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

TL;DR

This paper introduces a nonsymmorphic symmetry adapted finite element method for efficient and systematic band structure analysis of photonic structures with nonsymmorphic groups, enhancing design capabilities in nanophotonics.

Contribution

It develops a formal finite element approach that incorporates nonsymmorphic symmetries, including non-primitive translations and hidden symmetries, for photonic band structure calculations.

Findings

Method shows excellent agreement with standard finite element results.

Improves computational efficiency in band structure analysis.

Facilitates classification and analysis of photonic bands.

Abstract

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 accounting for non-primitive translations and nonstructural symmetries like time-reversal symmetry and hidden symmetries. We demonstrate the effectiveness of our method via computing the band structure of photonic structures with a layer 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.