Ellipsoidal models of small non-spherical scatterers

We review a novel approach to the light scattering by small layered particles in the electrostatic limit when the particle is considered to be in the uniform field. We use the expansions of all the fields in terms of the spheroidal functions related to the layer boundaries and the relations between such functions obtained by us. The approach provides the theoretical grounds for several new approximations. We demonstrate that the solution, e.g. the polarizability, given by the approach is similar to that of a small ellipsoid. We suggest two versions of the ellipsoidal model being the replacement of the particle with an ellipsoid of similar optical properties: the uniform field and form-fitting approximations. In the former, we assume that the field inside the particle is uniform and find that, for some kinds of the scatterers, such approximation is analytical. In the latter, we select the ellipsoid with the volume and the ratio of the maximum dimension to the transverse one equal to those of the particle. For small scatterers, such analytical approximation gives good results for particles of various shapes. The approximation can be also useful for quasi-axisymmetric scatterers as large as the wavelength. We consider the first two terms in the solution given by our approach for the layered particles with the concentric coaxial, but non-confocal spheroidal boundaries as new approximations. Numerical calculations demonstrate that these approximations, being analytical, have the accuracy as high as 0.1–1%. The approximations can be applied to the light scattering as well.