An ellipsoidal model for small nonspherical particles

Abstract

We have proposed an ellipsoidal model (ElM) for small nonspherical particles, i.e., we have proposed a method to construct “effective” ellipsoids the light scattering properties of which are similar to those of original particles. It has been shown that the semiaxes of a model ellipsoid should be determined from the requirement of equality of the volumes of particles, as well as of the equality of the ratios of their maximal longitudinal and transverse dimensions. Along with the ElM, the uniform internal field approximation (UFA) has also been considered, which is the first approximation in terms of the rigorous ЕВСМ solution of the electrostatic problem. In order to analyze the applicability of the ElM and UFA approximate approaches, rigorous methods for solving the problem of light scattering have been used, such as the discrete dipole approximation (DDA) and the SVM. The comparison of results of numerical calculations for parallelepipeds, finite circular cylinders and cones, Chebyshev particles and pseudospheroids has shown that the relative errors of calculations of the particle polarizability using ElM approximate formulas do not exceed 1–5%, while, for the absorption and scattering cross sections, they are roughly twice as large, since they depend on the squared polarizability module. As a rule, the ElM is preferable to the uniform field approximation, which is advantageous only in the case of a circular cylinder with close longitudinal and transverse dimensions.