Research in metamaterials and plasmonics both involve the study of light in electromagnetic structures. Metamaterials are engineered structures, which are not found in nature, that have an ability to guide light around objects rather than reflecting or refracting it. Plasmonic systems, in turn, exploit surface plasmon polaritons (SPPs), which are electromagnetic waves with wavelengths shorter than the incident light that can propagate at metal–dielectric interfaces. Although incorporation of metamaterials and plasmonics into practical devices promises many exciting applications, their use is limited by significant dissipative losses. These occur because the noble metals used in these photonic structures are poor conductors at high frequencies. Recently, P. Tassin and colleagues at Ames Laboratory—US DOE and the Department of Physics and Astronomy, Iowa State University, and co-researchers at the Institute of Electronic Structure and Lasers, Heraklion, Crete, Greece, have addressed the question of what makes a good conductor for metamaterials and for plasmonic systems. To this end, they have derived two different figures of merit, one for each type of electromagnetic structure.
In their article recently published online in Nature Photonics (DOI: 10.1038/NPHOTON.2012.2), Tassin and co-researchers consider metamaterials as an array of subwavelength conducting elements, which effectively captures the physics of the most commonly studied systems. The researchers derived an expression for the dissipated power fraction as a function of four independent parameters. However, only two parameters depend on the material’s properties—the dissipation factor, ζ, and the kinetic inductance factor, ξ, which are proportional to the real and imaginary parts of the resistivity, respectively. A small ζ allows for large currents, while a small ξ prevents saturation of the resonance frequency. Furthermore, at frequencies where the permeability is −1, the dissipative loss depends, to a good approximation, only on ζ. This establishes it as a good figure of merit for conducting materials in resonant metamaterials, although geometrical factors are important when comparing samples of different thicknesses.
The researchers said that although charge-neutral graphene displays minimal resistivity in the mid-infrared and visible band, it is not a good candidate for metamaterial applications because ζ and ξ for graphene are several orders of magnitude larger than those for gold. Similarly, silver performs better as a conducting material at terahertz frequencies than high-Tc superconductors because it has significantly smaller ζ and ξ values. Transparent conducting metal oxides, such as indium tin oxide and aluminum tin oxide, have also recently been proposed for use in metamaterials, but the researchers found that their microwave resistivities are two orders of magnitude larger than the optical resistivity of silver.
For plasmonics, the researchers use the ratio of the propagation length to the surface plasmon wavelength as the measure of loss performance. The larger kinetic inductance of biased graphene makes it a better candidate for plasmonic applications than charge-neutral graphene. However, the researchers also showed that the propagation length is, at best, on the order of a few SPP wavelengths, which is too short for most plasmonic applications.
The researchers also discussed why alkali–noble intermetallics, such as KAu and LiAg, are not good candidates for use in metamaterials, although they said, “These examples show, nevertheless, the possibility of band engineering to tune the resistivity of alloys,” and that, “it is worth continuing the research effort to develop better conducting materials, because of the considerable improvement such materials would bring.”
