Magnetic metamaterials with correlated disorder

Abstract

We examine the transport of magnetic energy in a simplified model of a magnetic metamaterial, consisting of a one-dimensional array of split-ring resonators (SRR), in the presence of correlated disorder in the resonant frequencies. The computation of the average participation ratio (PR) reveals that on average, the modes for the correlated disorder system are less localized than in the uncorrelated case. The numerical computation of the mean square displacement of an initially localized magnetic excitation shows an asymptotic behavior 〈n2〉∼tα, where α∼0 for uncorrelated disorder, and α>0 for the correlated case, spanning a whole range of behavior ranging from localization to super-diffusive behavior at finite system sizes. The transmission coefficient of a plane wave across a single magnetic dimer reveals the existence of well-defined regions in disorder strength-magnetic coupling space, where unit transmission for some wavevector(s) is possible. This explains the finite degree of mobility for magnetic excitations in the presence of correlated disorder, in the spirit of the random dimer model (Dunlap et al., 1990 [14]). Finally, the transmission of plane waves across an array with correlated disorder shows a power-law decrease with system size, in contrast to the exponential decrease found in the standard Anderson model.