Degree of paraxiality for Gaussian vortex beams

The degree of paraxiality for Gaussian vortex beams is studied based on the definition of the degree of paraxiality for monochromatic light beams. By using the angular spectrum representation, the analytical expression for the degree of paraxiality for Gaussian vortex beams is derived, and used to study the dependence of the degree of paraxiality on the Gaussian vortex beam parameters. It is shown that the degree of paraxiality for Gaussian vortex beams increases with increasing the waist width of background Gaussian beams or increasing the off-axis distance of optical vortices, and with decreasing the topological charge of optical vortices. The results are interpreted physically by using the relation between the degree of paraxiality and the far-field divergence angle.