Effect of spatial orientation and thickness of Bi$_{12}$GeO$_{20}$ crystal on the gain of the subject light wave: theory and experiment

The dependence of the gain of an object light wave in two-wave interaction on the orientation angle and the thickness of the photorefractive $(\overline{1}\,\overline{1}\,0)$-cut Bi$_{12}$GeO$_{20}$ crystal using only a single crystal sample with a thickness of $16$ mm has been experimentally investigated. The technique of carrying out the experiment and processing the results is described. The decisive role of the inverse piezoelectric and photoelastic effects in the theoretical interpretation of the experimental data is shown. Theoretical optimization of the gain of the object light wave in this crystal is performed.