On Scattering of Waves by Random Distributions. I. Free-Space Scatterer Formalism

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Abstract
Approximations are derived for the bulk parameters of the coherent multiple scattered field in a slab region of randomly distributed arbitrary scatterers. (The one-, two-, and three-dimensional cases are treated simultaneously.) The propagation number K, and, e. g., ε and μ, are given explicitly in terms of conventional free-space isolated scattering amplitudes; these results generalize existing special forms for monopoles, dipoles, cylinders, and spheres. Corresponding approximations are obtained for the differential-scattering cross section per unit volume (i.e., the incoherent scattering), such that the total flux (coherent plus incoherent) fulfills the energy principle explicitly. Scattering and reciprocity theorems are derived for a ``multiple scattering amplitude'' of a scatterer within the distribution, and these are used to trace the energy ``losses'' of the coherent field which ``reappear'' as incoherent scattering. Several applications are considered.

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