Titre : Radiation condition for a non-smooth interface between a dielectric and a metamaterial
Année : 2013
Type : article (revue avec comité de lecture)
Auteurs : A.-S. Bonnet-BenDhia, L. Chesnel, X. Claeys
Résumé : We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real valued negative permittivity/permeability which models an ideal metamaterial. When the interface between the two media has a corner, according to the value of the contrast (ratio) of the physical constants, this non-coercive problem can be ill-posed (not Fredholm) in $H^1$. This is due to the degeneration of the two dual singularities which then behave like $r^{\pm i\eta}=e^{\pm i\eta\ln\,r}$ with $\eta\in\mathbb{R}^{\ast}$. This apparition of propagative singularities is very similar to the apparition of propagative modes in a waveguide for the classical Helmholtz equation with Dirichlet boundary condition, the contrast playing the role of the wavenumber. In this work, we derive for our problem a functional framework by adding to $H^1$ one of these propagative singularities. Well-posedness is then obtained by imposing a radiation condition, justified by means of a limiting absorption principle, at the corner between the two media.
Thèmes : Guides d'ondes
Ondes harmoniques
Référence : Math. Models Meth. App. Sci. - vol. 3 images/icons/doctype_pdf.gif