AN IONIC GROUPING THEORY OF THE ELECTRO-OPTICAL AND NON-LINEAR OPTICAL EFFECTS OF CRYSTALS (Ⅲ)——A THEORETICAL CALCULATION OF THE ELECTRO-OPTICAL AND OPTICAL SECOND HARMONIC COEFFICIENTS FOR LiNbO<sub>3</sub>, LiTaO<sub>3</sub>,KNbO<sub>3</sub>, AND BNN CRYSTALS BASED ON A DEFO

Abstract

Based on (MO6) ionic grouping model as previously proposed in (I), we have calculated the various electro-optical coefficients as well as the optical second harmonic coefficients for LiNbO3, LiTaO3, KNbO3, and BNN crystals. If we assume that the oxygen-octahedra in the crystal lattice of these crystals of Oh symmetry all possess the same energy level and wavefunctions, then the energy level and the wavefunction for LiNbO3, LiTaO3, KNbO3, and BNN erystals of C3ν, or C2ν symmetry can be found upon applying the theory of group representations. Furthermore, by using the ABDP theory, we have calculated their electro-optical and optical second harmonic coefficients. It is interesting to note that without introducing any adjustable parameters the calculated values agree satisfactorily with the experimental data. The dependence of the magnitude and the sign of the optical second harmonic coefficients for these crystals upon the degree of the oxygen-oetahedra distortion has also been interpreted theoretically in this paper. We have thus arrived at the following conclusions:(1) The ionic grouping theory of the deformed oxygen-octahedra model proves to be appropriate not only for the perovskite-type structure but also for the tungsten bronze and LiNbO3 type structures.(2) In crystals of the tungsten bronze and LiNbO3 type structure, it is the ionic bonds that make major contribution to the electro-optical and optical second harmonic effects. As the covalent nature of bonds in the LiTaO3 crystal exceeds that in the LiNbO3 crystal, the non-linear optical effects in the LiTaO3 erystal are weaker than those in the LiNbO3 crystal.(3) The magnitude and the sign of the optical second harmonic coefficients for these crystals depend upon the degree of the oxgen-octahedra distortion.