High-order harmonic generation in atomic gases driven by a double-ring vortex beam and an optical ring lattice

Orbital angular momentum (OAM) beams have brought the nonlinear light-matter interaction to a novel, to our knowledge, regime. In this work, we investigate the generation of high-order harmonics in atomic gases when the extreme nonlinear optical process is driven by the coaxial superposition of linearly polarized Laguerre-Gaussian (LG) modes. Specifically, we discuss the cases when the waist sizes of the two superposed LG modes are different (double-ring vortex beam) or the same (optical ring lattice). Within the framework of the strong-field approximation (SFA), utilizing the thin-slab model (TSM) and the Fraunhofer diffraction integral, we compute the near- and far-field complex amplitude of the harmonic vortices. Furthermore, we demonstrate the conservation rule for the OAM by examining the far-field divergence and phase profiles. The topological richness present in the resulting superposed beams translates to a well-known OAM selection rule. Moreover, different harmonics are emitted with similar divergence. Our research provides an alternative route to customize the spatial shape of higher-order harmonics with precise control over the OAM and extend the range of application of these exotic beams down to the extreme-ultraviolet (XUV) spectral regime.