Fig. 1: Comparison between the conventional Doppler effect and the structured beam-induced Doppler effects.

a Conventional linear Doppler effect, where a planar phase beam is normally incident on a moving object and the Doppler shift is related to the linear velocity of the object and the phase velocity of the beam. b Rotational Doppler effect (RDE), where a vortex beam with angular wavevector is illuminated onto a spinning object, and the rotational Doppler shift is dependent upon the angular velocity of the object and topological charge of the beam’s orbital angular momentum (OAM). c Structure-shearing Doppler effect (SDE), where a Bessel beam with radial wavevector shines on a moving object and the observed Doppler shift would get an extra redshift compared with (a) due to the superluminal phase velocity of the beam.