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Arxiv – 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
* Radio Frequency Superconducting Metamaterials
Superconducting thin film wires can create large inductance values without the associated losses found in normal metals. This offers the opportunity to extend metamaterial atom structures to lower frequencies where larger inductance values are required to build resonant structures. In the past, three-dimensional structures have been employed to create artificial magnetism below 100 MHz. The use of two-dimensional spiral resonators to create negative effective permeability atoms has been developed in the sub-GHz domain using thick normal metal wires. However, such spirals are too lossy to resonate below 100 MHz for reasons similar to those discussed. Superconducting thin film spirals have low losses, but also have enhanced inductance from the kinetic inductance of the superfluid flow. Superconducting spiral metamaterials operating near 75 MHz have been developed with Nb thin films, and show strong tunability as the transition temperature is approached. Such metamaterials may be useful for magnetic resonance imaging,near-field imaging, and compact RF resonator applications.
* Superconducting Photonic Crystals
Photonic crystals (PCs) are generally constructed from a modulated dielectric function contrast with a spatial scale on the order of the wavelength. As such, they fall outside the domain of what are usually called metamaterials, but we shall consider them here nonetheless. A PC made up of superconducting cylinders embedded in a dielectric medium. They found that temperature tuning of the superfluid density, and therefore of the effective superfluid plasma frequency, can produce a tunable band of all-angle negative refraction, as well as tunable refracting beams. The angle of refraction can be tuned from positive to negative values, and achieve up to 45o of sweep.
* Novel Applications Enabled by Superconducting Metamaterials
The combination of left-handed and right-handed propagation media creates opportunities for new types of resonant structures. Engheta predicted that a resonant structure created by laminating two materials with opposite senses of phase winding can create a new class of resonant structures. He proposed a resonator consisting of two flat conducting plates separated by a sandwich of left-handed and right-handed metamaterials. A wave propagating in the direction normal to the plates will suffer a combination of forward and reverse phase windings before reaching the other reflecting boundary.
A related theoretical proposal was to add Josephson inductance to the superconducting dual transmission line to enhance nonlinearity. This can result in a tunable dispersion relation for propagating waves in the structure. Considering a metamaterial made up of a Josephson quantum bit (qubit) array leads to a number of interesting predictions, including the development of a quantum photonic crystal that derives its properties from the quantum states accessible to the qubits.
A one-dimensional SQUID array nonlinear transmission line has been used as a parametric amplifier, tunable for microwave signals between 4 and 8 GHz, and providing up to 28 dB of gain. This amplifier is suitable for use in detecting signals from low temperature qubits operating at microwave frequencies, and can squeeze quantum noise.
* Future Directions and Conclusions
There are many exciting future directions of research in superconducting metamaterials. Their low loss, compact structure, and nonlinear properties make them ideal candidates for realization of the landmark predictions of metamaterial theory, including the near-perfect lens, evanescent wave amplification, hyper-lensing, transformation optics and illusion optics.
There are many exciting possibilities to extend the frequency coverage of superconducting metamaterials from the low-RF range (below 10 MHz) to the upper limits of superconductivity in the multi-THz domain. Low frequencies offer the opportunity to create deep sub-wavelength structures to act as energy storage devices, imaging devices, or as filters. The THz domain brings many exciting possibilities for spectroscopy and imaging as well.
Josephson-based metamaterials offer many interesting opportunities for novel meta material structures. Their nonlinear response can be used to introduce parametric amplification of negative-index photons, further reducing the deleterious effects of loss. They also have extreme tunability with both DC and RF magnetic fields due to changes in the Josephson inductance. Their properties can also be made broad-band using a plurality of junction critical currents in the design.
Many superconductors have intrinsic properties that make them quite suitable for use as metamaterials or photonic crystals. For example, the anisotropic dielectric function in the layered high-Tc cuprate superconductors offers an opportunity to realize a hyperlens in the THz and far-infrared domain. The cuprates also have a built-in plasmon excitation for electric fields polarized along their c-axis (the nominally insulating direction), which can be exploited for plasmonic applications. Conventional superconductors have also shown conventional propagating plasmon excitations, suggesting that low loss microwave plasmonics, analogous to optical plasmonics, can be developed using superconducting thin films
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