Vortex solitons in twisted circular waveguide arrays

TL;DR

This paper investigates how twisting circular waveguide arrays influences the formation, stability, and properties of vortex solitons, revealing that twist induces novel topological states and stabilizes certain vortex modes.

Contribution

It demonstrates that twisting affects vortex soliton stability and topological properties, introducing new stable states and instability domains in circular waveguide arrays.

Findings

Twisting stabilizes vortex solitons with topological charges m=±1.

Twisting creates instability domains for m=±2 solitons.

Vortex modes with charges m=±3 emerge due to twisting.

Abstract

We address the formation of topological states in twisted circular waveguide arrays and find that twisting leads to important differences of the fundamental properties of new vortex solitons with opposite topological charges that arise in the nonlinear regime. We find that such system features the rare property that clockwise and counter-clockwise vortex states are nonequivalent. Focusing on arrays with C_{6v} discrete rotation symmetry, we find that a longitudinal twist stabilizes the vortex solitons with the lowest topological charges m=+-1, which are always unstable in untwisted arrays with the same symmetry. Twisting also leads to the appearance of instability domains for otherwise stable solitons with m=+-2 and generates vortex modes with topological charges m=+-3 that are forbidden in untwisted arrays. By and large, we establish a rigorous relation between the discrete rotation symmetry of the array, its twist direction, and the possible soliton topological charges.