Enhancement of the efficiency of acousto-optic Bragg diffraction due to optical activity. A case of Pb$_5$Ge$_3$O$_{11}$ crystals

We show that the existence of optical activity in an optical material can lead to essential enhancement of acousto-optic (AO) figure of merit for this material. The reason is that the ellipticity of interacting optical eigenwaves approaches unity near the optic axis and so additional elasto-optic (EO) tensor components with relatively large values become involved into the effective EO coefficient. We demonstrate on the example of lead germanate crystals, Pb$_5$Ge$_3$O$_{11}$, that the increase in the efficiency of AO diffraction manifests itself for all the types of isotropic and anisotropic interactions, whenever the incident optical wave propagates close to the optic axis. We find that, in the particular case of diffraction in the interaction plane XZ of Pb$_5$Ge$_3$O$_{11}$ crystals, the maximal enhancement of the AO figure of merit takes place under conditions of the types V and VI of isotropic diffraction, with the AO figure of merit increasing from zero up to 13.3x10$^{-15}$ s$^3$/kg, and the type IX of anisotropic diffraction when the AO figure of merit increases more than twice (from 12.5x10$^{-15}$ up to 26.5x10$^{-15}$ s$^3$/kg). The maximal AO efficiency in the XZ interaction plane is reached at the types I and II of isotropic AO interactions. In these cases the AO figure of merit increases from 6.8x10$^{-15}$ up to 37.9x10$^{-15}$ s$^3$/kg and from 31.1x10$^{-15}$ to 37.9x10$^{-15}$ s$^3$/kg, respectively.