Analysis for the nonlinear electro-optic modulation effect of BaTiO3 crystal thin-film waveguide modulators

Abstract

Quadratic-order electro-optic (EO) modulation of BaTiO3 crystal thin-film devices has stimulated increasing research on high-bandwidth modulators and other functions. The quadratic-order EO modulation is created by an outside electric field with respect to the EO coefficient r42 or r51. In this work, the entire changing process of refractive index ellipsoid of BaTiO3 crystal driven by an outside electric field is investigated, and two nonlinear EO modulation processes of quadratic and quartic nonlinearities are found for defining the relationship between drive voltage and interaction length. Theoretical investigation shows the dominations of two nonlinear processes—the quadratic and quartic modulations strongly depend on the birefringence, the electric field intensity applied, and the interaction length. The condition for defining the two effective high-order nonlinear modulation processes is that at 1550 nm wavelength when the absolute birefringence is close to 0.001, the quadratic model is challenged and instead the quartic one is more effective. An absolute birefringence of 0.001 can make the r51 of 250 pm/V meet a half-wave drive voltage of 5 V and an interaction length of 1 mm, which has the same role as 600 pm/V r51 value at an absolute birefringence of 0.007. Such an important finding is also verified by the simulation results of optical output operations of the EO modulator. This work has theoretically explained an incredible phenomenon reported that the dramatically different values of an effective EO coefficient are measured for the same device sample at different experimental conditions: the electric field intensity applied and axis-orientation of crystal.