The Neumann-Poincaré operator naturally appears in the context of metamaterials as it may be used to represent the solutions of elliptic transmission problems via potentiel theory. Its spectral properties are closely related to the well-posedness of these PDE's, in the typical case where one considers a bounded inclusion of homogeneous plasmonic metamaterial embedded in a homogeneous background dielectric medium.

The NP operator of a 2D domain with corners is not compact and has an essential spectrum which depends only on the angles of the corners. We characterize this essential spectrum in terms of elliptic corner singularity functions, which gives insight on the behavior of generalized eigenmodes.