We have observed sustained self-pulsing in a continuously pumped, triply resonant, optical parametric oscillator. From the analysis of our experimental data, we conclude that the instability mechanism is different from the Hopf bifurcation predicted by the classical model of parametric interaction. Self-pulsing results from the interplay of a slow variable ͑temperature͒ and the optical bistability cycle, leading to a singularly perturbed system. From simple arguments, we propose a minimal dynamical model that reproduces well the observed behaviors.PACS number͑s͒: 42.65.Yj, 42.65.Sf Continuous-wave optical parametric oscillators ͑OPOs͒ have recently received increased interest both experimentally and theoretically. Due to their tunability and to their quantum properties, OPOs are promising sources of coherent light. They have applications in high-resolution spectroscopy ͓1͔, implementation of reference standards ͓2͔, and can be used to generate squeezed states of light ͓3͔.It is thus important to understand the instabilities that cw OPOs may display, especially as they have been recognized as a system of choice for the study of complex nonlinear dynamics. In particular, theoretical studies have shown that OPOs are good candidates for the observation of various fundamental phenomena, such as transition to chaos ͓4͔, spatiotemporal dynamics ͓5͔, including localized structures and topological defects ͓6͔, as well as quantum images ͓7͔.Yet, such a simple dynamical phenomenon as the selfpulsing instability observed in a triply resonant OPO ͓8͔ has not so far been given a clear interpretation. On the one hand, theoretical studies of the classical mean-field model of parametric interaction have predicted the existence of periodic behaviors originating in a Hopf bifurcation ͓4,9͔. On the other hand, the first experimental observation of a selfpulsing regime suggested that a different mechanism might be involved ͓8͔: transverse, thermal, and/or multimode effects possibly have to be taken into account. The nature of the self-pulsing instability thus remains an open and important question, especially as a good understanding of the temporal dynamics of OPOs is a first step towards investigating more sophisticated phenomena such as spatiotemporal dynamics.In this paper, we identify a generic instability mechanism leading to self-pulsing behaviors, which differs from the Hopf bifurcation of the parametric model, and can result from several physical effects. The main ingredient is the interplay between the dynamics of a slow variable and the hysteresis cycle of a fast variable. Slow dynamics can be due to, e.g., thermal ͓10͔ or photorefractive effects ͓11͔, which are generally ignored in the modeling of OPOs.Such instabilities are classical in perturbation theory ͓12,13͔: adding a slow variable with a small relaxation rate ⑀ is known to lead to a singularly perturbed system, which can display a dynamical instability not present in the ⑀ϭ0 case, even for small ⑀. Examples of such instabilities are found in various fields, a cl...
