# 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〉

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

### 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〉

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