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

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.

References in corpus (7)

• Topological Photonics
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Scheme to Achieve Silicon Topological Photonics
• Topological Acoustics
• Two-dimensional Mott-Hubbard electrons in an artificial honeycomb lattice
• Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene
• A $C^0$ linear finite element method for sixth order elliptic equations

Cited by in corpus (5)

• Superconvergent Gradient Recovery for Virtual Element Methods
• Linear and nonlinear electromagnetic waves in modulated honeycomb media
• Edge states and the Valley Hall Effect
• Wave packets in the fractional nonlinear Schrödinger equation with a honeycomb potential
• Unfitted Nitsche's method for computing wave modes in topological materials