Numerical scattering analysis for two-dimensional dense random media: characterization of effective permittivity

Abstract
In this paper, a new numerical method for de- termining effective permittivity of dense random media in two dimensions is presented. The core of the method is to compare the average scattered field of a random collection of scatter- ers confined within an imaginary boundary with the scattered field from a homogeneous dielectric of the same shape as the imaginary boundary. The two-dimensional (2-D) problem is ag- gressively studied here to provide insight into the dependence of the method's convergence on particle size, boundary shape, and boundary dimension. A novel inverse scattering method is introduced based on the method of moments (MoM), which greatly reduces the computation time and increases the flexibility of the procedure to analyze a variety of geometries. Results from this 2-D method may be used directly to compare with theoretical methods for determining effective permittivity such as the Polder-Van Santen mixing formula or field techniques such as the quasi-crystalline approximation.