Vortex Propagation in Orbital Angular Momentum Beams and the Effects of a Limited Aperture

When generating light with orbital angular momentum by imprinting orbital phase onto a standard Gaussian beam, it is often assumed that the propagation of the generated spatial mode is a Laguerre-Gaussian. However, the true propagation of this beam in a realistic, aperture-limited optical system is non-trivial and has not been thoroughly explored in existing literature. We explore a numerical model that shows the development of an optical vortex mode, propagating from the plane of phase modulation, and the relation of these dynamics to the orbital phase factor $\ell$ and the spatial bandwidth of the optical system. The results of this model are compared to experimental data for beams with $\ell$ values 1, 2, 5, and 10 propagating through a range of spatial filters, with the described model showing agreement in the near field regime.