“…With a wide OAM spectrum, the vortex beam can be used in the ultrasensitive angular measurement, [25] the generation of arbitrary su-perpositions of atomic rotational states in a Bose-Einstein condensate, [26] the measurement of object parameters, [27] the performance of rotations and reflections on images, [28] and so on. To generate OAM spectra in the infrared (IR) and visible spectral ranges, there are several methods available including computer-generated holograms on the spatial light modulators, [29] specially designed metasurfaces, [30] integrated angular momentum gratings, [31,32] and coherent mixing of pre-generated vortex beams. [33] However, using optical elements is difficult to generate and tailor the OAM spectrum of light in the extreme ultraviolet (XUV) or soft x-rays.…”