Determination of Closed-form Expressions for Rayleigh Scattering of Polarized Light from Adsorbed Particles on or below a Substrate

An integral equation formulation describing the scattered field from a distribution of optically small Rayleigh objects of arbitrary shape adsorbed onto a planar dielectric substrate is presented. When certain approximations are introduced concerning the scatterers’ permittivity contrast and small size compared to the wavelength, simple closed-form expressions are obtained for the ellipticity ratio and reflectivity which can be readily related to the surface coverage and average height of the surface layer. The formulation is an alternative to thin-island film theory often used to describe electromagnetic scattering from such configurations. Results derived from the integral equation model are compared with previously published measurements of ellipticity ratio and reflectivity and are found to be in good agreement with observation.