Spatial fluctuations in an optical parametric oscillator below threshold with an intracavity photonic crystal

We show how to control spatial quantum correlations in a multimode, degenerate, type-I optical parametric oscillator below threshold by introducing a spatially inhomogeneous medium, such as a photonic crystal, in the plane perpendicular to light propagation. We obtain the analytical expressions for all of the correlations in terms of the relevant parameters of the problem and study the number of photons, entanglement, squeezing, and twin beams. Considering different regimes and configurations, we show that it is possible to tune the instability thresholds as well as the quantumness of correlations by breaking the translational invariance of the system through a photonic-crystal modulation.