From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency selective feedback

TL;DR

This paper extends the analysis of laser models with frequency-selective feedback from one-dimensional to two-dimensional solitons, including stripe-shaped and vortex types, revealing their properties and potential physical applications.

Contribution

It introduces a study of 2D vortex and stripe solitons in a laser model, expanding understanding beyond previously known 1D localized modes.

Findings

Vortex radius increases linearly with topological charge

Stripe solitons can be viewed as vortices with infinite charge

Results are applicable to various physical systems

Abstract

We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, $m$, therefore the flat-stripe soliton may be interpreted as the vortex with $m=\infty$, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicable to a broad class of physical systems. There is a qualitative agreement between our results and those recently reported for models with saturable nonlinearity.