Study on self pumped phase conjugation and four wave mixing in a BaTiO_3 photorefractive crystal.

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The location and profile of phase conjugate image produced by Gaussian beam pumped DFWM are studied. The equation describing the dependence of the conjugate image location and the transverse magnification factor on the gaussian beam parameters are derived. The reconstructed images of distorted probe object are calculated numericallyand it is found that the quality of the image is limited by the curvature, as well as, by the spot size of the Gaussian pump beams.Ordinary Self-Pumped Phase Conjugator (SPPCM) is demonstrated with use of a BaTiO_3 photorefractive crystal and analyzed. The comparison between the experiment and the theoretical analysis makes it possible to control the reflectivity of the SPPCM.Self-Pumped Four Wave Mixing (SPFWM) in a single BaTiO_3 crystal is demonstrated, which means that a simple phase conjugator with two incident beams is realized. At first, the conjugator was unstable and it is found that refractive index gratings were produced at a same region in the crystal and they sompete with each other. The competition is the origin of unstableness, so that separating the two index gratings leads to stable operation of SPFWN.The reflectivity and the response time of SPFWM are measured and found that it is as fast as ordinary four wave mixing and is faster than SPPCM by the order of two.As a result of this study, SPFWM in a BaTiO_3 crystal which uses phase conjugate beam as one of the pump beams which is generated by SPPCM in the same crystal is realized with rather simple optical system. It is found that the response of the SPFWM is as fast as ordinary four wave mixing.