Zhou G, Feng S, Xu Y, Zhou Y. Beam propagation factor and kurtosis parameter of hollow vortex Gaussian beams: an alternative method.
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2019;
36:1908-1916. [PMID:
31873709 DOI:
10.1364/josaa.36.001908]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2019] [Accepted: 10/04/2019] [Indexed: 06/10/2023]
Abstract
Based on the second-order moments, an analytical and concise expression of the beam propagation factor of a hollow vortex Gaussian beam has been derived, which is applicable for an arbitrary topological charge $m$m. The beam propagation factor is determined by the beam order $n$n and the topological charge $m$m. With increasing the topological charge $m$m, the beam propagation factor increases. However, the effect of the beam order $n$n on the beam propagation factor is associated with the topological charge $m$m. By using the transformation formula of higher-order intensity moments, an analytical expression of the kurtosis parameter of a hollow vortex Gaussian beam passing through a paraxial and real $ABCD$ABCD optical system has been presented. The kurtosis parameter is determined by the beam order $n$n, the topological charge $m$m, and the position of observation plane $ \eta $η. The influence of the beam order $n$n on the kurtosis parameter is related with the topological charge $m$m and the position parameter $ \eta $η. When the beam order $n$n is larger than 1, the kurtosis parameter in different observation $\eta$η-planes decreases and tends to a stable value with increasing the topological charge $m$m. When $m = \pm {2}n$m=±2n, the kurtosis parameter is independent of the position parameter $ \eta $η and keeps unvaried during the beam propagation. Regardless of the values of $n$n and $m$m, the kurtosis parameter must tend to a saturated value or a stable value as the position parameter $ \eta $η increases to a sufficiently large value. This research is beneficial to the practical application of a hollow vortex Gaussian beam.
Collapse