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

摘要

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 calculations carried out for iron inclusions at 670 nm free-space wavelength indicate that the inclusion volume fraction at the percolation threshold is direction-dependent, being lower in those directions that the ellipsoids have longer extents. When the longest principal semi-axis of an ellipsoidal inclusion exceeds a certain relative size - about three to five times as large as the 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 materials in relation to their volume fractions.