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Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

We study numerically and experimentally the process of cascaded four-wave mixing of a vortex beam imposed on short laser pulses propagating in a gas cell. We demonstrate that such cascaded nonlinear process leads to the generation of white-light optical vortices with well preserved vortex phase profile.

Optical vortices (OVs) are singular optical beams with a spiral phase dislocation in their wavefront. When two pump beams at the frequencies1 and2 interact in a Kerr-type nonlinear medium, the degenerate four-wave mixing (FWM) process results in the generation of new distinct sum and difference frequency components at the output. Importantly, the FWM process is expected to preserve the topological charge of the OVs, and thus it can be employed for the generation of white-light vortices, in contrast to the vortex propagation in a Raman nonlinear medium [1]. However, as the FWM process is accompanied by noticeable nonlinear instabilities due to self- and cross-phase modulation, the phase information in the newly generated frequency components may be destroyed [2]. Therefore, it is important to reveal the possible regimes where the FWM process will dominate nonlinear instabilities, leading to the stable generation of white-light optical vortices.

We study numerically and experimentally the propagation of pulsed singular beams, including dark crosses and optical vortices, in self-focusing nonlinear media, resulting in filamentation and supercontinuum generation. Our results show that the singular beams survive the process of modulation instability and appear well preserved in both the near and far field.

We employ an optical vortex beam for the generation of femtosecond supercontinuum in a solid state medium. We demonstrate that the continuum generation process is initiated by the filamentation of the vortex, resulting in a spatially divergent continuum. Despite the strong self-focusing and the formation of multiple hot-spots along the vortex ring, the singularity is preserved in both the near- and far-fields.

We study the ability of beams with complex phase dislocations to guide and steer signal beams in self-focusing nonlinear media. In particular, we report on the experimental demonstration of signal deflection by beams carrying step-screw phase dislocation

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.

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.

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.

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.

We present the first observation of simultaneous spatio-spectral localization and formation of a supercontinuum gap soliton in an optical waveguide array, demonstrating new possibilities for tunable reshaping of polychromatic light in nonlinear periodic photonic structures.