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May 01, 2010

The Physics and Applications of Superconducting Metamaterials

We summarize progress in the development and application of metamaterial structures utilizing superconducting elements. After a brief review of the salient features of superconductivity, the advantages of superconducting metamaterials over their normal metal counterparts are discussed. We then present the unique electromagnetic properties of superconductors and discuss their use in both proposed and demonstrated metamaterial structures. Finally we discuss novel applications enabled by superconducting metamaterials, and then mention a few possible directions for future research.



The Advantages of Superconducting Metamaterials

Metamaterials are typically constructed of “atoms” that have engineered electromagnetic response. The properties of the artificial atoms are often engineered to produce non-trivial values for the effective permittivity and effective permeability of a lattice of identical atoms. Such values include relative permittivities and permeabilities that are less than 1, close to zero, or negative. For concreteness, we shall consider below the scaling properties of metamaterials made of traditional “atomic” structures, like those used in the early metamaterials literature. Traditional metamaterials utilize wires to influence the dielectric properties by manipulating the effective plasma frequency of the medium. The magnetic properties of Split-Ring Resonators (SRRs) are utilized to create a frequency band of sub-unity, negative or near-zero magnetic permeability.

Substantial losses are one the key limitations of conventional metamaterials. As discussed in detail below, Ohmic losses place a strict limit on the performance of metamaterials in the RF – THz frequency range. In contrast to normal metals, superconducting wires and SRRs can be substantially miniaturized while still maintaining their low-loss properties. For comparison, as the size of normal metal wires and SRRs are decreased. These deleterious effects do not happen with superconducting wires and SRRs because the resistivity is orders of magnitude smaller, and the electromagnetic response is dominated by the reactive impedance. Superconductors will only break down when the dimensions become comparable to the coherence length, or when the induced currents approach the critical current density (Jc ~ 10^6 – 10^9 A/cm2).



Novel Superconducting Metamaterial Implementations

A number of novel implementations of superconducting metamaterials have been achieved in addition to superconducting split rings and wires. Here we present results on several classes of superconducting metamaterials.

* Superconductor/Ferromagnet Composites
* DC Magnetic Superconducting Metamaterials

The general idea is to take a solid diamagnetic superconducting object and divide it into smaller units, arranging them in such a way as to tailor the magnetic response. The cloak would shield a region of space from external DC magnetic fields, and not disturb the magnetic field distribution outside of the cloaking structure.


* SQUID Metamaterials

They considered a two-dimensional array of RF SQUIDs in which the Josephson junction was treated as a parallel combination of resistance, capacitance and Josephson inductance. Near resonance, a single RF SQUID can have a large diamagnetic response. In an array, there is a frequency and RF-magnetic field region in which the system displays a negative real part of effective permeability. The permeability is in fact oscillatory as a function of applied magnetic flux, and will be suppressed with applied fields that induce currents in the SQUID that exceed the critical current of the Josephson junction. Related work on a one-dimensional array of superconducting islands that can act as quantum bits (qubits) was considered by Rakhmanov, et al. When interacting with classical electromagnetic radiation, the array can create a quantum photonic crystal that can support a variety of nonlinear wave excitations. A similar idea based on a SQUID transmission line was implemented to perform parametric amplification of microwave signals

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