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Applied Optics

Photorefractive coupling in ring resonators

Pochi Yeh

Published Sep 1, 1984• 30 citations
Publisher

Abstract

The photorefractive coupling of the oppositely directed traveling waves in ring resonators is analyzed. The nonlocal response of the crystal gives rise to an asymmetrical coupling of the waves which results in unequal transmissivities and unequal phase shifts when the two waves traverse through the photorefractive material. The inequality in transmissivities and phase shifts removes the degeneracy and leads to a splitting in both oscillation frequency and intensity.

DOI
10.1364/ao.23.002974

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Physical Review A•Oct 11, 2002•2 citations
The photorefractive coupling of the oppositely directed traveling waves in ring resonators is analyzed. The nonlocal response of the crystal gives rise to an asymmetrical coupling of the waves which results in unequal transmissivities and unequal phase shifts when the two waves traverse through the photorefractive material. The inequality in transmissivities and phase shifts removes the degeneracy and leads to a splitting in both oscillation frequency and intensity.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
We develop a numerical method to solve the coupled-wave equations for four-wave mixing phase conjugation in a photorefractive crystal with unequal complex coupling constants; by this method we can obtain both the intensities and the phases of various beams. We discuss the intensities and the phases of the interacting beams in a photorefractive crystal for the cases in which the phase shifts between the refractive-index gratings and the interference pattern are all π/2 and in which they are not all π/2.
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.