A 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 3D evolution of important waves as Bessel beams, plane waves, gaussian beams, Bessel-Gauss beams, when truncated by finite apertures. One of the byproducts of our mathematical method is that one can get in few seconds, or minutes, high-precision results which normally require quite long times of numerical simulation. The method works in Electromagnetism (Optics, Microwaves,...), as well as in Acoustics.   OCIS codes: (999.9999) Non-diffracting waves; (260.1960) Diffraction theory; (070.7545) Wave propagation; (070.0070) Fourier optics and signal processing; (200.0200) Optics in computing; (050.1120) Apertures; (070.1060) Acousto-optical signal processing; (280.0280) Remote sensing and sensors; (050.1755) Computational electromagnetic methods. 
Michel Zamboni-Rached, Erasmo Recami, and Massimo Balma
physics.optics physics.comp-ph