Ball lens modeling for laser/fiber coupling. A direct solution of Maxwell's equations

We present optical designs for coupling between a commercial laser and a single mode fiber using one or two ball lenses. Our approach exploits the fact that the scattering of an arbitrary electromagnetic beam from a sphere is an exactly solvable problem. By solving Maxwell's equations directly using spherical harmonic expansion of the input field, we can account for effects (spherical aberration, polarization, astigmatism) which are not easy to include by other approaches. We are able to implement this method to calculate reflection and transmission accurately with modest computational effort.