A Potential of Incoherent Attraction Between Multidimensional Solitons

We obtain analytical expressions for an effective potential of interaction between two- and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by cross-phase modulation. The derivation is based on calculation of the interaction term in the full Hamiltonian of the system. An essential peculiarity is that, in the 3D case, as well as in the case of 2D solitons with unequal masses, the main contribution to the interaction potential originates from a vicinity of one or both solitons, similarly to what was recently found in the 2D and 3D single-mode systems, while in the case of identical 2D solitons, the dominating area covers all the space between the solitons. Unlike the single-mode systems,_stable_ bound states of mutually orbiting solitons are shown to be possible in the bimodal system.Comment: latex, no figures, submitted to Physics Letters

Families of Bragg-grating solitons in a cubic-quintic medium

We investigate the existence and stability of solitons in an optical waveguide equipped with a Bragg grating (BG) in which nonlinearity contains both cubic and quintic terms. The model has straightforward realizations in both temporal and spatial domains, the latter being most realistic. Two different families of zero-velocity solitons, which are separated by a border at which solitons do not exist, are found in an exact analytical form. One family may be regarded as a generalization of the usual BG solitons supported by the cubic nonlinearity, while the other family, dominated by the quintic nonlinearity, includes novel ``two-tier'' solitons with a sharp (but nonsingular) peak. These soliton families also differ in the parities of their real and imaginary parts. A stability region is identified within each family by means of direct numerical simulations. The addition of the quintic term to the model makes the solitons very robust: simulating evolution of a strongly deformed pulse, we find that a larger part of its energy is \emph{retained} in the process of its evolution into a soliton shape, only a small share of the energy being lost into radiation, which is opposite to what occurs in the usual BG model with cubic nonlinearity.Comment: 15 pages, 4 figures, Physics Letters A (in press

Turning light into a liquid via atomic coherence

We study a four level atomic system with electromagnetically induced transparency with giant $\chi^{(3)}$ and $\chi^{(5)}$ susceptibilities of opposite signs. This system would allow to obtain multidimensional solitons and light condensates with surface tension properties analogous to those of usual liquids

Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

In case of the nonlinear Schr\"odinger equation with designed group velocity dispersion, variable nonlinearity and gain/loss; we analytically demonstrate the phenomenon of chirp reversal crucial for pulse reproduction. Two different scenarios are exhibited, where the pulses experience identical dispersion profiles, but show entirely different propagation behavior. Exact expressions for dynamical quasi-solitons and soliton bound-states relevant for fiber communication are also exhibited.Comment: 4 pages, 5 eps figure

Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation

We investigate stability of (2+1)-dimensional ring solitons of the nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. Computing eigenvalues of the linearised equation, we show that rings with spin (topological charge) s=1 and s=2 are linearly stable, provided that they are very broad. The stability regions occupy, respectively, 9% and 8% of the corresponding existence regions. These results finally resolve a controversial stability issue for this class of models.Comment: 10 pages, 5 figures, accepted to Phys. Lett.

Partially incoherent optical vortices in self-focusing nonlinear media

We observe stable propagation of spatially localized single- and double-charge optical vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of partially incoherent light carrying a phase dislocation, and they are stabilized when the spatial incoherence of light exceeds a certain threshold. We confirm the vortex stabilization effect by numerical simulations and also show that the similar mechanism of stabilization applies to higher-order vortices.Comment: 4 pages and 6 figures (including 3 experimental figures

On the theory of adiabatic field dynamics in the Kerr medium with distributed gain and dispersion

A general theory is presented for the adiabatic field evolution in a nonlinear Kerr medium with distributed amplification and varying dispersion. Analytical expression is derived linking parameters of the adiabaticity, gain distribution, and dispersion profile. As a particular example, an optical pulse compressor based on the adiabatic dynamics is examined

Stable ring vortex solitons in Bessel optical lattices

Stable ring vortex solitons, featuring a bright-shape, appear to be very rare in nature. However, here we show that they exist and can be made dynamically stable in defocusing cubic nonlinear media with an imprinted Bessel optical lattice. We find the families of vortex lattice solitons and reveal their salient properties, including the conditions required for their stability. We show that the higher the soliton topological charge, the deeper the lattice modulation necessary for stabilization.Comment: 14 pages, 4 figures, submitted to Physical Review Letter

Radially symmetric and azimuthally modulated vortex solitons supported by localized gain

We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We uncover that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.Comment: 11 pages, 4 figures, to appear in Optics Letter

Non-quantum liquefaction of coherent gases

We show that a gas-to-liquid phase transition at zero temperature may occur in a coherent gas of bosons in the presence of competing nonlinear effects. This situation can take place both in atomic systems like Bose-Einstein Condensates in alkalii gases with two and three-body interactions of opposite signs, as well as in laser beams which propagate through optical media with Kerr (focusing) and higher order (defocusing) nonlinear responses. The liquefaction process takes place in absence of any quantum effect and can be formulated in the frame of a mean field theory, in terms of the minimization of a thermodynamic potential. We also show numerically that the effect of linear gain and three-body recombination also provides a rich dynamics with the emergence of self-organization behaviour.Comment: 6 pages, 5 figures. Submitted to Physica D: Nonlinear Phenomen