Superlensing using hyperbolic metamaterials: the scalar case

Bonnetier, Eric; Nguyen, Hoai-Minh

Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 973-1003.

Dans cet article, on s’intéresse à la propriété de superlensing des méta-matériaux, c’est-à-dire à la possibilité d’imager un objet arbitraire, sans condition sur le rapport entre sa taille et la longueur d’onde de la lumière incidente. Nous proposons et analysons deux types de dispositifs constitués de méta-matériaux hyperboliques, qui possèdent cette propriété. L’étude de tels milieux est délicate, car les EDP qui les modélisent changent de type : elles sont elliptiques dans certaines régions de l’espace et hyperboliques dans les autres.

This paper is devoted to superlensing using hyperbolic metamaterials: the possibility to image an arbitrary object using hyperbolic metamaterials without imposing any conditions on the size of the object and the wave length. To this end, two types of schemes are suggested and their analysis are given. The superlensing devices proposed are independent of the object. It is worth noting that the study of hyperbolic metamaterials is challenging due to the change of type of the modeling equations, elliptic in some regions, hyperbolic in some others.

Classification : 35B30, 35B40, 35J05, 35J70, 35M10, 35L53, 78A25
Keywords: Negative index materials, hyperbolic meta-materials, superlensing, degenerate elliptic equations
Mot clés : Matériaux à indice négatif, méta-matériaux hyperboliques, superlensing, équations elliptiques dégénérées

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