Bessel-like beams with controllable rotation of local linear polarization upon propagation are generated, which in fact achieve the evolution of polarization states along the equator of the Poincaré sphere during propagation. Based on the amplitude–phase joint modulation method, the rotation direction and rate of polarizations of the Bessel-like beam can be controlled easily by adjusting the radial indices and intensity ratio of two superposed beams. A rotation angle of ∼ 800 deg has been achieved after a propagation distance of 120 mm, corresponding to a rotation rate of ∼ 6.7 deg/mm, which is about three times higher than in previous works.

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The linear Doppler effect has been widely used to detect the translational motion of objects. However, it suffers difficulties in measuring the angular motion of a rotating target. In recent years, the rotational Doppler effect based on a vortex beam has been helpful to solve the problem of rotational measurement and has attracted extensive attention in remote sensing. This paper expounds the theoretical and experimental basis of the rotational Doppler effect and briefly summarizes its development for the detection of macro and micro targets. Specifically, the properties and analysis methods of a rotational Doppler shift when the vortex beam is misaligned with the rotation axis are described in detail. In addition, the existing problems and further developments in rotation detection based on the rotational Doppler effect are discussed.

The vector optical beam with longitudinally varying polarization during propagation in free space has attracted significant attention in recent years. Compared with traditional vector optical beams with inhomogeneous distribution of polarization in the transverse plane, manipulating the longitudinal distribution of polarization provides a new dimension for the expansion of the applications of vector optical beams in volume laser machining, longitudinal detection, and in vivo micromanipulation. Two theoretical strategies for achieving this unique optical beam are presented in the way of constructing the longitudinally varying phase difference and amplitude difference. Relevant generation methods are reviewed which can be divided into the modulation of complex amplitude in real space and the filtering of the spatial spectrum. In addition, current problems and prospects for vector optical beams with longitudinally varying polarization are discussed.