Efficient finite element modeling of photonic modal analysis augmented by combined symmetry

TL;DR

This paper introduces an efficient finite element method for photonic modal analysis that exploits symmetry operations, significantly reducing computation time and enabling direct mode classification, demonstrated on complex optical waveguides.

Contribution

The work develops a symmetry-augmented finite element approach with rigorous boundary conditions, achieving substantial speedups and improved modal classification in photonic systems.

Findings

Calculation speed increased by a factor of 23 in hollow-core fiber

Excellent agreement with standard FEM results

Facilitates modal analysis of complex waveguides

Abstract

In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in pseudo-Hermiticity systems. We provide a formal and rigorous treatment, specifically deriving the boundary constraint conditions corresponding to symmetry constraints. Without loss of generality, we illustrate our approach via computing the modes of optical waveguides with complex cross-sections, accompanied with performance benchmark against the standard finite element method. The obtained results demonstrate excellent agreement between our method and standard FEM with significantly improved computational efficiency. Specifically, the calculation speed increased by a factor of $23$ in the hollow-core fiber. Furthermore, our method directly classifies and computes the modes based on symmetry, facilitating the modal analysis of complex waveguides.