Macroscopic quantum fluctuations in noise-sustained optical patterns

We investigate quantum effects in pattern-formation for a degenerate optical parametric oscillator with walk-off. This device has a convective regime in which macroscopic patterns are both initiated and sustained by quantum noise. Familiar methods based linearization about a pseudo-classical field fail in this regime and new approaches are required. We employ a method in which the pump field is treated as a $c$-number variable but is driven by the $c$-number representation of the quantum sub-harmonic signal field. This allows us to include the effects of the fluctuations in the signal on the pump, which in turn act back on the signal. We find that the non-classical effects, in the form of squeezing, survive just above the threshold of the convective regime. Further above threshold the macroscopic quantum noise suppresses these effects.