Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media

We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant exceeds a certain critical value, that is inversely proportional to the range of nonlocality of nonlinear response. All spinning three-dimensional STSs are found to be unstable.Comment: 14 pages, 6 figures, accepted to PRE, Rapid Communication

Soliton eigenvalue control with optical lattices

We address the dynamics of higher-order solitons in optical lattices, and predict their self-splitting into the set of their single-soliton constituents. The splitting is induced by the potential introduced by the lattice, together with the imprinting of a phase tilt onto the initial multisoliton states. The phenomenon allows the controllable generation of several coherent solitons linked via their Zakharov-Shabat eigenvalues. Application of the scheme to the generation of correlated matter waves in Bose-Einstein condensates is discussed.Comment: 13 pages, 4 figures, to appear in Physical Review Letter

Dynamics of Vortex Dipoles in Confined Bose-Einstein Condensates

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.Comment: 8 pages, 3 figures, to appear in Phys. Lett.

Spatiotemporal discrete multicolor solitons

We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even and twisted stationary solutions are thoroughly characterized and their stability against perturbations is investigated. We show that the twisted and even solutions display instability, while most of the odd solitons show remarkable stability upon evolution.Comment: 18 pages,7 figures. To appear in Physical Review

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable against small perturbations if their energy exceeds a certain critical value, so that the stability domain occupies about 10% of the existence region of the solitons. We also demonstrate that the s=1 solitons are stable against very strong perturbations initially added to them. However, on the contrary to spatial vortex solitons in the same model, the spatiotemporal solitons with s=2 are never stable.Comment: latex text, 10 ps and 2 jpg figures; Physical Review E, in pres

Multicolor vortex solitons in two-dimensional photonic lattices

We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable almost in the entire domain of their existence, and that the instability domain decreases with the increase of the lattice depth. We also show the generation of the solitons, and the feasibility of the concept of lattice soliton algebra.Comment: 18 pages,6 figures. To appear in Physical Review

Electromagnetic surface waves guided by the planar interface of isotropic chiral materials

The propagation of electromagnetic surface waves guided by the planar interface of two isotropic chiral materials, namely materials \calA and \calB, was investigated by numerically solving the associated canonical boundary-value problem. Isotropic chiral material \calB was modeled as a homogenized composite material, arising from the homogenization of an isotropic chiral component material and an isotropic achiral, nonmagnetic, component material characterized by the relative permittivity \eps_a^\calB. Changes in the nature of the surface waves were explored as the volume fraction f_a^\calB of the achiral component material varied. Surface waves are supported only for certain ranges of f_a^\calB; within these ranges only one surface wave, characterized by its relative wavenumber $q$, is supported at each value of f_a^\calB. For \mbox{Re} \lec \eps_a^\calB \ric > 0 , as \left| \mbox{Im} \lec \eps_a^\calB \ric \right| increases surface waves are supported for larger ranges of f_a^\calB and \left| \mbox{Im} \lec q \ric \right| for these surface waves increases. For \mbox{Re} \lec \eps_a^\calB \ric < 0 , as \mbox{Im} \lec \eps_a^\calB \ric increases the ranges of f_a^\calB that support surface-wave propagation are almost unchanged but \mbox{Im} \lec q \ric for these surface waves decreases. The surface waves supported when \mbox{Re} \lec \eps_a^\calB \ric < 0 may be regarded as akin to surface-plasmon-polariton waves, but those supported for when \mbox{Re} \lec \eps_a^\calB \ric > 0 may not

Stable spatiotemporal solitons in Bessel optical lattices

We investigate the existence and stability of three-dimensional (3D) solitons supported by cylindrical Bessel lattices (BLs) in self-focusing media. If the lattice strength exceeds a threshold value, we show numerically, and using the variational approximation, that the solitons are stable within one or two intervals of values of their norm. In the latter case, the Hamiltonian-vs.-norm diagram has a "swallowtail" shape, with three cuspidal points. The model applies to Bose-Einstein condensates (BECs) and to optical media with saturable nonlinearity, suggesting new ways of making stable 3D BEC solitons and "light bullets" of an arbitrary size.Comment: 9 pages, 4 figures, Phys. Rev. Lett., in pres

Two-dimensional solitary pulses in driven diffractive-diffusive complex Ginzburg-Landau equations

Two models of driven optical cavities, based on two-dimensional Ginzburg-Landau equations, are introduced. The models include loss, the Kerr nonlinearity, diffraction in one transverse direction, and a combination of diffusion and dispersion in the other one (which is, actually, a temporal direction). Each model is driven either parametrically or directly by an external field. By means of direct simulations, stable completely localized pulses are found (in the directly driven model, they are built on top of a nonzero flat background). These solitary pulses correspond to spatio-temporal solitons in the optical cavities. Basic results are presented in a compact form as stability regions for the solitons in a full three-dimensional parameter space of either model. The stability region is bounded by two surfaces; beyond the left one, any two-dimensional (2D) pulse decays to zero, while quasi-1D pulses, representing spatial solitons in the optical cavity, are found beyond the right boundary. The spatial solitons are found to be stable both inside the stability region of the 2D pulses (hence, bistability takes place in this region) and beyond the right boundary of this region (although they are not stable everywhere). Unlike the spatial solitons, their quasi-1D counterparts in the form of purely temporal solitons are always subject to modulational instability, which splits them into an array of 2D pulses, that further coalesce into two final pulses. A uniform nonzero state in the parametrically driven model is also modulationally unstable, which leads to formation of many 2D pulses that subsequently merge into few ones.Comment: a latex text file and 11 eps files with figures. Physica D, in pres