Efficient Finite Element Modeling of Light Scattering in Symmetric Structures: A Nondegenerate Case

In recent years, advancements in optical scattering of nanostructures have significantly driven the development of telecommunications, medical imaging, detection, and novel light sources. However, due to the structural complexity of nanostructures, particularly metasurfaces and metamaterials, traditional methods of full-wave modeling for simulating optical scattering face substantial challenges due to increased degrees of freedom. In this work, we propose a symmetry-adapted finite element method to reduce the computational domain and enhance the efficiency of optical scattering simulations. By introducing the concepts of symmetry group and projection operator, we offer a formal and rigorous framework for decomposing the original problem, i.e., the incident condition, boundary constraints, and the finite element method implementation in decoupled subtasks. To demonstrate its broad applicability, we present three numerical examples: the enhancement of light confinement via quasi-bound states in the continuum in a photonic crystal slab, the scattering cross sections of incident configurations, and the calculation of transmission spectra in the metasurface. These examples illustrate the use of the symmetry finite element method under different symmetry conditions, including mirror symmetry, rotational symmetry, and the combination of Bloch’s theorem. Our method significantly reduces computation time and memory usage, thereby greatly improving the computational efficiency. Given the universality of symmetry principles, our method has important applications in the optical analysis and design of symmetric photonic devices, especially for symmetric yet large-sized optical structures.