July 2013 Phys. Chem. News 69 (2013) 44-51 PCN 44 A THEORETICAL INVESTIGATION OF THE AXIAL INTENSITY DISTRIBUTION OF TRUNCATED MQBG BEAM IN A TURBULENT ATMOSPHERE S. Hennani 1,2 , S. Barmaki 2 , L. Ez-zariy 1 , H. Nebdi 1 , A. Belafhal 1 * 1 Laboratoire de Physique Nucléaire, Atomique et Moléculaire, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali B.P. 20, El Jadida 24000, Morocco 2 Laboratoire de Physique Computationnelle et Photonique Secteur des Sciences, Université de Moncton-campus de Shippagan, Shippagan, New-Brunswick, E8S 1P6, Canada * Corresponding author. E-mail: belafhal@gmail.com Received: 20 December 2012; revised version accepted: 29 April 2013 Abstract Based on Huygens-Fresnel diffraction integral, by means of the expansion of a hard-edged aperture function into a finite sum of complex Gaussian function and with help of the Rytov approximation, an approximate analytical expression of modified Bessel modulated Gaussian beam with quadrature radial dependence (MQBG beam) passing through an apertured turbulent atmosphere is derived in this work. The influence of some factors, including incident beam parameters, size aperture and turbulence parameters on propagation characteristics are numerically analyzed in this study. Keywords: MQBG beam; Huygens-Fresnel integral; Hard aperture function; Turbulence; Rytov approximation. 1. Introduction Hypergeometric (HyG) beams as solution of Helmholtz paraxial wave equation was first devoted in optical field by Kotlyar et al. [1] in 2007. HyG beams constitute a complete and orthogonal family of nondiffracting beams. For reason of their realization in practice, HyG beams are apodized with a radial Gaussian transmittance to give Hypergeometric Gaussian (HyGG) beams [2]. Unlike HyG beams, their modulated version carries a finite power and therefore can be generated experimentally. MQBG beams are regarded as particular case of HyGG beams or of HyGG modes of type-II under somme conditions [3]. Such beams can be generated using diffraction theory by means of a spiral phase plate instrument [4] or with help of the “fork” Computer-generated holograms [5]. HyGG and MQBG beams are the subject of several studies in the past few years [6- 12]. Particularly, Hennani et al. [11] have treated the transformation of a MQBG beam by any axisymetric ABCD optical system and simulated the propagation in free space, thin lens and in a factional Fourier transform. In another work [12], the same research group have examined the diffraction of MQBG beam by misaligned optical system. On other hand, considerable interest was paid to studying the propagation of laser beams through atmospheric turbulence for a long time, because of its wide practical applications, including optical communications, imaging and remote sensing [13- 15]. A large amount of work, concerning the propagation of various laser beams through a turbulent atmosphere, has been carried out in the past years [9,10,16-28]. In literature, it's appreciated that partially coherent beams are less affected by atmospheric turbulence than fully coherent ones [29-31]. Up to now, to the best of our knowledge, the axial intensity distribution of MQBG beams through a turbulent atmosphere hasn’t been studied elsewhere. In this paper, our aim is to etablish a theoretical study concerning the axial intensity distribution of a truncated MQBG beam propagating through a turbulent atmosphere. The paper is structured as follows. Section 2 is conserved to the theoretical study of the work using the extended Huygens-Fresnel integral formula in the paraxial approximation, and by expanding of the hard aperture function into a finite sum of complex Gaussian functions. In section 3, we calculate the analytical expression of the axial intensity distribution of truncated MQBG beams in a turbulent atmosphere. In section 4, we show and discuss the results of our performed numerical simulations. A final conclusion is given in section 5. 2. Expression of the axial intensity distribution of MQBG beams in a turbulent atmosphere By the use of the analytical geometry polar coordinates ( ) z r , , 1 1 θ , we assume that an incident MQBG beam in the source plane 0 = z is given by