Self-focusing and filamentation of optical vortex beams: Spatiotemporal analysis

We report numerical simulations supported by experimental observations of self-focusing, fillamentation, and supercontinuum generation by an optical vortex beam in a Kerr nonlinear medium in the regime of dominating nonlinearity. Despite the strong self-focusing resulting in multiple filaments ordered along the vortex ring the optical vortex remains well preserved at the exit of the nonlinear medium and in the far-field. The presented quasi-(3+1)- dimensional numerical simulations under azimuthal initial vortex ring perturbations confirm qualitatively the experimentally observed survival of the optical vortex in the course of the white light generation

Bright optical beams in weakly nonlocal media: variational analysis

We employ a variational technique to describe the propagation of a Gaussian beam in a nonlinear, weakly nonlocal medium and derive the conditions for breathing soliton formation in both one and two transverse dimensions. The reduced one-dimensional results agree quantitatively with known exact nonlocal soliton solutions. We subsequently formulate a simple procedure for estimating the strength of a weak nonlocality and verify its applicability by direct numerical simulations

Spatial phase dislocations in femtosecond laser pulses

We show that spatial phase dislocations associated with optical vortices can be embedded in femtosecond laser beams by computer-generated holograms, provided that they are built in a setup compensating for the introduced spatial dispersion of the broad spectrum. We present analytical results describing two possible arrangements: a dispersionless 4 setup and a double-pass grating compressor. Experimental results on the generation of optical vortices in the output beam of a 20 fs Ti:sapphire laser and the proof-of-principle measurements with a broadband-tunable cw Ti:sapphire laser confirm our theoretical predictions.This research was partially supported by the National Science Fund (Bulgaria), under contract F-1303/2003, and the Australian Research Council

Observation of polychromatic vortex solitons

We demonstrate experimentally the formation of polychromatic single- and double-charge optical vortex solitons by employing a lithium niobate crystal as a nonlinear medium with defocusing nonlinearity. We study the wavelength dependence of the vortex core localization and observe self-trapping of polychromatic vortices with a bandwidth spanning over more than 70 nm for single-charge and 180 nm for double-charge vortex solitons.This work was supported by the Australian Research Council through Discovery and Linkage International projects and by the National Science Foundation (NSF)-Bulgaria, project WUF-02/05

Nonlinear dynamics of two-color optical vortices in lithium niobate crystals

We study experimentally the nonlinear dynamics of two-color optical vortex beams in the presence of second-harmonic generation combined with the effects of photo- and thermal refraction, as well as self- and induced-phase modulation.We use an iron-doped lithium niobate crystal as a nonlinear medium for the vortex propagation and observe experimentally, depending on the laser wavelength, a decay of a double-charge vortex, splitting and reshaping of background beam, pattern formation, and controllable nonlinear rotation of a vortex pair

Observation of polychromatic gap solitons

We study theoretically and observe experimentally polychromatic gap solitons generated by supercontinuum light in an array of optical waveguides. The solitons are formed through a sharp transition from diffraction-induced broadening and color separation to the simultaneous spatio-spectral localization of supercontinuum light inside the photonic bandgap with the formation of the characteristic staggered phase structure for all colors

Nonlinear spectral-spatial control and localization of supercontinuum radiation

We present the first observation of spatiospectral control and localization of supercontinuum light through the nonlinear interaction of spectral components in extended periodic structures. We use an array of optical waveguides in a LiNbO3 crystal and employ the interplay between diffraction and nonlinearity to dynamically control the output spectrum of the supercontinuum radiation. This effect presents an efficient scheme for optically tunable spectral filtering of supercontinua

Azimuthal Modulational Instability of Vortices in the Nonlinear Schr\"odinger Equation

We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schr{\"o}dinger (NLS) equation. The method of studying the stability relies on freezing the radial direction in the Lagrangian functional of the NLS in order to form a quasi-one-dimensional azimuthal equation of motion, and then applying a stability analysis in Fourier space of the azimuthal modes. We formulate predictions of growth rates of individual modes and find that vortices are unstable below a critical azimuthal wave number. Steady state vortex solutions are found by first using a variational approach to obtain an asymptotic analytical ansatz, and then using it as an initial condition to a numerical optimization routine. The stability analysis predictions are corroborated by direct numerical simulations of the NLS. We briefly show how to extend the method to encompass nonlocal nonlinearities that tend to stabilize solutions.Comment: 8 pages, 6 figures, in press for Optics Communication

Observation of attraction between dark solitons

We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as Bose-Einstein condensates with repulsive long-range interparticle interaction

Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors

We formulate higher derivative gravity with Lagrange multiplier constraint and scalar projectors. Its gauge-fixed formulation as well as vector fields formulation is developed and corresponding spontaneous Lorentz symmetry breaking is investigated. We show that the only propagating mode is higher derivative graviton while scalar and vector modes do not propagate. Despite to higher derivatives structure of the action, its first FRW equation is the first order differential equation which admits the inflationary universe solution.Comment: Physics Letters B published version. LaTeX 12 page