Rotating vortex solitons supported by localized gain

Abstract

We show that ring-like localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.Vortex solitons are self-sustained excitations carrying a nonzero angular momentum and topological phase singularities [1]. In uniform focusing local media, vortex solitons exhibit ring-like profiles, a property that makes them prone to azimuthal modulation instabilities. Such instability can be suppressed in conservative materials by several mechanisms, including competing nonlinearities, external potentials, or nonlocalities. Stable vortex solitons form also in dissipative settings [2,3]. Dissipative vortex solitons have been found in laser amplifiers [4], in Bose-Einstein condensates [5,6], and in systems described by the complex cubic-quintic Ginzburg-Landau equation [7][8][9]. Vortex solitons in uniform dissipative media may experience considerable dynamical shape deformations, as it occurs in suitable GinzburgLandau systems [8,9] and in wide-aperture lasers with a saturable absorber [4].Recently it was predicted that the evolution of nonlinear excitations in dissipative medium is affected dramatically by a spatially modulated gain. Such evolution has been studied in Bragg gratings and optical waveguides [10,11], in materials with periodic refractive index modulation [12,13], and in Bose-Einstein condensates [14]. In such systems solitons form due to the interplay between localized gain and nonlinear absorption, and a spatial localization of the gain landscape ensures the stability of the background field. Such interplay may result in suppression of azimuthal modulation instabilities and formation of stable stationary vortex solitons [15]. However, the possibility to excite rotating vortex states in such systems has never been addressed to date.In this Letter we reveal that ring-like gain landscapes imprinted in cubic media with two-photon absorption support rich families of rotating vortex states exhibiting multiple phase singularities embedded into a single vortex core and possessing azimuthally modulated shapes. Notice that while in some conservative systems the formation of vortex solitons with multiple singularities may be stimulated by external factors, such as large sample asymmetry in nonlocal media [16] or the presence of strong optical lattices [17], in our dissipative setting the asymmetric rotating vortices appear despite the fact that all parameters are either spatially uniform (diffraction and nonlinearity) or radially symmetric (gain). This indicates that the formation of such states is mediated by complex internal energy flows that may be highly asymmetric in a system with localized gain.We consider the propagation of laser radiation along the  -axis in a...

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates

“…Solutions with this symmetry were previously identified in other contexts, e.g., Ref. 46. Nevertheless, these results, and the absence of vortex lattice formation in this case, are in accordance with the results of the stability analysis of the GR soliton presented above and its fundamentally different instability mechanism in comparison to the NC or CV configurations.…”

Rotating solitons supported by a spiral waveguide

“…Further stabilisation can be achieved by introducing a composite (rotating "propeller") soliton made of a rotating dipole jointly trapped with a bell-shaped component [5]. Ringlike localized gain landscapes imprinted in focusing cubic nonlinear media support stable higher-order vortex solitons [6].…”

Localized solutions of Lugiato-Lefever equations with focused pump

“…Stable LDSs pinned to one or two gain-carrying "hot spots", shaped as narrow Gaussians, were reported too [58,62]. Further, stable 2D LDSs, including ones with an intrinsic vortex structure, supported by hot spots in the 2D geometry, were predicted in works [55,56,57,59,61].…”

“…The objective of the present work is to introduce localized pump in the framework of the 1D and 2D LL equations, and find stable confined modes, which may be supported by the spatially focused pump. The difference from the previous works, which were dealing with the CGL equations [54,55,56,57,58,59,60,61,64,62], is that the pump is represented by free terms in the LL equations, which do not multiply the field variable, while in the models of the CGL type the gain terms provide the parametric pump, i.e., they multiply the field variable.…”

“…In many physically relevant contexts, especially as concerns realizations in optics, one-and two-dimensional (1D and 2D) LDSs supported by localized gain were studied in detail in the context of complex Ginzburg-Landau (CGL) equations [54,55,56,57,58,59,60,61,62], see also reviews in [63] and [64]. Specifically, by considering a 1D model with the tightly localized gain in the form of a delta-function, placed on top of the spatially uniform linear loss, analytical solutions for pinned LDSs pinned to the delta-function were found in [54,60] (see also a review in [64]).…”