Numerically stable algorithm for scattering of spherical particles embedded in an absorbing medium

Abstract This study aims to develop a numerically stable Mie algorithm for solving the scattering problem of spherical particles in absorbing media. First, a new stable recursive algorithm for computing Bessel functions is presented. Compared to other algorithms, this new method can automatically determine the correct recurrence steps and construct more robust error analyses. Furthermore, we propose a new numerically stable algorithm based on the Lorenz-Mie theory framework. This algorithm employs forward recurrence formulas for Riccati-Hankel functions and backward recurrence formulas for ratios of Bessel functions. Numerical experiments demonstrate that this algorithm effectively handles the scattering phenomena of spherical particles in absorbing media. It not only accounts for the influence of absorbing media but also accurately computes scattering characteristics, including scattering and absorption coefficients, and other important parameters. Additionally, we also introduce a rescaling method to eliminate the overflow problem of Bessel functions as z → ∞ . This rescaling method can significantly extend the computational limits of traditional methods.