PerspectiveMaterials Science

Pursuing Near-Zero Response

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Science  19 Apr 2013:
Vol. 340, Issue 6130, pp. 286-287
DOI: 10.1126/science.1235589

In most wave phenomena, the interplay between the spatial and temporal features of a wave is influenced by the medium in which the wave propagates. For example, the wavelength λ (a spatial feature) and the frequency f (a temporal feature) of a propagating signal are related via the phase velocity v of the wave in the medium as v = fλ. For electromagnetic waves such as radio, microwave, and optical waves, the phase velocity is determined by the medium's electromagnetic parameters of permittivity ε and permeability µ, which is then given as √εμ . When a wave interacts with a structure embedded in a host medium, both these temporal and spatial features play key roles in determining the scattering response of the structure. The recent development of a class of metamaterials in which the electric (ε) and magnetic (µ) properties can be tuned by design is providing a platform to engineer optical devices with unconventional properties.

Features of ENZ metamaterials.

(A) The wavelength can be “stretched” within materials with low permittivity, whereas for high permittivity it is compressed. (B) A judicious mixture of a permittivity-positive and a permittivity-negative constituent structure may provide an effectively ENZ metamaterial. (C) Supercoupling phenomenon in ENZ-filled ultranarrow channels between two similar, but arbitrarily oriented, waveguides, in which an efficient tunneling occurs regardless of the length, shape, bending, and twisting of the ultranarrow channel.

The frequency of the wave tells us how the structure's materials behave, whereas its wavelength in the host medium is the yardstick by which the physical dimensions of the structure affect the wave-structure interaction. These two aspects of interaction are often closely intertwined because any physical structure is made of a material and has certain physical dimensions. Of course, as we go to higher frequencies, wavelengths are generally shortened. However, metamaterials allow the link between the frequency and the wavelength to be relaxed. If either the permittivity or the permeability (or both) can be designed to be relatively low values near zero, the phase velocity of the wave will approach a very high value, resulting in long wavelengths at high frequencies (see the figure, panel A).

The class of materials in which the relative permittivity ε attains near-zero values around a given frequency is called Epsilon-Near-Zero (ENZ) metamaterials (1). When the operating frequency is near the plasma frequency of transparent conducting oxides [e.g., indium-tin-oxide (ITO)] (2), the real part of the permittivity gets near zero (whereas its imaginary part is small). Alternatively, metamaterials can be designed to achieve effective permittivity near zero by mixing constituent materials with permittivity-positive (oxides) and permittivity-negative (metal) structures, such as the stacks of thin layers of pairs of such structures (see the figure, panel B). Another way to imitate propagation in an ENZ medium is to exploit the structural dispersion of metal-clad waveguides near their cut-off frequencies (3, 4).

ENZ metamaterials offer unprecedented wave properties. One such property is the phenomenon of supercoupling (1), in which the wave in one waveguide can efficiently tunnel through a very narrow, ENZ-filled channel to reach another waveguide, regardless of the channel's length, shape, bending and twisting, and the relative orientation of the two waveguides (see the figure, panel C). Counterintuitively, the narrower the channel's height, the better the tunneling. The consequence of this unusual tunneling is threefold: (i) because the energy has to squeeze through the narrow channel with no reflection, the wave intensity is enhanced along the entire narrow channel, and such enhancement is inversely proportional to the ratio of the channel's height to the port waveguide's height; (ii) because the wavelength in the ENZ region is very long due to the low value of permittivity, the enhanced intensity maintains an approximately uniform phase along the entire channel's length; and (iii) this enhancement and its uniformity along the channel are essentially independent of the length, shape, and bending of the channel. Because of its high wave intensity enhancement over an extended region, this phenomenon has been studied for boosting nonlinear effects (5) and second-harmonic generation and has also been used for enhancing the photon density of state for emitters embedded in such ENZ structures (6, 7). This platform has also been proposed for sensing a defect in the channel (8), thus opening the possibility for fluidic- and biosensing applications. The supercoupling concept has now been extended to other wave phenomena, such as acoustic and matter waves (9).

Because the permittivity of these materials is near zero, the electric displacement vector may also be near zero for a finite electric field. Therefore, an ENZ material can be used as a platform for “shielding” the displacement current, just as a dielectric insulator may shield the conduction current in a metallic wire (10, 11).

ENZ structures may provide a useful mechanism for enhancing the effects of nonreciprocity and time-reversal symmetry breaking, when they are combined with magneto-optical materials. Such composites may favorably change the balance between the parameter of the magneto-optical activity and the dielectric parameters, causing pronounced nonreciprocal effects such as wave isolation based on circular polarization and Faraday rotation (12).

In conventional media, random displacement of tiny scatterers causes temporal decoherence of the scattered signals. Because the wavelength is increased in ENZ media, random fluctuation of scatterers embedded in these media may lead to decreased incoherence and thus may maintain a more coherent signal compared with conventional materials.

Finally, when the permeability µ of ENZ metamaterials is also near zero, the refractive index of the medium again approaches nearzero value; however, here the wave impedance is preserved (1315). In such a scenario, a large volume of this medium may occupy appreciable physical space, while still being tiny from the wave point of view (because the wavelength has become long). This will provide an interesting possibility to “stretch” and “open up” a part of a physical system by expanding the region and filling it with index-near-zero medium. Such “opening up” of the space should not affect the wave interaction in the external region but could provide a platform to insert objects and elements that ordinarily would not fit in the region with standard materials. This concept may open doors to novel spectroscopy of nanostructures in which the effects of the size of the object may be decoupled from its material dispersion.

References and Notes

  1. Acknowledgments: This work is supported in part by the U.S. Office of Naval Research Multidisciplinary University Research Initiatives grant N00014-10-1-0942.
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