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Soviet Journal of Quantum Electronics

Conditions for generation of a phase-conjugate wave in a ring resonator with a local transient nonlinear response of the medium

Yu A Arutyunov, A I Khizhnyak

Published Apr 30, 1989• 0 citations
Publisher

Abstract

An approximation of a constant intensity of two counterpropagating noncollinear waves in a ring system is used to consider phase conjugation as a result of a four-beam interaction in a medium with a transient nonlinear response. An analytic solution is obtained of a system of equations for weak waves consisting of an arbitrary set of quasiplane components. It is shown that when the absolute instability threshold is exceeded by a nonlinear phase shift, the maximum increment is exhibited by those components which are inclined at a certain angle to the phase-conjugate wave. The conditions for reliable phase conjugation by introduction of a phase screen into the ring are identified.

DOI
10.1070/qe1989v019n04abeh007908

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An approximation of a constant intensity of two counterpropagating noncollinear waves in a ring system is used to consider phase conjugation as a result of a four-beam interaction in a medium with a transient nonlinear response. An analytic solution is obtained of a system of equations for weak waves consisting of an arbitrary set of quasiplane components. It is shown that when the absolute instability threshold is exceeded by a nonlinear phase shift, the maximum increment is exhibited by those components which are inclined at a certain angle to the phase-conjugate wave. The conditions for reliable phase conjugation by introduction of a phase screen into the ring are identified.
An analysis is made of double phase conjugation in media with a local response. A threshold is found for the generation of a phase-conjugated wave by the double process in a medium with a local response and with additional amplification. An analysis is made of the further possibilities of generation of phase-conjugated radiation in the case of a four-wave interaction characterized by a feedback loop established when double phase conjugation takes place in a nonlinear medium. The threshold intensity of the input radiation ensures possible generation of a phase-conjugated wave as a result of a four-wave interaction characterized by a feedback loop and merging of counterpropagating beams in a nonlinear medium.
The diffraction approximation is used to determine the structure of the radiation generated as a result of a four-wave interaction with feedback and the conditions for phase conjugation are identified. Phase conjugation can be expected in the case of a signal beam with a smooth distribution of the amplitude if the transverse size of this beam decreases as a result of passing through a feedback loop. In the case of a multimode signal beam it is additionally necessary to ensure that the resonator length or the length of the nonlinear medium exceeds the spreading length of the transverse inhomogeneity of the field.
The effects of side diffractions, generated from the interaction of a weak probe beam and its phase conjugate with two strong counterpropagating pump waves, and the effect of various intensity-dependent self- and mutual-phase modulations on the intensities of the probe beam and its phase conjugate are analytically studied in the nonpump-depletion limit. The results show that the conditions for the existence of, and threshold pump intensity parameters for, the divergence in the intensities of the probe and other generated beams are highly dependent on the wave-mixing angles and are different from the usual four-wave mixing phase conjugation process where the diffractions are not taken into account.>
Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.