  A detailed description is provided of a numerical model of the microcavity
optical parametric oscillator (OPO). The model is solved on a two dimensional
grid, in the time domain, using an alternating-direction implicit method.
Results are presented for a system pumped with a gaussian spatial profile beam.
It is shown that at high pump powers the OPO signal forms a ring, with low
emission at the centre where the pumping is strongest.
