Strong transmission and reflection of edge modes in bounded photonic graphene

TL;DR

This paper investigates how edge modes in bounded photonic honeycomb lattices propagate with strong transmission or reflection depending on topological properties, and develops an asymptotic theory to explain these phenomena.

Contribution

It introduces an asymptotic theory for edge states in photonic graphene, highlighting the role of topology in edge mode behavior and nonlinear soliton persistence.

Findings

Edge modes exhibit strong transmission or reflection depending on topological triviality.

Topologically protected edge states can support long-distance nonlinear solitons.

Asymptotic theory predicts presence or absence of edge states on all sides of the lattice.

Abstract

The propagation of linear and nonlinear edge modes in bounded photonic honeycomb lattices formed by an array of rapidly varying helical waveguides is studied. These edge modes are found to exhibit strong transmission (reflection) around sharp corners when the dispersion relation is topologically nontrivial (trivial), and can also remain stationary. An asymptotic theory is developed that establishes the presence (absence) of edge states on all four sides, including in particular armchair edge states, in the topologically nontrivial (trivial) case. In the presence of topological protection, nonlinear edge solitons can persist over very long distances.