Modèle effectif de couche mince rugueuse périodique sur une structure semi-infinie

Jean-Baptiste Bellet (1) , Gérard Berginc (2)

1 IECL - Institut Élie Cartan de Lorraine
2 Thalès Optronique

We study the effect of a periodic rough thin layer above a semi-infinite medium, in a bi-dimensionnal Helmholtz context. Effective transmission conditions are formally derived using homogenization type techniques. Then the solution to the problem of the effective medium illuminated by a plane wane is computed using Fourier analysis. So is the effective Green function. The second step is dedicated to the scattering problem from an embedded inclusion in the semi-infinite medium that is covered by the rough layer. It is solved by the boundary element method in the effective medium. Some numerical results are shown. To finish with, the effective model is validated in the case of a flat layer, and the BEM code is checked with the Born approximation.

Mots clés: asymptotic analysis; rough layer; Electromagnetics; Optics; Boundary Element Method; scattering; effective transmission conditions

Domaines: Analyse numérique [math.NA]; Electromagnétisme; Optique / photonique

Jean-Baptiste Bellet, Gérard Berginc. Modèle effectif de couche mince rugueuse périodique sur une structure semi-infinie. ESAIM: Mathematical Modelling and Numerical Analysis, 2013, 47 (5), pp.1367-1386. ⟨10.1051/m2an/2013073⟩. ⟨hal-00719857⟩