Nonsymmorphic symmetry adapted finite element modeling of glide-symmetric photonic structures

Space group theory is pivotal in the design of nanophotonics devices, enabling the characterization of periodic optical structures such as photonic crystals. The aim of this study is to extend the application of nonsymmorphic space groups in the field of numerical analysis for research and design of nanophotonics devices. In this work, we introduce the nonsymmorphic symmetry adapted finite element method and provide a systematic approach for efficient band structure analysis of photonic structures with nonsymmorphic groups. We offer a formal and rigorous treatment by specifically deriving the boundary constraint conditions associated with the symmetry operations and their irreducible representations, and decomposing the original problem into different subtasks. Our method fully accounts for non-primitive translations and nonstructural symmetries like time-reversal symmetry and hidden symmetries. We demonstrate the effectiveness of our method by computing the band structure of photonic structures with a rod group, a plane group, and a space group. The results exhibit excellent agreement with those obtained using the standard finite element method, showcasing improved computational efficiency. Furthermore, the decomposition of the original problem facilitates band structure classification and analysis, enabling the identification of the different bands among the band structure in various subtasks. This advancement paves the way for innovative designs in nanophotonics.