Collisions and inhomogeneous forces between solitons of different dimensionality

Splitting after collision of high-order bright spatial solitons in Kerr media

By numerically studying the collision between (1 + 1)-Dimensional high order bright spatial solitons in a Kerr nonlinear media we show that after the collision, the high order solitons split into a number of first order solitons that corresponds to its order. Two different collision scenarios are considered: collision between two independent high order solitons and a collision with a virtual soliton simulated by the reflection at an angle of a high order soliton at a linear interface. The results demonstrate that in both cases the high order solitons split showing minor differences.

X , Y , and Z waves: extended structures in nonlinear lattices

We propose a new type of waveforms in two-dimensional (2D) and three-dimensional (3D) discrete media-multilegged extended nonlinear structures (ENSs), built as arrays of lattice solitons (tiles and stones, in the 2D and 3D cases, respectively). We study the stability of the tiles and stones analytically, and then extend them numerically to complete ENS forms for both 2D and 3D lattices, aiming to single out stable ENSs. The predicted patterns can be realized in Bose-Einstein condensates trapped in deep optical lattices, crystals built of microresonators, and 2D photonic crystals. In the latter case, the patterns provide for a technique for writing reconfigurable virtual partitions in multipurpose photonic devices.

Mechanisms supporting long propagation regimes of photorefractive solitons

We extend investigation of one-dimensional solitons in biased photorefractive crystals to long propagation regimes, where self-trapping over a large number of linear diffraction lengths combines with the progressive growth of generally distortive spatially nonlocal components. Results indicate that saturation halts the radiative misshaping of the soliton, which follows that specific bending trajectory along which its evolution is governed by the same local screening nonlinearity that intervenes in short propagation conditions, where spatial nonlocality has a negligible effect. This finding not only allows the prediction of the curvature and of the relative role of charge displacement and diffusion, but implies a set of interesting observable effects, such as boomerangs, counterpropagating and cavity geometries, quasirectilinear and anomalous collisions, along with specific consequences on soliton arrays and on coupling to bulk gratings.

Soliton stripes in two-dimensional nonlinear photonic lattices

We study experimentally the interaction of a soliton with a nonlinear lattice. We observe the formation of a novel type of composite soliton created by strong coupling of mutually incoherent periodic and localized beam components. By imposing an initial transverse momentum on the soliton stripe, we observe the effect of lattice compression and deformation.

Collisions between spatiotemporal solitons of different dimensionality in a planar waveguide

A (2+1)-dimensional nonlinear Schrödinger equation including third-order dispersion is a natural model of a waveguide, in which strong temporal dispersion is induced by a grating in order to make the existence of two-dimensional spatiotemporal solitons possible. By means of analytical and numerical methods, we demonstrate that this model may support, simultaneously, stable dark quasi-one-dimensional (stripe) solitons and two-dimensional elevation solitons ("antidark solitons") in the form of weakly localized "lumps." The spatial position of lumps can be controlled by passing stripe dark solitons through them in an arbitrary direction. To substantiate this mechanism, we analytically calculate a position shift generated by a headon collision between the stripe and lump. The obtained results are in good agreement with direct numerical simulations.

A one- and two-dimensional nonlinear pulse interaction

The peculiar intergrability of the Davey-Stewartson equation allows us to analytically find solutions describing the simultaneous formation and interaction of one-dimensional and two-dimensional localized coherent structures. The predicted phenomenology allows us to address the issue of interaction of solitons of different dimensionality that may serve as a starting point for the understanding of hybrido-dimensional collisions recently observed in nonlinear optical media.