Physica B 394 (2007) 351–356 Spiraling solitons and multipole localized modes in nonlocal nonlinear media Daniel Buccoliero a,b , Servando Lopez-Aguayo a,c , Stefan Skupin b,d , Anton S. Desyatnikov a , Ole Bang e , Wieslaw Krolikowski b,Ã , Yuri S. Kivshar a a Nonlinear Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia b Laser Physics Center, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia c Photonics and Mathematical Optics Group, Tecnologico de Monterrey, Monterrey 64849, Me´xico d CEA-DAM/Ile de France, B.P. 12, 91680 Bruyeres-le-Chatel, France e COMDTU Department of Communications, Optics and Materials, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark Abstract We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form. r 2007 Elsevier B.V. All rights reserved. PACS: 42.65.Tg; 42.65.Jx; 42.65.Sf Keywords: Spatial solitons; Nonlocality; Nonlinear optics 1. Introduction It is well known that nonlinear optical media support the formation of spatially localized structures—spatial optical solitons [1]. Nonlinearity of optical media is usually approxi- mated by a local function of the light intensity assuming the refractive index change at a given spatial location depends solely on the light intensity at the same location. However, this local nonlinearity often supports only a certain type of stable optical solitons, such as the fundamental single-peak solitons. While in principle more complex optical structures such as multihump and vortex solitons can be predicted to exist as stationary states, such higher-order localized modes do not survive even weak perturbation and they break up into low- order solitons. For example, in the case of vortex solitons the ring-shaped beam with a helical phase structure disintegrates during the propagation in local nonlinear media due to the azimuthal instability [2]. However, as has been shown recently, the soliton stability may be enhanced dramatically if a nonlinear response of the medium is spatially nonlocal [3,4]. Nonlocality means that the change of the refractive index in a particular point is determined by the light intensity not only in the same point but also in its vicinity. Nonlocality appears naturally in many nonlinear systems including, for instance, self-action of laser beams in thermal media [5] and atomic vapors [6], as well as the dipole–dipole interaction of cold atoms in condensates [7]. Recent interest in the study of nonlocal nonlinear media has been stimulated by the experiments with spatial solitons in nematic liquid crystals [8] as well as the analysis of nonlocal interaction in dipolar Bose–Einstein conden- sates [7]. Various aspects of the impact of nonlocality on the propagation of finite-size beams and the formation of stable solitons in nonlocal media have been studied [9–12]. It has been shown that the stabilization of finite-size optical structures in nonlocal media is caused by the spatial averaging-out of low-scale intensity modulations, which results in the formation of broad and smooth waveguide ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.12.063 Ã Corresponding author. E-mail address: wzk111@rsphysse.anu.edu.au (W. Krolikowski).