Localized Structures in Dissipative Nonlinear Systems - Abstract

Firth, William

Stable localized vortices and solitons in a laser model with cubic nonlinearity

The simplest model for solitonic beams or pulses in a laser is the cubic complex Ginzburg-Landau model (CGL3). It has no stable solitonic solutions, so higher-order nonlinearity is usually invoked to obtain stable solitons (but only exceptionally as analytic solutions). In this paper we show that coupling the CGL3 to a resonant linear system is a simple, physically-relevant, and general route to stabilization. It encompasses and extends to higher dimensions a previous instance in the time domain. In one spatial dimension, the fundamental soliton is analytic, with chirped-sech form. We also show, for the first time in a CGL3 model, stable fundamental and vortex solitons in two spatial dimensions, with stable coexistence of m=0,1,2 states in some cases (including models of VCSELs with grating feedback).