Noise in one-dimensional metamaterials supporting magnetoinductive lattice waves

Abstract

Equivalent circuit models are presented for the propagation of noise in one-dimensional negative-index metamaterials based on split-ring resonators (SRRs) and rods. The SRRs are modeled as lossy lumped-element $L$-$C$ resonators, whose reactive components provide the effect of a negative relative permeability over a restricted frequency range but whose resistive elements act as sources of propagation loss and Johnson noise. Similarly, the rod loading is modeled as lumped-element inductors, whose reactive components provide the effect of a negative relative permittivity but whose resistive elements introduce further loss and noise. Coupling between the magnetic resonators allows the propagation of magnetoinductive lattice waves. The effect on the effective medium properties is to shift the apparent magnetic resonance up in frequency by an amount depending on the coupling coefficient and to allow the propagation of noise waves within the resonator array over the entire magnetoinductive band. The model predicts all the details of the electromagnetic and magnetoinductive noise inside the array. However, it is shown that the observable effect outside the array matches the prediction of a simplified model based only on the modified effective medium properties.