Light scattering by small pseudospheroids

Abstract

The Rayleigh approximation and solution of the electrostatic problem are considered for pseudospheroids that are obtained as a result of inversion of usual spheroidal particles: $$r\left( \theta \right) = ab/{r_{{\text{spheroid}}}}\left( \theta \right) = a\sqrt {1 - { \in ^2}{{\cos }^2}\theta } $$ , where e2 = 1 - (b/a)2. The approach is based on using the extended boundary condition method (EBCM) for the calculation of polarizability. The approach is studied analytically. The study has been shown that, in the near zone with respect to the particle, expansions of potentials of the “scattered” and internal fields in terms of the spherical basis converge up to the surface only under the conditions $$a/b \prec \sqrt 5 $$ and $$a/b \prec \sqrt 2 $$ (the external and internal Rayleigh hypotheses, respectively). In the far zone, the ЕВСМ can be justifiably applied for the ratio of pseudospheroid parameters $$a/b \prec \sqrt 2 + 1$$ . In this case, there exists a nonempty intersection of analytical continuations of expansions in terms of the spherical basis of the “scattered” and internal fields. The radii of convergence R 1, R 2 of these expansions have been found; they are determined by the presence of singular points. The relation between singular points for pseudospheroids and corresponding spheroids is considered. Numerical analysis of the problem under consideration has completely verified results of the analytical study, in particular, the presence of corresponding singular points. To obtain the necessary accuracy in calculations of elements of linear algebraic systems, the corresponding integrals are transformed into series containing gamma functions. Numerical calculations involving the EBCM were successfully verified using the condition of symmetry of the T matrix. For the applicability area of the ЕВСМ, calculation results for the polarizability of pseudospheroids are discussed according to the exact algorithm and within the approximation of the homogeneous internal field.