Energy exchange at counterpropagating two-wave mixing in a Bi$_{12}$GeO$_{20}$ crystal of (001) cut

The regularities of energy transfer between two linearly polarized light waves as their contra-directional mixing on a volume reflection holographic grating formed in a photorefractive Bi$_{12}$GeO$_{20}$ crystal of the (001)-cut are analyzed. The values of the crystal thickness and the azimuths of the linear polarization of the light waves, at which the amplification of the object wave is achieved, are determined. The change in the direction of energy transfer to the opposite, depending on the thickness of the crystal, has been experimentally demonstrated.