Exact solution for the scattering and absorption properties of sphere clusters on a plane surface

Abstract

A formulation and computational scheme are presented for predicting the scattering and absorption cross-sections, and the scattering matrix elements, of clusters of non-intersecting spheres that are lying on or above an infinite plane surface and exposed to plane-wave radiation. The formulation provides an exact solution to Maxwell's equations and the associated boundary conditions on the spheres and the plane surface, and is applicable for arbitrary refractive indices for the spheres and the surface. A simplified strategy is presented for the calculation of the surface reflection matrix, which transforms the reflected scattered field from one sphere into a regular vector spherical harmonic expansion centered about another sphere. The calculation results are presented for the clusters of one, two, and four polystyrene spheres, with size parameters of one and 10, lying on a silicon substrate, and are compared with the predictions from the normal incidence approximation (NIA) in which the reflectance of the surface is assumed constant at the normal incidence value. The results show that the accuracy of the NIA is highly dependent on the extent of the sphere cluster, the angle of incidence, and the particular quantity (cross-sections, scattering matrix elements) under examination.