Diffraction of Finite Airy-Hermite-Gaussian Beams

by an Apertured Misaligned Optical System


A. A. A. Ebrahim1, L. Ez-zariy1, M. Boustimi2, A. Chafiq3, H. Nebdi1, A. Belafhal1*

1Laboratory of Nuclear, Atomic and Molecular Physics
Department of Physics, Faculty of Sciences, Choua´b Doukkali University,

P. B 20, 24000 El Jadida, Morocco

2 Physics Department, College of Applied Sciences, Umm Al-Qura University,

P.O. Box : 715 , Makkah 21955, Saudi Arabia.

3 CRMFE de Safi, 46000, Safi, Morocco

* Corresponding author. E-mail: belafhal@gmail.com

Received: 14 December 2013; revised version accepted: 05 July 2014



     An analytical expression to study the propagation properties of an Airy-Hermite-Gaussian beam passing through an apertured misaligned optical system is developed, in this paper, by using the generalized Huygens-Fresnel diffraction integral and by means of expansion of the hard-edged aperture into a finite sum of complex-Gaussian 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 Huygens-Fresnel diffraction integral; Airy-Hermite-Gaussian beam; Aligned optical system; Misalignment; Circular aperture; Circular thin lens.



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