Features of vortex high harmonics generated by the Laguerre-Gaussian beam with nonzero radial node

High harmonic generation (HHG) with orbital angular momentum in the extreme ultraviolet could be produced by the interaction between vortex ultrafast infrared laser pulse and gas medium. In this paper, Laguerre-Gaussian (LG) beam with nonzero radial node was used as the driving laser. And through computing the single-atom response with the quantitative rescattering model, distributions of intensity and phase of HHG in the near and far fields were obtained by solving the three-dimensional Maxwell’s equation in the medium and the Huygens’ integral in the paraxial approximation, respectively. With the increase of the radial node in the driving laser, it is indicated that the distribution of HHG intensity shows the multiple-ring structure, the radial-node structure appears in the distribution of HHG phase, and the spatial region of intensity distribution is decreased in the near field, but increased in the far field. The phase-matching analysis showed that maps of spatial coherence length of short- and long-trajectory HHG are very sensitive to the mode of driving laser, qualitatively consistent with the maps of evolution of HHG field inside gas medium, which explained the features of vortex HHG under the LG beam with nonzero radial node.