Dynamics of vortex and anti-vortex solitons in a vectorial cubic-quintic complex Ginzburg-Landau equation

Abstract

In this paper, we present a study of vortex and anti-vortex dynamics within a complex cubic-quintic Ginzburg-Landau vector equation (CCQGLVE). We employ a variational approach to address the analytical aspects, and the results obtained are subsequently confirmed numerically. The vortex vector (VV) and the anti-vortex vector (anti-VV) are defined with topological charges: m = 1 for VV and m = − 1 for anti-VV. Our investigation reveals that the stability zone map corresponds to the region where greater stability can be achieved for the two studied solutions. Notably, the radius of the vortex craters experiences variations either an increase or decrease depending on the competition between the coupling parameters associated with cubic and quintic cross-phase modulation (XPM). During the propagation, the interaction between a fundamental soliton and anti-VV transforms the soliton into a vortex after a short time, but both finally undergo self-confinement which probably will generates solitons. In the case of the interaction between a VV and a fundamental soliton, we observed a self-confinement and a transformation into solitons. Considering the interaction between a VV and an anti-VV, we found that both solutions are also self-confined but the anti-VV solution turns into a soliton faster than the VV solution. This confirms that the anti-VV is the better solution that can be managed with system coupling parameters than the VV one.