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

Abstract

We present an experimental study on wave propagation in highly nonlocal optically nonlinear media, for which far-away boundary conditions significantly affect the evolution of localized beams. As an example, we set the boundary conditions to be anisotropic and demonstrate the first experimental observation of coherent elliptic solitons. Furthermore, exploiting the natural ability of such nonlinearities to eliminate azimuthal instabilities, we perform the first observation of stable vortex-ring solitons. These features of highly nonlocal nonlinearities affected by far-away boundary conditions open new directions in nonlinear science by facilitating remote control over soliton propagation. DOI: 10.1103/PhysRevLett.95.213904 PACS numbers: 42.65.Tg, 42.65.Jx, 47.27.Te Nonlocality plays an important role in many areas of nonlinear physics. Nonlocality typically arises from an underlying transport mechanism (heat [1], atoms in a gas [2], charge carriers [3,4], etc.) or from long-range forces (e.g., electrostatic interactions in liquid crystals [5]) and many-body interactions as with matter waves in BoseEinstein condensates [6] or plasma waves [7]. In nonlinear optics specifically, nonlocality was found in photorefractives [3,[8][9][10], in thermal nonlinear media [11][12][13][14], in atomic vapors [2], and in liquid crystals [5,15]. In principle, nonlocality acts to spread out the effects of localized excitations, and as such it can suppress modulation instabilities of homogeneous states [16]. However, in spite of the natural ''averaging'' tendency inherent to nonlocality, even highly nonlocal nonlinear media can support solitons [2,5,[17][18][19][20]. 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].Here we present an experimental study on solitons in a nonlinear medium with an extremely large range of nonlocality, such that far-away boundary conditions directly affect the soliton beam. We use the thermal optical nonlinearity in lead glass, which is of the self-focusing type. The nonlocal nature of this thermal nonlinearity is manifested in the heat-transfer (Poisson-type) equation, for which boundary conditions greatly influence the temperature distribution. The nonlinear index change is proportional to the temperature change; hence, the boundary conditions, even from afar, significantly affect the refractive index structure supporting solitons. We show that setting transversely anisotropic boundary conditions (e.g., rectangular boundaries in the transverse plane) f...

Stabilization of dipole solitons in nonlocal nonlinear media

“…The heat diffusion results in transversely inhomogeneous temperature distributions which depend on the temperatures at the sample boundaries and on the sample geometry. Temperature redistribution leads to a variation of local refractive index proportional to the temperature change [9,16]. The governing system of equations in dimensionless form thus writes as ν ≪ by many orders of magnitude, and it is justified to simplify the system (1) by neglecting nonlocality in the longitudinal direction.…”

Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media

“…2D spatial solitons stabilized by the nonlocality were observed in vapors [14] and lead glasses featuring strong thermal nonlinearity [15]; in the latter case, elliptic and vortex-ring solitons were reported. Optical 1D solitons supported by a nonlocal χ (3) nonlinearity were also created in liquid crystals [16].…”

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

“…This latter aspect, i.e. the effect of a nonlocal boundary potential on the propagation of spatial solitons, has been recently addressed with specific reference to thermo-optical and reorientational solitons in glass and in liquid crystals, respectively [16][17][18][19][20]. In this paper we undertake the ambitious task of providing a theoretical background to describe the boundarynematicon interaction, analysing the boundary induced motion of these self-localized beams by means of modulation theory, modelling the problem in one transverse dimension, but extending some of the results to the full two-dimensional scenario.…”