Design principles for high-speed barium titanate on-insulator electro-optic modulators

Barium titanate (BTO) has emerged as a key material in the development of electro-optic modulators (EOMs) for its outstanding electro-optic (EO) coefficients and its compatibility with rapidly evolving thin-film integrated photonic platforms. However, its high-speed performance is severely constrained by microwave-optical velocity mismatch, due to its exceptionally high microwave permittivity. While shortening the modulation length can increase the EO bandwidth, it exacerbates the voltage-bandwidth trade-off. The plasmonic waveguide configuration has been demonstrated to reduce such trade-off to the greatest extent, yet it also induces severe optical loss, compromising the practicability of certain applications. Here, we establish simulation-guided design principles for high-speed BTO-on-insulator EOM, with simulated EO bandwidth of over 100 GHz within a modulation length of 1 cm and half-wave voltage around 1 V, while achieving low microwave and optical losses and ensuring impedance matching. We emphasize that the velocity-matching condition should be achieved within a thin a -axis BTO slab, eliminating the influence of its huge permittivity on the microwave effective refractive index. The ridge optical waveguide and coplanar microwave waveguide configuration are employed to achieve both low optical loss and low microwave loss. Meanwhile, for c -axis BTO, the combination of higher permittivity and the fact that modulation will yield misalignment between the material’s birefringence and the waveguide structural birefringence is not conducive to high-speed applications. Our work identifies the physical origin of the high-frequency limitation in existing BTO modulators and provides a device physics-based principle for alleviating this bottleneck.