Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene

TL;DR

This paper introduces a high-accuracy gradient recovery method based on Bloch theory for computing topological edge modes in photonic graphene, enhancing the precision of electromagnetic mode simulations.

Contribution

It presents a novel gradient recovery technique that improves finite element methods for calculating topological edge modes in honeycomb photonic structures.

Findings

The method achieves superconvergence and higher order accuracy.

Numerical examples validate efficiency in symmetry-breaking cases.

Enhanced mode computation for optical applications.

Abstract

Photonic graphene, a photonic crystal with honeycomb structures, has been intensively studied in both theoretical and applied fields. Similar to graphene which admits Dirac Fermions and topological edge states, photonic graphene supports novel and subtle propagating modes (edge modes) of electromagnetic waves. These modes have wide applications in many optical systems. In this paper, we propose a novel gradient recovery method based on Bloch theory for the computation of topological edge modes in the honeycomb structure. Compared to standard finite element methods, this method provides higher order accuracy with the help of gradient recovery technique. This high order accuracy is highly desired for constructing the propagating electromagnetic modes in applications. We analyze the accuracy and prove the superconvergence of this method. Numerical examples are presented to show the efficiency by computing the edge mode for the $\mathcal{P}$-symmetry and $\mathcal{C}$-symmetry breaking cases in honeycomb structures.