Homogenization near resonances and artificial magnetism in 3D dielectric metamaterials

Abstract : It is now well established that the homogenization of a periodic array of parallel dielectric fibers with suitably scaled high permittivity can lead to a (possibly) negative frequency-dependent effective permeability. However this result based on a two-dimensional approach holds merely in the case of linearly polarized magnetic fields, reducing thus its applications to infinite cylindrical obstacles. In this paper we consider a dielectric structure placed in a bounded domain of $\mathbb{R}^3$ and perform a full 3D asymptotic analysis. The main ingredient is a new averaging method for characterizing the bulk effective magnetic field in the vanishing-period limit. We evidence a vectorial spectral problem on the periodic cell which determines micro-resonances and encodes the oscillating behavior of the magnetic field from which artificial magnetism arises. At a macroscopic level we deduce an effective permeability tensor that we can be make explicit as a function of the frequency. As far as sign-changing permeability are sought after, we may foresee that periodic bulk dielectric inclusions could be an efficient alternative to the very popular metallic split-ring structure proposed by Pendry.
Type de document :
Article dans une revue
Archive for Rational Mechanics and Analysis, Springer Verlag, 2017, 225 (3), pp.1233 - 1277. 〈10.1007/s00205-017-1132-1〉
Liste complète des métadonnées

https://hal-univ-tln.archives-ouvertes.fr/hal-01557764
Contributeur : Guy Bouchitte <>
Soumis le : jeudi 6 juillet 2017 - 15:26:58
Dernière modification le : jeudi 11 janvier 2018 - 06:23:21

Identifiants

Relations

Citation

Guy Bouchitté, Christophe Bourel, Didier Felbacq. Homogenization near resonances and artificial magnetism in 3D dielectric metamaterials. Archive for Rational Mechanics and Analysis, Springer Verlag, 2017, 225 (3), pp.1233 - 1277. 〈10.1007/s00205-017-1132-1〉. 〈hal-01557764〉

Partager

Métriques

Consultations de la notice

92