Permittivity of lossy heterostructures: effects of finite conductivity and anisotropy

The complex values of the permittivity of two-component lossy heterostructures, composed of inclusions of permittivity ε₁ embedded in a host matrix of permittivity ε₂, are rigorously evaluated with use of the finite element method and the code FLUX3D. Numerical results concerning spherical and rodlike inclusions with various radius-to-length ratios, of finite conductivity, periodically arranged in a simple cubic lattice configuration are provided. For illustrative purpose, a single set of permittivities was investigated: ε₁=80-i10⁶ and ε₂ =2-i0. The percolation threshold volume concentration is strongly dependent on the inclusion shape. Increasing the radius-to-length ratio by one order of magnitude has the effect of shifting upwards the percolation threshold by two decades. The exponents which determine how the real and imaginary parts of the effective permittivity scale with the distance from the percolation threshold are determined and are compared with the scaling predictions of percolation theory for infinite three-dimensional lattices of insulator-normal metal composite systems