A modified recursive transfer matrix algorithm for radiation and scattering computation of a multilayer sphere

TL;DR

This paper introduces a modified transfer matrix algorithm that enhances the stability and efficiency of electromagnetic scattering calculations for multilayered spheres, especially in complex scenarios like thin shells and absorbing media.

Contribution

It combines recursive methods with the transfer matrix approach, incorporating Debye potentials and a hybrid strategy to improve numerical stability and handle singularities.

Findings

Demonstrates superior stability over previous methods

Effective in complex cases like thin shells and absorbing media

Reduces numerical overflow issues with Bessel functions

Abstract

We discuss the electromagnetic scattering and radiation problems of multilayered spheres, reviewing the history of the Lorentz-Mie theory and the numerical stability issues encountered in handling multilayered spheres. By combining recursive methods with the transfer matrix method, we propose a modified transfer matrix algorithm designed for the stable and efficient calculation of electromagnetic scattering coefficients of multilayered spheres. The new algorithm simplifies the recursive formulas by introducing Debye potentials and logarithmic derivatives, effectively avoiding numerical overflow issues associated with Bessel functions under large complex variables. Moreover, by adopting a hybrid recursive strategy, this algorithm can resolve the singularity problem associated with logarithmic derivatives in previous algorithms. Numerical test results demonstrate that this algorithm offers superior stability and applicability when dealing with complex cases such as thin shells and strongly absorbing media.