RETARDED TREATMENT OF SUBSTRATE-RELATED EFFECTS ON GRANULAR FILMS .1. POLARIZABILITY OF A SINGLE SPHERE

A multipolar treatment of the retarded fields radiated by a metal sphere on a dielectric substrate under the influence of an incident plane wave is described. Unlike previous treatments, the present one allows boundary conditions, both on the spherical surface and on the substrate interface, to be matched by simply solving an adequate number of linear equations. The problem is thus reduced to inverting three complex matrices, whose sizes depend on the number of multipoles included in the field forms. The solutions, which represent the object and image multipoles (both in the incidence and in the transmission media) associated with the polarized sphere, are given the form of linear combinations of the multipoles associated with the unperturbed field (incident and reflected waves).