Banachraum

We consider the diffraction of a finite dielectric crystal at a fixed wavelength. The cristal contains a periodic structure made of dielectric material with large permittivity and small period. We describe the asymptotic behavior of the electromagnetic fields as the period tends to zero by determining their two-scale limit. We evidence a microscopic spectral problem which accounts the resonances of the crystal. The artificial magnetism is then described by a frequeny dependent effective permeability possibly negative. Also, a random perturbation of the structure will be discuss.

Christophe Bourel

Calais