PerspectiveMaterials Science

Metamaterials Beyond Optics

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Science  22 Nov 2013:
Vol. 342, Issue 6161, pp. 939-940
DOI: 10.1126/science.1246545

So far, the field of metamaterials has largely dealt with negative refractive indices in optics and invisibility cloaks (13). However, the underlying idea of designing material properties is not that narrow. More broadly, one rationally designs a subwavelength unit cell from existing constituent materials and (periodically) arranges it into an artificial solid. The properties of that solid are then determined by structure rather than chemistry and can be tailored, extreme, or even qualitatively unprecedented. Rational design is the key and makes metamaterials a rather particular class of composite materials.

In terms of application, some aspects of metamaterials such as negative phase velocities of light (1, 2), invisibility cloaking (4, 5), or unusual optical nonlinearities (6) are fascinating but are not likely to soon appear in products, because optical absorption (loss) is too high and in part fundamentally unavoidable. Moreover, the inexpensive manufacturing of complex large-volume three-dimensional optical metamaterials is still a formidable challenge in itself (2).

Why, then, don't we go beyond optics and also consider other material aspects (7) such as thermal, acoustic, elastic, or irreversible nonlinear mechanical properties? The corresponding wavelengths and length scales range from tens of micrometers to centimeters, rather than nanometers in optics. Hence, fabrication limitations are relaxed, thus easing real-world applications. Moreover, one lesson learned from electromagnetism is that off-resonant constituents enable low losses. In the visible spectrum, however, this results in a contrast in refractive index of no more than 3 for available nonabsorbing dielectrics. Some theoretical blueprints demand constituent-material contrasts in the range of tens or hundreds. Such values are accessible in mechanics and thermodynamics (see the figure).

Seeing, hearing, feeling.

While optics has been in the foreground of metamaterials research, opportunities arise in other areas such as acoustics, mechanics, and thermodynamics (heat conduction and diffusion). In all of these, larger lattice constants ease the fabrication requirements and losses can be much lower or absent.


Consider simple mechanical waves in elastic solids. They exhibit three orthogonal polarizations, one longitudinal (like sound waves in air or water) and two transverse (like electromagnetic waves). This complex elastic behavior gets simpler in so-called pentamode metamaterials, in which the longitudinal polarization dominates because the effective metamaterial shear modulus is small relative to the bulk modulus. Pentamode metamaterials were proposed years ago (8) but have been realized only recently (9). In these materials, wave propagation is scalar, thereby allowing analogies to optics. For example, the elastic counterpart of an optical invisibility cloak becomes possible (7). Such elastic structures would also work in the static limit. One could then mechanically protect or hide sensitive objects within the mechanical cloak.

In more detail, the elastic compressibility plays the same role that electric permittivity plays in electromagnetism; likewise, the mass density plays the role of magnetic permeability (7). Mechanical metamaterials that offer low mass density together with reasonable mechanical stability have been realized (10). Negative mass densities and anisotropic mass-density tensors are well established theoretically (7, 11), and one-dimensional model systems have been demonstrated experimentally (12) as well. Still, experimentalists need feasible blueprints to fabricate three-dimensional microstructures to achieve specific anisotropic mass-density tensors. Progress here would greatly enhance the possibilities in elasticity.

An elastic solid can be viewed as the generalization of a passive reversible linear Hooke spring. But why limit ourselves to this linear mechanical regime? Metamaterial unit cells could be constructed that break or buckle to dissipate mechanical shock energy. We also could work toward active mechanical metamaterials, integrating miniature energy sources together with sensors, actuators, and feedback loops into the individual unit cells. Nonlinear and active mechanical metamaterials are wide open for innovation.

As a second group of examples, consider thermodynamic material properties such as heat conduction or diffusion (7). Much of optical metamaterials is about molding the flow of the Poynting vector—that is, the energy flux per unit time and area. The heat current density in thermodynamics has the same meaning and units. It also follows a related continuity equation, even though waves do not occur in thermodynamics. Material contrast in thermal conductivity can exceed 1000, and thermal metamaterial lattice constants can be made smaller than the thermal diffusion length (the counterpart of the optical wavelength). Losses are absent because heat is at the bottom of the energy food chain. Consequently, free-space omnidirectional broadband thermal cloaks work nearly perfectly (13). Objects can transiently be protected from overheating while keeping the heat flow in their surroundings as though nothing was there.

Still, the metamaterial cloak needs to be wrapped around the object. It would be yet more stunning and useful if it could rather be spatially separated from the object. Such exterior cloaking is possible and has been demonstrated experimentally in dc electrical conduction using effectively negative electric conductivities (14) of active metamaterials [see also absolute negative mobility (15)]. By analogy, exterior thermal cloaking requires effectively negative metamaterial heat conductivities. Heat would flow from the cold to the hot. The second law of thermodynamics forbids that for passive but not for active materials containing heat sources or sinks. Mathematically, negative heat conductivity is analogous to negative phase velocity in electromagnetism (1, 2).

Yet further opportunities arise in airborne acoustics. Just think more broadly about metamaterials.

References and Notes

  1. Acknowledgments: I thank R. Schittny for preparing the figure and for careful reading of the manuscript, and T. Bückmann, J. Christensen, S. Guenneau, P. Gumbsch, M. Kadic, G. W. Milton, and M. Thiel for discussions. Supported by the DFG Center for Functional Nanostructures and the Karlsruhe School of Optics and Photonics.
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