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

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.

arXiv comment11 pages, 5 figure

References in corpus (7)

• Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials
• Impact of the inherent periodic structure on the effective medium description of left-handed and related meta-materials
• Permittivity and Conductivity Measured using a Novel Toroidal Split-Ring Resonator
• Using split-ring resonators to measure the electromagnetic properties of materials: An experiment for senior physics undergraduates
• Ferromagnetic resonance in the complex permeability of an Fe${}_3$O${}_4$ nanosuspension at radio and microwave frequencies
• Design and characterization of a novel toroidal split-ring resonator
• Probing Split-Ring Resonator Permeabilities with Loop-Gap Resonators

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