Computation of the beam-shape coefficients in the generalized Lorenz–Mie theory by using the translational addition theorem for spherical vector wave functions

The generalized Lorenz-Mie theory describes the electromagnetic scattering of a Gaussian laser beam by a spherical particle. The most intensive computational aspect of the theory concerns the evaluation of the beam-shape coefficients in the general case of an off-axis location of the scatterer. These beam-shape coefficients can be computed starting from the set of beam-shape coefficients for an on-axis location by using the addition theorem for the spherical vector wave functions of the first kind under a translation of the coordinate origin.