OPTICAL-RESPONSE OF A THIN-FILM OF SPHERICAL-PARTICLES ON A DIELECTRIC SUBSTRATE - RETARDED MULTIPOLAR TREATMENT

Multipolar expansions have recently been used to describe the polarizability of a metal sphere on a dielectric substrate. The same technique may be applied to calculating the optical behavior of a square network of identical spheres sitting upon a flat substrate. It is shown how to relate the image multipoles to the object multipoles, which are in turn related to the applied field carried by the unperturbed incident and reflected waves. Retarded-field forms are consistently used throughout the treatment. The scattered fields are also calculated and the optical response determined. This requires summing up the multipole-multipole interactions. Numerical calculations have been performed, showing that a quadrupolar treatment is needed to define the transmittance of an ideal sample.