Angular momentum density of a linearly polarized Lorentz–Gauss vortex beam

Based on the vectorial Rayleigh–Sommerfeld integral formulae, the analytical propagation equation of a linearly polarized Lorentz–Gauss vortex beam is derived in free space. By taking curl of the electric field, the propagating magnetic field of the linearly polarized Lorentz–Gauss vortex beam is also presented. By using the analytical propagation equation of the Lorentz–Gauss vortex beam beyond the paraxial approximation, the analytical expression of the angular momentum density of a Lorentz–Gauss vortex beam is obtained. The effects of the linearly polarized angle and the beam parameters on the three components of the angular momentum density of a Lorentz–Gauss vortex beam are analyzed in detail. The two transversal components of the angular momentum of a Lorentz–Gauss vortex beam beyond the paraxial approximation must be zero in an arbitrary reference plane. The longitudinal component of the angular momentum is determined by the linearly polarized angle and the beam parameters. The distributions of the angular momentum densities of the Lorentz–Gauss vortex beam are also compared with those of the Gaussian vortex beam. This research is very useful to the optical trapping, the optical guiding, and the optical manipulation of microscopic particles using the single mode diode laser beams.