THE POLARIZABILITY AND THE OPTICAL-PROPERTIES OF LATTICES AND RANDOM DISTRIBUTIONS OF SMALL METAL SPHERES ON A SUBSTRATE

We give expressions for the reflection and transmission amplitudes for two-dimensional distributions of small monodisperse metal spheres on a substrate in terms of interfacial susceptibilities. These susceptibilities are related to the averaged polarizability of the spheres. Using a multipole expansion, we derive an infinite coupled set of linear equations for this polarizability which contains all the interactions between the spheres and the substrate. By truncating this set, one can calculate the polarizability as accurately as desired for regular arrays and uncorrelated distributions. For random distributions we approximated multiparticle correlations in terms of pair correlations. The ellipsometric angles and normal transmittance as a function of the coverage are analysed in detail. Up to a coverage of about 40% the results are almost independent of the sphere distribution on the substrate. For larger coverages we find considerable differences. Regular arrays of spheres show a coverage-dependent resonance frequency.