Light scattering by axisymmetric multilayer particles

Abstract

A new recursive algorithm for solving the problem of scattering a plane electromagnetic wave by axisymmetric dielectric multilayer particles is constructed. The approach that was proposed earlier and demonstrated for uniform axisymmetric particles is used. It has the following basic features: (1) the fields are represented in the form of a sum of two terms, one of which is independent of the azimuthal angle, whereas averaging of the second term over this angle gives zero; (2) the axisymmetric problem is solved by using the scalar potentials related to the azimuthal components of electromagnetic fields; and (3) the non-axisymmetric problem is solved by using the superposition of Debye potentials and vertical components of the magnetic and electric Hertz vectors. It is of principal importance for the solution proposed here that the scattering problem is formulated in the form of surface integral equations in these scalar potentials, which are represented in the form of expansions in wave spherical functions. Infinite systems of linear algebraic equations for unknown expansion coefficients are obtained, which are rather simple in structure. The reduced systems for multilayer particles have the same dimension as the systems for identical uniform particles. In the case of multilayer spherical particles, the algorithm gives an explicit solution to the problem, and the dependence on the radial spherical functions for the layers is specified in terms of the derivative of the logarithm (i.e., the ratio of the derivative to the function itself) and the ratio of the functions of neighboring layers. Numerical calculations demonstrated the high efficiency of the algorithm.