Comptes Rendus
Mathematical Physics
Homogenization near resonances and artificial magnetism from dielectrics
Comptes Rendus. Mathématique, Volume 339 (2004) no. 5, pp. 377-382.

The homogenization of periodic dielectric structures in harmonic regime usually leads to an effective permittivity tensor ɛeff. 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 μeff(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 ɛeff. 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 μeff(ω) qui peut éventuellement être négative.

Received:
Published online:
DOI: 10.1016/j.crma.2004.06.018
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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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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[5] D. Felbacq; G. Bouchitté Homogenization of a set of parallel fibers, Waves Random Media, Volume 7 (1997), pp. 245-256

[6] J.B. Pendry; A.J. Holden; D.J. Robbins; W.J. Stewart Magnetism from conductors, and enhanced non-linear phenomena, IEEE T. Microw. Theory, Volume 47 (1999), pp. 2075-2084

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