“…Although metasurfaces and multiple microring lasers can form many discrete singularities, and their topological charge can be tuned at will, these approaches require the manufacturing of optical elements through nano-technology. In traditional laser systems, by utilizing a nonlinear process in the gain medium, the transverse mode locking of the same or different frequency-degenerated cavity modes such as Hermite-Gaussian (HG), Laguerre-Gaussian (LG) or Ince-Gaussian (IG) modes with π/2 phase shift forms an array of vortices with topological charge 1 in laser resonator [45][46][47][48][49][50][51][52]. These laser cavities with different schemes, such as off-axis pumping [45], shaped pumping [48][49][50], cavity elements misalignment [51], or cavity length [52] to select multi-modes simultaneously lasing, leading the change in the intensity distribution of the output vortex array.…”