Abstract
We present a model of intracavity frequency doubler in the presence of two-photon dissipation processes. We find that the possible operation regimes are substantially different from those for pure second harmonic generation. In particular, the system is characterized by two critical points and a limited self-pulsing instability domain. Control of the instabilities is demonstrated, and complete quenching of self-pulsing and stabilization of the steady states for the entire domain of the driving field intensity are shown.
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