Transmission and Anderson localization in dispersive metamaterials

Comprehensive theoretical and numerical studies of the effects of dispersion and absorption on the Anderson localization of classical waves in weakly disordered, one-dimensional stacks composed of dispersive metamaterials and normal materials are presented. An asymptotic analysis for studying the effects of dispersion and absorption is developed. It is shown that the localization of waves in random stacks composed entirely of either metamaterial or normal dielectric layers is completely suppressed at frequencies where the magnetic permeability or the dielectric permittivity is zero. In mixed stacks of alternating layers of normal and metamaterials with disorder present in either the dielectric permittivity or the magnetic permeability, localization is substantially suppressed not only at these frequencies but in essentially wider frequency ranges. When both the permittivity and the permeability are random, the localization behavior is similar to that in monotype stacks. At the transition from a double negative metamaterial to a single negative metamaterial, the transmission length drops dramatically in a manner that might be useful in optical switching. Polarization effects are also considered and it is shown that localization is suppressed at the Brewster angle, in a manner dependent on both the polarization and the nature of the disorder. Theoretical predictions are in excellent agreement with numerical calculations.