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The refocusing of femtosecond laser pulses forming the filament in air is studied both numerically and experimentally. The evolution of fundamental as well as third harmonic pulses and spectra during propagation in the filament is discussed. It is shown that the refocusing of the pulse gives rise to enhanced spectral shifts of fundamental and third harmonic waves.

The large spectral shifts of the fundamental and third harmonic waves (up to 20 nm and 50 nm, respectively) during femtosecond laser pulse filamentation in air have been demonstrated by using focusing lenses of long focal length. It was shown that in a wide range of laser intensities this process does not saturate and linearly depend on the pump pulse energy.

We investigate theoretically the parametric diffraction effect in the two-beam-pumped optical parametric amplifier. The analytical solutions for the signal as well as diffracted beams in the linear regime are obtained. We demonstrate that at large intersection angles the parametric diffraction can be suppressed simultaneously with an increase of conversion efficiency to signal beam when the seed intensity is combined with an intensity of the pump beams. The analytical results are in good agreement with the numerical simulations.

Parametric diffraction at small intersection angles of pump beams is investigated theoretically as well as experimentally in the case of optical parametric amplification. It is revealed that the parametric diffraction can be avoided at smaller critical intersection angles and proper phase difference of the pump beams. In the case of random phase difference of the pump beams the fluctuations in signal energy can be reduced by increasing the seed energy.

Optical parametric chirped pulse amplifiers (OPCPAs) are widely recognized and rapidly developing devices for high-power femtosecond pulse generation. In this paper we reveal the main issues of OPCPA gain bandwidth extension for amplification of pulses with octave-spanning spectra.

We present simple analytical solutions of coupled wave equations describing chirped pulse parametric amplification under pump depletion. The evolution of the duration and spectrum of amplified pulses in OPA pumped by Gaussian and supergaussian pulses has been investigated both numerically and analytically. Also, the dependence of the energy conversion efficiency from pump to signal was determined for a range of parameter values, and an optimum ratio of signal and pump pulse durations was evaluated.

The modifications of an angular spectrum of the intense Bessel J 0 and J 1 beams caused by self-action in the medium with large cubic nonlinearity are investigated. The appearance of an outer ring of triple radius was observed. The phenomenon can be explained as Bragg diffraction of Bessel beam on Bessel lattice in nonlinear medium. Experimental results are in qualitative agreement with the theoretical predictions.

It is revealed that orbital angular momentum can be conserved within the spontaneous parametric down-conversion of higher-order Bessel beam. That is the result of strong transverse selection of spontaneously arising optical fields in optical parametric generator pumped by Bessel beam due to transverse phase-matching of interacting waves in nonlinear medium. A qualitative agreement of theoretical predictions with experimental results is obtained.

A vorticity of the light field created by interference of two intersecting Laguerre–Gaussian singular beams is analysed. It is demonstrated that the number and location of the vortices present in the field depend on the propagation length as well as on the topological charges of the individual beams, their intersection angle and amplitude ratio.

The propagation of a combined beam consisting of two noncoaxial vortex beams is investigated. It is demonstrated that the vortical properties of the combined beam under diffraction depend on propagation length as well as on amplitude ratio of individual beams.

The noncollinear interaction of singular light beams (degenerate four-wave mixing) in Kerr nonlinear medium is analyzed. It is demonstrated that vorticity of diffracted beams significantly depends on the topological charges of pump beams. The results of an experimental observation of the phenomenon are presented.

The parametric amplification of the signal beam with a narrow angular spectrum in the field of an incoherent broadband pump is investigated theoretically as well as experimentally. It is demonstrated that in the absence of beam walk-off a significant enhancement of the parametric gain takes place, and the power of the incoherent pump can be effectively transferred into the signal beam. The background of the signal spectrum appearing in the process of amplification due to pump amplitude fluctuations can be removed by filtering, and the coherence of the input signal can be recovered.

Generation of terahertz (THz) radiation in gaseous media by focused bichromatic femtosecond laser pulses is simple, efficient and well-established technique. However, despite the very high THz field strengths and extremely broadband spectral widths achieved by this method, THz generation efficiency strongly depends on the relative phase difference between two pump waves. Although this phase difference could be easily optimised by adjusting optical path length in the experimental setup, the exact value of this parameter is very useful both in theoretical modelling and in analysis of the experimental data. In the theoretical model, the input wave was a forward-propagating two-colour wave and the relevant Maxwell equations were solved numerically. Calculations show that the obtained maxima of the x-polarised THz wave do not depend on the phase difference. In contrast, significant shifts of the maxima positions have been obtained for the y-polarised THz wave. These findings have been confirmed experimentally, when dependencies of the THz field strength on pump polarisation angle for different fundamental pulse energies have been registered. Note that theoretically obtained results were found to be in good agreement with the experiment only when the nonlinear phase shifts of interacting waves were taken into account. In conclusion, it is shown that even at moderate pump powers the nonlinear Kerr-induced phase shifts of the fundamental and its second harmonic play an important role in THz wave generation from the laser-induced air plasma.

We report on the development of the theory of second-harmonic generation by an incoherent pump with broad angular and frequency spectra. We show that spatial as well as temporal walk-off effects in a nonlinear crystal result in angular dispersion of the second-harmonic radiation. We demonstrate that the acceptance angle in second-harmonic generation by incoherent light is caused by the width of the pump angular spectrum and the resulting angular dispersion of second-harmonic radiation but does not depend on crystal length. In this case the frequency spectrum of second-harmonic radiation is determined by its angular dispersion and the pump angular spectrum. The theory is supported by an experiment in which a LiIO${}_{3}$ crystal was pumped by a tungsten halogen lamp.

It is revealed that the generation of a coherent wave by frequency conversion of incoherent waves is a characteristic feature of three-wave interaction in a nonlinear medium when angular dispersion of input waves is properly chosen. In this case the combining action of the pairs of spectral components of incoherent waves may result in the cumulative driving of a single plane monochromatic wave in up-conversion and down-conversion processes. As a fundamental result we point out an enhancement of the spectral radiance of the generated wave in comparison with incoherent waves.

This study predicts and demonstrates that orbital angular momentum (OAM) is conserved within the spontaneous down-conversion of Bessel vortex beam in optical parametric generators (OPG). Results show that the output radiation of CDA-based OPG pumped by Bessel vortex beam consists of two pairs of OAM-free axial (Gaussian-like) beam and the conical (Bessel-like) beam, the OAM of which is equal to OAM of pump beam. Hence, the OAM is conserved within the spontaneous parametric down-conversion of higher-order Bessel beams in contrary to OPG pumped by Laguerre-Gaussian modes. That is the result of strong transverse selection of spontaneously arising fields in OPG pumped by Bessel beams.

It is revealed that orbital angular momentum can be conserved within the spontaneous parametric down-conversion of higher-order Bessel beam. A qualitative agreement of theoretical predictions with experimental results is obtained.