Propagating free-space nonparaxial beams

We use a method based on the simultaneous combination of the propagation operator and the Fourier transform with arbitrary index in propagating the transverse component of a nonparaxial beam in free space from an arbitrary initial transverse field structure. Being an iterative method, this approach can easily be implemented computationally. As an example of its efficiency, we derive the closed-form nonparaxial corrections to a Bessel-Gaussian beam, showing that our results differ strongly from those reported previously. The validity of our approach is supported by an analysis of the paraxiality estimator recently introduced in the literature.