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, 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 for the correlated case shows a substantial departure from the uncorrelated (Anderson-like) case. A long-time asymptotic fit $\langle n^2\rangle \sim t^\alpha$ reveals that, for the uncorrelated system $\alpha\sim 0$, while for the correlated case $\alpha>0$, spanning a whole range of behavior ranging from localization to super-diffusive behavior. 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 implies, according to the random dimer model (RDM) of Dunlap et al., a degree of mobility. A comparison between the mobilities of the correlated SRR system and the RDM shows that the RDM model has better mobility at low disorder while our correlated SRR model displays better mobility at medium and large disorder.