Thresholdless discrete surface solitons and stability switchings in periodically curved waveguides

TL;DR

This paper investigates how periodic driving in curved waveguide arrays affects discrete surface solitons, revealing thresholdless solitons and stability switches driven by parametric resonance effects.

Contribution

It introduces the concept of thresholdless discrete surface solitons and analyzes their stability switching due to parametric drives in curved waveguides.

Findings

Discrete surface solitons can exist without a power threshold under certain drives.

Critical drive values cause the threshold power to vanish.

Stability of solitons switches at critical drive values, confirmed by Floquet analysis.

Abstract

We study numerically a parametrically driven discrete nonlinear Schr\"odinger equation modelling periodically curved waveguide arrays. We show that discrete surface solitons persist, but their threshold power is altered by the drive. There are critical drives at which the threshold values vanish. We also show that parametric drives can create resonance with a phonon making a new barrier for discrete solitons. By calculating the corresponding Floquet multipliers, we find that the stability of symmetric and antisymmetric off-side discrete surface solitons switches approximately at the critical drives for thresholdless solitons.