Floquet states on disclinations

TL;DR

This paper demonstrates that periodic modulation of waveguide arrays with disclinations can generate unique Floquet modes localized at the disclination core, revealing new localization regimes in photonic systems.

Contribution

It introduces a novel method to create and control Floquet states bound to disclinations through periodic waveguide modulation, linking topology, Floquet engineering, and nonlinearity.

Findings

Floquet modes appear due to waveguide oscillations switching the structure between topological and trivial phases.

Localized Floquet states depend on oscillation amplitude and array symmetry.

Localized states can form Floquet solitons below a critical power threshold.

Abstract

We show that periodic longitudinal modulation of waveguide arrays with disclination can result in the appearance of previously unexplored Floquet modes bound to the disclination core. Such modes arise due to oscillations of the waveguides in the array, periodically switching the structure between topological and trivial phases on each modulation period, so that on average it seems trivial. Localization of such modes depends on the amplitude of waveguide oscillations. Depending on the discrete rotational symmetry of the arrays with disclinations, these modes exhibit distinct spatial profiles unattainable in periodic lattices. Propagation in a medium with focusing cubic nonlinearity reveals that these Floquet states remain localized below a critical power threshold, indicating the possibility of the formation of disclination-bound Floquet solitons. Our results unveil a new regime of localization in photonic systems, bridging disclination topology, Floquet engineering, and nonlinearity.