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Annual Meeting Optical Society of America

Mutually pumped phase conjugation in Kerr media

Ragini Saxena, Pochi Yeh

Published Jan 1, 1989• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1989.tul3

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Photorefractive self-pumped phase conjugation is attractive for its simplicity and high reflectivity with low-power light sources. In order to realize its potential applications, it is important to study its response. So far the response of a phase-conjugate wave has been described with its rise time. It has not studied how the phase-conjugate wave responds when the spatial structure of an input probe wave is changed dynamically. We investigated the response of the phase conjugate wave by using two mutually coherent input beams, which can be regarded as components of a probe wave, and by introducing sinusoidal phase changes into one of them with varied frequencies. Each input beam has a power of 6 mW at the wavelength of 515 nm. A BaTiO3 crystal was employed as a self-pumped phase-conjugate mirror.1 By measuring relative phase between the two output beams, which can be regarded as components of a phase-conjugate wave, we found the response characteristic represented by a time-lag of first order, which is similar to RC circuit. The response time thus determined was 0.32 s, which was much shorter than the rise time of 30 s obtained with the same condition.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
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.
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 demonstrate for the first time, to our knowledge, second harmonic optical phase conjugation, using the second spatial harmonics of a nonsinusoidal grating formed in a photorefractive material. The possibility of harmonic phase conjugation has been considered previously for artificial Kerr media.1 We have applied the same idea to barium titanate, since the existence of the higher-order gratings in this material has been known to us for some time. In our experiment, two 1.06-µm cw Nd:YAG laser beams wrote a grating in a poled photorefractive barium titanate crystal. Then a second harmonic of the YAG at 0.532 µm read out the grating in a counterpropagating direction to one of the writing beams. In this geometry, the usual Bragg condition is not satisfied. The reflectivity of the 0.532-µm signal was rather weak, ~0.01%, with ~0.1-mW reading beam power. The buildup time was around 3 s, with loosely focused writing beams with 50-mW power in each beam. The same experiment with a SBN crystal showed no significant harmonic phase conjugation. Finally, we stress that this effect is different from the previously published result.2
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.
Photorefractive self-pumped phase conjugation is attractive for its simplicity and high reflectivity with low-power light sources. In order to realize its potential applications, it is important to study its response. So far the response of a phase-conjugate wave has been described with its rise time. It has not studied how the phase-conjugate wave responds when the spatial structure of an input probe wave is changed dynamically. We investigated the response of the phase conjugate wave by using two mutually coherent input beams, which can be regarded as components of a probe wave, and by introducing sinusoidal phase changes into one of them with varied frequencies. Each input beam has a power of 6 mW at the wavelength of 515 nm. A BaTiO3 crystal was employed as a self-pumped phase-conjugate mirror.1 By measuring relative phase between the two output beams, which can be regarded as components of a phase-conjugate wave, we found the response characteristic represented by a time-lag of first order, which is similar to RC circuit. The response time thus determined was 0.32 s, which was much shorter than the rise time of 30 s obtained with the same condition.