Oxygen-Octahedra Ferroelectrics. I. Theory of Electro-optical and Nonlinear optical Effects

A microscopic tensor theory of the electro-optical and nonlinear optical effects in oxygen-octahedra ferroelectrics is presented. The theory stresses the importance of the basic BO6 octahedron building block in this class of materials. This common structural unit leads to similarities in band structure and similarities in polarization-induced, Stark-like energy band shifts. Using the polarization-potential tensor concept to describe these shifts, we relate the quadratic electro-optic g coefficients and the nonlinear optic δ coefficients to static and optical-frequency polarization-potential tensors, respectively. These tensors are found to be nearly the same in all oxygen-octahedra ferroelectrics, leading us to conclude that these materials possess the same fundamental electro-optical and nonlinear optical properties. The physical origin of both effects is shown to be related to polarization-induced modulation of the (pdπ) energy overlap integral. The resulting static and optical-frequency polarization potentials are found to be almost, but not exactly, equal. We also show that in the ferroelectric phase the linear electro-optic effect is fundamentally a quadratic effect biased by the spontaneous polarization, which enables us to calculate the important r coefficients. An analysis of optical-refractive-index-dispersion data shows that oxygen-octahedra ferroelectrics, and many other materials as well, have nearly the same dispersion behavior described by the parameter ε0/S0=6±0.5×10−14 eV·m2 where ε0 is an average interband-oscillator energy in eV and S0 is an average interband-oscillator strength defined by a single-term Sellmeier description of optical index data.