We deal with the vectorial equations of two-wave mixing without an external field (diffusion response) in Bi<sub>12</sub>SiO<sub>20</sub> and Bi<sub>12</sub>TiO<sub>20</sub> by splitting the vectorial amplitudes of signal and reference waves into a parallel part whose direction is determined by the optical activity rotation and into a perpendicular part. By doing so we obtain an approximation scheme that works particularly well after optimization with respect to the input polarization. Exploring the relevant crystal configurations [L, T, and D geometry of the (110) cut and T<sup>′</sup> and D<sup>′</sup> geometry of the (111) cut], we show that for common crystal thicknesses our approximate solution is almost as precise as the numeric solution.
© 2001 Optical Society of America
Yi Hu, K. H. Ringhofer, and E. Shamonina, "Parallel subsystem: An almost precise solution for two-wave mixing in sillenites," J. Opt. Soc. Am. B 18, 1137-1143 (2001)