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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Study of the threshold coupling strength for mutually pumped phase conjugator

Lin Ma, Zhiguo Jiang, Jifang Liu, Xin Liu

Published Nov 29, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.999966

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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.
Based on the four-wave mixing mechanism and light fanning effect, a mutually pumped phase conjugator(MPPC) model is proposed to analyze the variation of MPPC output response with time for different scattering seed value. It shows that preset grating can enhance the fan light intensity when it satisfies Bragg condition and also can shorten MPPC response time. In experiment the bird-wings MPPC is done with or without the preset grating and the variation of MPPC reflectivity with time is obtained in two cases, and simulation conclusion is in agreement with the experimental result. These results have importance for applications of MPPC on optical heterodyne detection.
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.
We present a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of four-wave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.
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 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.