Characterization of the essential spectrum of the Neumann-Poincaré operator in 2D domains with corner via Weyl sequences

Abstract

The Neumann-Poincaré (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.

References in corpus (3)

• The plasmonic eigenvalue problem
• On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients
• Spectral resolution of the Neumann-Poincaré operator on intersecting disks and analysis of plasmon resonance

Cited by in corpus (4)

• Surface Riesz transforms and spectral property of elastic Neumann--Poincaé operators on less smooth domains in three dimensions
• Embedded eigenvalues for the Neumann-Poincaré operator
• Stable determination of polygonal inclusions in Calderón's problem by a single partial boundary measurement
• The spectra of harmonic layer potential operators on domains with rotationally symmetric conical points