We have observed low-threshold optical hyperparametric oscillations in a high-Q fluorite whispering gallery mode resonator. The oscillations result from the resonantly enhanced four-wave mixing occurring due to Kerr nonlinearity of the material. We demonstrate that, because of the narrow bandwidth of the resonator modes as well as the high efficiency of the resonant frequency conversion, the oscillations produce stable narrow-band beat-note of the pump, signal, and idler waves. A theoretical model for this process is described.
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