Discrete dissipative localized modes in nonlinear magnetic metamaterials

TL;DR

This paper investigates the existence, stability, and dynamics of dissipative localized modes in nonlinear magnetic metamaterials composed of coupled split-ring resonators, highlighting the role of electric coupling and nonlinear effects.

Contribution

It introduces a nonlinear model for magnetic metamaterials, analyzing localized modes, domain walls, and modulational instability in one- and two-dimensional lattices.

Findings

Electric coupling can reverse the sign of interactions between resonators.

Bistable domain wall velocity depends on external field.

Larger localized modes can undergo modulational instability and splitting.

Abstract

We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in one- and two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting.