Classical electrodynamics of non-specular dielectric surfaces

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Abstract
The effect of spatial dispersion on the electrodynamics of surfaces is studied for a phenomenological model which describes the surface scattering of the elementary excitations in terms of a parameter p, the specular surface being the case p = 1. Surface impedance, reflectivity and surface mode dispersion relation are obtained for arbitrary p without resorting to additional boundary conditions. It is thus shown that the problem is sufficiently defined if the model, including the effect of the surface, is specified. Various forms of additional boundary conditions used in the literature are discussed and characterized as models corresponding to particular values of p. The different roles of the longitudinal and transverse dielectric constants are discussed in physical terms