Domain engineering in ferroelectric nematics for nonlinear optical modulation.

Domain engineering is essential in ferroelectric materials for controlling polar properties and attracts considerable attention because of its induced exotic phenomena and underlying rich physics. In recently discovered fluid ferroelectrics, dubbed ferroelectric nematics, the flexoelectric effect, which couples the gradient of the orientational field and the magnitude of polarizations, favors a splay polar field and can dominate over controlling polarization configurations. However, rationally designing and fabricating polarization fields with combinations of bend and twist, as well as the splay, remain a challenge. Here, we manipulate the competition between electrostatics and surface anchoring to tailor diverse polar fields including twisted vortices in ferroelectric nematic liquid crystals via the photopatterning technique. We successfully fabricate a periodic splay-bend polarization structure that enables the regulation of the polarizations of second harmonic waves at multiple diffraction orders. The flexible domain engineering opens a promising route for developing applications in nonlinear geometrical phase devices and optical information multiplexing.