Mutually pumped phase conjugation in Kerr media

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.