ON DIFfRACTION OF A Hyperbolic-Cosine-Gaussian Beam


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 January 2014; revised version accepted: 23 May 2014



     Based on the generalized Collins integral diffraction and by means of the expansion method of a hard-edged aperture into finite sum of complex Gaussian terms, an approximate analytical expression of the propagation properties of Hyperbolic-Cosine-Gaussian (ChG) beam passing through a misaligned annular aperture coupled with a misaligned optical system is devoted as the main result of this work. The propagation properties of the fundamental Gaussian beam through a misaligned annular aperture followed by a misaligned optical system and those of ChG and Gaussian beams passing through an unapertured misaligned or aligned optical system or truncated by an aligned or misaligned: annular aperture, circular aperture and black screen are derived in the article as particular cases of the main finding. Some numerical simulations are performed in the study to examine the impact of misalignment elements, especially those of the annular and circular apertures, on shape and profile of the beam exiting the optical system captured at the output plane. Some numerical calculations are performed in the work.


Keywords: Hyperbolic-Cosine- Gaussian (ChG) beam; Generalized Collins integral diffraction; ABCD optical system; Annular aperture; Circular aperture; Black screen; Misalignment.



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