AN IONIC GROUPING THEORY OF THE ELECTRO-OPTICAL AND NON-LINEAR OPTICAL EFFECTS OF CRYSTALS (Ⅰ)——A THEORETICAL CALCULATION OF ELECTRO-OPTICAL AND SECOND OPTICAL HARMONIC COEFFICIENTS OF BARIUM TITANATE CRYSTALS BASED ON A DEFORMED OXYGEN-OCTAHEDRA

Abstract

In order to elucidate the relationship between the structure and the electro-optical and nonlinear optical effects in crystals of the perovskite type, we have here proposed a deformed oxygen-octahedra model for these crystals. On the basis of quasi-molecular orbitals and ionic bond orbitals for the ionic grouping TiO6 formulated under the imposed crystal field, we have calculated the various electro-optical and second optical harmonic coefficients for the BaTiO3 crystal without introducing any adjustable parameters. It is gratifying to note that the calculated values of the electro-optical and second optical harmonic coefficients agree satisfactorily with the experimental values. As is to be expected, the quasi-molecular orbitals contribute very little to these optical effects. We have been led to the following conclusions:1) The electro-optical and second optical harmonic effects of the BaTiO3 crystal arise as a direct consequence of the deformation of the TiO6 oxygen-octahedra. The more these octahedra are deformed, the larger are these optical effects.2) When BaTiO3 is present as the ferroelectric phase, a strong odd ordered-term crystal field arises as a result of the spontaneous polarization within the crystal. This explains why BaTiO3 possesses such large electro-optical and second harmonic optical effects. The covalent bonds in the ionic group TiO6 tend to cancel each other in their contribution to these effects.3) The electro-optical and second harmonic optical coefficients are directly proportional to the degree of spontaneous polarization.