Simple and effective method for the analytic description of important optical beams when truncated by finite apertures

In this paper we present a simple and effective method, based on appropriate superpositions of Bessel–Gauss beams, which in the Fresnel regime is able to describe in analytic form the threedimensional evolution of important waves as Bessel beams, plane waves, Gaussian beams, and Bessel–Gauss beams when truncated by finite apertures. One of the by-products of our mathematical method is that one can get in a few seconds, or minutes, high-precision results, which normally require quite lengthy numerical simulations. The method works in electromagnetism (optics, microwaves) as well as in acoustics.