Percolation theory in the design of artificial dielectrics

Percolation theory presents the electromagnetic engineer with a novel approach for the modeling of random particle dispersions. Its ability to model realistic manufacturing processes in terms of their stochastic behavior and to yield the effective media parameters for the permittivity and the permeability of the aggregate structure make it a powerful tool in the design of synthetic electromagnetic materials. However, the results are cast in such a form that it is difficult to separate the probabilistic contributions from the purely electromagnetic effects. If properly recast into the language of artificial dielectrics, the percolation theory model should separate into two effects: a probabilistic model of the dispersion, which yields the mean geometry of the array of particles (or clusters), and an electromagnetic model of the properties of that assemblage of particles (or clusters) resulting from the interaction of their intrinsic properties with the geometry of the array. In other words, the stochastic model of percolation theory should be reducible to a deterministic model of a classic artificial dielectric. That reduction is presented for the specific case of the permittivity of a dispersion of conducting particles in a dielectric binder at a sample volume fraction. Similarities to the behavior of a classic frequency selective surface are demonstrated as a distributed circuit model is determined for the dispersive behavior predicted by percolation theory.