Stable algorithm for the computation of Mie coefficients for scattered and transmitted fields of a coated sphere

Abstract

The Mie coefficients and the electric-field vector inside a spherical, layered particle are presented in a form which is more suitable for computations. Difficulties in the computation occur especially for large, absorbing spheres, due to numerical instabilities in the computation of Besselfunctions with complex arguments. This can be avoided by rearranging the Mie coefficients, so that only ratios and logarithmic derivatives of Besselfunctions are used. A suitable analytical expression for the coefficients of the scattered and transmitted fields and the electric-field vector is given.