The radial Doppler effect of optical vortex beams induced by a surface with radially moving periodic structure

Recent studies have highlighted that the rotational Doppler effect arises from rotational motion and optical orbital angular momentum (OAM), which has potential to detect rotating objects. Here, we investigate the frequency shift when an OAM beam is scattered from a surface with a radially periodic structure moving in the radial direction. This kind of frequency shift is related to the radial velocity and the harmonic components of the radially periodic structure of the surface. We support our conclusion by means of calculating time-evolution phase of light beam theoretically and measuring the rotating interference patterns through coherent detection. Furthermore, a more general theoretical model for the complex frequency shift resulting from the concurrence of both the angular and radial Doppler effects, is proposed. The complex frequency shift characteristics are associated with harmonic components and the velocity of the structural surface in both radial and angular directions. Interestingly, the frequency shift resulting from the moving surface may be spatially variant, because of the combination of the angular and radial Doppler effects. This scheme is useful for analyzing the light-moving matter interaction. Meanwhile, it might be applicable to transverse velocity measurement and frequency modulation.