Wavelength-dependent electromagnetic parameters for coherent propagation in correlated distributions of small-spaced scatterers

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Abstract
Earlier results for coherent propagation of electromagnetic waves in pair-correlated random distributions of scatterers (of radius a and physical parameters ε′,μ′) with minimum separation of centers b≥2a small compared to wavelength (2π/k) are generalized to obtain polarization, refraction, and absorption terms to order k2. The development includes multiple scattering and multipole coupling by electric and magnetic dipoles, as well as quadrupoles to appropriate order. The correlation aspects are determined by simple integrals of the statistical mechanics radial distribution function f for impenetrable particles (spheres, cylinders, and slabs) of diameter b. For slab scatterers, in terms of the exact Zernike–Prins f, the correlation integrals are expressed as algebraic functions of the volume fraction w; the resultant bulk values reduce to those of one particle at full packing, w=1. Similar results are obtained for spheres in terms of the Wertheim–Thiel solution of the Percus–Yevick approximation of f at the unrealizable bound w=1.