Homogenization near resonances and artificial magnetism from dielectrics

Guy Bouchitté; Didier Felbacq

doi:10.1016/j.crma.2004.06.018

Mathematical Physics

Homogenization near resonances and artificial magnetism from dielectrics

Presented by: Philippe G. Ciarlet

Guy Bouchitté ¹; Didier Felbacq ²

¹ Laboratoire ANAM, université de Toulon et du Var, BP 132, 83957 La Garde cedex, France
² Groupe d'étude des semiconducteurs, université de Montpellier 2, place Eugène Bataillon, CC 074, 34095 Montpellier cedex 05, France

Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 377-382.

Abstract (OV)
Résumé

The homogenization of periodic dielectric structures in harmonic regime usually leads to an effective permittivity tensor $ɛ^{eff}$ . It has been observed by Bouchitté and Felbacq [Waves Random Media 7 (1997) 245–256], that in the high contrast case (high conductivity fibers), this tensor depends on the angular frequency ω. In this Note, we enlight a new effect induced by microscopic resonances which leads in parallel to a possibly negative effective permeability $μ^{eff} (ω)$ (although the original medium is assumed to be nonmagnetic i.e. $μ = 1$ ).

L'homogénéisation de structures diélectriques périodiques en régime harmonique fait apparaitre en général un tenseur de permittivité effective $ɛ^{eff}$ . Il a été remarqué par Bouchitté et Felbacq [Waves Random Media 7 (1997) 245–256] que dans le cas de forts contrastes (fibres de grande conductivité), ce tenseur peut dépendre de la fréquence ω. Dans cette note, nous mettons en évidence un effet nouveau dû à des micro-résonances et qui conduit, malgré l'absence initiale de propriétés magnétiques (i.e. $μ = 1$ ), à une perméabilité effective $μ^{eff} (ω)$ qui peut éventuellement être négative.

Received: 2004-06-19
Published online: 2004-08-06

DOI: 10.1016/j.crma.2004.06.018

Author's affiliations:

Guy Bouchitté ¹; Didier Felbacq ²

¹ Laboratoire ANAM, université de Toulon et du Var, BP 132, 83957 La Garde cedex, France
² Groupe d'étude des semiconducteurs, université de Montpellier 2, place Eugène Bataillon, CC 074, 34095 Montpellier cedex 05, France

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     author = {Guy Bouchitt\'e and Didier Felbacq},
     title = {Homogenization near resonances and artificial magnetism from dielectrics},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {377--382},
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     number = {5},
     year = {2004},
     doi = {10.1016/j.crma.2004.06.018},
     language = {en},
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Guy Bouchitté; Didier Felbacq. Homogenization near resonances and artificial magnetism from dielectrics. Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 377-382. doi : 10.1016/j.crma.2004.06.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.018/

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