A vectorial Doppler effect with spatially variant polarized light fields

The Doppler effect of light was implemented by interference with a reference wave to infer linear velocities in early manifestations, and more recently lateral and angular velocities with scalar phase structured light. A consequence of the scalar wave approach is that it is impossible to deduce the motion direction and position of moving targets directly. Here we overcome this limitation with vectorially structured light, exhibiting spatially variant polarization, allowing both the position and velocity of a particle to be robustly determined by a new vectorial Doppler effect. We use this to successfully implement real time monitoring of instantaneous angular position and velocity of a complicated moving particle, and interpret its physical mechanism as evidence of time reversal symmetry breaking in classically entangled light fields. Our demonstration can easily be extended with arbitrary vector structured fields for complete motion tracking of nontrivial trajectories, offering new vectorial Doppler metrology for universal motion vectors.