Negative index materials: at the frontier of macroscopic electromagnetism

Boris Gralak

doi:10.5802/crphys.29

Negative index materials: at the frontier of macroscopic electromagnetism
[Matériaux d’indice négatif : à la frontière de l’électromagnétisme macroscopique]

Boris Gralak ¹

¹ CNRS, Aix Marseille Univ, Centrale Marseille, Institut Fresnel, Marseille, France

Comptes Rendus. Physique, Volume 21 (2020) no. 4-5, pp. 343-366.

Résumé
Abstract

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 $- 1$ . 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 $- 1$ 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.

Publié le : 2020-12-16

DOI : 10.5802/crphys.29

Keywords: Negative index, Metamaterials, Frequency dispersion, Corner mode, Spatial dispersion, Passivity, Permeability
Mot clés : Indice négatif, Métamatériaux, Dispersion en fréquence, Mode de coin, Dispersion spatiale, Passivité, Perméabilité

Affiliations des auteurs :

Boris Gralak ¹

¹ CNRS, Aix Marseille Univ, Centrale Marseille, Institut Fresnel, Marseille, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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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/

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