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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01240316
Contributor : Christophe Bourel <>
Submitted on : Wednesday, December 9, 2015 - 9:31:21 AM
Last modification on : Wednesday, May 29, 2019 - 9:46:13 AM
Long-term archiving on : Saturday, April 29, 2017 - 10:21:05 AM

Files

BouBouFel.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01240316, version 1
  • ARXIV : 1512.02463

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. ⟨https://link.springer.com/article/10.1007/s00205-017-1132-1⟩. ⟨hal-01240316⟩

Share

Metrics

Record views

808

Files downloads

248