Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

Abstract

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s = 1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10 % of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s = 2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

Formation and stability of multidimensional structures in optics and atomic condensate: recent theoretical studies

“…This result also holds for the case of competing quadratic and self-defocusing cubic nonlinearities 25 . A general conclusion of these studies is that stable spinning solitons are possible as a result of competition between focusing and defocusing optical nonlinearities.…”

“…The (2+1)-dimensional light bullet formation was achieved in quadratically nonlinear crystals by generating the necessary anomalous GVD via achromatic phase matching 19 . I mention several promising physical settings for the generation of light bullets, such as the use of saturable 20,21 and nonlocal 22,23 optical media, materials with competing nonlinearities 24,25 , the propagation of (3+1)-dimensional localized structures in confining two-or three-dimensional optical lattices [26][27][28][29][30] , the formation of multidimensional fundamental and vortex (spinning) dissipative solitons in media with gain and loss described by the cubic-quintic Ginzburg-Landau equation 31,32 , and the existence, stability and collision scenarios of discrete light bullets in one-and two-dimensional photonic lattices [33][34][35][36] .…”

Vortex solitons in an off-resonant Raman medium

“…quintic) are assumed to dominate over the lower order ones (e.g. cubic), see, e.g., [7,20]. Our model is particularly interesting because, as we will demonstrate below, it allows the existence of a sufficiently broad parameter range, where stable vortex solitons exist with the local type of nonlinearity derived from the first principles.…”

Stable spatiotemporal dissipative soliton clusters in the complex Ginzburg–Landau equation

“…Soliton clusters in 2D saturable self-focusing media having a staircaselike phase distribution that leads to rotation of the cluster were revealed [7]. Soliton clusters in 2D and 3D, respectively, may be viewed as a nontrivial generalization of the 2D bright or dark vortex solitons [8][9][10][11], and 3D 'spinning' solitons [12,13]. These new concepts of complex soliton structures may be applied to other nonlinear physical media, including the prediction of Skyrmions in a two-component Bose-Einstein condensate (BEC) [14,15].…”