Floquet edge solitons in modulated trimer waveguide arrays

TL;DR

This paper demonstrates the existence of two co-existing topological Floquet edge states and their nonlinear soliton counterparts in modulated trimer waveguide arrays, revealing new topological phenomena in periodically driven photonic systems.

Contribution

It introduces the concept of co-existing Floquet topological edge states in a single system and explores their nonlinear soliton formations, a novel finding in topological photonics.

Findings

Two types of Floquet edge states coexist in the system.

Nonlinear topological Floquet edge solitons can bifurcate from linear edge states.

Both types of edge solitons can be stable and generated dynamically.

Abstract

We show that one-dimensional Floquet trimer arrays with periodically oscillating waveguides support two different and co-existing types of topological Floquet edge states in two different topological gaps in Floquet spectrum. In these systems nontrivial topology is introduced by longitudinal periodic oscillations of the waveguide centers, leading to the formation of Floquet edge states in certain range of oscillation amplitudes despite the fact that the structure spends half of the period in ``instantaneously'' nontopological phase, and only during other half-period it is ``instantaneously'' topological. Two co-existing Floquet edge states are characterized by different phase relations between bright spots in the unit cell -- in one mode these spots are in-phase, while in other mode they are out-of-phase. We show that in focusing nonlinear medium topological Floquet edge solitons, representing exactly periodic nonlinear localized Floquet states, can bifurcate from both these types of linear edge states. Both types of Floquet edge solitons can be stable and can be created dynamically using two-site excitations.