A Surface Plasmon Dispersion Relation in the Presence of Spatial Dispersion.

A dispersion relation for surface plasmons retardation neglected is obtained in the presence of spatial dispersion. The physical system considered is one of vacuum separated by a plane interface from a dielectric medium occupying the half-space x3 0, and characterized by a nonlocal dielectric function assumed to be symmetric in x3 and x3. Here k-parallel is a two-dimensional wave vector whose components are parallel to the interface, and omega is the frequency of the electromagnetic field in the medium. The use of the dispersion relation is illustrated by applying it to two examples a local dielectric constant and the nonlocal dielectric function used previously by Maradudin and Mills. In both cases previously obtained results are recovered.