Sh-matrices method as applied to scattering by particles with layered structure

We develop a modification of the T-matrix method that allows for fast calculations of light-scattering properties of non-spherical particles with layered structure. This modification uses the Sh-matrices that depend on the shape of particles only and do not depend on the particle size or optical constants. The matrices are obtained for any number of discrete layers of a particle with different thickness and refractive indices. This solution is generalized for continuously varying refractive index as a function of distance from the particle center. Solutions are considered for the cases when the refractive index changes linearly as well as with the exponential, normal, and Poisson's laws.