Anderson localization in metamaterials with compositional disorder

We consider one-dimensional periodic-on-average bi-layered models with random perturbations in dielectric constants of both basic slabs composing the structure unit-cell. We show that when the thicknesses da and db of basic layers are essentially nonequal, da not = db, the localization length L-l-o-c is described by the universal expression for two cases: (a) both layers are made from right-handed materials (the RH-RH model), (b) the a layers are of a right-handed material while the b layers are of a left-handed material (the RH-LH model). For these models the derived expression for L-l-o-c includes all possible correlations between two disorders. However, when da = db the RH-LH model exhibits a highly nontrivial properties originated from inhomogeneous distribution of the phase of propagating wave, even in the case of white-noise disorder. We analytically show that in this case the localization length diverges in the conventional second order in perturbation parameters. Therefore, recently numerically discovered anomalies in L-l-o-c are due to the next order of approximation. On the other hand, for the RH-RH model the general expression for Lloc remains valid for da = db as well.