Anderson localization in metamaterials with compositional disorder

Анотація

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 d_a and d_b of basic layers are essentially nonequal, d_a ≠ d_b, the localization length L_loc 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_loc includes all possible correlations between two disorders. However, when d_a = d_b 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_loc are due to the next order of approximation. On the other hand, for the RH–RH model the general expression for L_loc remains valid for d_a = d_b as well.