Calculation of the electro-optical and nonlinear optical coefficients of ferroelectric materials from their linear properties

The polarization function, for electrons in an ionic frame that possess a single degree of freedom and two electronic quantum levels, is used to derive formulas for calculating the linear electro-optical coefficients and the coefficient for second harmonic generation (SHG). The resultant analytical formulas contain no adjustable parameters besides the band gap, the index of refraction, and the dielectric constant of the materials that are involved. Because of the inclusion of the ionic coordinate, the model can be used to treat such materials as ferroelectrics in which lattice polarization plays an important role. The electro-optical coefficients and the SHG coefficients, in the case where the electric fields are parallel to the optical axis, are calculated for a large number of materials. The results agree with experimental values within a factor of 2 for most of the materials studied.