Investigation of Profiled Beam Propagation through a Turbulent Layer and Temporal Statistics of Diffracted Output for a Modified von Karman Phase Screen

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.