Generalized M2-factor of hard-edged diffracted

Hypergeometric-Gaussian type-II beams


A.A.A. Ebrahim, F. Khannous, H. Nebdi, A. Chafiq, A. Belafhal*

Laboratoire de Physique Nucléaire, Atomique et Moléculaire

Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali,

B. P.: 20, 24000 El Jadida, Morocco

* Corresponding author. E-mail:

Received: 06 February 2013; revised version accepted: 20 May 2014



     Based on the truncated second-order moments definition, the generalized M²-factor of the hypergeometric-Gaussian type-II beams in the cylindrical coordinate system through a hard-edged circular aperture is derived. The effects of the beam truncation parameter d and the beam orders on the beam propagation factor have been investigated. The theoretical results show that the generalized M²-factor can be simplified to four special cases, among of them, the truncated and untruncated Gaussian beams. The power fraction of the hypergeometric-Gaussian type-II beams is calculated analytically and illustrated numerically.


Keywords: Generalized M²-factor; Hard-edged; Hypergeometric-Gaussian type-II beams; Power fraction.



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