Analysis of extreme-ultraviolet vortex high-order harmonics generated by few-cycle Laguerre-Gaussian beams carrying orbital angular momentum

Recent advances in generating high-energy, few-cycle, carrier-envelope phase (CEP)-stabilized vortex lasers has opened the possibility of producing novel vortex light sources in the extreme ultraviolet (XUV) and soft x-ray regions via high-order harmonic generation (HHG) in gases. However, this area remians underexplored and poorly understood, both experimentally and theoretically. In this work, we investigate the characteristics of vortex high harmonics driven by few-cycle Laguerre-Gaussian (LG) beams using an improved three-dimensional propagation model in which the nonlinear polarization is efficiently computed via a two-dimensional interpolation method. We demonstrate that the intensity profiles of generated vortex high harmonics exhibit discontinuous bright-spot patterns along the azimuthal direction, and the orbital angular momentum (OAM) carried by the $q\mathrm{th}$ harmonic contains multiple modes with topological charges $\ensuremath{\ge}q{l}_{0}$, where ${l}_{0}$ is the topological charge of the fundamental laser. These features are distinctly different from those observed with long-duration LG beams. Such phenomena arise from the strong CEP dependence of few-cycle laser waveforms, which induces variations in the quantum-trajectory phase accumulated during electron ionization and recombination, effects that are especially pronounced for long trajectories. Additionally, we show that the harmonic intensity profiles, OAM spectra, and helical attosecond pulses depend sensitively on the position of the gas medium. We expect that this work will stimulate further experimental and theoretical investigations into strong-field phenomena driven by few-cycle vortex laser pulses.