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Journal Articles Archive for Rational Mechanics and Analysis Year : 2017

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.
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Dates and versions

hal-01240316 , version 1 (09-12-2015)

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Guy Bouchitté, Christophe Bourel, Didier Felbacq. Homogenization near resonances and artificial magnetism in 3D dielectric metamaterials. Archive for Rational Mechanics and Analysis, 2017, 225 (3), pp.1233-1277. ⟨10.1007/s00205-017-1132-1⟩. ⟨hal-01240316⟩
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