  Multipole expansion of an incident radiation field - that is, representation
of the fields as sums of vector spherical wavefunctions - is essential for
theoretical light scattering methods such as the T-matrix method and
generalised 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 only approximations of
radiation fields. This results from the standard laser beam representations
being solutions to the paraxial scalar wave equation. We present an efficient
method for determining the multipole representation of an arbitrary focussed
beam.
