Numerical testing of dielectric mixing rules by FDTD method

The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of the mixture is calculated by FDTD simulations of such a sample in a TEM-waveguide. The mixture consists of a homogeneous free space background in which circular cylinders are embedded in random positions. Clustering of the inclusions is allowed. The choice of two-dimensional spheres allows us to make much more use of the numerical capacity than what would be the case in three-dimensional inclusions. Various dielectric contrasts are studied from permittivity ratio 2 to 50. Numerical results are compared with classical mixing rules, and they show moderate agreement with the Bruggeman rule rather than the Maxwell Garnett approach. However, another key finding of this paper is that obtained mixing results are not symmetric with respect to inclusions and background. This makes the exact validity of the symmetric Bruggeman formula questionable.