Electromagnetic scattering for multilayered sphere: Recursive algorithms

We have proposed more stable and accurate recursing equations and a computing procedure to calculate scattering coefficients for a multilayered sphere. The procedure involves three logarithmic derivatives of Ricatti‐Bessel functions ψ n ′( z )/ ψ n ( z ), χ n ′( z )/ χ n ( z ), and ξ n ′( z )/ξ n ( z ), as well as the ratio ψ n ( z )/χ n ( z ). The asymptotic behavior, stability, and accuracy of the procedure and scattering coefficients a n and b n are discussed for any complex refractive indices. This procedure can be used for large and small inhomogeneous spherical particles.