Composite vortices in nonlinear circular waveguide arrays

TL;DR

This paper investigates the stability of composite vortex states in nonlinear circular waveguide arrays, revealing that unlike in continuous media, explicit vortices can be stable in discrete systems, with diverse stable states and dynamic phenomena.

Contribution

It demonstrates the stability properties of composite vortices in discrete media, contrasting with continuous media, and explores the existence of long-lived breather states with vortex charge flipping.

Findings

Explicit vortices are stable in discrete media with stable scalar vortex states.

Hidden vortex states become unstable as power increases in small ring chains.

Existence of long-lived breather states with vortex charge flipping.

Abstract

It is known that, in continuous media, composite solitons with hidden vorticity, which are built of two mutually symmetric vortical components whose total angular momentum is zero, may be stable while their counterparts with explicit vorticity and nonzero total angular momentum are unstable. In this work, we demonstrate that the opposite occurs in discrete media: hidden vortex states in relatively small ring chains become unstable with the increase of the total power, while explicit vortices are stable, provided that the corresponding scalar vortex state is also stable. There are also stable mixed states, in which the components are vortices with different topological charges. Additionally, degeneracies in families of composite vortex modes lead to the existence of long-lived breather states which can exhibit vortex charge fipping in one or both components.