Browsing by Author "Pack, Jeong-Ki"
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- Numerical simulation of optical wave propagation through random mediaPack, Jeong-Ki (Virginia Polytechnic Institute and State University, 1988)The propagation of optical plane waves through a one-dimensional Gaussian phase screen and a two-dimensional Gaussian extended medium are simulated numerically, and wave statistics are calculated from the data obtained by the numerical simulation. For instantaneous realization of a random medium, a simplified version of the random-motion model [77] is used, and for wave-propagation calculation the wave-kinetic numerical method and/or the angular-spectral representation of the Huygens-Fresnel diffraction formula are used. For the wave-kinetic numerical method, several different levels of approximations are introduced, and the region of validity of those approximations is studied by single-realization calculations. Simulation results from the wave-kinetic numerical method are compared, either with those from the existing analytical expressions for the phase-screen problem, or with those from the Huygens-Fresnel diffraction formula for the extended-medium problem. Excellent agreement has been observed. Extension to two-dimensional media with the power-law spectrum or three-dimensional problems is straight-forward. We may also deal with space-time correlations using, for example, Taylor's frozen-in hypothesis.
- A wave-kinetic numerical method for the propagation of optical wavesPack, Jeong-Ki (Virginia Polytechnic Institute and State University, 1985)A new wave-kinetic numerical method for the propagation of optical waves in weakly inhomogeneous media is discussed, and it is applied to several canonical problems: the propagation of beam and plane waves through a weak 3-D ( or 2-D ) Gaussian eddy. The numerical results are also compared to those from a Monte-Carlo simulation and the first Born approximation. Within the validity of the Liouville approximation, the Wigner distribution function ( WDF ) is conserved along the conventional ray trajectories, and, thus, by discretizing the input WDF with Gaussian beamlets, we can represent the output WDF as a sum of Gaussians, from which irradiance can be obtained by analytical integration of each Gaussian with respect to wavevector. Although each Gaussian beamlet propagates along a geometrical optics ray trajectory, it can correctly describe diffraction effects, and the propagation of optical waves through caustics or ray crossings. The numerical results agree well with either the Monte-Carlo method or the first Born approximation in regions where one or both of these are expected to be valid.