The effect of cumulative forward and single large-angle scattering of an electromagnetic wave in a random medium

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Virginia Polytechnic Institute and State University

A general discussion on propagation of an electromagnetic wave in a random medium is presented. Emphasis is placed on the bistatic scattering problem. The first phase of the investigation is focused on a random continuum. This is an extension of work done by de Wolf [19] recently. He derives a formal expression for the enhancement factor of the electromagnetic flux at large angles (excluding backscatter) from an extended weakly random medium. Enhancement describes the factor by which the singly-scattered flux is modified when the effects of cumulative forward scatterings are taken into account before and after one large-angle scattering. Explicit results are calculated here for a two-dimensional geometry describing cylindrical scattering from a slab of width L filled with a uniformly turbulent dielectric described by a power-law spectrum in the inertial subrange. The results show that the enhancement factor is close to unity beyond the mean free path of the small-angle scatterings and it increases when the medium width L exceeds the mean free path of a large-angle scattering. This result is extended for a generalized power-law structure function of the dielectric permittivity fluctuation, which shows a possibility of using the cumulative forward and single large-angle scattered flux to detect the statistical properties of a random continuum. The negligence of the Fresnel terms in the expression of the scattered flux is justified by including those in the phase term and investigating the resulting effects. This investigation reveals that the inclusion of the Fresnel terms makes the scattered flux complex, an error arising from the truncation of the higher-order phase terms, which is not observed when the Fresnel terms are neglected.

The second phase of the investigation involves discrete random media. A mathematical model is developed for the purpose of deriving an integral equation of the coherent field and autocorrelation function in the very general case of an electromagnetic wave propagating in a medium of densely packed nontenuous particles. All orders of N-tuple particle correlation function are included. The resulting equations are a generalization of those derived recently by Tsolakis et al. [23]; the four lowest-order terms of each equation include those of Tsolakis et al.'s equations which incorporate only binary correlation between particles. The mathematical model is then used to derive an expression for the scattered flux of an electromagnetic wave under a first-order cumulative forward and single large-angle scattering approximation. The resulting expression is valid at high frequencies under Twersky's approximation [5]. It is shown that the discrete scatterer case may be treated by an approach similar to the continuum case by using the new formulation.