Propagation within fractal composite systems with strong permittivity fluctuations

In random complex composite systems such as a forest environment or a composite mixture, at volume fractions or biomass levels near the percolation threshold fractal or self similar behavior will be seen over a large scale. To describe the propagation of an electromagnetic wave through these systems an extension of the treatment of Tsang and Kong (1981) of the average field in an infinite, random medium, with strong permittivity fluctuations is considered, with scattering clusters whose correlation function is fractal from a minimum inclusion size a/sub 0/ up to a much larger scale. The case investigated is of a spherical minimum inclusion size, with radius a/sub 0/, above the scale of which there is an isotropic fractal fluctuation of the clusters' correlation function, with a maximum cluster size, still much smaller than the electromagnetic wavelength so that the bilocal approximation as described in Tsang and Kong can be used. The system is considered as an isotropic mixture in order to represent a completely random distribution in which no favorable orientations are present in the system. An effective permittivity is presented from this fractal correlation function which is an extension of the Bruggerman effective medium theory to include the scattering size effects of the fractal clusters within a random, composite system.