Investigation of Profiled Beam Propagation through a Turbulent Layer and Temporal Statistics of Diffracted Output for a Modified von Karman Phase Screen Monish R. Chatterjee 1,* and Fathi H. A. Mohamed 1 1 Department of Electrical & Computer Engineering University of Dayton, Dayton, Ohio 45469 * Corresponding author ABSTRACT Gaussian beam propagation through a turbulent layer has been studied using a split-step methodology. A modified von Karman spectrum (MVKS) model is used to describe the random behavior of the turbulent media. Accordingly, the beam is alternately propagated (i) through a thin Fresnel layer, and hence subjected to diffraction; and (ii) across a thin modified von Karman phase screen which is generated using the power spectral density (PSD) of the random phase obtained via the corresponding PSD of the medium refractive index for MVKS turbulence. The random phase screen in the transverse plane is generated from the phase PSD by incorporating (Gaussian) random numbers representing phase noise. In this paper, numerical simulation results are presented using a single phase screen whereby the phase screen is located at an arbitrary position along the propagation path. Specifically, we examine the propagated Gaussian beam in terms of several parameters: turbulence strength, beam waist, propagation distance, and the incremental distance for Fresnel diffraction for the case of extended turbulence. Finally, on-axis temporal statistics (such as the mean and variance) of the amplitude and phase of the propagated field are also derived. Keywords: Atmospheric turbulence, Gaussian beam, Modified von Karman spectrum, split-step beam propagation method, random phase screen. 1. INTRODUCTION Atmospheric turbulence effects may have a strong influence on several laser applications whereby the turbulence causes fluctuations in both the intensity and the phase of the received light signal. Experimental studies of atmospheric turbulence effects on laser beam propagation is of importance in relating environmental parameters to beam propagation effects and estimate magnitudes of perturbations which degrade the performance of laser systems [1]. Theoretical descriptions in the intermediate and strong turbulence regimes are less well developed than for weak turbulence. Knowledge of atmospheric turbulence effects is helpful in the development of a wide class of atmospheric- optics systems including laser communication, energy transfer, remote sensing, and active and passive imaging systems. Inhomogeneities in the temperature and pressure of the atmosphere lead to variations of the refractive index along the transmission path. Index inhomogeneities can deteriorate the quality of the received signal and cause fluctuations in both the intensity and the phase of the received signal. Several atmospheric turbulence spectral models use random phase screens to model the turbulence [2-5]. Common among these are the Kolmogorov, Tatarski, von Karman and modified von Karman spectra (MVKS). The phase fluctuations of the phase screen used to model the random phase distribution within the aperture are parameterized by the Fried parameter, which describes the transverse coherence length, and the inner and outer scales that determine the amount of aberration seen by the propagating beam. The split- step propagation method involving the Fresnel-Kirchhoff diffraction integral is used to model the propagation of the Free-Space Laser Communication and Atmospheric Propagation XXVI, edited by Hamid Hemmati, Don M. Boroson, Proc. of SPIE Vol. 8971, 897102 · © 2014 SPIE · CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2033442 Proc. of SPIE Vol. 8971 897102-1 Downloaded From: http://spiedigitallibrary.org/ on 05/27/2014 Terms of Use: http://spiedl.org/terms