Eigenenergy braids in 2D photonic crystals

TL;DR

This paper explores the topological properties of eigenenergy braids in 2D photonic crystals, revealing how symmetry and reciprocity influence band topology and transitions at exceptional points.

Contribution

It introduces a novel analysis of eigenenergy braids in 2D non-Hermitian systems, linking braid conjugacy classes to band topology changes at exceptional points.

Findings

Eigenenergy braids determine point-gap topology in 2D photonic crystals.

Symmetry and reciprocity constrain eigenenergy braid structures.

Transitions in braid conjugacy classes correspond to band number changes at exceptional points.

Abstract

We consider non-Hermitian energy band theory in two-dimensional systems, and study eigenenergy braids on slices in the two-dimensional Brillouin zone. We show the consequences of reciprocity and geometric symmetry on such eigenenergy braids. The point-gap topology of the energy bands can be found from the projection of the eigenenergy braid onto the complex energy plane. We show that the conjugacy class transitions in the eigenenergy braid results in the changes in the number of bands in a complete point-gap loop. This transition occurs at exceptional points. We numerically demonstrate these concepts using two-dimensional reciprocal and nonreciprocal photonic crystals.