In a parallel approach to recently-used transfer function formalism, a study involving diffraction of modulated electromagnetic (EM) waves through uniform and phase-turbulent atmospheres is reported in this paper. Specifically, the input wave is treated as a modulated optical carrier, represented by use of a sinusoidal phasor with a slowly timevarying envelope. Using phasors and (spatial) Fourier transforms, the complex phasor wave is transmitted across a uniform or turbulent medium using the Kirchhoff-Fresnel integral and the random phase screen. Some preliminary results are presented comparing non-chaotic and chaotic information transmission through turbulence, outlining possible improvement in performance utilizing the robust features of chaos.
The impact of atmospheric phase turbulence on Gaussian beam propagation along propagation paths of varying lengths is examined using multiple random phase screens. The work is motivated by research involving generation and encryption of acousto-optic chaos, and the interest in examining propagation of such chaotic waves through atmospheric turbulence. A phase screen technique is used to simulate perturbations to the refractive index of the medium through the propagation path. A power spectral density based on the modified von Karman spectrum model for turbulence is used to describe the random phase behavior of the medium. In recent work, results for the numerical simulation of phase turbulence over a narrow region of space implemented by placing a planar aperture representing a (narrow) random phase screen were presented. Results are presented pertinent to extended phase screens (via multiple random-phase apertures) through which an incident Gaussian beam propagates incrementally via alternate phase transmission and diffraction along the propagation path. Additionally, for profiled electromagnetic waves (such as Gaussian), the scintillation index is evaluated for extended phase turbulence, and finally, fringe visibility due to the interference of double-Gaussian beams passing through extended turbulence is examined.
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.
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.
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