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

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. • A new recursive algorithm for the scattering and radiation computation of multilayered sphere. • New recursive formulas for the outgoing wave scenario. • A hybrid strategy for addressing the singularity problem with existing recursive algorithms.