Frequency locking in the photorefractive phase-conjugate ring oscillator

In the absence of backscattering, the frequency difference between the oscillating and the pump waves in a photorefractive phase-conjugate ring oscillator is linearly proportional to the small nonreciprocal phase shift applied in the ring. We show that coupling that is due to backscattering can result in frequency locking in the photorefractive oscillator. A seed beam is used to simulate scattering of the pump beam in the oscillation direction. Close to locking threshold, harmonics of the beat frequency lead to nonsinusoidal oscillations in the beat signal. The nonreciprocal phase shift at which locking occurs is directly proportional to the field strength of the coherent seed beam. Frequency locking is absent with an incoherent seed.