Spatio-temporal instabilities and threshold condition in a broad-area optical parametric oscillator

The role of diffraction on the threshold condition for signal generation in a broad-area, doubly-resonant optical parametric oscillator (OPO) operating close to degeneracy is analytically investigated starting from a three-dimensional model of the OPO equations. The instability domain for signal generation, as derived in terms of general cavity parameters, is shown to be composed by two families of multiballoon (or multiconical) regions, which correspond to the two discrete sets of longitudinal modes for the OPO. Depending on the cavity detuning parameter, parametric oscillation is preferred to occur on either one of the two mode families, and may be associated to an off-axis emission. Due to the conservation of the photon momentum in the nonlinear down-conversion process, a discrimination among the different instability balloons exists, which explains the asymmetric behavior of threshold curves versus cavity length tuning and makes unlikely the occurrence of multiconical emission in the OPO. (C) 1998 Elsevier Science B.V. All rights reserved.