Photonic Spin Hall Effect by Electro-optically Induced Pancharatnam-Berry Phases.

Here, a novel photonic spin Hall effect is demonstrated based on the spatially varying Pancharatnam-Berry (PB) phases, aroused naturally in an X-cut LiTaO_{3} crystal via the Pockels effect. Applied with an electric field, the principal axes of crystal will rotate around the x-axis with the rotation angle varying linearly with the y component of the applied field. By depositing an asymmetric electrode pair on the crystal to induce inhomogeneously distributed electric fields, spatially varying rotations of the principal axes of crystal are generated, resulting in spatially varying PB phases. These spatially varying PB phases are redistributable by the applied voltage, different from those unchangeable PB phases aroused by the spatially varying orientations of anisotropic structure units such as patterned liquid crystals and metasurfaces. The redistributable PB phases can cause tunable separations of spin photons in the momentum space. The separation speed is measured as ∼0.16  GHz. These findings deepen the understanding of the geometric phase and pave the way for high-speed control of spin photons.