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Wave propagation in focusing random media
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1982
[PDF-116.64 MB]
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Description:The problem considered Is that of calculating the moments of waves propagating 1n a medium with random refractive Index fluctuations and deterministic focusing. Focal regions produced by deterministic refractive index variations are defined within the ray approximation and classified into two types: the caustic and the cusp. The caustic and the cusp are the only focal regions in two dimensions which are stable to small perturbations of the refractive index.
It is shown that the problem of waves propagating 1n a random medium can be approximated by a phase screen problem in which the waves freely propagate to a plane, where they are perturbed in phase and then propagate freely to the observation point. This is done first within the ray approximation by considering higher order terms in an expansion about a deterministic ray. The approximation is also derived using the path integral solution to the parabolic wave equation; this derivation of the approximation gives an improved estimate of the range of validity of the phase screen approximation. A theorem concerning the expansion of functionals at singularities is generalized, showing that moments of waves propagating in a random medium can always be expressed in terms of generalized Airy functions. Since a generalized Airy function can be interpreted as the field beyond a phase screen, this shows that some phase screen problem is a good approximation to the wave propagation problem.
A phase screen model with deterministic focusing is defined which includes as special cases the phase screen approximations to propagation 1n random media. An additional focal type, perfect focusing with a Gaussian amplitude window at the screen, is also
allowed. Non-dimensiona1iz1ng the integral expressions for the field beyond the screen produces dimensionless parameters. The strength parameter can be identified with the strength parameter in a propagation problem in an extended medium, but the
diffraction parameter for the approximating phase screen 1s a generalization of the usual diffraction parameter for propagation problems. The multi-dimensional integrals for the moments of the field beyond the screen are evaluated by the method of steepest
descent for several cases. A new method for evaluating multidimensional integrals is developed. With this method, the moments of the field can be expressed as an operator acting on the deterministic field in the absence of random fluctuations. This operator is conveniently expressed as a filter acting on the transform of the deterministic field. This method is applied analytically to a few cases, and numerically to calculate the intensity near a caustic. The effect of the fluctuations is to decrease local intensity maxima and to increase local intensity minima.
A Monte-Carlo simulation is used to estimate the moments of the field 1n several cases of Interest. The moments are found to depend on the strength of the fluctuations in a complicated way when the generalized diffraction parameter 1s near unity. In particular, the scintillation Index 1s large at local Intensity minima even for relatively weak fluctuations. Fluctuation parameters for focal regions produced 1n underwater sound propagation are estimated.
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Rights Information:CC0 Public Domain
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