Propagation of a Lorentz–Gauss vortex beam through a paraxial ABCD optical system

Based on the Collins integral, an analytical expression of a general Lorentz–Gauss vortex beam passing through a paraxial ABCD optical system is derived by means of the mathematical technique. As a numerical example, the normalized intensity distribution, the phase distribution, and the orbital angular momentum density distribution of Lorentz–Gauss vortex beams propagating in free space are graphically demonstrated. The influences of Gaussian waist, the width parameters of Lorentzian part, and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density distribution of Lorentz–Gauss vortex beams propagating in free space are discussed in detail. This research is useful to the optical trapping, guiding, and manipulation of microscopic particles involved in the single mode diode laser beams.