Designer materials render objects nearly invisible to microwaves

Optical design is largely a matter of choosing the right material for the job and then optimizing its geometry—say, a glass lens to form images, a metal cage to screen sensitive electronics, or a polymer film to reduce surface reflections. But the range of electromagnetic properties available to optical engineers from materials found in nature falls far short of what is theoretically possible.

In 1999 John Pendry and colleagues from Imperial College London dramatically extended the palette of realizable electromagnetic properties by proposing a variety of artificial structures—metamaterials—whose response to radiation could be custom-designed. ¹ Although the field of artificial materials dates back to the 1940s, it took advances in computation and fabrication technology made in the 1990s, along with a surge of interest in negative refraction, to set the stage for engineering composite materials whose effective magnetic permeability tensor μ and electric permittivity tensor ε could be tailored.

Essentially miniature inductive and capacitive circuits composed of copper loops built into a repeated array of unit cells, Pendry’s metamaterials owe their electromagnetic properties to subwave-length details of geometric structure rather than to chemical composition. As long as the size and spacing of circuit components are small compared to wavelengths of interest, incident radiation cannot distinguish circuits from conventional materials. Adjusting a circuit’s geometry tunes its resonant frequency and the strength of its electromagnetic response to the incident radiation.

To understand how, think of each circuit as a magnetic atom. Just as a magnetic atom produces a net magnetic dipole in response to a field, so do these metamaterials, at least in the microwave regime where metals react strongly to applied fields. A time-varying electromagnetic field induces an electromotive force that drives a current in a conducting loop. A gap in the loop introduces a capacitance into the circuit and produces a resonance at a frequency set by the loop’s geometry. Similarly, the electric component of the field induces an electric dipole that oscillates with a large amplitude near its resonant frequency. Because the resonant frequency of a metamaterial can be set to virtually any value, one has tremendous control over ε and μ .

Armed with this powerful design flexibility, researchers have since created metamaterials with properties impossible to find in nature. If fashioned so that both ε and μ are negative at some frequency, for instance, metamaterials can form exotic lenses that bend light at that frequency in a direction opposite that of ordinary materials and produce images with a level of detail beyond the diffraction limit (see the article by Pendry and David Smith in Physics Today, June 2004, page 37 ).

Pendry, along with Duke University’s Smith and postdoc David Schurig, has taken the notion of flexible design to its logical conclusion: If, they reasoned, something can be constructed with ε and μ varying independently and arbitrarily throughout the material, then one can redirect electromagnetic waves at will. The researchers set themselves a problem straight out of Star Trek—electromagnetic cloaking, the deflection of waves completely around an object so that the waves return to their original trajectories on the other side, which effectively renders the object invisible. ² Five months later they had a working device. ³

Curved spaces

Designing an invisibility cloak is straightforward, in principle: Find the coordinate transformation that distorts in just the right way the underlying space and thus the paths that electromagnetic fields are constrained to follow. The desired effect is to squeeze space from a volume into a shell. Interestingly, Maxwell’s equations are form-invariant to coordinate transformations, so only the components of ε and μ would be affected, each multiplied by the same factor. Pendry and company “are essentially applying the recipes of general relativity, mapping free space into curved space,” explains Ulf Leonhardt, a theorist from the University of St. Andrews in Scotland who has outlined a similar protocol to achieve cloaking. ⁴ The anisotropic variation in ε and μ takes the place of mass in deflecting the light rays to avoid certain regions of space, in this case a hole where an object might be hidden.

Building a cloak is more complicated. The tensor quantities ε and μ are each three-dimensional matrices, whose components are spatially varying. To simplify the problem, Schurig and coworkers restricted their implementation to an effectively 2D one and adopted a reduced set of parameters using cells that are diagonal in the cylindrical basis. So although the r, θ, and z components of ε and μ each vary with radius in an exact transformation, the actual cloak accounts only for radial variation in μ _r . The only other relevant parameters are μ _θ and ε _z , and they’re held fixed.

The cover and figure 1 show the device: 10 nested fiberglass cylinders, each containing hundreds of wire loops, or split-ring resonators, that scatter incident microwaves through the cloak and around the innermost cylinder. Although variations in the unit-cell geometry affect both ε and μ , Schurig found that he could tune the values of both parameters independently through minor adjustments in the length of the split and the curvature at the corners of each square loop. That curvature and the amount of metal at each corner have little effect on the area threaded by the magnetic flux, but they tweak the electric coupling between adjacent unit cells enough so that ε _z can be held constant while μ _r is increased.

To test the degree to which their device approximates perfect invisibility, the researchers placed it in a parallel-plate waveguide and measured the electric-field amplitude and phase inside and outside the cloak as polarized microwaves were directed toward it. Figure 2 compares theoretical simulations with those experimental results, revealing deviations from the ideal. In each case, as waves propagate through the cloak and approach the inner radius, the wavefronts begin to lag with a concomitant compression in wavelength and a reduction in intensity. The penalty for using the reduced parameter set for ε and μ is nonzero reflectance of the incident radiation, as pictured in figures 2b and 2d. Real materials, of course, also absorb some fraction of incident radiation. Nevertheless, the device dramatically reduces backward and forward scattering of microwaves, compared with the case where the waves are incident to an uncloaked copper cylinder (figure 2c).

Other researchers have recently proposed alternative invisibility schemes. ⁵ In 2005 the University of Pennsylvania’s Andrea Alù and Nader Engheta proposed the use of a plasmonic shell that suppresses scattering by resonating in tune with the incident radiation. The exciting electromagnetic field induces in the shell a series of multipole moments that effectively cancel some of those of the object inside it. But the properties of the object being cloaked and of the cloak itself would have to be carefully matched. The scheme thus lacks the generality that Schurig and his colleagues achieved: In their device anything—from mouse to missile—can be cloaked, provided it fits within the cloak’s dimensions.

Romulan dreams

Because the cloak is dispersive—as it must be since the phase velocity of waves inside the cloak exceeds the speed of light in free space—the bandwidth over which it works well is narrow; Schurig and coworkers performed their proof-of-principle demonstration at a single frequency of 8.5 GHz. The microwave-frequency region has plenty of relevance in today’s world, though, and one can imagine an eventual replacement to radar evasion and stealth technologies in aircraft—à la Romulan cloaking of Star Trek fame. According to the University of Rochester’s Allan Greenleaf and colleagues, invisibility is not restricted to passive objects. Active sources and sinks—cell phones and computers, say, or anything else that emits or receives a signal—may also be cloaked, at least in principle. ⁶

Metamaterials based on a nonresonant circuit design might overcome the bandwidth problem to some degree. But extending the response to optical frequencies is trickier. Today the nanometer-scale lithography required to shrink circuit components to fractions of the wavelength of visible light is routine. But the electric permittivity of metals at optical frequencies is several orders of magnitude lower than it is in the microwave region. Electrons simply can’t follow the oscillations in the electric field nearly as well at such high frequencies.

Creating 3D cloaks isn’t easy either. The difficulty lies in designing a cloak’s configuration to produce all the needed variations in the tensor components of ε and μ . Traditional metamaterials are assembled from 2D planar sheets that typically intersect each other in a cubic lattice. The Duke–Imperial College design veered from tradition by bending sheets into cylinders to form a metamaterial that is semicrystalline—periodic in θ and z but amorphous in the radial direction. The next-generation design may incorporate spherical circuit configurations and more exotic topologies. But according to Pendry, that shouldn’t surprise us. “The more you think about Maxwell’s equations, the more you realize that geometry is at their heart.”