Spatial Photo-Patterning of Nematic Liquid Crystal Pretilt and its Application in Fabricating Flat Gradient-Index Lenses

Liquid crystals offer a dynamic platform for developing advanced photonics and soft actuation systems due to their unique and facile tunability and reconfigurability. Achieving precise spatial patterning of the liquid crystal alignment is critical to developing electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, we demonstrate a simple method to achieve continuous three-dimensional control of the directions of liquid crystal mesogens using a two-step photo-exposure process. In the first step, polarized light sets the orientation in the plane of confining substrates; the second step uses unpolarized light of a prescribed dose to set the out-of-plane orientation. The method enables smoothly varying orientation patterns with sub-micrometer precision. As a demonstration, we design gradient-index lenses with parabolic refractive index profiles that remain stable without external electric fields. We characterize the lenses' focal length and sensitivity to light polarization through experimental and numerical methods. Our findings pave the way for developing next-generation photonic devices and actuated materials, with potential applications in molecular self-assembly, re-configurable optics, and responsive matter.