The Electromagnetic Field Near a Metal Surface

Abstract

We have given here a formulation for calculating the electromagnetic fields near a metal surface exposed to an external radiation. For the sake of simplicity, the metal has been treated as a semi-infinite jellium with no restriction on the surface profile. The solutions of Maxwell's wave equations have been considered separately in three regions, vacuum, bulk and surface. In the first two regions, the solutions have simple forms and correspond to asymptotic forms of the electromagnetic fields. In the surface region, introducing "surface solutions" as the modifications in the fields over their asymptotic forms, an exact procedure for their determination has been developed. It is a computationally tractable method and has allowed discussions of various approximations. In particular, we have examined in detail the "surface solutions" and their physical origin, and as illustration, discussed extensively the limiting cases of semi-classical infinite barrier model, and long wavelength limit. We have shown explicitly that the surface solutions arise essentially from the particle-hole excitations.