Modeling of power spectral density of modified von Karman atmospheric phase turbulence and acousto-optic chaos using scattered intensity profiles over discrete time intervals

In recent research, propagation of plane electromagnetic (EM) waves through a turbulent medium with modified von Karman phase characteristics was modeled and numerically simulated using transverse planar apertures representing narrow phase turbulence along the propagation path. The case for extended turbulence was also studied by repeating the planar phase screens multiple times over the propagation path and incorporating diffractive effects via a split-step algorithm. The goal of the research reported here is to examine two random phenomena: (a) atmospheric turbulence due to von Karman-type phase fluctuations, and (b) chaos generated in an acousto-optic (A-O) Bragg cell under hybrid feedback. The latter problem has been thoroughly examined for its nonlinear dynamics and applications in secure communications. However, the statistical characteristics (such as the power spectral density (PSD)) of the chaos have not been estimated in recent work. To that end, treating the chaos phenomena as a random process, the time waveforms of the chaos intensity and their spectra are numerically evaluated over a (large) number of time iterations. These spectra are then averaged to derive the equivalent PSD of the A-O chaos. For the turbulence problem, an optical beam passing through an input pinhole is propagated through a random phase screen (placed at different locations) to a desired distance (typically near-field) under different levels of turbulence strength. The resulting spatial intensity profile is then averaged and the process repeated over a (large) number of pre-specified time intervals. From this data, once again, the turbulence PSD is calculated via the Fourier spectra of the average intensity snapshots. The results for the two systems are compared.