volume 46 (2012), 001363 | MR | Zbl
[85] Radiation condition for a non-smooth interface between a dielectric and a metamaterial, Math. Models Methods Appl. Sci., Volume 23 (2013), 001629 | MR | Zbl
[86] Two-dimensional Maxwell’s equations with sign-changing coefficients, Appl. Numer. Math., Volume 79 (2014), 000029 | MR | Zbl
[87] T-coercivity for the Maxwell problem with sign-changing coefficients, Commun. Part Differ. Equ., Volume 37 (2014), 001007 | MR | Zbl
[88] Spectral analysis of polygonal cavities containing a negative-index material, Annales Henri Lebesgue, Volume 3 (2020), pp. 1161-1193 | DOI
[89] Optical Waves in Layered Media, John Wiley and Sons, New York, 1988
[90] Electromagnetic Fields, IEEE Press Series on Electromagnetic Wave Theory, Whiley-Interscience, Hoboken, NJ, USA, 2007
[91] Calculation and analysis of the complex band structure of dispersive and dissipative two-dimensional photonic crystals, J. Opt. Soc. Am. B, Volume 33 (2016), 000691 | DOI
[92] Quasinormal mode solvers for resonators with dispersive materials, J. Opt. Soc. Am. A, Volume 36 (2019), 000686 | DOI
[93] Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures, Comput. Phys. Commun., Volume 257 (2020), 107509 | DOI | MR
[94] On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients, J. Comput. Phys., Volume 322 (2016), 000224 | MR | Zbl
[95] Negative refractive index materials, J. Comput. Theor. Nanosci., Volume 3 (2006), p. 1 | DOI
[96] Resonant and antiresonant frequency dependence of the effective parameters of metamaterials, Phys. Rev. E, Volume 68 (2003), 065602(R) | DOI
[97] Comment i on “resonant and antiresonant frequency dependence of the effective parameters of metamaterials”, Phys. Rev. E, Volume 70 (2004), 048601
[98] Comment ii on “resonant and antiresonant frequency dependence of the effective parameters of metamaterials”, Phys. Rev. E, Volume 70 (2004), 048602
[99] Electromagnetic Surface Modes, Whiley, New York, 1982
[100] Transformation-optics description of nonlocal effects in plasmonic nanostructures, Phys. Rev. lett., Volume 108 (2012), 106802
[101] Electrodynamics of media with spatial dispersion, Usp. Fiz. Nauk, Volume 74 (1961), 000223
[102] Causality, nonlocality, and negative refraction, Phys. Rev. Lett., Volume 1180 (2017), 134301
[103] Band structure of absorptive photonic crystals, J. Phys. A: Math. Gen., Volume 33 (2000), 006223 | MR | Zbl
[104] Flat optics with designer metasurfaces, Nat. Mater., Volume 13 (2014), 000139
[105] Dielectric gradient metasurface optical elements, Science, Volume 345 (2014), 000298
[106] Photonic floquet topological insulators, Nature, Volume 496 (2013), 000196
[107] Honeycomb Schrödinger operators in the strong binding regime, Commun. Pure Appl. Math., Volume 71 (2018), 001178 | Zbl
[108] Metamaterials and Plasmonics, Volume 2: Elastic, Acoustic, and Seismic Metamaterials, World Scientific Series in Nanoscience and Nanotechnology, World Scientific Publishing, London, UK, 2017
Cité par Sources :
Commentaires - Politique