Quantum spatial correlations in the optical parametric oscillator with spherical mirrors

We consider a quantum model for a degenerate optical parametric oscillator below threshold in a cavity with spherical mirrors. The spatial correlation function of a generic quadrature component of the signal field is calculated analytically in terms of an expansion over the Gauss-Laguerre modes. The critical behavior and the quantum image phenomenon, which emerge when threshold is approached, are described in detail. We calculate also the spatial correlation function of the intensity fluctuations, which can be more easily measured by direct detection and exhibits the same qualitative features.