Direction-discriminated rotational Doppler velocimetry with circularly polarized vortex beams

The rotational Doppler effect can be exploited in laser rotational Doppler velocimetry to detect the angular velocity of a moving object. Recently, its vectorial counterpart was revealed, which uses vectorial polarization fields and shows the potential to retrieve the full vectorial motion information of a moving object. Here, we further develop the general model for direction-discriminated rotational Doppler velocimetry by considering two optical degrees of freedom (DoFs), i.e., the orbital angular momentum (OAM) and polarization. Analyses indicate that the two optical DoFs of light play different roles in rotational velocity measurement. On the one hand, the OAM DoF enables the detection of the magnitude of rotational velocity; on the other hand, the circular polarization DoF facilitates the determination of the rotation direction by analyzing the relative phase difference between two intensity signals of the superposed light field after two polarizers. We demonstrate an interferometric scheme with two orthogonally circularly polarized beams of opposite OAM for detecting a rotating small object. These demonstrations may provide abundant alternatives for achieving robust Doppler velocimetry in more complicated sensing and metrology applications.