Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Journal of Quantum Electronics

Effects of side diffractions and phase modulations on phase conjugation in a Kerr medium

I. C. Khoo, W. Wang

Published Jun 1, 1991• 6 citations
Publisher

Abstract

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.>

DOI
10.1109/3.89947

Related papers

Pump-depletion effects in noncollinear degenerate four-wave mixing in Kerr media

Richard S. Lytel

This paper presents an exact solution to the slowly varying envelope equations for the probe and signal fluxes in degenerate four-wave mixing in Kerr media. The analysis is performed for a noncollinear geometry, and all beams have the same linear polarization in the nonlinear medium. It is assumed that the angle separating the directions of the counterpropagating pumps and probe and signal beams is large enough so that cross-coupled waves do not contribute to the envelope equations describing the spatial evolution of the pump, probe, and signal beams. Multiple values of the transmitted probe are obtained for equal pump fluxes above a threshold determined by the nonlinear phase shift in the medium. Significant pump depletion occurs in this regime, but it can also occur without the appearance of multiple solutions. Since exact optical phase conjugation occurs only in the limit where the pumps are undepleted in Kerr media, this result implies that there are fundamental upper limits on the pump intensity that can be used to increase signal reflectivities in optical phase conjugation.

Journal of the Optical Society of America B•Nov 1, 1986•11 citations

Mutually pumped phase conjugation in Kerr media and the effects of external seeding

Ragini Saxena, P. Yeh

Mutually pumped phase conjugation, a process by which two incident laser beams can mutually pump each other to generate the phase-conjugate replica of the other beam, is studied in a transparent Kerr medium with an electrostrictive nonlinearity. The nonlinear medium acts as a phase-conjugating mirror to both of the incident beams and generates their Stokes-shifted phase-conjugated outputs by the nearly degenerate four-wave mixing process. Our results show that this process will occur only if the coupling strength, defined by the product of the Kerr amplitude gain coefficient, the total input intensity, and the interaction length, is above the threshold value of 2. If the intensity of one of the input beams exceeds the threshold value and the second input beam is weaker than the first, then the weak beam is phase conjugated with a large reflectivity that has a maximum value of the intensity ratio of the strong to the weak input beam. For negligible absorption in the medium, a complete transfer of energy of both the incident beams into the phase-conjugate beams can occur for finite interaction lengths that are only slightly larger than the threshold value. Seeding the oscillation beams tends to lower the phase-conjugate power reflectivities, probably because of increased contribution from the competing two-wave mixing process.

Journal of the Optical Society of America B•Mar 1, 1990•9 citations

Probe beam amplification and phase conjugation self-oscillation in a Kerr medium

I. C. Khoo, Y. Zhao

In a highly-nonlinear thin Ker medium, the intersection of a strong pump beam and a much weaker probe beam produces a sizeable diffracted beam whose presence changes both the transmitted probe beam gain and the phase conjugation self-oscillation thresholds. An analytical calculation of these effects involving degenerate multiwave mixing processes is presented.>

IEEE Journal of Quantum Electronics•Mar 1, 1989•5 citations

Degenerate four-wave mixing in Kerr media in the presence of nonlinear refraction, pump depletion, and linear absorption

Shekhar Guha, Philip Conner

We consider degenerate four-wave mixing in a Kerr medium with a standard noncollinear geometry and the polarization directions of all the beams parallel to one another. The two pump beams, the probe beam, and the phase-conjugate beam are denoted by the subscripts 1,2,4 and 3, respectively. The nonlinear medium is placed between z = 0 and z = 1; the values of the intensities of the beams at z = 0 and 1 are denoted by Ii0 andIi1, where i = 1,2,3,4. Beams 2 and 4 are incident at z = 1; and beam 1 is incident at z = 0. We have determined the dependence of the phase-conjugate reflectivity R = I31/I41 and the pump transmission T = I11/I10 on the following parameters: the probe ratio, q=I41/(I10 + I21); the pump ratio, r = I21/I 1 0; the absorption coefficient–path length product, al; and the coupling constant of the medium, q. In the absence of nonlinear refraction, pump depletion, and linear absorption in the medium, R = tan2q. When all of these effects are taken into account, the maximum value of R is given by Rmax = exp (-2α1)/(q(1 + r)). The minimum value that T can reach is proportional to q for q < 1. Even for small values of q, multistable solutions for R and T are obtained when q is greater than a threshold value, which we denote by qth. We have determined the dependence of qth on the parameters q and r.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations

Effects of side diffraction and phase modulation on optical multiwave mixing and phase conjugation

I. C. Khoo, Y. Zhou, R. R. Michael +3 more

We report several recently observed optical wave mixing effects in thin films of nonlinear materials, such as liquid crystals and silicon. Kerrlike local and nonlocal and diffusive nonlinear resonses are studied. The presence of the diffracted beam is, theoretically and experimentally, shown to have a pronounced effect on the amplification of the probe beam in pump–probe wave mixing. The diffracted beam also drastically alters the phase conjugation reflection of the probe beam, phase conjugation self-oscillation threshold, and aberration correction characteristics.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Nonlinear phase distortion in phase conjugation by degenerate four-wave mixing in Kerr media

S. Trillo, Stefan W. Wabnitz

We derive an exact solution for both amplitude and phase of a signal that is back-reflected by collinear nonlinear degenerate mixing of four circularly polarized waves of arbitrary intensity in a Kerr-like medium. Our analysis suggests that taking pump depletion into account may spoil the ideal phase-conjugation condition, even in the limit of weak nonlinear coupling, and indicates that substantial deterioration of the probe phase-reversal property may occur for strongly interacting waves in a manner that is highly sensitive to the anisotropy of the nonlinear susceptibility.

Journal of the Optical Society of America B•Feb 1, 1988•8 citations
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.>
This paper presents an exact solution to the slowly varying envelope equations for the probe and signal fluxes in degenerate four-wave mixing in Kerr media. The analysis is performed for a noncollinear geometry, and all beams have the same linear polarization in the nonlinear medium. It is assumed that the angle separating the directions of the counterpropagating pumps and probe and signal beams is large enough so that cross-coupled waves do not contribute to the envelope equations describing the spatial evolution of the pump, probe, and signal beams. Multiple values of the transmitted probe are obtained for equal pump fluxes above a threshold determined by the nonlinear phase shift in the medium. Significant pump depletion occurs in this regime, but it can also occur without the appearance of multiple solutions. Since exact optical phase conjugation occurs only in the limit where the pumps are undepleted in Kerr media, this result implies that there are fundamental upper limits on the pump intensity that can be used to increase signal reflectivities in optical phase conjugation.
Mutually pumped phase conjugation, a process by which two incident laser beams can mutually pump each other to generate the phase-conjugate replica of the other beam, is studied in a transparent Kerr medium with an electrostrictive nonlinearity. The nonlinear medium acts as a phase-conjugating mirror to both of the incident beams and generates their Stokes-shifted phase-conjugated outputs by the nearly degenerate four-wave mixing process. Our results show that this process will occur only if the coupling strength, defined by the product of the Kerr amplitude gain coefficient, the total input intensity, and the interaction length, is above the threshold value of 2. If the intensity of one of the input beams exceeds the threshold value and the second input beam is weaker than the first, then the weak beam is phase conjugated with a large reflectivity that has a maximum value of the intensity ratio of the strong to the weak input beam. For negligible absorption in the medium, a complete transfer of energy of both the incident beams into the phase-conjugate beams can occur for finite interaction lengths that are only slightly larger than the threshold value. Seeding the oscillation beams tends to lower the phase-conjugate power reflectivities, probably because of increased contribution from the competing two-wave mixing process.
We consider degenerate four-wave mixing in a Kerr medium with a standard noncollinear geometry and the polarization directions of all the beams parallel to one another. The two pump beams, the probe beam, and the phase-conjugate beam are denoted by the subscripts 1,2,4 and 3, respectively. The nonlinear medium is placed between z = 0 and z = 1; the values of the intensities of the beams at z = 0 and 1 are denoted by Ii0 andIi1, where i = 1,2,3,4. Beams 2 and 4 are incident at z = 1; and beam 1 is incident at z = 0. We have determined the dependence of the phase-conjugate reflectivity R = I31/I41 and the pump transmission T = I11/I10 on the following parameters: the probe ratio, q=I41/(I10 + I21); the pump ratio, r = I21/I 1 0; the absorption coefficient–path length product, al; and the coupling constant of the medium, q. In the absence of nonlinear refraction, pump depletion, and linear absorption in the medium, R = tan2q. When all of these effects are taken into account, the maximum value of R is given by Rmax = exp (-2α1)/(q(1 + r)). The minimum value that T can reach is proportional to q for q < 1. Even for small values of q, multistable solutions for R and T are obtained when q is greater than a threshold value, which we denote by qth. We have determined the dependence of qth on the parameters q and r.
We report several recently observed optical wave mixing effects in thin films of nonlinear materials, such as liquid crystals and silicon. Kerrlike local and nonlocal and diffusive nonlinear resonses are studied. The presence of the diffracted beam is, theoretically and experimentally, shown to have a pronounced effect on the amplification of the probe beam in pump–probe wave mixing. The diffracted beam also drastically alters the phase conjugation reflection of the probe beam, phase conjugation self-oscillation threshold, and aberration correction characteristics.
We derive an exact solution for both amplitude and phase of a signal that is back-reflected by collinear nonlinear degenerate mixing of four circularly polarized waves of arbitrary intensity in a Kerr-like medium. Our analysis suggests that taking pump depletion into account may spoil the ideal phase-conjugation condition, even in the limit of weak nonlinear coupling, and indicates that substantial deterioration of the probe phase-reversal property may occur for strongly interacting waves in a manner that is highly sensitive to the anisotropy of the nonlinear susceptibility.