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.
© 2012 Optical Society of America
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