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Artificial Ferro-Magnetic Anisotropy: Homogenization of 3D Finite Photonic Crystals

  • F. Zolla
  • S. Guenneau
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)

Abstract

In this paper, we attempt to replace heterogeneous ferro-magnetic photonic crystals by homogeneous structures with anisotropic matrices of permittivity and permeability, both deduced from the resolution of annex problems of electrostatic type on a periodic cell. The asymptotic analysis relies on the multi-scale method which is a tool in the theory of homogenization with rapidly oscillating coefficients [2]. We note a singular perturbation for the divergence of the electromagnetic field associated to scaled permittivity ε(x/η) and permeability μ(x/η), which are periodic functions of period η≪1. We establish the sharp convergence of the oscillating field towards the homogenized one via the notion of two-scale convergence [1]. We finally solve numerically the associated system of partial differential equations with a Finite Element Method in order to exhibit the matrices of effective permittivity and permeability for given 2D ferro-magnetic periodic composites.

Keywords

Photonic Crystal Relative Permeability Maxwell System Anisotropic Matrice Condense Matter Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • F. Zolla
    • 1
  • S. Guenneau
    • 2
    • 3
  1. 1.Institut Fresnel, UMR 613SFaculté de saint-JérômeMarseille Cedex 20France
  2. 2.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK
  3. 3.Condensed Matter Theory Group, Blackett LaboratoryImperial CollegeLondonUK

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