Intensity distribution of Four-Petal Gaussian beams

illuminating an apertured misaligned ABCD optical system


L. Ez-zariy, H. Nebdi, A. Belafhal*

Laboratory of Nuclear, Atomic and Molecular Physics

 Department of Physics, Faculty of Sciences, Choua´b Doukkali University,

P. B 20, 24000 El Jadida, Morocco

* Corresponding author. E-mail:

Received: 08 September 2013; revised version accepted:27 December 2013



     The aim of this paper is to develop the propagation characteristics of the four-petal Gaussian (FPG) beam through a misaligned circular annular aperture followed by a misaligned optical system. Based on the diffraction theory, an analytical expression of the FPG beam transformation by this considered system was obtained. Several particular cases corresponding to the transformation of FPG beam by an unapertured misaligned optical system or the latter with misaligned circular aperture or misaligned black screen and other special cases concerning the transformation of a FPG beam by aligned optical system with aligned/misaligned: annular aperture, circular aperture or black screen could be deduced in this paper. Some numerical simulations describing the effect of misalignment of annular aperture, circular aperture and black screen on propagation properties are also investigated. The current work generalizes about 31 investigations of FPG and fundamental Gaussian beams through misaligned and aligned various kinds of apertures followed by aligned or misaligned optical system.


Keywords: Four-petal Gaussian beam; ABCD optical system; Annular aperture; Misalignment. 


ę 2015