Bounded dynamics in finite PT -symmetric magnetic metamaterials

Abstract

We examine the PT-symmetry-breaking transition for amagnetic metamaterial of a finite extent, modeled as an array of coupled split-ring resonators in the equivalent circuit model approximation. Small-size arrays are solved completely in closed form, while for arrays larger than N = 5 results were computed numerically for several gain and loss spatial distributions. In all cases, it is found that the parameter stability window decreases rapidly with the size of the array, until at N = 20 approximately it is not possible to support a stable PT -symmetric phase.