  The Neumann-Poincar\'e (NP) operator naturally appears in the context of
metamaterials as it may be used to represent the solutions of elliptic
transmission problems via potentiel theory. In particular, 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. In a
recent work, M. Perfekt and M. Putinar have shown that the NP operator of a 2D
curvilinear polygon has an essential spectrum, which depends only on the angles
of the corners. Their proof is based on quasi-conformal mappings and techniques
from complex-analysis. In this work, we characterize the spectrum of the NP
operator for a 2D domain with corners in terms of elliptic corner singularity
functions, which gives insight on the behavior of generalized eigenmodes.
