Composite spatial solitons in a saturable nonlinear bulk medium

We review the generation of the recently predicted multi-component spatial optical solitons in a saturable nonlinear bulk medium. We present numerical simulations for an effectively isotropic model and experimental results for a set of different combinations of a Gaussian beam co-propagating incoherently with a beam of a more complex internal structure, such as a higher order transverse laser mode. We discuss the different formation processes and the general properties of a variety of different dipole-mode composite solitons and expand our investigations to the generation of a quadrupolemode composite soliton. PACS: 42.65.Tg; 05.45.Yv; 42.65.Hw Stable self-focusing of light in two transverse dimensions in a bulk nonlinear material has been a fast growing and attractive topic of research during the last decade [1]. The diffraction of a Gaussian beam is counterbalanced by a self-focusing effect in a material that exhibits a Kerr-like but saturable nonlinearity (e.g. a photorefractive nonlinear crystal). The beam shape remains constant during propagation, and it can be regarded as the fundamental Gaussian mode that propagates in its self-induced waveguide [2]. Self-trapped beams that consist of only one optical field are called scalar solitons, whereas vector or composite solitons represent the selftrapped beams that result from an incoherent superposition of several optical fields. Typically they consist of a fundamental Gaussian beam that co-propagates with one (or more) mutually incoherent higher-order mode of the induced multimode waveguide. Both beams remain mutually trapped due to the self-consistent change of the refractive index induced by both beams. Such types of spatial solitons have been extensively studied in the planar (1+1)D geometry [3]. Single and multihump structures as well as collision-induced shape transformation of the composite solitons have been demonstrated both experimentally and theoretically [4, 5]. Within the last year various configurations of composite solitons in two transverse ∗Corresponding author. (Fax: +49-6151/164-123, E-mail: [email protected]) dimensions have been predicted theoretically [6, 7] and subsequently verified experimentally [8, 9]. Here, we give a review of the various classes of composite solitons that have been realized so far. When expanding the problem to two transverse dimensions, the number of possible types of beams with different shapes becomes large. A Gaussian beam that induces a refractive index profile with an almost circular symmetry is expected to host higher-order-mode beams that are well-known from linear waveguide theory. Examples of these modes are depicted in Fig. 1. However, this linear principle can only be applied to multimode solitons if the higher-order mode is much weaker than the fundamental component that creates a multimode waveguide structure in which a less-intense probe beam is guided. Here we investigate composite structures that consist of two components of nearly equal intensity. The nontrivial question is whether these combined structures form a bound vector soliton state during propagation, or break apart forming several separated structures. In this paper we analyze and observe experimentally three different kinds of two-dimensional spatial vector solitons. First, we review the generation of a dipole-mode vector soliton, which is a combination of a nodeless bell-shaped Gaussian fundamental component (Fig. 1a) with a Hermite– Gaussian (HG10)-like dipole-mode (Fig. 1b). Second, we generate a similar dipole-mode vector soliton through the decay of a vortex beam of Laguerre–Gaussian (LG01)-type (Fig. 1c) into a dipole-mode beam in the presence of a stabilizing Gaussian component. The resulting dipole-mode vector soliton displays a non-vanishing transverse angular momentum Fig. 1a–d. Examples of the transverse intensity distributions of the a fundamental, b dipole, c vortex and d quadrupole modes that become constituents of multi-component spatial optical solitons