Surface Plasmon‐Polaritons in a Spatially Dispersive Inhomogeneous Medium

The dispersion of surface plasmon‐polaritons and their associated fluctuation densities and electric fields are calculated for a spatially dispersive semi‐infinite electron plasma, with, parameters appropriate to the metallic state. The model is hydrodynamic and the electron density is assumed to be uniform and equal to the bulk value, except for a small region near the surface. In this surface neighbourhood the electron density is assumed to fall in a step‐function manner as in previously reported successful models of surface profile properties. The momentum range covers that which is experimentally available and includes both the retardation and electrostatic regimes. It is emphasised that the inclusion of spatial dispersion, by the introduction of a pressure gradient, is an essential feature. This is because the distance over which the surface density changes is such that the transit time of the carriers is the same order of magnitude as the inverse plasma frequency. Resonances are possible, therefore, which are entirely absent in pure retardation models which ignore spatial dispersion. Fluctuation densities, electric fields, and polarisation plots are presented. The previously reported assertion that the charge distributions can be rigorously classified into multipoles is investigated numerically.