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Comptes Rendus Mathématique
Volume 339, n° 5
pages 377-382 (septembre 2004)
Doi : 10.1016/j.crma.2004.06.018
Received : 19 June 2004 ; 
Homogenization near resonances and artificial magnetism from dielectrics
Homogénéisation de diélectriques près des résonances et magnétisme artificiel.
 

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

Abstract

The homogenization of periodic dielectric structures in harmonic regime usually leads to an effective permittivity tensor  . 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 . In this Note, we enlight a new effect induced by microscopic resonances which leads in parallel to a possibly negative effective permeability   (although the original medium is assumed to be nonmagnetic i.e.  ). To cite this article: G. Bouchitté, D. Felbacq, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

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Résumé

L'homogénéisation de structures diélectriques périodiques en régime harmonique fait apparaitre en général un tenseur de permittivité effective  . 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 . 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.  ), à une perméabilité effective   qui peut éventuellement être négative. Pour citer cet article : G. Bouchitté, D. Felbacq, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.


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