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Soviet Journal of Quantum Electronics

Double phase conjugation in media with a local response

Igor' M Bel'dyugin, M V Mel'kumov, K. A. Sviridov

Published Sep 30, 1990• 4 citations
Publisher

Abstract

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.

DOI
10.1070/qe1990v020n09abeh007420

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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.
A theoretical analysis is made of wavefront reversal which is not sensitive to the optical quality of the nonlinear wavefront-reversing medium when complex-conjugate reference waves are formed spontaneously. An investigation is made of the linear and nonlinear stages of reversed wave generation in various nonlinear media using feedback in degenerate and nondegenerate four-wave interaction. It is shown that in nonamplifying nonlinear media this method can only be achieved by additional amplification of the radiation reflected from the 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.
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.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.
In the case of disordered nonlinear media, it is shown that in four-wave mixing a phenomena analogous to phase conjugation may occur. In contrast to the case of transparent media in which two counterpropagating pump waves (with frequency ${\ensuremath{\omega}}_{p}$) are required, phase conjugation may occur in the presence of a single pump wave injected into the disordered nonlinear material. We find that in the angular distribution of radiation of frequency ${\ensuremath{\omega}}_{s}$ (${\ensuremath{\omega}}_{s}$=2${\ensuremath{\omega}}_{p}$-${\ensuremath{\omega}}_{i}$, where ${\ensuremath{\omega}}_{i}$ is the frequency of probe wave) there is a narrow peak in the backscattered direction associated with the probe wave. The intensity of this peak may be some orders of magnitude larger than the diffuse background at the frequency ${\ensuremath{\omega}}_{s}$.