Negative Refractive Index at Optical Wavelengths

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Science  05 Jan 2007:
Vol. 315, Issue 5808, pp. 47-49
DOI: 10.1126/science.1136481

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Although discovered only 6 years ago, negative refractive index materials (NIMs) have been the target of intense study, drawing researchers from physics, engineering, materials science, optics, and chemistry. These artificial “metamaterials” are fascinating because they allow the design of substances with optical properties that simply do not occur in nature (14). Such materials make possible a wide range of new applications as varied as cloaking devices and ultrahigh-resolution imaging systems. The variety of possible applications would be even greater if such materials could be engineered to work at optical wavelengths.

For the ultimate control of light, one needs a handle on both the electric and the magnetic components of the electromagnetic (EM) light wave. To achieve this control, normally one would think about modifying the microscopic electric and magnetic fields in a material. However, in most cases it is easier to average over the atomic scale and consider the material to be a homogeneous medium characterized by the electric permittivity ϵ and the magnetic permeability μ. These two quantities describe the EM response of a given material. More specifically, Veselago showed nearly 40 years ago (5) that the combination ϵ < 0 and μ < 0 leads to a negative refractive index, n < 0. This means that the phase velocity of light is negative; in other words, light waves now have a “reverse gear.”

Veselago's idea remained obscure because no such natural materials were known to exist at any frequency. Although electric resonances with ϵ < 0 do occur up to the visible and beyond, magnetic resonances typically die out at microwave frequencies. Moreover, the electric and magnetic resonances would need to overlap in frequency, which seemed improbable. However, by making use of artificially structured metamaterials, in which inclusions smaller than a wavelength replace the atoms and molecules of a conventional material, scientists can circumvent this limitation. Metamaterials can be designed to exhibit both electric and magnetic resonances that can be separately tuned to occur in spectra from the low radiofrequency to the visible.

Since the first demonstration (6) of an artificial NIM in 2000, metamaterials have exhibited a broad range of properties and potential applications: nearly zero reflectance; nanometer-scale light sources and focusing; miniaturization of devices, such as antennas and waveguides; and novel devices for medical imaging, especially magnetic resonance imaging. For example, metamaterials may lead to the development of a flat superlens (7) that operates in the visible spectrum, which would offer superior resolution over conventional technology and provide image resolutions much smaller than one wavelength of light.

Advances in metamaterials.

The solid symbols denote n < 0; the open symbols denote μ < 0. Orange: data from structures based on the double split-ring resonator (SRR); green: data from U-shaped SRRs; blue: data from pairs of metallic nanorods; red: data from the “fishnet” structure. The four insets give pictures of fabricated structures in different frequency regions.

Subsequent theory and experiment (822) confirmed the reality of negative refraction. The development of NIMs at microwave frequencies (6, 811) has progressed to the point where scientists and engineers are now vigorously pursuing microwave applications. In contrast, research on NIMs that operate at higher frequencies (1222) is at an early stage, with issues of material fabrication and characterization still being sorted out.

The figure gives a detailed history of the development of the magnetic resonance frequency and/or the frequency of negative n as a function of time. In the early years of the field (2000 to 2003), the design of choice to obtain μ < 0 was an artificial structure proposed by Pendry, the so-called split-ring resonator (SRR). This structure exhibits a band of negative μ values even though it is made of nonmagnetic materials. A double SRR is shown at the lower left of the figure. A negative μ at 10 GHz requires SRR dimensions on the order of 1 mm. To obtain negative ϵ, one needs to arrange long and thin wires in a simple cubic lattice, so as to mimic the response of a metal to electromagnetic waves—that is, below a frequency called the plasma frequency, ϵ is negative. Negative ϵ at gigahertz frequencies might be obtained with wires a few tens of micrometers in diameter and spaced several millimeters apart. By using an array of SRRs and thin wires in alternating layers, several groups (6, 811) showed negative n at gigahertz frequencies.

As can be seen from the figure, a negative μ at terahertz and infrared frequencies was achieved in 2004. The idea underlying that work was that the magnetic resonance frequency of the SRR is inversely proportional to its size. Thus, the concepts from the microwave regime could simply be scaled down to shorter wavelengths. For ease of fabrication, a transition from double SRR to single SRR took place (see the figure). Indeed, this approach works up to about 200 THz. Unfortunately, it was found that this scaling breaks down for yet higher frequencies for the single SRR. The reason is that the metal of which the SRR is composed starts to strongly deviate from an ideal conductor.

Although these developments have been important proofs of principle, progress was hindered by several experimental details. For example, the combination of these SRRs with metal wires to form a three-dimensional structure is very challenging on the nanometer scale. Thus, there was a hunt for alternative designs that are more suitable for the terahertz or even for the visible regime. The key idea to make this possible was independently realized and published by three different groups in 2005 (16, 18, 19). These designs all show that pairs of metal wires or metal plates, separated by a dielectric spacer, can provide the magnetic resonance. The magnetic resonance originated from the antiparallel current in the wire pair with an opposite sign charge accumulating at the corresponding ends. This resonance provides μ < 0. In addition, an electric resonance with ϵ < 0 results for excitation of a parallel current oscillation. In the transmission measurements, the EM waves were incident normal to the sample surface. This setup is much simpler than that for conventional SRRs and wires, where the incident EM waves must propagate parallel to the sample surface.

Overlap (18, 19) of the regions where ϵ and μ are both negative with only wire pairs is difficult, so new designs were needed. One way is to introduce extra continuous wires next to the pairs, or to change the shape of the wires. The best design that has been used in 2005 and 2006 is the so-called “double-fishnet” structure, which consists of a pair of metal fishnets separated by a dielectric spacer. This design is shown in the lower right of the figure. Although the choice of the metal constituting the structure is not critical in the microwave regime, it is crucial in the optical and the visible regime because the metamaterial losses are dominated by metal losses. Silver exhibits the lowest losses at optical frequencies, and indeed, going from gold (16, 18, 20) to silver drastically reduced the losses at similar frequencies (21). A suitable measure for the losses is the figure of merit (FOM), defined as the negative ratio of the real to the imaginary part of n. Dolling et al. (21) obtained FOM = 3 at a wavelength of 1400 nm, which compares to FOM < 1 for other groups (16, 19, 20). Furthermore, the use of silver has enabled the first negative-index metamaterials at the red end of the visible spectrum (22) (wavelength 780 nm). Another group has also reported a negative n (23, 24), but this has been questioned recently (25).

Only 6 years after their first demonstration, negative-index metamaterials have been brought from microwave frequencies toward the visible regime. However, for applications to come within reach, several goals need to be achieved: reduction of losses (by using crystalline metals and/or by introducing optically amplifying materials), three-dimensional rather than planar structures, isotropic designs, and ways of mass production of large-area structures. With emerging techniques such as microcontact printing, nanoembossing, holographic lithography, and quantum tailoring of large molecules, it seems likely that these technical challenges can be successfully met. The spirit of metamaterials is to design materials with new and unusual optical properties. In that enterprise, only our imagination and creativity set the limits.

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