In this thesis work, the photorefractive two wave mixing in Fe-doped $LiNbO_3$ crystal has been studied. Experiments have been performed with a crystal, where the diffusion and the photovoltaic effect contribute to the charge transport mechanism with about the same order of magnitude. In contrast with the diffusion dominant or drift dominant process, somewhat different dependencies of the energy transfer effect and the diffraction efficiency upon experimental parameters such as grating spacing and beam intensity ratio have been observed, and compared with theoretical calculation. We have observed a significant transient energy transfer between two writing beams without applying any external electric field, which had been reported to be observed with applying a large electric field. In addition, we have observed that a self enhancement effect may occur without respect to the direction of the reading beam, while the previous authors had reported that a self enhancement occurs only when the reading beam has the component in $^+$c axis direction. Possible application fields including the coherent light amplification are discussed. Methods for improving the characteristics such as a response time are suggested.