A model is developed to explain the hysteretic electric field dependence of the electrooptic coefficient in ferroelectric thin films. The reversible electric polarization and the tunable dielectric susceptibility of the ferroelectric thin film are proposed to explain the hysteretic ρ-E (electrooptic coefficient- applied electric field) loop. An empirical model used in ferroelectric capacitors to predict the high frequency C-V curve is utilized here to find the field dependence of the nonlinear susceptibility. The tunable susceptibility can also explain the peaked characteristics of the ρ-E loop. We also show that the linear electrooptic effect in ferroelectric thin films could produce the pseudo-quadratic electrooptic effect on field-induced birefringence as a result of the switchable spontaneous polarization of ferroelectrics. Thus, a careful interpretation of the field-induced birefringence is required to avoid misleading conclusions. This model provides a fundamental understanding to the tunability of the electrooptic coefficient and is useful for the electrooptic characterization of the ferroelectric thin films.
The intensity-voltage output characteristics of thin-film linear electro-optic Mach-Zehnder interferometer modulators can be nonperiodic for configurations where the optic axis is perpendicular to the applied electric field. As a result, the electro-optic coefficient for the material can not be determined assuming a periodic half-wave voltage. From the Jones matrix calculation, an analytic expression of the output intensity is derived in terms of the phase retardation. A method of determining the linear electro-optic coefficient is proposed based on the determination of the first intensity minimum in intensity-voltage characteristics. This method provides a simple expression for determining the electro-optic coefficient given values for the ordinary and extraordinary refractive indices, the modulator geometry, and the first half-period voltage. The first half-period voltage is found to be approximately inversely proportional to the square root of the electrode length. The method shows close agreement to the exact Jones matrix method for the case where the sum of the principal refractive indices in one arm of Mach-Zehnder interferometer is close to that of the other arm under an electric field.