Periodically-Modulated Unipolar and Bipolar Orders in Nematic Fluids: Towards Miniaturized Microscopic Nonlinear Photonics

Complex polar topological configurations are the foundation for exploring exotic phases and nontrivial emergent phenomena in condensed-matter physics. While numerous topological configurations like skyrmions and merons are known to occur spontaneously in various materials, achieving the designability of magnetically- and electrically-polar textures in a controlled manner is a long-standing challenge in domain engineering. Here, we discover an unprecedented mesophase that exhibits unipolar and bipolar orders, where both the apolar and polar orientational order parameters are modulated. The polar state enables defect-free polar patterning with designability and controllability at large scales. We succeed in scaling down the volume of the nonlinear vectorial beam generation devices by a factor over 10 ^-6 , providing a foundation for the microscopic nonlinear optical apparatuses.