Abstract
Maxwell's equations are solved in the presence of a metal slab. The response of the electrons in the slab to an electromagnetic wave is a current charge density which appears to be a non-local pseudopotential in the Helmholtz equation. This pseudopotential comprises Lindhard's longitudinal and transverse dielectric functions internally, the scattering at the surfaces, and the vacuum dielectric function externally. External magnetic modes couple to internal magnetic modes; external electric modes couple to internal electric and longitudinal modes; bound longitudinal modes and bound electric and magnetic modes are shown to arise as well. Explicit secular equations for the frequency of longitudinal and transverse bulk modes are derived which include the scattering at the surface. The phase shift of the free transverse modes at the slab is calculated and related to the reflectivity and the surface energy of the slab. The phase shift of the free electric modes is governed by the internal longitudinal dielectric function and that of the free magnetic modes by the internal transverse dielectric function.
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