Coherent electromagnetic wave propagation through randomly distributed dielectric scatterers

We present a vector multiple-scattering analysis of the coherent wave propagation through an inhomogeneous media consisting of a random distribution of identical, oriented, nonspherical, dielectric scatterers. The single-scattering aspect of the problem is dealt with through application of the transition or $T$ matrix. Configurational averaging techniques are employed to determine the "hole" correction integrals which are subsequently solved to yield the dispersion relations characterizing the bulk or effective properties of the medium. Closed-form solutions in the Rayleigh limit are derived for both spherical and spheroidal scatterer geometries. These solutions, together with the $T$ matrix, form the basis of our computational method for determining the coherent wave phase velocity and attenuation as a function of frequency ($\mathrm{ka}$) and scatterer concentration. Numerical results are presented for spherical and oblate spheroidal geometries over a range of $\mathrm{ka}$ values (0.05-2.0) and scatterer concentrations (0.05-0.20).