0 D ec 2 00 5 Stable rotating dipole solitons in nonlocal optical media

Recently increased interest in the study of self-trapped optical beams in nonlocal nonlinear media is explained by experimental observations of nonlocal spatial solitons in liquid crystals and lead glasses as well as a number of many interesting theoretical predictions, including stabilization of vortex solitons against symmetry breaking instability in the media with nonlocal optical response. Many of the predicted and demonstrated properties of nonlocal nonlinear modes suggest that in such optical media we should expect stabilization of many different types of spatial nonlinear structures such as necklaces, soliton clusters, and recently introduced broader classes of modulated optical vortices or azimuthons. One of the simplest multi-hump solitons predicted in nonlinear optics is a dipole-like structure composed of two interacting fundamental beams with opposite phases that undergo angular rotation during the propagation. Such a localized structure can be viewed as a special type of strongly modulated single-charge vortex soliton or azimuthon and it can also be linked to the problem of soliton spiraling, as discussed e.g. in §6.1 of Ref. [13]. However, in spite of its broad applicability and deep physical context, the rotating dipoles are known to be always unstable in all types of realistic optical media with local response. In this Letter, we study the effect of nonlocal response of an optical medium on the stability of rotating dipole solitons. We demonstrate that such solitons can be stabilized when the nonlocality parameter exceeds some threshold value that decreases with the angular momentum and angular velocity, i.e. the dipoles rotating faster are more robust. We describe a continuous family of twolobe localized structures (or azimuthons) that extend from non-rotating dipole solitons to radially symmetric vortex solitons by continuous azimuthal transformations. We consider the propagation of paraxial optical beams in a nonlinear medium described by the nonlinear Schrödinger equation for the scalar field envelope E