Topological Floquet edge states in periodically curved waveguides

TL;DR

This paper investigates Floquet edge states in periodically curved optical waveguides, revealing how band topology and modulations influence the existence and coexistence of topological and non-topological edge states.

Contribution

It provides an analytical framework for understanding the phase boundaries and edge state coexistence in modulated topological systems, extending the bulk-edge correspondence concept.

Findings

Topological and non-topological edge states cannot coexist in the same spectral gap.

Analytical phase boundaries are derived in the high-frequency limit.

Periodic modulations can induce or tune edge states beyond static topological properties.

Abstract

We study the Floquet edge states in arrays of periodically curved optical waveguides described by the modulated Su-Schrieffer-Heeger model. Beyond the bulk-edge correspondence, our study explores the interplay between band topology and periodic modulations. By analysing the quasi-energy spectra and Zak phase, we reveal that, although topological and non-topological edge states can exist for the same parameters, \emph{they can not appear in the same spectral gap}. In the high-frequency limit, we find analytically all boundaries between the different phases and study the coexistence of topological and non-topological edge states. In contrast to unmodulated systems, the edge states appear due to either band topology or modulation-induced defects. This means that periodic modulations may not only tune the parametric regions with nontrivial topology, but may also support novel edge states.