Analytical method for the description of important obstructed optical beams and the Poisson-Arago spot

In this work, we describe analytically the diffraction of some important beams due to a circular obstacle. In order to obtain the desired results, we deal with the wave equation in paraxial approximation together with the diffraction Fresnel integral and apply the analytical method proposed by Zamboni-Rached et al. [Appl. Opt.51, 3370-3379 (2012)APOPAI0003-693510.1364/AO.51.003370]. As a byproduct of our method, we notice the formation of the Poisson-Arago spot for ordinary beams (plane wave and Gaussian beam) and a reconstruction of the beam for nondiffracting beams (Bessel beam). Then, we pass to a vectorial analysis for better describing the electromagnetic beams.