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 $m$. The beam propagation factor is determined by the beam order $n$ and the topological charge $m$. With increasing the topological charge $m$, the beam propagation factor increases. However, the effect of the beam order $n$ on the beam propagation factor is associated with the topological charge $m$. 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 $ABCD$ optical system has been presented. The kurtosis parameter is determined by the beam order $n$, the topological charge $m$, and the position of observation plane $ \eta $. The influence of the beam order $n$ on the kurtosis parameter is related with the topological charge $m$ and the position parameter $ \eta $. When the beam order $n$ is larger than 1, the kurtosis parameter in different observation $\eta$-planes decreases and tends to a stable value with increasing the topological charge $m$. When $m = \pm {2}n$, the kurtosis parameter is independent of the position parameter $ \eta $ and keeps unvaried during the beam propagation. Regardless of the values of $n$ and $m$, the kurtosis parameter must tend to a saturated value or a stable value as the position parameter $ \eta $ increases to a sufficiently large value. This research is beneficial to the practical application of a hollow vortex Gaussian beam.

© 2019 Optical Society of America

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