Nonlinear magnetoinductive transmission lines

TL;DR

This paper investigates power transmission in nonlinear magnetic metamaterials modeled as magnetoiductive lines, revealing that nonlinear effects enable power transfer in additional frequency bands beyond the linear regime, with implications for metamaterial design.

Contribution

It provides analytical solutions for magnetoinductive waves in nonlinear regimes and demonstrates power transmission in new frequency bands through numerical simulations.

Findings

Power transmission occurs in nonlinear frequency bands near resonances.

Transmission effectiveness in nonlinear bands is comparable to linear bands.

Power transfer involves linear modes and mode instabilities at the driven site.

Abstract

Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent capacitance. Extended numerical simulations reveal that power transmission along the array is also possible in other than the linear frequency bands, which are located close to the nonlinear resonances of a single nonlinear RLC circuit. Moreover, the effectiveness of power transmission for driving frequencies in the nonlinear bands is comparable to that in the linear band. Power transmission in the nonlinear bands occurs through the linear modes of the system, and it is closely related to the instability of a mode that is localized at the driven site.