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

Mutually-Pumped Phase Conjugation In Kerr Media

Ragini Saxena, P. Yeh

Published Aug 8, 1989• 0 citations
Publisher

Abstract

Mutually-Pumped Phase Conjugation (MPPC) in a transparent Kerr medium is considered. A pair of mutually incoherent light beams pump each other to generate the phase-conjugate replica of the other beam via Nondegenerate Four Wave Mixing (NFWM) in the nonlinear medium.
DOI
10.1117/12.951730

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Annual Meeting Optical Society of America•Jan 1, 1989•1 citation

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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.
Several mutually pumped phase conjugation configurations have been experimentally demonstrated and theoretically studied in photorefractive media.1 Although these materials are very efficient at low operating power, the process is inherently slow due to the need to generate a large number of photo-induced charge carriers.2 This paper examines the possibility of the same process occurring in a transparent Kerr medium which offers the advantage of faster response times. Due to an electrostrictive nonlinearity in the medium, a photon from either of the two input beams can be spontaneously converted into a frequency downshifted Stokes photon and an acoustic phonon, a process better known as Brillouin scattering.3 The presence of phonons due to noise will also help in Stokes scattering the incident photons. Each pair of incident beam and its coherently generated scattered beam will then write a grating that is moving at the phonon velocity. Reading of this moving hologram by the other incoherent input beam may generate the cross-readout phase conjugated beam that is frequency shifted from the read beam by the frequency of the acoustic field. The nonlinear medium thus acts like a phase conjugate mirror to both of the incident beams. Since the read-write processes occur simultaneously, the dynamics of the beam coupling are described by NFWM equations in the nonlinear medium with appropriate boundary conditions. Our calculations show that it is indeed possible to phase conjugate the two mutually incoherent input beams simultaneously when the coupling strength is above a threshold value. If one of the input beams is very weak compared to the other input beam, it is phase conjugated with a very high reflection coefficient. We have also examined the effects of seeding the phase conjugated beams.
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.
Recent interest in degenerate four-wave mixing in artificial Kerr media to produce phase conjugate waves has concentrated on the visible and infrared spectra. Attempts to extend this technique to the millimeter wave and microwave spectral regions encounter severe difficulties arising from the requirements of medium nonlinearity and high beam intensities. The former problem may be solved by the use of artificial Kerr media and the latter by confinement in a waveguide. In a single-mode waveguide, however, wavefront perturbations cannot propagate. Phase conjugation therefore reduces in this case to a 1-D conjugation capable only of correcting for longitudinal phase error. Observation of this conjugate wave with a slow response medium is made possible by using a sequential method. The general concept is to first write the nonlinear refractive index grating using counterpropagating pump and probe waves. Subsequently, both waves are turned off, and a pump wave approaching from the opposite side reads (scatters from) the grating to produce the phase conjugate wave.
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.
The demonstration of optical phase conjugation in photorefractive materials has been accomplished by numerous methods, including i) externally-pumped four-wave mixing,1ii) self-pumped (passive) phase conjugation,24iii) stimulated backscattering,5,6and iv) mutually-pumped phase conjugation.7-10Stimulated backscattering and self-pumped phase conjugators have only a single incident beam. On the other hand, externally-pumped four-wave mixing has two auxiliary pumping beams in addition to the incident probe beam. Different still is the cross-conjugation of the two incident beams in mutually pumped phase conjugators. To use these conjugators in a given application, the compatibility between the processes generating the phase-conjugate wave(s) and the application must be considered. The distinguishing features of the different conjugators translate to advantages or disadvantages for certain applications.