Propagation evolution of an off-axis high-order cylindrical vector beam

Abstract

The propagation characteristics of an off-axis high-order cylindrical vector beam (OHCVB) are studied in this paper. The analytic expressions for the electric field and intensity distribution of the OHCVB propagating in free space are presented, to our knowledge for the first time. The transverse intensity of the OHCVB, different from that of the input Gaussian beam, does not have an axially symmetric distribution, owing to a slight dislocation between the polarization singularity located in the vector field generator and the center point of the Gaussian beam. Numerical results show that the intensity distribution during propagation strongly depends on the propagation distance, dislocation displacement, and topological charge. Accompanied by beam expansion, the intensity distribution of the OHCVB tends to eventually become steady, and the dark core of the vector beam will disappear gradually during the process of propagation. Moreover, with the increase of the topological charge, more energy will be transferred from the $x$ axis to the $y$ axis, and the annular intensity is split into two parts along the $y$-axis direction. The results help us to investigate the dynamic propagation behaviors of the HCVB under the off-axis condition and also guide the calibration of the off-axis high-order cylindrical vector field in practice.