T-Matrix determination of effective permittivity for three-dimensional dense random media

In this paper, we present a full wave method for determining the effective permittivity for random media in three dimensions. The type of media addres sed is composed of spherical dielectric particles in a homogeneous dielectr ic background. The particle volume fraction ranges from 0 to 40% and dielec tric contrast may be significantly different from the background medium. Th e method described relies on the T-matrix approach for solving Maxwell's eq uations using a spherical wave expansion in conjunction with a Monte-Carlo simulation for calculating the mean scattered field confined within a presc ribed fictitious boundary. To find the effective permittivity, the mean sca ttered held is compared with that of a homogeneous scatterer whose shape is defined by the fictitious boundary and its dielectric constant is varied u ntil the scattered fields are matched. A complete description of the T-matr ix approach is given along with an explanation of why the recursive form of this technique (RATMA [3]) cannot be used for addressing this problem, Aft er the method development is completed, the results of our numerical techni que are compared against the theoretical methods of the quasi-crystalline a pproximation and the effective field approximation to demonstrate the regio n of validity of the theoretical methods. The examples contained within the paper use between 30 and 120 included spheres (with radii ranging from fro m ka = 0.6 to 0.8) within a larger, fictitious sphere of diameter kD = 8.4.