Spatiotemporal Doppler Effect

ABSTRACT The Doppler effect refers to the frequency shift when there is a relative motion between a wave‐emitting source and an observer. Vortex beams are capable of measuring the rotation frequency of a spinning object whose rotation axis is aligned with the optical axis based on the rotational Doppler effect. Here we demonstrate that spatiotemporal optical vortices with the Poynting vector circling in spacetime can induce a novel Doppler effect. The spatiotemporal Doppler effect features a time‐variant linear frequency shift and a time‐invariant rotational frequency shift. The spatiotemporal Doppler effect enables measurement of the rotation frequency of a spinning object with an arbitrarily oriented rotation axis. Furthermore, when the illumination comprises spatiotemporal vortices of different topological charges, a Doppler frequency shift spectrum is uncovered that consists of the double frequency, sum frequency, and difference frequency of individual Doppler frequency shifts. The observation of the spatiotemporal Doppler effect is a direct manifestation of transverse orbital angular momentum of photons. The multiplicative and multiple frequency shift features of spatiotemporal Doppler effect may find applications in remote sensing of turbulence in hydrodynamics and aerodynamics, and detection of rotating bodies in astronomy.