Rotational Doppler Effect of Vector Beams

The optical rotational Doppler effect occurs when vortex beams are scattered by rotating objects and demonstrate the Doppler frequency shifts in scattered beams, which are associated with the optical angular momentum of vortex beams and the relative rotating angular velocity. Here, we investigate the rotational Doppler effect of a rotating vector beam in its tight focusing and find that similar Doppler frequency shifts arise when the polarization order and vortex charge satisfy some specific relations. We note that the vortex charge is the indispensable parameter in the rotational Doppler effect of the vector vortex beam. Nonetheless, the sign and magnitude of the frequency shift are only determined by the angular frequency of the rotating beam and are irrelevant to the vortex charge of the beam. In addition, the on-axis energy flow and spin angular momentum in the focal plane can also be well modulated, accompanying the rotational Doppler effect of the vector vortex beam. Our results may be applied to an optical micro-manipulation, especially for some kinds of microparticles which are sensitive to frequency changes.