Abstract
Complex Ginzburg-Landau (CGL) models of laser media (with cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-peak) vortices, but the most fundamental “crater-shaped” vortices (CSVs), alias vortex rings, which are essentially squeezed into a single cell of the potential, have not been found before in a stable form. In this work we report on families of stable compact CSVs with vorticity in the CGL model with the external potential of two different types: an axisymmetric parabolic trap and the periodic potential. In both cases, we identify a stability region for the CSVs and for the fundamental solitons (). Those CSVs which are unstable in the axisymmetric potential break up into robust dipoles. All the vortices with are unstable, splitting into tripoles. Stability regions for the dipoles and tripoles are identified, too. The periodic potential cannot stabilize CSVs with either; instead, families of stable compact square-shaped quadrupoles are found.
12 More- Received 20 June 2010
DOI:https://doi.org/10.1103/PhysRevA.82.023813
©2010 American Physical Society