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

Abstract

We have measured the relative permeability of splitring resonator (SRR) arrays used in metamaterials designed to have µ < 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 µ < 0 when compared to the ESRRs. The observed differences in damping, however, were diminished considerably when the array size was expanded from a onedimensional array of N SRRs to a 2 × 2 × N array. Our method can also be used to experimentally determine the effective permeability of other metamaterial designs.