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Étude mathématique et numérique de cristaux photoniques fortement contrastés

Abstract : This thesis is to develop the macroscopic behavior of highly contrasted composite materials in an electromagnetic framework. We consider structures made of periodically (or randomly) distributed micro-inclusions made of high conductivity or high permittivity medium. Actually, such a structure is to be found in a three-dimensional bounded domain which is illuminated by an infinity-coming monochromatic incident wave. Our mathematical approach consists in passing to the limit in the Maxwell system describing the diffraction problem when the distance between inclusions goes to zero while the electromagnetic constant of inclusions goes to infinity ("high contrast"). We are studing two 3D diffracting structures which lead to negative permittivity or permeability materials. The asymptotic study is based on the two-scale convergence method (sometimes in a stochastic way), and the resulting unit cell problems are solved by spectral method. This leads to an explicit formulation of the effective tensor according to the frequency, which highlights their huge variations around the so-called resonant frequencies.
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Contributor : Christophe Bourel <>
Submitted on : Wednesday, February 2, 2011 - 7:14:21 PM
Last modification on : Tuesday, June 19, 2018 - 3:50:01 PM
Long-term archiving on: : Tuesday, May 3, 2011 - 3:37:41 AM


  • HAL Id : tel-00562138, version 1



Christophe Bourel. Étude mathématique et numérique de cristaux photoniques fortement contrastés. Mathématiques [math]. Université du Sud Toulon Var, 2010. Français. ⟨tel-00562138⟩



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