Finite-size scaling and disorder effect on the transmissivity of multilayered structures with metamaterials

We investigate the influence of metamaterials on the scaling laws of the transmission on multilayered structures composed of random sequences of ordinary dielectric and metamaterial layers. The spectrally averaged transmission in a frequency range around the fully transparent resonant mode is shown to decay with the total number of layers as 1/N. Such thickness dependence is faster than the 1/N(1/2) decay recently reported to take place in random sequences of ordinary dielectric slabs. The interplay of strong localization and the emergence of resonant modes within the gap leads to a non-monotonous disorder dependence of the transmission that reaches a minimum at an intermediate disorder strength.