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.