Open AccessThe beam propagation factor and the kurtosis parameter of a Gaussian vortex beam
Author(s) -
Guoquan Zhou
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.174102
Subject(s) - physics , topological quantum number , kurtosis , m squared , paraxial approximation , gaussian , gaussian beam , beam (structure) , vortex , moment (physics) , parameter space , beam diameter , quantum mechanics , optics , geometry , mechanics , mathematics , statistics , laser , laser beams
Based on the definition of the second-order moment of intensity, the analytical expression for the beam propagation factor, namely the M2 factor, of a Gaussian vortex beam is derived, which is uniquely determined by the topological charge n. The numerical result indicates that the M2 factor of a Gaussian vortex beam increases with the increase of topological charge n. By means of the higher-order moment of intensity, the analytical expression for the kurtosis parameter of a Gaussian vortex beam passing through a paraxial ABCD optical system is also presented, which depends on topological charge n, parameter δ, transfer matrix elements A and D. When propagating in free space, the kurtosis parameter of a Gaussian vortex beam is determined by topological charge n and parameter δ. With the increase of parameter δ, the kurtosis parameter of a Gaussian vortex beam in free space first decreases and finally tends to a minimal value. Moreover, the kurtosis parameter of a Gaussian vortex beam in free space decreases with the increase of topological charge n. This research is helpful for the practical application of the Gaussian vortex beam.