Studies on polarizabilities and scattering behavior of small spherical particles

Abstract

It is possible to relate the response of a sphere to an applied uniform static electric field with the scattering from a small spherical particle due to plane wave incidence. The limits up to which these relations between the polarizability and the extinction, scattering, and radar cross sections of a sphere are valid in the dynamic range are presented here. From the observations it can be concluded that radar cross section is a very good measure in predicting the polarizability. A related aspect studied here is the evaluation of the effective permittivity of a sparse mixture of spherical inclusions using a generalized Maxwell Garnett mixing rule. This is compared with extinction of a plane wave by a slab of n spherical inclusions sparsely located. The extinction by such a slab is calculated using the quasistatic approximation to Mie theory, and also using the full Mie theory, as the size of the inclusions is increased. The studies have been carried out for both lossless and lossy inclusions. The generalized mixing rule was found to be quite accurate in predicting the value of effective permittivity up to size parameters of 0.5 at least for small εr of the inclusion.