Simulation of granular media by numerical characterization in the microwave range in coaxial line and in free space

Heterogeneous materials, composed of several elementary constituents, are often used in the field of microwaves, for absorption, shielding, or antenna substrate applications. The consideration of these materials for the design of such devices requires the knowledge of their effective properties (dielectric permittivity and magnetic permeability) as a function of frequency. These parameters can be approximated with the help of mixing laws, which have a limited range of validity. The experimental characterization in the microwave domain in transmission lines, waveguides, or in free-space can be considered, but sensitivity studies require numerical simulation. In this paper, a numerical method is proposed, allowing us to conduct sensitivity studies, and to determine the occurrence of the percolation phenomenon. The method, which gives an equivalence between the reflection and transmission coefficients of a material sample, and electromagnetic properties of the material, is declined in two configurations: in transmission line and in free space.