Accurate calculation of the optimum phase-matching parameters in three-wave interactions with biaxial nonlinear-optical crystals

The effective nonlinear coefficients and the optimum phase-matching angles for three-wave mixing processes in biaxial crystals are calculated, and their analytical expressions are obtained. We carried out the calculations by taking into consideration the difference between the directions of the electric field vector E and the electric displacement vector D in biaxial crystals. Using the small-signal approximation, we also derived expressions for acceptance parameters and calculated their values for some typical three-wave interaction processes. In addition we obtained a theoretical curve for the energy conversion efficiency of three-wave interactions as a function of phase mismatch by numerically solving the coupled wave equations describing the processes. With this curve we are able to define and to compute the acceptance parameters for any type of three-wave mixing process. Finally, the numerical values of the phase-matching parameters are obtained for such biaxial crystals as KTiOPO4 and LiB3O5, and the results are graphically presented.