We study numerically the statistics of the formation of local intensity maxima in the focal plane of a collecting lens after a Gaussian beam passes through a spiral phase transparency in the presence of amplitude‒phase noise in the beam. It is shown that when the amplitude of field fluctuations is about 15

The results of experimental and theoretical study of the self-action of femtosecond optical vortices in the region of anomalous group velocity dispersion in fused silica and fluorides are presented. Multiple filamentation of an axially asymmetric annular beam with a phase dislocation of topological charge m = 1 at a wavelength of 1800 nm in a LiF crystal is investigated. It is found that for the experimentally recorded intensity profile of a vortex beam with two maxima on the diameter, the critical self-focusing power is approximately two times larger than the critical power of a unimodal Gaussian beam. In pulses with supercritical power in the vicinity of the intensity maxima, two coupled filaments, separated by a phase dislocation, are formed on the annular profile of the optical vortex, which prevents energy exchange during their formation. The length of vortex-beam plasma channels in a single pulse is found to be about 300 μm at a diameter of about 2 μm, which is close to the characteristics of plasma channels in a Gaussian beam.

We numerically study the dynamics of the formation of optical vortex from collimated Gaussian beam behind a spiral phase plate, and assess the characteristic scale of azimuthal instability developing in a Kerr medium. The near zero values of intensity on axes arise shortly after the plate but the ring profile is formed at the distance of approximately half of the diffraction length. The break-up of the vortex into several hot spots in the Kerr medium is more rapid for the large-scale noise. The transformation of the vortex spatial spectrum is analyzed along with changes in its phase profile. The interference of the self-focusing mode and the radiation extending to the periphery leads to the formation of rings in the beam spectrum.

We numerically studied the transformation of Gaussian beam passed through phase plate with singularity into vortex beam. The modulation instability development in the vortex beam was studied for different noise parameters.

Filamentation of powerful femtosecond beams with a vortex of the topological charge l = 2 in sapphire is studied. A method to control the azimuthal position of filaments by changing the phase difference between two coherent co-axial beams, vortex and vortex-free reference ones, is proposed and demonstrated. The observed misalignment between the paths of filaments generated by the vortex and vortex-free beams, when they cross at a small angle is explained in terms of the spiral propagation of filaments around the vortex optical axis.

An influence of pass-through optics on femtosecond laser pulse filamentation in ambient air is analyzed for the first time both experimentally and numerically. Propagation of high-power femtosecond laser pulse through solid optical elements introduces spatiotemporal phase modulation due to the Kerr effect. This modulation may have a strong ef-fect on the pulse filamentation in air. We demonstrated that the phase modulation obtained in the thin pass-through dielectric plate reduces the distance to the filament onset and increases the plasma channel length

The filamentation of focused beams at wavelength of 800 and 248 nm in air is studied experimentally and numerically. The results indicate that relatively tight focusing can lead to the coalescence of individual regions of high fluence and high plasma density that result from multiple refocusing, whereas in the case of weak focusing such regions are separated in the pulse propagation direction. The lower multiphoton ionization order in the case of UV radiation leads to a stronger effect of geometric focusing on filament formation. We show the possibility to control the parameters of femtosecond laser plasma filaments by introducing astigmatism in laser beam wavefront. Strong astigmatism can lead to the splitting of the channel into two separate regions. We demonstrate that the self-phase modulation in the thin passthrough dielectric plate decreases the distance to the filament start in air and increases the length of plasma channel.

Propagation of high-power femtosecond laser pulse in transparent dielectric medium leads to beam filamentation [1]. Filamentation of collimated beams is widely studied by different scientific groups [1], unlike the propagation of tightly focused laser pulses. Experiment [2] showed that very tight beam focusing leads to dense plasma region generation in geometrical focal area. Also tight focusing [3] can result in plasma channels passing through system focal plane. Hypothesis of energy reservoir, sustaining extended filament existence in case of collimated beam, was proved in experiment [4]: placing of a small diaphragm, passing only high energy beam core and absorbing peripheral parts of the pulse, led to filament termination. Energy reservoir role in filamentation of focused beam has not been studied before, so we experimentally and numerically studied the reservoir influence on plasma channel formation in case of tight beam focusing.

The influence of the energy reservoir on plasma channel formation during the filamentation of tightly focused femtosecond laser beams was studied both experimentally and numerically. It was found that for the reservoir localized near the propagation axis, its diameter is much smaller than in the case of a collimated beam and decreases in the vicinity of the focus. A small diaphragm placed in the focal area does not eliminate the plasma channel behind the focal point.

We have demonstrated experimentally and numerically the possibility of controlling parameters of plasma channels formed during filamentation of a femtosecond laser pulse by introducing astigmatism in the laser beam wavefront. It is found that weak astigmatism increases the length of the plasma channel in comparison with the case of aberration-free focusing and that strong astigmatism can cause splitting of the plasma channel into two channels located one after another on the filament axis.

Filamentation of focused femtosecond laser pulse in the vicinity of the geometric focus is studied both theoretically and experimentally.

Influence of transparent dielectric media in the beam optical path on plasma channel characteristics formed during intense femtosecond laser pulse filamentation was numerically and experimentally studied. Total length of plasma channel proved to be longer with additional pass-through optics.

The filamentation of IR and UV laser pulses has been studied numerically and experimentally for different initial beam focusing geometries, and linear electron density profiles along the plasma channel of filaments have been obtained. The results demonstrate that changes in laser beam focusing have a stronger effect on filament and plasma channel parameters for UV radiation than for IR radiation. Focusing causes individual high fluence regions produced by refocusing to merge to form a continuous extended filament with a continuous plasma channel.

The interaction of two coherent femtosecond laser pulses, propagating at a small angle with respect to each other in a sapphire crystal in the filamentation regime, has been investigated numerically and experimentally. Distributions of the fluence and free-electron density in the laser-plasma channels formed in the crystal are obtained. Additional filaments are found to form outside the plane of initial pulse propagation.

Modification of Zn-containing H-ZSM-5 pentasil by tin and lead reduces the yield of C10+ aromatic hydrocarbons from alkanes C3–C4. The high selectivity of formation of the aromatization products is retained.

The results of a comparative study of the catalytic properties of gallium and platinum pentasil (ZSM-5) zeolites, prepared according to the solid-state modification and impregnation techniques, in the ethane aromatization reaction are reported. It has been found that the procedure for the preparation of bimetallic catalysts has no substantial effect on their activity and selectivity for aromatic hydrocarbons. The formation of the active sites of the catalysts obtained by solid-state modification was investigated with the use of X-ray diffraction and X-ray photoelectron spectroscopy, and it has been supposed that Ga-Pt clusters similar to the species revealed earlier in bimetallic pentasil catalysts prepared by impregnation are produced as a result of topochemical reactions involving hydrogen. Based on the catalytic and physicochemical data, a reaction scheme for the ethane aromatization on Ga-Pt/HZSM-5 is proposed, which suggests the involvement of bimetallic clusters in a key step, the dehydrogenation of ethane followed by the formation of ethylene oligomers and their dehydrocyclization.