Limits for the effective permittivity of mixtures: numerical validation by the FDTD method

Reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional dielectric mixture is calculated by FDTD simulations of such a sample in a TEM-waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits.