Self-enhanced diffraction from fixed photorefractive gratings during coherent reconstruction

Photorefractive (PR) holograms can be fixed with various degrees of success.1-4 These usually involve the replacement of the original electronic charge by a relatively immobile ionic charge. When such holograms are reconstructed, by illuminating with the readout wave, a new dynamic electronic hologram is generated by the spatial interference of the readout and the diffracted waves. The superposition of the original (ionic) and the new (electronic) holograms, which are of the same period, can lead to self-enhancement*>2 or self-depletion, depending on their relative phase. In this letter we revisit this problem theoretically and experimentally. Our analysis differs from previous ones, discussed by Gu and Yeh,516 which examined a PR twowave mixing process in the presence of a fixed uniform grating. We consider a realistic case of a fixed PR grating, solve, rather than assume, for its spatially varying profile, and then derive the conditions for self-enhanced (and selfdepleted) diffraction. This enables us to draw quantitative conclusions and to compare our theoretical results to experiments using known material parameters. Finally, we demonstrate these effects experimentally for thermally fixed holograms in a PR LiNbOs crystal, and show selfenhancement of the diffraction efficiency from 4% (of the fixed grating only) to 23%. We start the theoretical analysis by describing the holographic recording process, and assume an ordinary twowave mixing effect in a PR medium7 between two arbitrary input waves a, and a2 (represented here by their field amplitudes) in the transmission geometry