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 ℓ 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 ℓ = 1 , 2, 5, and 10 over a range of spatial bandwidths.