External modes of two-dimensional thin scatterers

Abstract

Two-dimensional wave scattering by open thin scatterers is studied. The current induced on the scatterer is expanded in modes, which are eigenfunctions of the singular part of the Green's function. The number of excited modes is a monotonic increasing function of the length of the scatterer and its curvature. An efficient numerical scheme for calculating the induced current emerges, with an explicit convergence criterion.