Excitation of surface plasmon polaritons by the scattering of a volume electromagnetic beam from a circularly symmetric defect on a planar metal surface

In a recent theoretical study of the scattering of a surface plasmon polariton by a circularly symmetric protuberance or indentation on an otherwise planar metal surface in contact with vacuum, it was found that the angular dependence of the intensity of the volume electromagnetic waves scattered into the vacuum region possesses a maximum in the plane of incidence at a polar scattering angle of approximately 28 degree(s). This suggests that if a p-polarized volume electromagnetic field in the form of a beam of finite width is incident on the same surface defect, the efficiency of exciting a surface plasmon polariton will be greatest for a polar angle of incidence close to 28 degree(s). To test this hypothesis, in this paper we study this problem theoretically. The reduced Rayleigh equations for the amplitudes of the p- and s-polarized components of the scattered field are reduced to a set of one-dimensional integral equations by exploiting the circular symmetry of the surface defect, which is assumed to have a Gaussian form. The efficiency of exciting surface plasmon polaritons in this fashion is calculated as a function of the polar angle of incidence, and is found to be maximal when this angle is close to 28 degree(s).