Vector solitons in (2 + 1) dimensions

Abstract

We address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.Recent experimental observations of multidimensional spatial optical solitons in different types of nonlinear materials [1] call for a systematic analysis of the selftrapping of light in higher dimensions. When two (or more) fields interact nonlinearly, they can form multicomponent trapped states, known as vector solitons. Vector solitons, first theoretically studied in a (1+1)-D models [2], were observed in birefringent fibers and planar waveguides [3]. Fabricated waveguiding structure localizes such solitons in one of the two directions transverse to the direction of propagation, hence these solitons are effectively one-dimensional. It is only recently, that the theory and experiments on incoherent interaction and truly two-dimensional self-trapping of beams in a bulk (saturable) medium merged [4], indicating progress towards the observation and study of different types of (2+1)-D vector solitons and their interactions.The practical possibility of such an observation greatly depends upon the soliton stability in the media with realistic, Kerr or saturable nonlinearity. It is known that scalar (one-component), fundamental (2+1)-D solitons are stable in saturable media [1], but they exhibit critical collapse in Kerr-type media [5]. However, as in the case of (1+1)-D vector solitons [6], both existence and stability of multi-dimensional vector solitons are nontrivial issues, which have not been systematically adressed so far.In this Letter, we study (2+1)-D vector solitons in Kerr and saturable media. We analyze two classes of such solitons. First, we consider solitons formed by the coupling of two fundamental modes; such solitons are always bellshaped. Secondly, we analyze the coupling between the fundamental mode of one field and the first-order mode (i.e. that carrying a topological charge) of the other field. In the latter case the vector solitons may possess a ring structure and are expected to be analogous to the twohump (1+1)-D vector solitons recently proved to be stable in a saturable medium [6].We consider two incoherently interacting beams propagating along the direction z in a bulk, weakly nonlinear optical medium. For a Kerr medium, the problem is described by the normalized, coupled equations for the slowly varying beam envelopes, E 1 and E 2 , (1) where ∆ ⊥ is the transverse Laplacian, and σ measures the relative strength of cross-and self-phase modulation effects. Depending on the polarization of the beams, the nature of nonlinearity, and anisotropy of the material, σ varies over a wide range. For a Kerr-type material with nonresonant electronic nonlinearity σ ≥ 2/3, whereas for a nonlinearity due to molecular orientation σ ≤ 7 [7]. We look for solutions of Eqs.(1) in th...

Vector vortex solitons in nematic liquid crystals

“…We are interested in a special class of vector solitons for which one of the components carries angular momentum and the other component describes a spatially localized mode in the form of a spatial bright beam. Solutions of this type have been discussed earlier for nonlinear systems with a local response [11,12] and they have been shown to be unstable in a large region of their existence domain [13]. For our system described by Eqs.…”

“…Solutions of this type have been discussed earlier for nonlinear systems with a local response [11,12] and they have been shown to be unstable in a large region of their existence domain [13]. For our system described by Eqs.…”

Observation of Dipole-Mode Vector Solitons

“…The limit s → 0 corresponds to the Kerr medium [4]. As has been recently shown in [2], when one of the beams components, say w, is weak, a soliton formed by the u-component induces a change in the refractive index of the PR material that traps and guides the weaker wcomponent.…”

Single- and double-vortex vector solitons in self-focusing nonlinear media

“…Model (1) provides a straightforward generalization to a number of important cases studied earlier. In particular, the limit σ → 0 corresponds to the Kerr medium with cubic nonlinearity [12] where all self-trapped beams may undergo collapse instability. The case of the saturable nonlinearity at µ = 1 corresponds to the incoherent beam interaction in photorefractive nonlinear media [10,11,14].…”

“…Mutual coupling between the fundamental beam and the vortex-carrying beam can create different novel types of composite vector solitons carrying an angular momentum [10,11,12]. The properties of such vector vortex solitons can differ substantially from the properties of one-component scalar vortices and scalar solitons.…”