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 ε{lunate}(k∥ω|x3x'3), assumed to be symmetric in x3 and x'3. Here k∥ is a two-dimensional wave vector whose components are parallel to the interface, and ω is the frequency of the electromagnetic field in the medium. The dispersion relation has the form 1 + k∥χ(k∥ω|x3 = 0, x′3 = 0) = 0, and an explicit prescription for obtaining the function χ(k∥ω|x3x'3) is presented. The use of the dispersion relation is illustrated by applying it to two examples: (1) a local dielectric constant; and (2) the nonlocal dielectric function used previously by Maradudin and Mills. In both cases previously obtained results are recovered. © 1979.