Propagation Characteristics of Lis Flattened Gaussian Beam Through A Misaligned ABCD Optical System

With A Misaligned Annular Aperture


L. Ez-zariy1, E. M. ElHalba1, M. Boustimi2, H. Nebdi1, M. Khouilid1, A. Belafhal1*

1Laboratory of Nuclear, Atomic and Molecular Physics
Department of Physics, Faculty of Sciences, Chouab 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 author. E-mail:

Received: 09 May2013; revised version accepted: 06 October 2013



     In this paper, an approximate analytical expression for description of the transformation properties of the 2D-Li's Flattened Gaussian beam by a misaligned annular aperture followed by a misaligned paraxial ABCD optical system is developed. The study of the fundamental Gaussian beam through the considered system is derived as a particular case. Yet, the propagation of the Li's Flattened Gaussian and the pure Gaussian beams through an unapertured misaligned optical system or this last with a misaligned circular aperture or a misaligned black screen cases are deduced here, independently, also as special cases of the misaligned annular apertured misaligned optical system case which considered the generalized one. So, other particular cases concerning the Li's Flattened Gaussian beam and pure Gaussian beam travelling an unapertured misaligned (aligned) optical system or coupled with misaligned (aligned) annular aperture, circular aperture or black screen can be derived in the investigation. Some numerical simulations are also performed in this work.   


Keywords: Li's Flattened Gaussian beam; Generalized Huygens-Fresnel integral; ABCD optical treatment; Annular aperture; Misalignment.