Rotating surface soliton complexes in annular waveguides

We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a p-phase difference between neighboring spots. It is shown that the multipole-mode solitons can rotate steadily upon propagation, and the existence domain is strongly affected by the rotation frequency. The rotation may enhance the stabilization of surface multipole-mode solitons. 2008 Elsevier B.V. All rights reserved. The study of light propagating at the interface between different materials is a fundamental problem of scientific and practical importance [1–4]. Such interfaces can support localized waves, i.e. surface states, which were encountered in various areas of physics. In optics, nonlinear surface waves have been investigated extensively during the last few years [5–8]. However, most of these works are focused on one-dimensional (1D) geometry. One natural question is whether the concept of 1D surface solitons can be extended to two-dimensional (2D) settings. In 2006, it was suggested that the edges and corners of finite two-dimensional lattices could support surface solitons [9]. Very recently, this idea was verified by two remarkable experiments, which demonstrated 2D surface solitons in optically induced lattices in photorefractive crystal [10] and fs-laser-written arrays in bulk fused silica [11], respectively. Soliton dynamics depends crucially on the overall geometry of the lattice. In this respect the lattices with radial symmetry afford the wealth of possibilities for soliton control [12,13], including the possibility to study mobility of solitons in experiment. In the circular geometry, in particular, the structures created by Bessel beams support rotary solitons, stable vortices in self-defocusing media, and multipole-mode solitons [14–17]. Note that solitons in the ring structure have been demonstrated in [18]. Very recently, surface ll rights reserved. Research School of Physical iversity, Canberra ACT, 0200, 8. solitons and switching with vortex beams have been discussed in circular guiding structures with limited number of rings [19,20]. The aim of this paper is to investigate the properties and stability of multipole-mode solitons residing in the outer ring of guiding structure consisting of several concentric rings. In particular, it will be shown that such surface multipole modes can rotate upon propagation. It is important to note that rotation may help to stabilize multipole-mode surface solitons. We consider the propagation of a light beam along the n axis in a Kerr-type medium with a transverse modulation of refractive index, described by the following equation for the complex field amplitude q: