Application of spheroidal functions in theory of light scattering by nonspherical particles: Separation of variables method

The separation of variables method (SVM), which uses a spheroidal basis, is proposed. According to this method, fields are presented in the form of expansion in terms of spheroidal functions. The previously conducted analysis of various methods using a spherical basis showed that the SVM is applicable in a broader area for numerical calculations, while the proposed approach using a spheroidal basis yields reliable results in the case of spheroids with a high degree of asphericity where other methods and approaches cannot be used. Importantly, the method includes an SVM that uses a spherical basis as the limiting case. Thus, the proposed method has all chances of being highly efficient for calculation of optical characteristics of various nonspherical particles in a wide range of parameters of the formulated problem.