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

Abstract

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 three-dimensional 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.