Virtual source for Lommel–Gauss beams

We introduce a group of virtual sources for generating Lommel–Gauss beams based on beam superposition to analyze nonparaxial propagation. We typically derive the paraxial approximation and integral representations of the nth-order Lommel–Gauss beams. The first three orders of the nonparaxial corrections for the on-axis field of the Lommel–Gauss beams are analytically obtained. The on-axis intensity distribution of the corresponding nonparaxial corrections is also provided.