  Polarisation effects in the microcavity parametric oscillator are studied
using a simple model in which two chi-three optical parametric oscillators are
coupled together. It is found that there are, in general, a number of steady
states of the model under continuous pumping. There are both continuous and
discontinuous thresholds, at which new steady-states appear as the driving
intensity is increased: at the continuous thresholds, the new state has zero
output intensity, whereas at the discontinuous threshold it has a finite output
intensity. The discontinuous thresholds have no analog in the uncoupled device.
The coupling also generates rotations of the linear polarisation of the output
compared with the pump, and shifts in the output frequencies as the driving
polarisation or intensity is varied. For large ratios of the interaction
between polarisations to the interaction within polarisations, of the order of
5, one of the thresholds has its lowest value when the pump is elliptically
polarised. This is consistent with recent experiments in which the maximum
output was achieved with an elliptically polarised pump.
