Earlier results for coherent propagation of light in correlated random distributions of dielectric particles of radius a (with minimum separation b ≥ 2a small compared with wavelength λ = 2π/k) are generalized to obtain the refractive and absorptive terms to order (ka)2. The present results include the earlier multiple scattering by electric dipoles as well as scattering and multipole coupling by magnetic dipoles and electric quadrupoles. The correlation aspects are determined by the statistical-mechanics radial distribution function f(R) for impenetrable particles of diameter b. The new terms for slab scatterers and spheres involve the integral of fR (first moment) or of f ln R for cylinders. The new packing factor is evaluated exactly for slabs as a simple algebraic function of the volume fraction w, and it is shown that the bulk index of refraction reduces to that of one particle in the limit w = 1. A similar result is achieved for spheres in terms of the Percus–Yevick approximation and the unrealizable limit w = 1.
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