Scattering resonances in unbounded transmission problems with sign-changing coefficient

Abstract It is well known that classical optical cavities can exhibit localized phenomena associated with scattering resonances, leading to numerical instabilities in approximating the solution. This result be established via ‘quasimodes resonances’ argument from black box framework. Those concentrate at inner boundary of cavity and are called whispering gallery modes. In this paper we investigate resonances for unbounded transmission problems sign-changing coefficient (corresponding negative properties, e.g. made metamaterials). Due change sign previous results cannot applied directly, interface metamaterial-dielectric (such as so-called surface plasmons) emerge. We establish existence arbitrary two-dimensional smooth metamaterial cavities. The proof relies on an asymptotic characterization shows naturally fit Our analysis reveals that, depending metamaterial’s situated close real axis plasmons. Examples several provided.