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.

中文翻译：

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三维电刺激液晶光子器件的高效非均匀有限差分法

近几十年来，液晶（LC）光子器件由于具有可调谐性、成本效益和高效率等优点而引起了人们的广泛关注。然而，大规模三维电刺激液晶光子器件的精确有效的模拟仍然具有挑战性且消耗资源。在这里，我们报告了一种简单的非均匀有限差分方法（NFDM），通过采用空间非均匀网格来有效地模拟大型液晶光子器件。我们证明，通过使用改进的逐次过松弛方法（12 倍）、对称边界（4 倍）、动量梯度下降算法（3.5 倍）和动量梯度下降算法（3.5 倍），NFDM 可以进一步加速大约 504 倍。多重网格（3倍）。我们通过实验制造了大规模电刺激液晶光子器件，测量结果证明了所提出的 NFDM 的有效性和有效性。 NFDM将更多的网格分配给电场梯度较陡的核心区域，从而减少了电场的畸变和计算的截断误差，使其在计算资源相近的情况下比有限元法和传统有限差分法更加精确。这项研究展示了一种高效且高度可靠的方法来模拟大规模电刺激液晶光子器件，并为定制具有可设计功能的大规模液晶光子器件铺平了道路。