An effective medium description for a random uniaxial anisotropic medium with small-scale fluctuations

Some properties of the electromagnetic field are determined for an unbounded medium characterized by a permittivity tensor whose elements can be expressed as the sum of two terms, one deterministic and the other random. The deterministic and random parts of the permittivity tensor are considered to be uniaxial anisotropic; thus it is a diagonal tensor where two of the three elments are equal. Starting from the bilocal approximation to Dyson's equation, an effective permittivity tensor and mean dyadic Green's function are obtained for small-scale fluctuations. Some important properties of the ordinary and extraordinary waves are also made known.