The Complex Permeability of Split-Ring Resonator Arrays Measured at Microwave Frequencies

TL;DR

This study measures the effective permeability of split-ring resonator arrays at microwave frequencies, revealing how array size and spacing influence negative permeability properties in metamaterials.

Contribution

It introduces a method to experimentally determine the permeability of SRR arrays and compares their behavior to extended ESRRs, highlighting effects of array size and damping.

Findings

SRR arrays exhibit narrower negative permeability frequency range than ESRRs.

Damping effects decrease as array size increases from 1D to 2x2xN arrays.

The measurement method is applicable to various metamaterial designs.

Abstract

We have measured the relative permeability of split-ring resonator (SRR) arrays used in metamaterials designed to have $\mu^\prime< 0$ over a narrow range of microwave frequencies. The SRR arrays were loaded into the bore of a loop-gap resonator (LGR) and reflection coefficient measurements were used to determine both the real and imaginary parts of the array's effective permeability. Data were collected as a function of array size and SRR spacing. The results were compared to those obtained from continuous extended split-ring resonators (ESRRs). The arrays of planar SRRs exhibited enhanced damping and a narrower range of frequencies with $\mu^\prime<0$ when compared to the ESRRs. The observed differences in damping, however, were diminished considerably when the array size was expanded from a one-dimensional array of $N$ SRRs to a $2\times 2\times N$ array. Our method can also be used to experimentally determine the effective permeability of other metamaterial designs.