LANGEVIN TREATMENT OF QUANTUM FLUCTUATIONS AND OPTICAL-PATTERNS IN OPTICAL PARAMETRIC OSCILLATORS BELOW THRESHOLD

yA Langevin model is introduced to study quantum fluctuations below th e threshold of pattern formation for optical parametric oscillators (O PO's). In particular we compare analytical and numerical results for t he OPO with one and two transverse spatial dimensions and in the prese nce of either plane or spherical cavity mirrors. The far-field structu re and the correlation functions of the fluctuating signal field antic ipate the onset of a transverse spatial pattern which arises classical ly even in the presence of Gaussian input beams. Correlation functions also reveal the squeezed nature of the OPO field, Numerical simulatio ns of the Langevin model describe the result of short time measurement s and show that close to threshold the near-field signal is a noisy sp ot pattern evolving on a time scale longer than the inverse decay rate of the resonator. This and other far-field features should be experim entally accessible.