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Soviet Journal of Quantum Electronics

Photorefractive-crystal loop oscillator with linear aberrations of the resonator

Adam Mazur, S. G. Odulov, M. S. Soskin

Published Mar 31, 1990• 0 citations
Publisher

Abstract

A nonreciprocal phase shift experienced by both the pump and output waves, which appeared in the presence of linear aberrations in a photorefractive-crystal loop resonator, was compensated by a frequency shift or by generation of other longitudinal and/or transverse modes. A theoretical model describing the experimental results was developed.

DOI
10.1070/qe1990v020n03abeh005636

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A nonreciprocal phase shift experienced by both the pump and output waves, which appeared in the presence of linear aberrations in a photorefractive-crystal loop resonator, was compensated by a frequency shift or by generation of other longitudinal and/or transverse modes. A theoretical model describing the experimental results was developed.
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.
Steady-state coherent oscillation in the ring-loop and double-side mirror geometries is first observed and studied in media with local nonlinear response. The results of calculation are presented stating that the oscillation becomes possible providing two necessary conditions are met: the oscillation waves appear 1) misaligned with respect to strictly backward to pumps directions to restore the phase matching, and 2) they are shifted in frequency with respect to the pump waves. By appropriate choice of frequencies of two incident waves in double-side mirror geometry one of oscillating waves may be done a perfect conjugate replica of an input wave with limited spatial spectrum.
Photorefractive resonators exhibit an extremely small frequency difference (Deltaomega/omega~10(-15)) between the oscillating and pumping beams. The observed frequency difference is proportional to cavity-length detuning. This dependence is explained by a photorefractive phase shift that is due to slightly nondegenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for steady-state oscillation. The measured onset or threshold of oscillation as a function of photorefractive gain and intensity agrees with theory.
A theory of the two-wave mixing in a photorefractive medium placed in a ring cavity is developped following the model first derived by Yariv and Kwong [1]: a steady refractive index involving the photorefractive effect is used as a non-linear source-term (PNL) in the Maxwell equations, and the cavity field is expanded on the transverse cavity modes. In this model we take into account the intensity change of both the pump and resonator beams inside the crystal due to the mutual power exchange: we have developed a multimode model which gives in the long-time limit the z-dependance of the fields (z is the optical axis) for a passage in the crystal, using the expansion in terms of the complete set of the cavity transverse modes. [2]