Rotational Doppler effect of vortex beam with frequency-shifted laser feedback

We propose and demonstrate a rotational Doppler measurement system based on frequency-shifted laser feedback interferometry. The system utilizes a vortex beam as the probe, which is modulated by the target and then reflected back into the laser cavity. Compared with the conventional rotational Doppler methods, this approach effectively enhances the amplitude of the generated beat signal through intra-cavity interference between the echo signal and local oscillator. Consequently, it improves sensitivity in weak-signal detection and enables measurement with low probe-beam power. A signal to noise (SNR) enhancement of over 15 dB was observed compare to the Mach-Zehnder structure. This system inherits the advantages of rotational Doppler effect, possessing the capacity to get a frequency proportional to the topological charge of vortex. Experimental validation demonstrates accurate measurement of rotational angle and velocity, with the ability to distinguish rotational direction through heterodyne detection. For vortices with topological charge ranging from 18 to 21 and rotational speeds in range of 150 to 600 revolutions per minute (RPM), the measurement error is within +/- 3 RPM. Overall, the proposed system possesses high sensitivity to echo signal, low photon consumption, and direction information availability, which provides a new approach for optimizing the rotational Doppler effect in practical applications.