Fig. 2: Coherent interference of multiple frequency comb lines leading to the dynamic rotation and revolution.

a \(LG_{\bar \ell ,0}\) beam on a single frequency whose center located at the central axis. b The interferogram of multiple \(LG_{\ell ,p}\) modes with multiple \(\ell\) values and p values carried by a single frequency line. It produces an \(LG_{\bar \ell ,0}\) beam whose beam center is offset from the original central axis. c Combining multiple frequency comb lines with each carrying a superposition of multiple \(LG_{\ell ,p}\) modes (a different \(\ell\) value and multiple p values). Δφ: time-variant relative phase delay between neighboring \(LG_{\ell ,p}\) modes, leading the generated light beam to dynamically revolve around the central axis; Δf: frequency spacing; Δθ: revolving angle; Δt: t1 – t2 is the temporal delay.