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Journal of the Optical Society of America B

Seeding and grating phase in mutually pumped phase conjugators

William R. Christian, Ragini Saxena, Ian C. McMichael

Published Jan 1, 1992• 5 citations
Publisher

Abstract

We present theoretical and experimental studies of mutually pumped phase conjugation when a seed beam is injected that is the conjugate of one of the pumping beams. Good agreement exists between the theoretical and the experimental functional dependencies of the conjugate reflectivities on seed-beam intensity. However, the calculated gain is lower than that measured by two-beam coupling by nearly a factor of 2. We found that the seed-to-pump intensity ratio needs to exceed approximately 10−6, greater than 100 times the scattering, before the phase of the grating in the mutually pumped phase conjugator will follow the phase of the seed beam when it is varied by a moving mirror.

DOI
10.1364/josab.9.000108

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We present theoretical and experimental studies of mutually pumped phase conjugation when a seed beam is injected that is the conjugate of one of the pumping beams. Good agreement exists between the theoretical and the experimental functional dependencies of the conjugate reflectivities on seed-beam intensity. However, the calculated gain is lower than that measured by two-beam coupling by nearly a factor of 2. We found that the seed-to-pump intensity ratio needs to exceed approximately 10−6, greater than 100 times the scattering, before the phase of the grating in the mutually pumped phase conjugator will follow the phase of the seed beam when it is varied by a moving mirror.
Much attention is focused on the mutually pumped phase conjugators (MPPCs). Their unique ability to operate with mutually incoherent pumping beams makes them ideal candidates for applications in communications, laser locking, fiber optic gyros, and optical information processing. In the simple physical picture of MPPCs, the conjugate beams result from gratings that form between each pump beam and amplified scattering from that pump beam. Therefore, one might expect that the phase of the grating is determined by the relative phase between the pumping beams and their scattering. That is, the scattering acts as a seed beam that interferes with the pumping beam to determine the phase of the grating. The situation is complicated by the possibility of moving gratings, multiple reflections, and the sharing of holograms written simultaneously by both pump beams and their corresponding scattering. The problem of MPPC driven by an external seed beam was analyzed by Kroli- kowski et al.1 They predicted temporal instabilities for low intensity seed beams and stable solutions for high intensity seed beams. However, it has not been demonstrated (at least experimentally) that a seed beam can control the phase of the diffracted beam without destroying its conjugate nature. To investigate this question, we have set up a MPPC with a variable (phase and amplitude) seed beam and an interferometer to measure the relative phase between an incident and diffracted beam, and thus the phase of the grating. The same interferometer is used to determine whether the seed beam is influencing the wavefront of the diffracted beam and therefore destroying the conjugation process. This effect might be used as a nonmechanical means of biasing phase conjugate interferometers.
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.
A study of the influence of the spatial structure and statistics of the pump beams in the phase-conjugation process is made, showing that the reflectivity varies along the phase-conjugation mirror when the phase factor in the coupling equations that describe the process is not constant. The mutual coherence function of the generated field is calculated from the mutual reflectivity of the mirror for two commonly used statistics for the partially coherent pump beams. Finally, the influence of diffractional effects is also analyzed, showing that, in general, the fidelity of the process is degraded.
We report for the first time a double 45°-cut mutually pumped phase conjugate mirror, which has high phase conjugate reflectivities and is highly insensitive to the alignment of the two incident beams. For example, two mutually incoherent incident beams can produce their own phase conjugate outputs when the angle between the incident beams is varied from as much as 7° to 140° and over 60% conjugate reflectivity can be obtained. Furthermore, the phase conjugate outputs are stable because the competition from the self-pumped phase conjugation can be avoided easily.
Based on the four-wave mixing mechanism and fanning effect, the threshold coupling constant for mutually pumped phase conjugator (MPPC) with one interaction region and two interaction regions is studied in theory. The relation of the the threshold coupling strength for MPPC and the fanning intensity is studied. Due to the more efficient fanning, preset grating in MPPC has the ability to reduce threshold coupling constant and improve output efficiency. These characteristics predicted by theory have been used to explain the previous experiment phenomenon. The dependence of threshold coupling constants for MPPC on the amplitude ratio of incident pump beams is presented. The threshold coupling constant for one-interaction-region MPPC is lower than that for two-interaction-regions MPPC.