Unified approach using spheroidal functions to solve the light scattering problem for axisymmetric particles

V. G. Farafonov

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 40, Tome 380 (2010), pp. 132-178

Résumé

We suggest a theory that joins three well-known methods – the separation of variables, extended boundary condition and point matching ones where the fields are represented by their expansions in terms of (spheroidal) wave functions. Applying similar field expansions, the methods essentially differ in formulation of the problem and hence were always discussed in the literature independently. We also utilize an original approach where 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 well to see similarity and differences of the methods under consideration. Analysis performed earlier shows that the methods essentially 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 algoritm for calculations of the optical characteristics of nonspherical scatterers in a very wide region of their parameter values. Bibl. 21 titles.