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 optical parametric oscillator type I 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 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 the possibility 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.