title: Stable vortex solitons supported by competing quadratic and cubic nonlinearities.
abstract: We address the stability problem for vortex solitons in two-dimensional media combining quadratic and self-defocusing cubic [chi(2):chi(3)- ] nonlinearities. We consider the propagation of spatial beams with intrinsic vorticity S in such bulk optical media. It was earlier found that the S=1 and S=2 solitons can be stable, provided that their power (i.e., transverse size) is large enough, and it was conjectured that all the higher-order vortices with S> or =3 are always unstable. On the other hand, it was recently shown that vortex solitons with S>2 and very large transverse size may be stable in media combining cubic self-focusing and quintic self-defocusing nonlinearities. Here, we demonstrate that the same is true in the chi(2):chi(3)- model, the vortices with S=3 and S=4 being stable in regions occupying, respectively, approximately 3% and 1.5% of their existence domain. The vortex solitons with S>4 are also stable in tiny regions. The results are obtained through computation of stability eigenvalues, and are then checked in direct simulations, with a conclusion that the stable vortices are truly robust ones, easily self-trapping from initial beams with embedded vorticity. The dependence of the stability region on the chi(2) phase-mismatch parameter is specially investigated. We thus conclude that the stability of higher-order two-dimensional vortex solitons in narrow regions is a generic feature of optical media featuring the competition between self-focusing and self-defocusing nonlinearities. A qualitative analytical explanation to this feature is proposed.
authors.affiliation: Department of Theoretical Physics, Institute of Atomic Physics, P.O. Box MG-6, Bucharest, Romania.
authors.forename: D
authors.initials: D
authors.lastname: Mihalache
authors.forename: D
authors.initials: D
authors.lastname: Mazilu
authors.forename: B A
authors.initials: BA
authors.lastname: Malomed
authors.forename: F
authors.initials: F
authors.lastname: Lederer