On Scattering of Waves by Random Distributions. II. Two-Space Scatterer Formalism

Abstract

The bulk parameters (propagation number K, etc.) of the coherent multiple scattered field in a slab region of randomly distributed scatterers are expressed functionally in terms of ``two-space'' isolated scatterer amplitudes. These amplitudes correspond to a single object excited by a wave traveling in ``K space'' (the medium associated with the coherent field) but radiating into ``k space'' (free space). The formalism is applied to small spheres of arbitrary ε′ and μ′, and the ``Lorentz-Lorenz'' form for each bulk parameter ε and μ is obtained. It is shown that ε and μ are independent of the direction and of the polarization of the incident field; thus, the coherent field for the distribution defines a unique Maxwellian medium. As a second approximation for small spheres, the ``loss terms'' corresponding to incoherent scattering are included; these appear in the bulk ε and μ in the roles of electric and magnetic ``conductivities.' As another illustration, we consider normal incidence on a slab of tenuous scatterers (parameters close to those of free space) large compared to wavelength; for this case the bulk parameters ε and μ are equal to the index of refraction. We consider the incoherent as well as the coherent effects.