Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation

Abstract

We establish spectral enclosures and spectral approximation results for the inhomogeneous lossy Drude-Lorentz system with purely imaginary poles, in a possibly unbounded Lipschitz domain of R3. Under the assumption that the coefficients θe, θm of the material are asymptotically constant at infinity, we prove that spectral pollution due to domain truncation can lie only in the essential numerical range of a curlcurl0−f(ω) pencil.As an application, we consider a conducting metamaterial at the interface with the vacuum; we prove that the complex eigenvalues with non-trivial real part lie outside the set of spectral pollution. We believe this is the first result of enclosure of spectral pollution for the Drude-Lorentz model without assumptions of compactness on the resolvent of the underlying Maxwell operator.