Self-mixing rotational Doppler effect for spinning velocity detection

The Doppler effect is a well-known phenomenon which has been widely applied in many areas. Less well-known than the traditional linear Doppler effect, the rotational Doppler effect (RDE) which arises from the transverse motion between the wave source and the object has attracted a lot of attention in recent years. Here, we report on the demonstration of RDE in a laser self-mixing framework and provide high-sensitivity, auto-alignment rotational velocity (magnitude and direction) detection. This novel self-mixing rotational Doppler detection scheme is different from the existing rotational Doppler detection schemes, with its light source also acts as a signal amplifier. Further, in the vortex retarder-based self-mixing interferometry, we find that the feedback light experience twice the rotational Doppler shift compared to traditional RDE detection methods. At the same time, the direction of rotation can be discriminated with the help of the light frequency modulators, i.e., we can realize the detection of velocity vectors. We demonstrate the mode selection properties of the self-mixing detection framework and successfully realized the high signal-to-noise ratio measurement of the rotational speed, which is expected to greatly expand the detection capability of the RDE-based metrology in the long-range and weak signal detection conditions. This demonstration is of significance as it provides us with insight into the production of the RDE in the new regimes.