Majority of existing codes for calculation of electromagnetic scattering by a single sphere is based on Mie theory which is an analytical solution of Maxwell's equations in terms of infinite series.
Other approximations to scattering by a single sphere include: Debye series, ray tracing (geometrical optics), ray tracing including the effects of interference between rays, Airy theory, Rayleigh scattering, diffraction approximation.
Even though Mie theory offers convenient and fast way of solving light scattering problem by homogeneous spherical particles, there are other techniques, such as discrete dipole approximation, FDTD, T-matrix, which can also be used for such tasks.
[1] The compilation contains information about the electromagnetic scattering by spherical particles, relevant links, and applications.
[2] Fortran IDLMatlab C Python Algorithmic literature includes several contributions [7] [8] [9] [10] Code dates from 1968 available here:[11] Web application is the part of package, available online on the website of Department of Physics and Engineering in ITMO University.