External modes of two-dimensional thin scatterers

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.