L. EZ-ZARIY ET AL. 325

[4] H. T. Eyyuboglu, Y. Baykal, E. Sermutlu, O. Korotkova

and Y. Cai, “Scintillation Index of Modified Bessel-

Gaussian Beams Propagating in Turbulent Media,” Jour-

nal of the Optical Society of America, Vol. 26, No. 2,

2009, pp. 387-394. doi:/10.1364/JOSAA.26.000387

[5] S. A. Ponomarenko, “A Class of Partially Coherent

Beams Carrying Optical Vortices,” Journal of the Optical

Society of America, Vol. 18, No. 1, 2001, pp. 150-156.

doi:/10.1364/JOSAA.18.000150

[6] L. Wang, X. Wang and B. Lü, “Propagation Properties of

Partially Coherent Modified Bessel-Gauss Beams,” Optik,

Vol. 116, No. 2, 2005, pp. 65-70.

doi:/10.1016/j.ijleo.2004.11.006

[7] Z. H. Gao and B. D. Lü, “Partially Coherent Nonparaxial

Modified Bessel-Gauss Beams,” Chinese Physics, Vol. 15,

No. 2, 2006, pp. 334-339.

doi:/10.1088/1009-1963/15/2/018

[8] L. Wang, M. Li, X. Wang and Z. Zhang, “Focal Switch-

ing of Partially Coherent Modified Bessel-Gaussian Beams

Passing through an Astigmatic Lens with Circular Aper-

ture,” Optics & Laser Technology, Vol. 41, No. 5, 2009,

pp. 586-589. doi:/10.1016/j.optlastec.2008.10.008

[9] K. C. Zhu, X. Y. Li, X. J. Zheng and H. Q. Tang, “Non-

paraxial Propagation of Linearly Polarized Modified Bes-

sel-Gaussian Beams and Phase Singularities of the Elec-

tromagnetic Field Components,” Applied Physics B: La-

sers and Optics, Vol. 98, No. 2-3, 2010, pp. 567-572.

doi:/10.1007/s00340-009-3807-2

[10] C. Ding, L. Pan and B. Lü, “Changes in the State of Po-

larization of Apertured Stochastic Electromagnetic Modi-

fied Bessel-Gauss Beams in Free-Space Propagation,”

Applied Physics B: Lasers and Optics, Vol. 99, No. 1-2,

2010, pp. 307-315. doi:/10.1007/s00340-009-3818-z

[11] A. A. A. Ebrahim, L. Ez-zariy and A. Belafhal, “Propaga-

tion of Modified Bessel-Gaussian Beams through an An-

nular Apertured Paraxial ABCD Optical System,” Physi-

cal and Chemical News, Vol. 61, 2011, pp. 52-58.

[12] G. Ding and B. Lu, “Decentered Twisted Gaussian Schell-

Model Beams and Their Propagation through a Mis-

aligned First-Order Optical System,” Optical and Quan-

tum Electronics, Vol. 35, No. 2, 2003, pp. 91-100.

doi:/10.1023/A:1022478608090

[13] M. Shen, S. Wang and D. Zhao, “Propagation of Flat-

tened Gaussian Beams Passing through a Misaligned Op-

tical System with Finite Aperture,” Optik, Vol. 115, No. 5,

2004, pp. 193-196. doi:/10.1078/0030-4026-00346

[14] J. Gu, D. Zhao and Z. Mei, “The Relative Phase Shift of

Off-Axial Gaussian Beams through an Apertured and

Misaligned Optical System,” Optik, Vol. 115, No. 4, 2004,

pp. 187-191. doi:/10.1016/S0030-4026(08)70009-3

[15] Y. Cai and L. Zhang, “Propagation of a Hollow Gaussian

Beam through a Paraxial Misaligned Optical System,”

Optics Communications, Vol. 265, No. 2, 2006, pp. 607-

615. doi:/10.1016/j.optcom.2006.03.070

[16] Y. Cai and X. Lu, “Propagation of Bessel and Bessel-

Gaussian Beams through an Unapertured or apertured

Misaligned Paraxial Optical Systems,” Optics Communi-

cations, Vol. 274, No. 1, 2007, pp. 1-7.

doi:/10.1016/j.optcom.2007.01.058

[17] C. Zhao, L. Wang, X. Lu and H. Chen, “Propagation of

High-Order Bessel-Gaussian Beam through a Misaligned

First-Order Optical System,” Optics & Laser Technology,

Vol. 39, No. 6, 2007, pp. 1199-1203.

doi:/10.1016/j.optlastec.2006.08.015

[18] H. T. Eyyuboglu, “Propagation Aspects of Mathieu-

Gaussian Beams in Turbulence,” Applied Physics B: La-

sers and Optics, Vol. 91, No. 3-4, 2008, pp. 629-637.

doi:/10.1007/s00340-008-3020-8

[19] A. Chafiq, Z. Hricha and A. Belafhal, “Propagation of

Generalized Mathieu-Gauss Beams through Paraxial Misa-

ligned Optical Systems,” Optics Communications, Vol.

282, No. 19, 2009, pp. 3934-3939.

doi:/10.1016/j.optcom.2009.03.062

[20] A. Belafhal, M. Yaalou and S. Hennani, “Propagation of

Bessel-Modulated Gaussian Beams through a Misaligned

First-Order Optical System,” Physical and Chemical

News, Vol. 61, 2011, pp. 34-43.

[21] A. Belafhal and S. Hennani, “A Note on Some Integrals

Used in Laser Field Involving the Product of Bessel

Functions,” Physical and Chemical News, Vol. 61, 2011,

pp. 59-62.

[22] S. Wang and L. Ronchi, “III Principles and Design of

Optical Arrays,” Progress in Optics, Vol. 25, 1988, pp.

279-348.

[23] I. S. Gradshteyn and I. M. Ryzhik, “Tables of Integrals,

Series, and Products,” 5th Edition, Academic Press, New

York, 1994.

Copyright © 2012 SciRes. OPJ