In 2006, a number of researchers made international headlines with the announcement that they had laid the theoretical foundations for the construction of an “invisibility cloak,” a device that has been a staple of horror, fantasy and science fiction for over 100 years earlier. Since then, new developments in optical cloaking have been a regular staple of the science news media, and every new discovery has been reported on with breathless, and often over-hyped, excitement.
It is with this in mind that I mention new results that hit the media over the past few days, with tantalizing headlines like “Invisibility cloaking in ‘perfect’ demonstration,” “Researchers at Duke are perfecting an invisibility cloak,” and “Scientists call their discovery a ‘perfect’ invisibility cloak.”
These are also experimental results! With this in mind, can we say that “perfect” cloaking has been achieved? Well, it really depends on your interpretation of the word “perfect!” In a very real technical sense, to be explained below, the researchers have demonstrated that optical cloaking can in principle work perfectly (with certain strong caveats), and make an object undetectable to an electromagnetic wave of a certain wavelength. However, it is nowhere near “perfect” cloaking in the sense that most of the public would interpret the word — the object is readily, obviously visible under most circumstances!
Though there are a lot of posts out there explaining the new developments, I thought I’d spare a few words to describe what exactly what was done and what is novel about it.
First, a refresher: in 2006, two research papers were published back-to-back articles in Science magazine postulating the possibility of “invisibility cloaks.” One of these, “Optical conformal mapping,” was written by U. Leonhardt*, and the other, “Controlling electromagnetic fields,” was written by J.B. Pendry, D. Schurig and D.R. Smith**. (My original post on these papers is here.)
Both of these theoretical articles introduced the same idea: that light travels through matter in very much the same way that light would travel through a region of warped space! All materials are characterized by a quantity called the refractive index, which represents the fraction by which the speed of light is reduced in the medium. When a ray of light travels in a medium with a continuously varying (i.e. gradient) refractive index, it follows a curved path, as illustrated below.
This curving is very much akin to the curved paths that light travels when in the vicinity of a strong gravitational object like a star or black hole. In the original cloaking papers, the authors pushed this analogy to a rigorous mathematical theory, now known as transformation optics. In order to design a cloak, one simply imagines how one would “pinch” space in order to leave a gap into which no light can enter. Then one uses the mathematics of transformation optics to determine what type of material will curve light in the same manner. The idea of “pinching” space is roughly illustrated below.
The actual transformations, and materials, needed to make a cloak are much more complicated, but the effect on light rays is quite straightforward: the rays enter the cloak on one side, are bent around the central, cloaked, region, and emerge from the other side, as if they had traveled without distortion. This is illustrated for the two original models below.
When these results first came out, it was expected that it would take a long, long time to actually implement a cloak experimentally. Among many challenges, a practical cloak requires complicated optical materials that must have unusual structures engineered on a scale smaller than the wavelength of light being cloaked. Visible light has wavelengths roughly 500 billionths of a meter, and bulk three-dimensional manipulations of matter at that scale is still outside the ability of science. The class of materials needed are not to be found in nature, and are known as metamaterials.
Nevertheless, it is possible to make crude cloaking devices at longer wavelengths! In 2006, the same year that cloaking was introduced, researchers D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith*** constructed a two-dimensional cloaking device that works at microwave wavelengths, roughly 3 cm. An illustration of the device, with its internal structure, is shown below.
The entire cloak is roughly 12 cm in diameter, and is in no way really invisible! The device was sandwiched between two metal plates, to keep the microwaves confined to two dimensions, and only cloaks the interior region for a narrow range of microwave wavelengths.
More significant, and relevant to our discussion, is that the creators of this first cloak “cheated” a bit in its design! I noted that the material properties of cloaks are very complicated; even in the microwave two-dimensional case, a true optical cloak requires internal structure that is extremely complicated and difficult to fabricate, at least for the original cylindrical design shown above. Schurig et al. made the process easier by noting that, at least within the limit of ray optics, much simpler structures will produce the same microwave ray bending.
The catch is that microwaves (and light) are waves, and the simplified cloak design therefore fell notably short of being “perfect.” In particular, the simple cloak reflected a significant amount of light from its surface, damaging the cloaking effect.
To fix this, researchers were faced with two choices: figure out how to fabricate the extremely complicated “perfect” cylindrical cloaking structure or, alternatively, find another type of cloaking design that does not need such complicated materials to achieve “perfection.”
Duke researchers took the second approach, and drew inspiration from a second category of optical cloaks, known as “carpet cloaks.” In 2008, J. Li and J.B. Pendry**** observed that it is possible to hide objects on a smooth surface by a modified cloak. The “carpet cloak” in principle makes a surface with an object on it appear flat, by curving the light rays appropriately; the strategy is called “hiding under the carpet,” and is illustrated below.
The carpet cloak is much simpler than the spherical or cylindrical ones considered earlier, and also can be built with much simpler materials; in fact, several experimental realizations (by no means invisible, however!) were demonstrated recently. Duke researchers N. Landy and D.R. Smith***** have introduced a cloak that uses similar mathematics to the carpet cloak, and in fact produces “perfect” cloaking! Simulations done by the researchers are shown below.
You can see that the plane waves coming from the left are diverted around the central diamond region and reconstructed as plane waves on the right side! We may crudely understand this diamond-shaped cloak as a pair of carpet cloaks, one above the other, each of which diverts the waves away from the interior region.
As I have said, this cloak is by no means “perfect” in a colloquial sense of the word: it functions only in two-dimensions, it works only for a narrow range of wavelengths and, most significant, it only works for one direction of illumination! Though microwaves from the left are diverted by the cloak without reflection or scattering, the same thing cannot be said for waves coming from the top or bottom or any other angle.
Though it suffers from many of the same limitations as earlier experimental cloaking designs (and the additional one of directionality), this cloak is still a significant development. This is the first cloaking design that does not make any approximations in its design, and is a precise implementation (and vindication) of the ideas of transformation optics. Its success demonstrates that “perfect” cloaking is feasible, if not possible at the moment.
Furthermore, these results demonstrate that there is more than one way to make a practical cloaking device! I expect that the diamond cloak will spur researchers to investigate more possible, and easier to fabricate, cloaks.
So the press releases may have been a bit misleading to emphasize the “perfect” aspects of the cloak, but the science is interesting nevertheless!
* U. Leonhardt, “Optical Conformal Mapping,” Science, 312 (2006), 1777-1780.
** J.B. Pendry, D. Schurig and D.R. Smith, “Controlling Electromagnetic Fields,” Science, 312 (2006), 1780-1782.
*** D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314 (2006), 977-980.
**** J. Li and J.B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101 (2008), 203901.
***** N. Landy and D.R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nature Materials (2012), online published.