Homogenization of similarly oriented, metallic, ellipsoidal inclusions using the Bruggeman formalism

The effective relative permittivity dyadic of a composite material made by randomly embedding parallel, ellipsoidal, isotropic, metallic inclusions in an homogeneous, isotropic, dielectric host material is computed using the Bruggeman formalism with exact depolarization dyadics. Numerical calculatio ns carried out for iron inclusions at 670 nm free-space wavelength indicate that the inclusion volume fraction at the percolation threshold is directi on-dependent, being lower in those directions that the ellipsoids have long er extents. When the longest principal semi-axis of an ellipsoidal inclusio n exceeds a certain relative size - about three to five times as large as t he other two principal semi-axes - the Bruggeman estimate of the effective permittivity along this direction does not indicate a percolation threshold , becoming merely a simple weighting of the permittivities of the two mater ials in relation to their volume fractions. (C) 2000 Published by Elsevier Science B.V. All rights reserved.