Optical reflectance of nonlocal systems

A microscopic perturbative theory developed earlier for the electric field near the surface of a metal having a nonlocal dielectric tensor is extended beyond the Born approximation. Expressions are derived for the reflection amplitudes of $s$- and $p$-polarized light, and they are compared with the results of previous workers by taking appropriate limits. A new, general dispersion relation of surface plasmons is given which takes into account possible band-structure effects near the surface. The influence of this more accurate theory on formulas for differential reflectance from an absorbate-covered metal surface is indicated.