Scattering of electromagnetic-plane waves by radially inhomogeneous spheres: a finely stratified sphere model

A new recursive algorithm to calculate the internal and scattered fields of finely stratified inhomogeneous spheres has been developed. No restriction on the number of layers-the thicknesses of which can be arbitrarily small-is imposed by this method. The number of layers is restricted only by the computer's capability: calculations with spheres with more than 10,000 layers were successfully performed with a HP work station. The new algorithm circumvents the limitations introduced by the numerical round-off errors encountered when using the previously developed recursive relations to calculate the ratios of Riccati-Bessel functions. Tests and calculations show that the method is stable and accurate for a large range of size parameters and optical properties. By employing the proposed algorithm, the problems encountered in analyzing the scattering by spheres with continuous-profile refractive indices can be solved with good accuracy.