Solitons in nonlinear media with infinite range of nonlocality: first observation of coherent elliptic solitons and 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 1D 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) fa...

Nematic liquid crystals: An excellent playground for nonlocal nonlinear light localization in soft matter

“…Nonlinear nonlocal media encompass a wealth of features unavailable in local Kerr-like materials, including increased stability, long-range interactions, modified spatial dispersion, etc. [4][5][6][7][8][9][10][11][12][13][14][15][16] Light beam localization in the form of optical spatial solitons was reported in nematic liquid crystals (NLC) in the year 2000 17 and was obtained by exploiting the large self-focusing response afforded by all-optical reorientation in a planar cell containing a (properly oriented) positive uniaxial fluid. The so-called "nematicons" could be generated at input powers of a few mW, 17 propagate stably and with invariant profile over several Rayleigh lengths and in two transverse dimensions, interact and mutually attract with other solitons, even at separations exceeding their transverse size, 6,18 survive collisional interactions with other nematicons or external beams or dielectric perturbations or boundaries, [19][20][21][22][23] refract or reflect when traveling across interfaces, [24][25][26][27] be deflected by electro-optically or self-induced changes in birefringent walkoff, [28][29][30][31][32] etc.…”

𝒫𝒯-symmetric nonlocal gap solitons in optical lattices

“…15 In the present work we study the existence and stability of PT -symmetric gap solitons in defocusing nonlocal media. Several material systems exhibit a diffusive (nonlocal) nonlinearity, particularly thermo-optic media [16][17][18][19] and nematic liquid crystals. 20,21 We extend these models to include PT -symmetric potentials.…”

Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media

“…It has been reported that nonlocality can suppress modulation instability of homogeneous states [1], eliminate azimuthal instability of vortex-ring beams [2][3][4][5], prevent the collapse of self-focusing beams in media with cubic nonlinearity [6], and give rise to attraction of nonlocal dark solitons [7,8]. The stable vortex-ring solitons was first experimentally observed [9] by exploiting the natural tendency of long-range nonlocal nonlinearities to eliminate azimuthal instabilities in lead glass. It has been discussed that synthetic nonlocal nonlinearities can support the stabilization of higher-order vortices and multihump solitons [10].…”

“…Many contributions have been made in the propagation of vortex solitons with linear polarization and phase singularities [2][3][4][5][9][10][11] in nonlocal nonlinear media, described by the nonlocal nonlinear Schrödinger equation (NNLSE), which is derived from the scalar Helmholtz equation based on paraxial approximations. Whereas the scalar Helmholtz equation can be used to describe the propagation of a linearly polarized scalar beam, it is the vector Helmholtz equation that describes the propagation of the vector beams with inhomogeneous polarization.…”