  We calculate the bi-photon state generated by spontaneous parametric down
conversion in a thin crystal and under collinear phase matching conditions
using a pump consisting of any superposition of Laguerre-Gauss modes. The
result has no restrictions on the angular or radial momenta or, in particular,
on the width of the pump, signal and idler modes. We demonstrate the strong
effect of the pump to signal/idler width ratio on the composition of the
down-converted entangled fields. Knowledge of the pump to signal/idler width
ratio is shown to be essential when calculating the maximally entangled states
that can be produced using pumps with a complex spatial profile.
