Phase-matching techniques and frequency-conversion efficiency in optically active crystals

Many materials of potential interest for nonlinear optical applications exhibit optical activity and this is generally not taken into account in the standard theoretical treatments of nonlinear optical effects. In this paper we examine the conditions under which optical activity significantly alters the nonlinear optical properties of a material and show how this mechanism might be used in designing a nonlinear optical device. First, an algorithm is developed to calculate the exact optimum phase-matching angles and conversion efficiency for three-wave interactions in optically active biaxial crystals. Corrections to the standard theoretical expressions for birefringent phase-matching angles and conversion efficiency are obtained for application to biaxial crystals with large natural birefringence. Second, a generalized quasi-phase-matching scheme based on the presence of optical activity is formulated for three-wave interactions in second-order nonlinear crystals. It is shown that quasi-phase-matching via optical activity can be achieved by way of an effective harmonic modulation of deff, the effective second-order nonlinear coefficient. For both these effects, it is found that optical activity makes a negligible change in the nonlinear optical properties of a material such as KTiOPO4, but they may become important for liquid crystals or polymers with high optical rotation and small birefringence.