Georgi Maleshkov

Supercontinuum generation with optical vortices

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.

Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams.

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.

Filamentation and supercontinuum generation by singular beams in self-focusing nonlinear media

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.

White light generated by femtosecond optical vortex beams

In this work we report detailed experimental and numerical investigation of the white light generation by singly and doubly charged optical vortices propagating in a Kerr medium, where spectral broadening and transfer of topological charge (TC) into emerging spectral satellites take place due to self-phase modulation and degenerate four-wave frequency mixing (FWFM). Experiments performed with different pump beams show excellent agreement with theory. Singly and doubly charged white light vortices are observed within more than ±200  nm bandwidth after nonlinear propagation in Argon gas. Our experiment and theory data confirm that the TC transformation of the newly generated spectral components follows a law analogous to the one for energy conservation in the FWFM process. We also present results on the white light vortex stability.

Fractional vortex dipoles of edge-screw type in self-focusing Kerr nonlinear media

In this work we study the evolution of dark beams of finite length carrying edge-screw phase dislocations in selffocusing Kerr nonlinear media aiming to find appropriate conditions to control the process of filamentation of the background beam. In the case of a single fractional vortex dipole, geometry-controlled conditions for changing the intensity ratio of the peaks and their offset are found. Depending on their orientation, two parallel or two in-line mixed phase dislocations carried by a common background beam are predicted to perturb it and to initiate filamentation of different number of peaks with different spatial distributions.

Degenerate four-wave mixing of optical vortices assisted by self-phase and cross-phase modulation

We study theoretically the non-phase-matched degenerate four-wave mixing of type ωs = 2ω1 ωω2 , involving beams carrying two-dimensional spatial phase dislocations in the form of singly-charged optical vortices (OVs). Accompanying third-order nonlinear processes in the non-resonant nonlinear medium (NLM), which are accounted for, are self- and cross-phase modulation. In the case of pump OV beams with identical topological charges the model predicts the generation of signal beams carrying OVs of the same charge. If the pump beams carry OVs with opposite charges, the generated signals are predicted to carry triply charged vortices which, in the case of a nonnegligible initial free-space propagation from the plane of vortex generation to the NLM, decay inside the NLM into three singly-charged vortices with highly overlapping cores.

Self-focusing and filamentation of optical vortex beams: Spatio-temporal 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.

Initiating self-focusing of beams carrying spatial phase singularities

In this work, we show both experimentally and by numerical simulations that the presence and evolution of a ring dark beam and/or an on-axis optical vortex nested on a bright background beam noticeably perturb the host background. In a photorefractive nonlinear medium (crystal SBN) these perturbations can initiate self-focusing of the background. By changing the dark ring radius and the presence of an optical vortex and keeping all other experimental parameters unchanged, we can control the dynamics at the initial stage of longitudinal self-focusing and the type of self-focusing structure (single peak or bright ring of variable radius). The presented results may appear especially important in experiments that involve cascaded nonlinear frequency mixing of singular beams, in which accelerated dark beam spreading is accompanied by self-focusing of certain portions of the perturbed host beam.

Controllable bright beam self-focusing initiated by singular dark beams

We study by computer simulations the initial stage of bright background beam self-focusing initiated by the energy density redistribution due to the presence of optical vortex and/or ring dark wave. Local self-focusing Kerr nonlinear medium is considered. When a single ring dark wave is nested on the background, ring radius-to-width ratio Δ=2 promises up to 4 times peak intensity increase at a propagation distance of 2 dark beam diffraction lengths. Δ=6 seems adequate when flat-toped super-Gaussian beam is desired. Self-focusing in bright rings of different radii and even in two coaxial rings (at Δ=3) is observed when initially optical vortex and ring dark wave are simultaneously nested on the background. The detailed numerical analysis of the evolution of azimuthal perturbations confirmed the physical intuition that self-focusing rings of small radii suffer much less (when at all) from ring filamentation, because the spatial frequency of the perturbations on the inner rings appear higher than the critical one.

Branching probe beams by fractional vortex dipoles: guiding vs. anti-guiding

In this work we study the evolution and interaction of semi-infinite dark beams carrying edge-screw phase dislocations in self-focusing and self-defocusing local Kerr nonlinear media aiming to find appropriate conditions to control the process of fusion/crossing the dark beams in a way suitable for probe-beam cross-switching. We show that a quasi-infinite vortex dipole (dipole much longer than the background beam) evolves into a one-dimensional dark spatial soliton with vanishing transverse velocity. Single semi-infinite fractional dipole develops snake instability near the dark beam end. Depending on their phase profiles, four parallel semi-infinite fractional vortex dipoles aligned to initially form two dark stripes can evolve into two different ‘cross-connects’ able to branch and route probe optical beams. Perpendicular probe beam propagation in the optically-induced guiding structures is modeled and analyzed with respect to the branching efficiency to respective virtual output channels for both self-focusing and self-defocusing conditions.