Theoretical description of a photonic topological insulator based on a cubic lattice of bianisotropic resonators

TL;DR

This paper provides a theoretical framework for a 3D photonic topological insulator using a cubic lattice of bianisotropic resonators, analyzing band structures, topological features, and localized states.

Contribution

It introduces a dyadic Green's function-based theoretical model for a 3D photonic topological insulator with detailed analysis of band topology and localized in-gap states.

Findings

Quadratic degeneracies near high-symmetry points without bianisotropy

In-gap states localized at domain walls with bianisotropy

Berry curvature distributions reveal topological properties

Abstract

In the present paper, we construct a theoretical description of a three-dimensional photonic topological insulator in the form of a simple cubic lattice of bianisotropic resonators that is based on a dyadic Green's function approach. By considering electric and magnetic dipole modes and the interactions between different numbers of the nearest resonators, we obtain the Bloch Hamiltonians and the corresponding tight-binding models and analyze the band diagrams, spatial structure of the eigenmodes, and their localization, revealing quadratic degeneracies in the vicinity of high-symmetry points in the absence of bianisotropy and the emergence of in-gap states localized at a domain wall upon the introduction of bianisotropy. Finally, we visualize the Berry curvature distributions to study the topological properties of the considered models.