Fig. 1. Generating a spatiotemporal beam exhibiting both dynamic rotation and revolution.

a, b Illustration of a light beam that dynamically rotates around its beam center and revolves around another central axis; this is analogous to the earth orbiting around the sun, exhibiting both rotation around its Earth center and revolution around the solar central axis. c, g A Gaussian beam on a single frequency exhibits no dynamic rotation/revolution. d, h An LG_3,0 beam on a single frequency exbibits only dynamic rotation. e, i Using multiple frequency comb lines, in which each carries an $L{G}_{\ell ,p}$ mode with a different $\ell$ value and the same p value, to generate a Gaussian-like beam dot exhibiting only revolution around a central axis. f, j Using multiple frequency comb lines, in which each carries a superposition of multiple $L{G}_{\ell ,p}$ modes with one different $\ell$ value and multiple p values, to generate an LG_3,0 beam exhibiting both dynamic rotation and revolution.