Propagation of Gaussian vortex beams from aperture-limited optics

We present the first rigorous experimental investigation of the propagation of Gaussian vortex beams, which are Gaussian beams imprinted with a spiral phase, under the realistic condition of an aperture-limited optical system. By combining approximate analytic results with a numerical solution of the paraxial wave equation, we produce a simple empirical model that describes the radius of the vortex singularity and its relationship with the imprinted orbital angular momentum (Formula presented) (Formula presented) and the spatial bandwidth of the optical system. We compare our empirical model with experimental data and show that we achieve excellent agreement for beams with (Formula presented) (Formula presented), 2, 5, and 10 over a range of spatial bandwidths.