Ring vortex solitons in nonlocal nonlinear media

Abstract

We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction.

Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality

“…Other types of localized response functions have been used to obtain qualitative analytical results that capture the physics of the effect of nonlocality, such as a Gaussian in connection with variational calculations [36,37]. The generic properties of the different types of response functions have been studied by Wyller et al in terms of modulational instability and it was shown that, in general, all types of localized response functions have the same generic properties, provided their Fourier transform is positive-definite [38].…”

Dynamics of two-dimensional coherent structures in nonlocal nonlinear media

“…Though vortices can be stabilized in media with competing local nonlinearities [12,13,14,15], it occurs only in the extreme regime when the higher-order contribution to the nonlinearity dominates. The recent investigations [16,17] have shown that the different kinds of nonlocality of the nonlinear response can also suppress or completely eliminate the symmetry-breaking azimuthal instability for one-ring and double-ring single-charge (m = 1) vortex solitons. The recent experiments [2] have confirmed an existence of stable single-charge vortex solitons in the the nonlocal media with thermal optical nonlinearity.…”

Solitons in Nonlinear Media with an Infinite Range of Nonlocality: First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons

“…Moreover, it was suggested that nonlocality can prevent the catastrophic collapse of self-focused beams, allowing 2 1 D solitons in Kerr-type media [2,17,21]. In a similar vein, it was proposed that nonlocality can suppress azimuthal instabilities of vortex-ring beams [22,23], but such an experiment has thus far never been reported. Finally, nonlocality can considerably alter soliton interactions, e.g., giving rise to attraction between out of phase solitons [19,20,24] and between dark solitons [25], which without nonlocality always repel, and causing attraction between well separated solitons [26].…”

“…(ii) Far-away boundary conditions significantly affect the self-trapping, controlling a soliton beam ''by remote.'' As discussed above, it has been proposed [22,23] that nonlocal nonlinearities suppress azimuthal instabilities of vortex-ring beams, but experimental observation of stable vortex-ring solitons has thus far not been reported. Exploiting this stabilizing feature, we demonstrate the first stable vortex-ring solitons.…”