Homogenization of the 3D Maxwell system near resonances and artificial magnetism - Archive ouverte HAL Access content directly
Journal Articles Comptes rendus de l'Académie des sciences. Série I, Mathématique Year : 2009

Homogenization of the 3D Maxwell system near resonances and artificial magnetism

Christophe Bourel
Didier Felbacq
  • Function : Author
  • PersonId : 860489

Abstract

It is now well known 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 micro resonator problem on the section of the fibers holds merely in the case of polarized magnetic fields, reducing thus its applications to infinite cylindrical obstacles. In this Note we propose a full 3D extension of previous asymptotic analysis based on a new averaging method for the magnetic field. We evidence a vectorial spectral problem on the periodic cell which accounts for micro-resonance effects and leads to a 3D negative effective permeability tensor. This suggests that periodic bulk dielectric inclusions could be an efficient alternative to the very popular metallic split-ring structure proposed by Pendry.

Dates and versions

hal-00385882 , version 1 (20-05-2009)

Identifiers

Cite

Christophe Bourel, Didier Felbacq, Guy Bouchitté. Homogenization of the 3D Maxwell system near resonances and artificial magnetism. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2009, 347, pp.571-576. ⟨10.1016/j.crma.2009.02.027⟩. ⟨hal-00385882⟩
123 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More