  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 suitable for real-time analysis of electromagnetic
scattering from electrically large objects, which is essential for monitoring
and control applications, such as optomechanical manipulation, scanning
microscope, and fast optimization algorithms.
