Beam propagation factors and kurtosis parameters of a Lorentz-Gauss vortex beam

Based on the second-order and the higher-order moments, analytical expressions for the beam propagation factors of a Lorentz-Gauss vortex beam with l=1 have been derived, and analytical propagation expressions for the kurtosis parameters of a Lorentz-Gauss vortex beam with l=1 through a paraxial and real ABCD optical system have also been presented. The M² factor is determined by the parameters a and b and decreases with increasing the parameter a or b. The M² factor is validated to be larger than 2. The kurtosis parameters depend on the diffraction-free ranges of the Lorentz part, the parameters a and b, and the ratio A/B. The kurtosis parameters of a Lorentz-Gauss vortex beam propagating in free space are demonstrated in different reference planes. In the far field, the kurtosis parameter K decreases with increasing one of the parameters a and b. Upon propagation, the kurtosis parameter K first decreases, then increases, and finally tends to a saturated value. In any case, the kurtosis parameter K is larger than 2. This research is beneficial to optical trapping, guiding, and manipulation of microscopic particles and atoms using Lorentz-Gauss vortex beams.