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) [CrossRef] ]. 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.

中文翻译：

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重要受阻光束和泊松-阿拉戈斑描述的解析方法

在这项工作中，我们分析地描述了由于圆形障碍物引起的一些重要光束的衍射。为了获得所需的结果，我们将近轴近似波动方程与衍射菲涅耳积分一起处理，并应用 Zamboni-Rached等人提出的解析方法。[申请。选择。51 , 3370–3379 (2012) [CrossRef] ]。作为我们方法的副产品，我们注意到普通光束（平面波和高斯光束）的泊松-阿拉戈光斑的形成和非衍射光束（贝塞尔光束）的光束重建。然后，我们进行矢量分析以更好地描述电磁波束。