Non-paraxial propagation of a circular Lorentz-Gauss vortex beam.

The optical field of a circular Lorentz-Gauss vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integrals. The expression of the longitudinal component of the angular momentum density of a circular Lorentz-Gauss vortex beam is also presented. The normalized intensity, the three components of intensity, and the longitudinal angular momentum density of a circular Lorentz-Gauss vortex beam are demonstrated in the reference plane, respectively. The effects of linearly polarized angle, topological charge, and Lorentzian width parameter on the intensity, the three components of intensity, and the longitudinal angular momentum density are analyzed, respectively. The normalized intensity and the longitudinal angular momentum density of a paraxial circular Lorentz-Gauss vortex beam are also shown in the same reference plane. The missing longitudinal component of the optical field will result in deficient patterns of the intensity and the longitudinal angular momentum density. In terms of the longitudinal angular momentum density, the longitudinal component of a circular Lorentz-Gauss vortex beam cannot be neglected under the condition that the Lorentzian width parameter and the Gaussian waist are of the order of the optical wavelength.