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Fast Photorefractivity and Energy and Momentum Transfer in Dense, Two-Level Media

B. A. Samson, Wojciech Gawlik

Published Jan 1, 1990• 0 citations
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Abstract

polymers, etc.). \-Vit.hin (\. t.wo-Ievel model we dellloll sll'aL<' creat.ion of t.he p()Luia.t.ioll gratillg that. is phase- shifted tda.iv 10 lite illeident fi,·It!. Tit pltase sitifl is duc 10 I.lte nonlinearity arising fr0 1ll lite local-field effects. Precisely I he sall rca.lttI'(' of I.ite phase-shined polari,alioll respons(, is cltaraclerist.ic for Ihe photomftacliv(' 1I1<'<lia. We int.crprcl, therefore, this effecl. as the IOeILl­ jidd-ind1tced lJ/lOtorcjmciilJ ily. It is nol,cwortity I.hal it can occur in any two-level mcdilltn and, most interestingly, it is a vcry fasl. phenomenon with response time not limiled hy (,harge l'cal'l'angement in st.!ldard phot.ordract.ivc materials. The appropriate pha.,� shift. between incident field and polarization grating r esul ts in unidirectional energy jmolllcntufli ,'xchange bciween the coupled beams and possible ampliGcation of one of them. We take the net light Geld in t.he IIwoium as omposed of two wave s The small frequency shift < « -: (: beillg t.he lincwidth) causes the movement of the i,t· t.erference pattern which eliminates all uncertailli(.y in a spatial distribution of the atomi(' variables whose dependence on IIIl' lighl. intensit.y is bistable under conditions of lOB. Thi, purpose can be achieved also by a slow f(·la.l.ive motion of the medium with resped (0 (.h(' ill tel-ference pattern and the polarization grating (2). Similarly as in Ref.(2J, we find t.he appcarence of a phase-shifted contribution to the polarizat.ion grating that is absent for a low· density medium. This phase-shifted component is responsible for the unidirectional energy flow determined by the sign of E, exactly in the same way as in the standard phol.orcfracl.iv ity.

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polymers, etc.). -Vit.hin (. t.wo-Ievel model we dellloll sll'aL<' creat.ion of t.he p()Luia.t.ioll gratillg that. is phase- shifted tda.iv 10 lite illeident fi,·It!. Tit pltase sitifl is duc 10 I.lte nonlinearity arising fr0 1ll lite local-field effects. Precisely I he sall rca.lttI'(' of I.ite phase-shined polari,alioll respons(, is cltaraclerist.ic for Ihe photomftacliv(' 1I1<'<lia. We int.crprcl, therefore, this effecl. as the IOeILl­ jidd-ind1tced lJ/lOtorcjmciilJ ily. It is nol,cwortity I.hal it can occur in any two-level mcdilltn and, most interestingly, it is a vcry fasl. phenomenon with response time not limiled hy (,harge l'cal'l'angement in st.!ldard phot.ordract.ivc materials. The appropriate pha.,� shift. between incident field and polarization grating r esul ts in unidirectional energy jmolllcntufli ,'xchange bciween the coupled beams and possible ampliGcation of one of them. We take the net light Geld in t.he IIwoium as omposed of two wave s The small frequency shift < « -: (: beillg t.he lincwidth) causes the movement of the i,t· t.erference pattern which eliminates all uncertailli(.y in a spatial distribution of the atomi(' variables whose dependence on IIIl' lighl. intensit.y is bistable under conditions of lOB. Thi, purpose can be achieved also by a slow f(·la.l.ive motion of the medium with resped (0 (.h(' ill tel-ference pattern and the polarization grating (2). Similarly as in Ref.(2J, we find t.he appcarence of a phase-shifted contribution to the polarizat.ion grating that is absent for a low· density medium. This phase-shifted component is responsible for the unidirectional energy flow determined by the sign of E, exactly in the same way as in the standard phol.orcfracl.iv ity.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
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.