TRANSFORMATION OF A TWO-DIMENSIONAL FINITE ENERGY AIRY BEAM BY AN ABCD OPTICAL SYSTEM

WITH A RECTANGULAR ANNULAR APERTURE

 

L. Ez-zariy1, H. Nebdi1, M. Boustimi2, 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

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

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

* Corresponding authors: belafhal@gmail.com

Received: 15 January 2014; revised version accepted: 02 March 2014

 

Abstract

     This paper deals with the propagation of a two-dimensional finite Airy beam through a rectangular aperture followed by a paraxial ABCD optical system. Based on the fact that a rectangular hard-edged 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 closed-form 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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