Theory of a “stimulated photorefractive backscattering and four-wave mixing” self-pumped phase conjugator

We give a theoretical analysis of a “stimulated photorefractive backscattering and four-wave mixing” (SPB-FWM) self-pumped phase conjugator (SPPC) in which the generation of the phase conjugate wave relies on both stimulated photorefractive backscattering (SPB) and four-wave mixing (FWM) processes. The two pumping beams in the FWM process are, respectively, the forward-propagating beam of which the generation is seeded by the fanning effect, and the backward-propagating beam that is generated by the SPB process. Assuming that the SPB interaction is seeded by the scattering centers in the crystal, we have calculated the threshold four-wave mixing coupling strength (γ₁l₁)_th as a function of the SPB two-wave mixing coupling strength (γ₂l₂) corresponding to the 2k grating and of the reflectivity R′ of the scattering centers. Above threshold, we have also calculated the phase-conjugate reflectivity with a numerical method. Our calculations show that the threshold as well as the reflectivity of a SPB-FWM SPPC strongly depend on γ₂l₂ and R′. It is also shown that a high phase-conjugate reflectivity can be easily realised in doped barium titanate crystals which are shown to have much larger γ₁ and γ₂ than an undoped one.