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
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