Scattering of surface-plasmon polaritons by a localized dielectric surface defect studied using an effective boundary condition

By the use of an effective boundary condition we derive a two-dimensional integral equation for the scattering amplitude in the Rayleigh representation of the electric field of a surface-plasmon polariton scattered from a two-dimensional dielectric surface defect. This integral equation is transformed into a set of coupled one-dimensional integral equations by representing the dependence of the amplitude on the azimuthal angle by means of a rotational expansion. Exemplifying the usefulness of this approach, numerical results are obtained for defects of the shape of an anisotropic Gaussian function and a hemiellipsoid with a finite footprint when the surface-plasmon polariton incident on the defect from an arbitrary direction is either a plane wave or a Gaussian beam. Inspecting the near-field distribution of the radiation caused by the scattering, we find a localized increase of surface-plasmon polariton intensity in the vicinity of the dielectric defect, which indicates a focusing for both forms of the incident surface-plasmon polariton.