Mathieu-Gauss beam and its propagation
L. Ez-zariy, H. Nebdi, A. Chafiq, A. Belafhal*
Laboratoire de Physique Nucléaire, Atomique et Moléculaire.
B.P. 20, Département de Physique, Faculté des sciences,
Université Chouaïb Doukkali, 24000 El Jadida. Maroc,
* Corresponding author: firstname.lastname@example.org
Received: 13 February 2012; revised version accepted: 21 March 2012
Based on the generalized Collins integral formula and using the expansion of the hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression of Mathieu-Gauss (MG) beams passing through a paraxial ABCD optical system with an annular aperture is derived. From this general analytical expression, the traveling of MG beams through free space, circular aperture and circular black screen are deduced as particular cases. Using the theoretical expressions developed in this work, some numerical simulations of normalized intensity distribution of MG beams are investigated.
Keywords: Mathieu-Gauss beams; Paraxial ABCD optical system; Free space; Annular aperture; Circular aperture ; Circular black screen.