Vector Spherical Wavefunction Expansion of a Strongly Focussed Laser Beam

Vector spherical wavefunction expansions of an incident radiation field are essential for theoretical light scattering methods such as the T-matrix method and generalized Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but approximations of radiation fields. We show that both integral and point-matching methods can be used to find vector spherical wavefunction expansions of laser beams, including strongly focussed beams