TRANSFORMATION OF A TWODIMENSIONAL FINITE ENERGY AIRY BEAM BY AN ABCD OPTICAL SYSTEM WITH A RECTANGULAR ANNULAR APERTURE
L. Ezzariy^{1}, H. Nebdi^{1}, M. Boustimi^{2}, 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 , * Corresponding authors: belafhal@gmail.com Received: 15 January 2014; revised version accepted: 02 March 2014
Abstract This paper deals with the propagation of a twodimensional finite Airy beam through a rectangular aperture followed by a paraxial ABCD optical system. Based on the fact that a rectangular hardedged aperture function can be expanded into a finite sum of complex Gaussian functions, and by using the generalized Collins diffraction integral, an approximate analytical expression of propagation properties is derived. From the main finding, the propagation characteristics formulas of the finite Airy beam through an unapertured ABCD optical system, or this last with a rectangular aperture, or a rectangular black screen are deduced. According to the closedform expressions developed the propagation characteristics of finite Airy beam through a free space with a square annular aperture or with a square aperture are illustrated numerically in the work.
Keywords: Finite Airy beam, ABCD Optical system, Rectangular annular aperture, Rectangular aperture, Rectangular black screen, Propagation, Generalized Collins formula, Hard aperture function.

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