Light scattering by multilayered nonspherical particles: a set of methods

An original approach to solution of the light scattering problems for axisymmetric particles was developed in our earlier papers. The approach is based on separation of the fields in two specific parts and a proper choice of scalar potentials for each of them. Applications to homogeneous scatterers made first in the framework of the separation of variables method (SVM) and later the extended boundary condition method (EBCM) led to more efficient solutions (at least in the case of the SVM) than the standard ones. The approach was recently applied to formulate new theoretical methods for multilayered axisymmetric particles. In this paper we further develop and systematically discuss the methods. One of them is a modification of the EBCM and another looking as (and wrongly called) a modification of the SVM is shown to be rather that of the EBCM formulated in spheroidal coordinates. The solutions are now presented in recursive forms. The ranges of applicability of the new methods are considered analytically for the first time in the literature on layered scatterers. The theoretical methods and their program implementations are compared with others available. We note that usage of scalar potentials (a feature of our approach) allowed us consistently to realize the EBCM in spheroidal coordinates. Advantages of this approach in the case of layered spheroidal particles with the confocal layer boundaries are noted. Earlier we have extended the quasistatic approximation (QSA), being a generalization of the Rayleigh (RA) and Rayleigh-Gans approximations, to layered ellipsoids in the general case of nonconfocal layer boundaries. Here the connection between the QSA and the asymptotic of the scattered field found in the framework of our SVM-like method in the limit of very large aspect ratios of spheroids is discussed. Keeping this fact in mind, the applicability regions of the QSA and RA are comparatively considered for multilayered ellipsoids. We also note that the formulations of the RA and QSA contains a quantity that can be interpreted as the average refractive index of a layered particle and thus gives a new rule of the effective medium theory more appropriate for such scatterers.