Highly efficient nonuniform finite difference method for three-dimensional electrically stimulated liquid crystal photonic devices

Abstract

Liquid crystal (LC) photonic devices have attracted intensive attention in recent decades, due to the merits of tunability, cost-effectiveness, and high efficiency. However, the precise and efficient simulation of large-scale three-dimensional electrically stimulated LC photonic devices remains challenging and resource consuming. Here we report a straightforward nonuniform finite difference method (NFDM) for efficiently simulating large-scale LC photonic devices by employing a spatially nonuniform mesh grid. We show that the NFDM can be further accelerated by approximately 504 times by using the improved successive over-relaxation method (by 12 times), the symmetric boundary (by 4 times), the momentum gradient descent algorithm (by 3.5 times), and the multigrid (by 3 times). We experimentally fabricated the large-scale electrically stimulated LC photonic device, and the measured results demonstrate the effectiveness and validity of the proposed NFDM. The NFDM allocates more grids to the core area with steep electric field gradient, thus reducing the distortion of electric field and the truncation error of calculation, rendering it more precise than the finite element method and traditional finite difference method with similar computing resources. This study demonstrates an efficient and highly reliable method to simulate the large-scale electrically stimulated LC photonic device, and paves the way for customizing a large-scale LC photonic device with designable functionalities.