Modeling the anisotropic electro-optic interaction in hybrid silicon-ferroelectric optical modulator.

We present a numerical method to accurately model the electro-optic interaction in anisotropic materials. Specifically, we combine a full-vectorial finite-difference optical mode solver with a radio-frequency solver to analyze the overlap between optical modes and applied electric field. This technique enables a comprehensive understanding on how electro-optic effects modify individual elements in the permittivity tensor of a material. We demonstrate the interest of this approach by designing a modulator that leverages the Pockels effect in a hybrid silicon-BaTiO slot waveguide. Optimized optical confinement in the active BaTiO layer as well as design of travelling-wave index-matched electrodes is presented. Most importantly, we show that the overall electro-optic modulation is largely governed by off-diagonal elements in the permittivity tensor. As most of active electro-optic materials are anisotropic, this method paves the way to better understand the physics of electro-optic effects and to improve optical modulators.