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.