Output characteristics of mixed holograms in the ($\overline{11}$0)-cut Bi$_{12}$TiO$_{20}$ crystal

An analytical solution to the system of linear differential equations that describe the reconstruction of object wave using a transmission holographic grating formed in a cubic photorefractive piezoelectric ($\overline{11}$0)-cut crystal with the 23 symmetry is derived. The solution is used to interpret the experimental results on the dependence of the diffraction efficiency of mixed holograms on the thickness of the Bi$_{12}$TiO$_{20}$ crystal at a fixed orientation angle and three azimuths of linear polarization of the readout reference beam. The best agreement of the theoretical and experimental results on mixed holograms is reached when the inverse piezoelectric effect and photoelasticity are taken into account in addition to the conventional electrooptic effect.