Fig. 4: Simulation results of diffraction effects for a spatiotemporal beam exhibiting both rotation and revolution.

Propagation over distance of an offset conventional LG3,0 in a the near-field and b the far-field for t = 0. Propagation along distance of a rotating-revolving LG3,0 in c the near-field and d the far-field for t = 0. The first and second rows in (a)–(d) are the intensity profiles of the propagating beams and the corresponding interferograms with Gaussian beams, respectively. As the propagation distance increases, the spatiotemporal beam counterclockwise revolves around the central axis. e The mode purity of a generated rotating-revolving LG3,0 beam with different revolving speed (0.02–2 THz) when the propagation distance is varied from 0 to 100zR, where zR = 45.6 mm is the Rayleigh range.