Light scattering by multilayer nonconfocal ellipsoids in the Rayleigh approximation

The Rayleigh approximation of light scattering by multilayer nonconfocal coaxial ellipsoids is constructed. The ellipsoids that form a multilayer particle have coincident centers, and their principal axes are parallel. A particle in a constant electric field is considered, and the corresponding system of Laplace equations and boundary conditions is solved. Since the ellipsoidal surfaces of the interlayer interfaces are not confocal, the layers are divided into many sublayers, in each of which the potential is written in the proper ellipsoidal systems of coordinates. The potentials are sewn together at the sublayer interfaces by approximate matching conditions (the continuity of potentials and their normal derivatives). The polarizability of a multilayer particle is expressed as a 2×2 matrix in terms of the parameters of the core and the subsequent layers.