Reflection and scattering of long-range surface plasmon-polaritons on boundary of free half-space

Abstract

We study the long-range surface plasmon-polariton (LRSPP) propagating along a thin metal film embedded in a homogeneous semi-infinite medium. The reflection and scattering of the LRSPP by the end face of the film at the boundary of free half-space are discussed. We apply the self-consistent electromagnetic approach using the expansion of the plasmon and scattered fields by the eigenfunctions of the structure. The Fredholm integral equation of the first kind appearing in the model has been solved with using the variational Ritz-Galerkin procedure. It is shown that the LRSPP reflection coefficient can be approximated by the Fresnel formula of reflection for normal incidence of a plane TEM wave. The power of the back-scattered radiation is predicted to be a considerable part (tens of percents) of the reflected LRSPP power. We discuss the far-field patterns of both the back- and forward-scattered radiation. It is shown that the back-scattered radiation form two narrow lobes directed symmetrically with regard to the metal film plane. The radiation scattered in the forward direction is presented by the one-lobe far-field pattern; decreasing the metal layer thickness results in the narrower lobe of the forward-scattered radiation.