Efficient computation of arbitrary beam scattering on a sphere

Electromagnetic scattering on a sphere is one of the most fundamental problems, which has a closed form analytical solution in the form of Mie series. Being initially formulated for a plane incident wave, the formalism can be extended to more complex forms of incident illumination. Here we present a fast calculation approach to address the scattering problem in the case of arbitrary illumination, incident on a spherical scatterer. This method is based on the plane wave decomposition of the incident illumination and weighted integration of Mie solutions, rotated to a global coordinate system. Tabulated solutions, sampled with an accurately level of sparsity, and efficient rotational transformations allow performing fast calculations on electrically large structures, outperforming capabilities relatively to other numerical techniques. Our approach is appropriate for real-time analysis of electromagnetic scattering from electrically large objects, which is essential for monitoring and control applications, such as optomechanical manipulation, scanning microscopy, and fast optimization algorithms.