Tunability of Superconducting Metamaterials

Metamaterials are artificial structures with unique electromagnetic properties, such as relative dielectric permittivity and magnetic permeability with values less than 1, or even negative. Because these properties are so sensitive to loss, we have developed metamaterials comprised of superconducting waveguides, wires, and split-ring resonators. An important requirement for applications of these metamaterials is the ability to tune the frequency at which the unique electromagnetic response occurs. In this paper we present three methods (unique to superconductors) to accomplish this tuning: temperature, dc magnetic field, and rf magnetic field. Data are shown for dc and rf magnetic field tuning of a single Nb split-ring resonator (SRR). It was found that the dc field tuning was hysteritic in the resonant frequency data, while the quality factor, $Q$, was less hystertic. The rf power tuning showed no hysteresis, but did show supression of the $Q$ at high power. Magneto-optical images reveal inhomogeneous magnetic vortex entry in the dc field tuning, and laser scanning photoresponse images for a YBa$_2$Cu$_3$O$_{7-\delta}$ SRR reveals the current distribution in the rings.