Beam energy exchange in sillenite crystals (Bi12SiO20 and Bi12TiO20), considering the variation of light modulation along sample thickness in a strong non-linear regime

The energy exchange during two-wave mixing can be increased in photorefractive sillenite crystals considering thick samples (i.e., large interaction lengths). Nevertheless, in thick samples under a non-linear regime, the light modulation does not remain constant along wave propagation, and there is a spatial non-uniform grating along sample thickness. Here, we study the optimization of the effective gain for non-moving gratings in thick samples, taking into account the spatial non-uniformity of the grating on the beam energy exchange. Optical activity, absorption of light, birefringence, polarization angles of the incident beams, different values of a static applied d.c. field were also considered. We did this by first solving numerically the material rate equations to obtain the time evolution of the space charge field up to the steady state, and then by numerically solving the coupled wave equations in a self-consistent way in order to take into account the variation of the magnitude and phase of the light modulation along sample thickness. We obtained the variation of the complex amplitudes of the interacting beams along sample thickness for both, when the grating vector is parallel to the face [0 0 1] and when it is perpendicular to the same face. We predict that an effective gain of 45 can be obtained for samples >2 cm. We also found that the influence of the initial polarization angles on the value of the gain is very different when considering the spatial non-uniformity of the grating.