Appl Phys B (2010) 98: 857–863 DOI 10.1007/s00340-009-3702-x Scintillations of Laguerre Gaussian beams H.T. Eyyubo˘ glu · Y. Baykal · X. Ji Received: 29 July 2009 / Published online: 16 September 2009 © Springer-Verlag 2009 Abstract By using the Rytov method, we formulate and nu- merically evaluate the scintillations of Laguerre Gaussian beams in weak atmospheric turbulence. Our results indi- cate that at on-axis positions, Laguerre Gaussian beams with zero angular mode number will have less scintillations than fundamental Gaussian beams, where the amount of scintillations will further decrease with rising radial mode number. When off-axis positions are considered, this situ- ation reverses however, and the scintillations of Laguerre Gaussian beams become generally higher than the funda- mental Gaussian beam. Plotted against the source size, the on-axis scintillations of Laguerre Gaussian beams fall below the fundamental Gaussian beam, following the same trend as the fundamental Gaussian beam all throughout the source size range examined. PACS 42.25.Dd · 42.25.Bs · 42.68.Bz · 42.68.-w H.T. Eyyubo˘ glu ( ) · Y. Baykal Department of Electronic and Communication Engineering, Çankaya University, Ö˘ gretmenler Cad. No. 14 Yüzüncüyıl, 06530 Balgat, Ankara, Turkey e-mail: h.eyyuboglu@cankaya.edu.tr Fax: +90-312-2848043 Y. Baykal e-mail: y.baykal@cankaya.edu.tr Fax: +90-312-2848043 X. Ji Department of Physics, Sichuan Normal University, Chengdu, 610068 China e-mail: jixl@163.com Fax: +86-28-84480787 1 Introduction In atmospheric optical links, it is well known that at- mospheric turbulence affects the received intensity and the intensity fluctuations take place at the receiver plane. Mani- festing itself as signal dependent noise, intensity fluctuations degrade the signal to noise ratio and, consequently, the bit error rate performance in atmospheric optics links. Scintil- lation theory and basic formulations can be found in [1, 2]. One factor that affects the intensity scintillations is the type of incidence used. Propagation in turbulence introduces different variations depending on the starting beam profile. The effect of beam types on the scintillation index in weakly turbulent atmosphere has been of interest in the last several years. Many researchers including our group scrutinized this topic in detail and presented results on the scintillation index in weak turbulence for sinusoidal-Gaussian [3, 4], higher order sinusoidal Gaussian [5], annular [3, 6, 7], higher or- der annular [5], flat-topped [8–10], dark hollow [11], astig- matic [12, 13], laser array [14] and Bessel [15–17] beams. We have recently presented a review on the effects of beam types on the scintillation index in weak atmospheric turbu- lence [18]. In this paper we extend our efforts in examining the intensity fluctuations for different beam types, and for- mulate by a Rytov method and evaluate the scintillations for a Laguerre Gaussian beam in atmospheric turbulence to un- derstand whether such beams will introduce any advantage in reducing scintillation noise. 2 Formulation Using radial coordinates s,φ s , the field of a Laguerre Gaussian beam on the source plane is [2] u s (s,φ s ) = A c  −j √ 2kαs exp(−jφ s )  m × exp ( −kαs 2 ) L m n ( 2kαs 2 ) , (1)