# Radiation condition for a non-smooth interface between a dielectric and a metamaterial

august, 2013
Publication type:
Paper in peer-reviewed journals
Journal:
Math. Models Meth. App. Sci., vol. 3
HAL:
Abstract:
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.
BibTeX:
@article{Bon-Che-Cla-2013,
author={Anne-Sophie Bonnet-BenDhia and Lucas Chesnel and Xavier Claeys },
title={Radiation condition for a non-smooth interface between a
dielectric and a metamaterial },
doi={10.1142/S0218202513500188 },
journal={Math. Models Meth. App. Sci. },
year={2013 },
month={8},
volume={3 },
}