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Physical Review A

Photorefractive ring resonator with seeding as an externally driven oscillator

Svetlana A. Tatarkova, Malgosia Kaczmarek, Changxi Yang, Robert W. Eason

Published Oct 11, 2002• 2 citations
Publisher

Abstract

We report on experimental and theoretical studies of a photorefractive ring resonator pumped by a 1.06 \ensuremath{\mu}m beam and injected with a weak, external, seeding beam. The competition between the two dominant gratings that form inside the photorefractive crystal leads to characteristic periodic oscillations in the intensity of the resonating beam, which originate from the frequency difference between the pump beam and the unidirectional oscillation beam. We show that such a system can be treated as a driven nonlinear oscillator.

DOI
10.1103/physreva.66.043807

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We report on experimental and theoretical studies of a photorefractive ring resonator pumped by a 1.06 \ensuremath{\mu}m beam and injected with a weak, external, seeding beam. The competition between the two dominant gratings that form inside the photorefractive crystal leads to characteristic periodic oscillations in the intensity of the resonating beam, which originate from the frequency difference between the pump beam and the unidirectional oscillation beam. We show that such a system can be treated as a driven nonlinear oscillator.
We report the observation of bistability in a unidirectional ring resonator that employs photorefractive barium titanate for gain and also for saturated loss. One photorefractive crystal provides gain via two-beam coupling in a conventional unidirectional ring configuration.1 A second crystal is arranged to couple light out of the resonator using two-beam coupling, thereby producing loss. The orientations of the two crystals are chosen so that the magnitude of the small signal loss is greater than the magnitude of the small signal gain. Thus the oscillation in the ring cannot build up from noise since there is no net gain. However, the pump intensity for the gain medium is made larger than that for the loss medium. This means that the loss saturates at a lower signal level. Hence, at large intensities, gain can exceed net loss so oscillation can occur.
A self-consistent theory is used to derive the frequency shift presented by the oscillating mode in a cavity that contains a photorefractive crystal. A long-time-limit theory has been used to get the steady characteristics of the cavity field. The problem of the weak-field approximation is avoided. This approximation is useless in the case studied because the interaction along the crystal is so strong that one has to take in account the intensity exchange occurring inside the material between the pump and oscillating beams (two-wave mixing). We have fully analyzed the influence of the transverse nature of the beams on the intensity exchange in the two-wave mixing situation. In the photorefractive resonator case, the frequency shift of the oscillating beam is expressed in terms of a ratio that presents poles. The dependence on the problem parameters of these poles is studied and a perturbative method is developed; it is based on the smallness of the transverse overlap between the pump and cavity modes. An analytical expression for this frequency shift is obtained.