Propagation of modified Bessel-Gaussian beams

through an annular apertured paraxial

ABCD optical system


A.A.A. Ebrahim, L. Ez-zariy, 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: 12 January 2011; revised version accepted:26 September 2011



     We investigate the propagation characteristics of modified Bessel-Gaussian (MBG) beams travelling through a paraxial ABCD optical system with an annular aperture. A novel analytical expression of MBG beams intensity distribution is examined by the use of the generalized Collins diffraction integral and the expansion of the hard aperture function into a finite sum of complex Gaussian functions. From our analytical expression, the free space, circular aperture and circular black screen are also treated as particular cases. The previous results concerning the propagation of Bessel-Gaussian, Bessel and Gaussian beams through the considered optical system are found as special cases. Some numerical examples are given to simulate the propagation of MBG beams.


Keywords: Modified Bessel-Gaussian beams; Collins diffraction integral; Annular aperture; Circular aperture; Circular black screen; Paraxial ABCD optical system; Hard aperture function.


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