Adiabatic Dynamics of Edge Waves in Photonic Graphene

TL;DR

This paper investigates the behavior of edge waves in photonic graphene with adiabatic parameter variation, revealing conditions for topologically protected states, soliton formation, and scattering phenomena in linear and nonlinear regimes.

Contribution

It provides an explicit asymptotic analysis of edge mode dynamics in adiabatically varying photonic honeycomb lattices, including nonlinear effects and topological protection.

Findings

Edge states can persist over entire or partial periods depending on parameters.

Nonlinear effects lead to soliton solutions in the envelope dynamics.

Certain long-lived modes exhibit topological protection with minimal backscattering.

Abstract

The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying dynamics. Depending on parameters, edge states can exist over an entire period or only part of a period; in the latter case an edge mode can effectively disintegrate and scatter into the bulk. In the presence of nonlinearity, a `time'-dependent one-dimensional nonlinear Schr\"odinger (NLS) equation describes the envelope dynamics of edge modes. When the average of the `time varying' coefficients yields a focusing NLS equation, soliton propagation is exhibited. For both linear and nonlinear systems, certain long lived traveling modes with minimal backscattering are found; they exhibit properties of topologically protected states.