Localization of electromagnetic waves in two-dimensional disordered systems

We calculate the average transmission for s- and p-polarized electromagnetic (EM) waves and consequently the localization length of two-dimensional (2D) disordered systems which are periodic on the average; the periodic systems form a square lattice consisting of infinitely long cylinders parallel to each other and embedded in a different dielectric medium. In particular, we study the dependence of the localization length on the frequency, the dielectric function ratio between the scatterer and the background, and the filling ratio of the scatterer. We find that the gaps of the a-polarized waves can sustain a higher amount of disorder than those of the p-polarized waves, due to the fact that the gaps of the a-polarized waves are wider than those of the p-polarized waves. For high frequencies, the gaps of both types of waves easily disappear, the localization length is constant and it can take very small values. The optimum conditions for obtaining localization of EM waves in 2D systems will be discussed.