, Volume 175, Issue 6, pp 698-723

A unified approach, using spheroidal functions, for solving the problem of light scattering by axisymmetric particles

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A theory that joins three well-known methods is suggested. These methods are the separation of variables, extended boundary conditions and point matching, where the fields are represented by their expansions in (spheroidal) wave functions. Applying similar field expansions, the methods essentially differ in formulation of the problem, and thus they were always discussed in the literature independently. An original approach is employed, in which the fields are divided in two parts with certain properties, and special scalar potentials are selected for each of the parts. The theory allows one to see the similarity and differences of the methods under consideration. Analysis performed earlier shows that the methods significantly supplement each other and the original approach used with a spheroidal basis gives reliable results for particles of high eccentricity for which other techniques do not work. Thus, the suggested theory provides a ground for development of a universal efficient algorithm for calculating optical characteristics of nonspherical scatterers in a very wide region of their parameter values. Bibliography: 21 titles.

Dedicated to Professor Vasilii Mikhailovich Babich with sincere gratitude
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 380, 2010, pp. 132–178.