A piece of information on the polarization effects on the effective dielectric constant εeff of a medium whose dielectric circular cylinders are randomly distributed is obtained by analyzing εeff for both E-wave and H-wave incidences. Our numerical analysis shows clearly the difference of εeff between E-wave and H-wave incidences and also shows the difference of εeff between our method and the Foldy's approximation.

Coherent and incoherent electromagnetic (EM) waves scattered by many particles are approximately expressed as solutions of integral equations by unconventional multiple scattering method. The particles are randomly displaced from a uniformly ordered distribution, and hence the distribution of particles can change from total uniformity to complete randomness. The approximate expressions of the EM waves are systematically given, independent of the distributions of particles, on the following assumptions. First the particles are identical in material, shape, size and orientation. Second each random displacement of particles from the ordered positions is statistically independent of each other and homogeneous in space. These assumptions may be extended to more general ones but have been used here to make clear the derivation process of the coherent and incoherent EM waves. The approximate expressions of the EM waves are reduced to known ones for both limiting cases: a periodic distribution and a very sparse random distribution. The effective dielectric constant of a random medium containing randomly distributed dielectric spheres can be calculated from the coherent EM wave and compared with those given by conventional methods such as the quasi-crystalline approximation, using the previous results. The comparison indicates the advantage of the method presented here. The present method is expected to be useful for the study of interaction of EM waves with many particles.