FIELD-FACTOR FORMALISM FOR THE STUDY OF THE TENSORIAL SYMMETRY OF 4-WAVE NONLINEAR-OPTICAL PARAMETRIC INTERACTIONS IN UNIAXIAL AND BIAXIAL CRYSTALS

We establish a complete treatment of the tensorial symmetry properties of the four-wave sum and difference frequency mixing, phase matched in uniaxial and biaxial crystals. This study is based on the formalism of the ''field factor'' which we have previously introduced [B. Boulanger and G. Marnier, Opt. Commun. 79, 102 (1990)]. The 14 configurations of polarization allowing phase matching are considered and the corresponding effective coefficient is calculated for the 19 uniaxial and 8 biaxial classes. The effective coefficient is nil in a few cases. The inequalities between refractive indices, which determine the collinear phase-matching directions, are given according to the optical sign. We calculate the field factors for three real nonlinear crystals: BaB2O4, KTiOPO4, and thiosemicarbazide cadmium chloride monohydrate.