Scattering of Surface Plasmon Polaritons by a Circularly Symmetric Surface Defect

By the use of the method of reduced Rayleigh equations, we develop a theory of the scattering of a surface plasmon polariton from a cirularly symmetric defect on a metal surface. We derive and solve one-dimensional integral equations for the scattering amplitudes corresponding to different rotational numbers $m$. We calculate the differential cross sections for scattering into the vacuum and into other surface waves, and the field intensity near the surface. The results show agreement with recent experimental data. We also consider resonant scattering due to surface shape resonances.