Homogenization near resonances and artificial magnetism in 3D dielectric metamaterials Auteur(s): Bouchitté Guy, Bourel Christophe, Felbacq D. (Article) Publié: Archive For Rational Mechanics And Analysis, vol. 225 p.1233-1277 (2017) Texte intégral en Openaccess : Ref HAL: hal-01240316_v1 Ref Arxiv: 1512.02463 DOI: 10.1007/s00205-017-1132-1 WoS: 000404633500008 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote 17 Citations Résumé: 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. |