Efficient Finite Element Modeling of Photonic Structures with Combined Symmetry Operations for Waveguide Modal Analysis

Symmetry is widely used to analyze the optical properties of photonic devices, which can improve the efficiency and accuracy of full-wave simulations. Existing optical full-wave simulations mostly use a single symmetry to simplify the calculations. In this work, we lay out the theoretical foundation and numerical implementation of the finite element method (FEM) that combines various symmetry operations, significantly improving the computational efficiency. Our method integrates multiple spatial or non-spatial symmetry operations, decomposing the original problem into several decoupled sub-problems for analyzing the vector eigenmodes of photonic devices. We employ our proposed method to compute the vector eigenmodes of two-dimensional optical waveguides and conduct a comparative analysis against the standard FEM. The obtained results demonstrate excellent agreement between our method and std. FEM while simultaneously showcasing enhanced computational efficiency multiple times at least. Furthermore, our method classifies the eigenmodes directly based on symmetry, with one category of eigenmode corresponding to one sub-task, which is beneficial for analyzing and designing waveguide modal characteristics.