A new approach to the problem of wave scattering in random media and its application to evaluating the effective permittivity of a random medium

The interaction of electromagnetic (EM) waves with matter is key to remote sensing technologies. Wave scattering by many particles is a typical example of the interaction. In the theoretical study, Floquet's theorem or so called multiple scattering methods has been used according as the distribution of particles is periodic or random. Although the periodic and random distributions are quite distinct from each other, the discrimination of the distributions becomes difficult when using EM waves of much longer wavelength than the average distance between particles. In this paper, many particles are assumed to be randomly displaced from a uniformly ordered distribution, and the distribution of particles can therefore change from total uniformity to complete randomness. Coherent and incoherent EM waves scattered by the particles are approximately expressed as solutions of integral equations by the unconventional multiple scattering method. The approximate expressions are systematically given, independent of the distribution of particles, and are reduced to known ones for both limiting cases: a periodic distribution and a very sparse random distribution. Using the above approach, the random condition is shown that the uniformity of distribution can be neglected in the expression of coherent EM wave, and a method is presented for evaluating the effective permittivity of a medium containing randomly distributed dielectric spheres. The effective permittivity is numerically compared with those of conventional methods such as the quasi-crystalline approximation, by changing the volume fraction and and the permittivity of spheres.