Diffraction of Finite AiryHermiteGaussian Beams by an Apertured Misaligned Optical System
A. A. A. Ebrahim^{1}, L. Ezzariy^{1}, M. Boustimi^{2}, A. Chafiq^{3}, H. Nebdi^{1}, A. Belafhal^{1}* ^{1}Laboratory of Nuclear, Atomic and Molecular Physics P. B 20, 24000 ^{2 }Physics Department, College of Applied Sciences, Umm P.O. Box : 715 , ^{3} CRMFE de Safi, 46000, Safi, Morocco * Corresponding author. Email: belafhal@gmail.com Received: 14 December 2013; revised version accepted: 05 July 2014
Abstract An analytical expression to study the propagation properties of an AiryHermiteGaussian beam passing through an apertured misaligned optical system is developed, in this paper, by using the generalized HuygensFresnel diffraction integral and by means of expansion of the hardedged aperture into a finite sum of complexGaussian functions. Some particular cases are deduced from the main theoretical formalism of our work. The propagation characteristics of the considered beam through an apertured aligned and misaligned circular thin lens are investigated numerically. The results of this finding show that the output beam shape remains unchanged and similar to that of the incident beam. However, it is slightly decentred in x or/and y directions and its deflection is related to the misalignment parameters.
Keywords: Generalized HuygensFresnel diffraction integral; AiryHermiteGaussian beam; Aligned optical system; Misalignment; Circular aperture; Circular thin lens.

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