Aspects of spatial dispersion in the optical properties of a vacuum-dielectric interface

We have examined the relationship between the polarizability for a two-phase (vacuum-dielectric) system and the use of additional boundary conditions and the like, as regards the response of systems exhibiting spatial dispersion. As a consequence we are able to derive information about induced-charge and current densities and the continuity of the field quantities across the interface. It is shown that it is not possible to resonantly excite longitudinal bulk modes with incident light in the formalism of Rimbey-Mahan. We have derived sum rules in wave-vector space on bulk polaritons in homogeneous isotropic systems. In the case of nonhomogeneous perfect crystals in which the bulk response is described by the matrix ε(→Q,→Q^'), we have solved formally for the surface impedance in terms of an assumed arbitrary ε(→Q,→Q^'), by means of an extension of the Fuchs-Kliewer formalism.