Anderson localization in metamaterials with compositional disorder

Abstract

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 ≠ db, the localization length Lloc 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 Lloc 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 Lloc 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.