Ulf Leonhardt is riding high these days, with a new award from the Royal Society of Great Britain to further develop his ideas on how to make things in plain sight disappear.
Born in East Germany and now occupying the theoretical physics chair at Scotland’s University of St. Andrews, Leonhardt is among the leaders of the worldwide race to realize an old dream of science fiction: cloaking devices. They would steer light or other electromagnetic waves around them like water around a stone in a smooth stream, leaving nary a ripple of difference in the flow. Such things, letting light swish past like a boxer ducking every punch, would be invisible.
Cloaking device is a common term in technical literature. It also deliberately evokes myth and popular fiction. Allusions include the Romulan technology that first amazed TV viewers of the old Star Trek in the episode “Balance of Terror,” when hostile Bird of Prey fighting vessels just disappeared, poof. One finds cloaking in J.K. Rowling’s novels about the young wizard Harry Potter with his invisibility cape. Farther back, H.G. Wells’ novel The Invisible Man (and the movie of the same name, along with its sequel The Invisible Woman) toyed with much the same idea. J.R.R. Tolkien assigned similar power to The One Ring in his tales of hobbits. Inspiration for the ring apparently came from way back — the magical ring that the shepherd Gyges recovered from an earthquake-spawned chasm in Plato’s The Republic.
Leonhardt’s role in the cloaking field’s rise to respectability did not get off to an encouraging start. The details of his initial frustration and eventual triumph illustrate the swiftness with which the field entered the mainstream — even surprising some experts. “I began my work at a time when invisibility was not fashionable at all,” he says. That was about a decade ago. After years of quiet work with a few colleagues, he wrote a paper titled “Optical conformal mapping.” The abstract’s first words come right to the point: “An invisibility device should guide light around an object as if nothing were there.”
In 2005 he sent the paper to Nature, which rejected it, and to Nature Physics. Editors at Nature Physics, Leonhardt recalls, took just two days to reject the paper as well. So, he says, he sent it to Science. There, it lasted two weeks before the heave-ho. In early 2006 he tried again, this time with Physical Review Letters, or PRL. Another no-go. One reviewer said the mathematics, while classical (the calculations refer to Maxwell’s and Newton’s equations of light and to other mathematical constructs credited to such titans as Fermat, Lagrange, Euler, Descartes, Euclid, Kepler, Einstein and Feynman), did not offer enough new physics. Ouch.
But it was another PRL reviewer’s rebuke that opened Leonhardt’s eyes wide. It said he was not alone. The assessment, routinely shared with Leonhardt, indicated that the reviewer had been to two meetings in the previous months “in which John Pendry discussed his group’s efforts on the same issue, calling it a cloaking device or their Hogwarts project in reference to the cloak of invisibility associated with the Harry Potter series.” Pendry and his colleagues, the assessment added, “supposedly have filed a patent related to this work.” Hence, the anonymous reviewer declared, the work was not new and did not merit publication in PRL.
It came as a surprise to Leonhardt that he had been in unwitting competition with Pendry, one of the most distinguished scientists in Britain. Pendry is not merely professor of theoretical physics at Imperial College London — he is Sir John. The queen knighted him in 2004 for his services to science. Much of his reputation is based upon achievements in optical theory and in metamaterials that refract light in a fashion — even backward — not found in natural substances. Leonhardt was pleased to have a rival of such eminence but furious over his paper’s treatment. Because Pendry’s team had not published its work, Leonhardt argued in a letter to PRL, the journal should publish promptly — not reject —his own paper. Further, Leonhardt averred that a pending patent provides no ethical reason to reject independent work by an outsider.
Then, abruptly, his fortunes took a 180-degree turn.
Science, he recalls, wanted to publish his paper after all. The journal had just received a paper from Pendry’s team, which includes his close collaborator David Smith, an electrical and computer engineer at Duke University in Durham, N.C. Titled “Controlling electromagnetic fields,” the work was strikingly similar in its overall message to what Leonhardt had already offered. In late May 2006 the two papers came out (SN: 7/15/06, p. 42). They were sensations. Dozens of groups around the world set to work to build devices that, however crudely, tested the elegant new mathematical prescriptions.
Later that year Science named the papers and cloaking as among the world’s top science breakthroughs of 2006. Scientific American named Pendry, Smith and Leonhardt to its list of top 50 research leaders of the year. Leonhardt recently won a prestigious Theo Murphy Blue Skies award from the Royal Society with two years’ full funding to pursue invisibility by manipulating light and other electromagnetic waves, and to follow indications that even sea waves might be steered around small islands or drilling platforms by altering the water nearby.
Pendry this year won the UNESCO-Niels Bohr gold medal for his work in the field.
Stabs at disappearance
During the past four years headlines have been reporting the baby-step progress by Leonhardt and a dozen or so other teams toward not only cloaking devices, but also supersharp lenses, omnidirectional reflectors (a specialty of Leonhardt’s) and artificial black holes that would swallow light much like a collapsed star in deep space would (SN: 10/10/09, p. 10). All such seeming trickery is born of the same underlying optical sleights of hand. On the physics website arXiv.org, more than 30 papers have appeared in the past year with variants of “cloak” or “cloaking” in their titles.
So far the devices have all been tests of the concept, with nothing close to practical. Furthermore, the small gadgets don’t yet cloak anything perfectly, or cloak anything very large. Some regions that have been made invisible are hard to see without a microscope. And because cloaks that shield longer wavelengths of light are easier to make, first successes came with microwaves — whose radiation can be measured in inches. Some devices work in the infrared with pinhead-sized or smaller wavelengths, with even shorter light waves just now showing up on the agenda.
Leonhardt and Pendry remain in the thick of it — and remain rivals. Each is easily goaded to murmurings that the other takes more than his fair share of credit for coaxing invisibility from obscurity.
While Pendry says Leonhardt’s first published paper “had a good scheme,” he adds that Leonhardt makes more of it than he should. “Ulf is not being straightforward, for his was not a full cloak, but an approximation” — because his approach did not have a full treatment of light as waves but handled it as a collection of rays. Leonhardt in turn says of Pendry: “He has done very important work, but he has not done everything. In particular the connection of this research area to general relativity, that is what we have done.… He makes the impression that this whole field is due to him, and he used results that I developed without referencing them.”
Sharp elbows are not uncommon in highly competitive, new fields of science. But the researchers agree on one thing: Progress has been fast. “The field has amazed me,” Pendry says. “People have jumped onto the theme, and how successful they have been. There are some wonderful ideas out there.” Says Leonhardt: “It has gotten more interesting than I expected. The theoretical side of the field was over very quickly. Now it is being turned into reality.”
A few examples:
Xiang Zhang of the University of California, Berkeley and the Lawrence Berkeley National Laboratory says he and a few others in the field have their eyes on a cloaking material that ought to work at visible wavelengths — but it’s a secret for now, so he can’t say what it is. “You could trip on it, and feel it, but you wouldn’t see it,” he predicts. The secret recipe needs more work, he says, and ought to be ready for publication in a year … or more.
At Purdue University in West Lafayette, Ind., physicist Vladimir Shalaev is pretty sure he can do it, too, and is happy to describe the material (basically, mirrors and air), but he isn’t yet sure how to shape it for practical use.
Physicist Michal Lipson of Cornell University and her group have demonstrated a microscopic “carpet cloak,” a miniature flat, reflective surface with a lump in it to hide the goods. The lumpy part looks as flat as the rest of the “rug,” the team reports in the August Nature Photonics. Zhang’s Berkeley group, led by grad student Jason Valentine, did the same thing, reporting the results in the July Nature Materials. “It’s like we ripped a hole in the fabric of space,” Valentine says. “Light won’t go there.”
This year in PRL, a team led by Che Ting Chan, a Berkeley-trained physicist at the Hong Kong University of Science and Technology, describes an approach called “remote cloaking.” It not only (in theory) renders an object invisible, but also does so with a device sitting next to rather than surrounding the thing to be hidden. Invisibility, says one of the team’s papers, is merely the process of altering the light so an object “looks like air.” Even better, the group claims, it may be possible to make one thing look like another — for example “change an apple optically to [a] banana.” The researchers call this offshoot “illusion optics.”
Some of these methods work only within a narrow range of wavelengths, often in flat, two-dimensional settings. It’s difficult to find anybody in the know who expects there will ever be a device that hides itself and its contents at all wavelengths — if you can’t see it in visible light, then perhaps radar, infrared, ultraviolet or X-rays would reveal it. But optimism for practical uses is growing. So are the sources of money to propel research.
In the United States, National Science Foundation program officer Robert Trew says that the main division supporting such work — Electrical, Communications and Cyber Systems — has about $15 million worth of contracts now out, shared among
16 awards. The Pentagon’s Defense Advanced Research Projects Agency, or DARPA, has been supporting such research — initially behind a cloak of semisecrecy (not quite classified, but not published in open media either) for most of this decade. While precise figures are hard to come by, DARPA has spent about $50 million in the last 10 years on metamaterials, including cloaking research.
In an allusion to the cloaking process, Pendry now thinks “much of this work will soon go dark” as military money in the United States, and in other nations, drops a cape on sensitive applications.
A hidey-hole in stretched space
While cloaking is the term that has caught the public’s eye, the broader field is known as transformation optics. Its power comes from a remarkable property of Maxwell’s classic equations describing the behavior of light and other electromagnetic radiation. The equations are invariant, meaning that they work the same in different coordinate systems. Thus physicists can keep track of how light will behave if a real object is mathematically warped into something shaped quite different — or, vice versa. A dimensionless point in one mathematical realm, unaffected by passing light waves, can be expanded into a 3-D void in another coordinate system. But light or other radiation remains oblivious to the void.
Leonhardt, in his seminal paper in Science, described this as conformal mapping. Just as a mapmaker drapes the geographic points on the Earth’s globe onto a flat sheet — such as for a Mercator projection — mathematicians can map, or conform, the surface of one object onto something else. And Maxwell’s equations still work there.
Pendry, in a review in the July 30 Nature, explained the concept clearly: “Imagine that the optical system in question … is embedded in a rubber medium. We then stretch and pull the rubber, taking with it all the rays of light passing … until the rays are traveling in the desired directions.” The same transformations that “stretched the rubber” also describe how the newly made cloak’s properties must change — how its refractive index at every point must be altered — to permit Maxwell’s equations to exert themselves as desired and steer the waves around the hiding place.
It is for this reason that papers on cloaking are often littered with the symbols μ. These are epsilon and mu, the electrical permittivity and the magnetic permeability of a material. The values describe the way a substance reacts to the oscillating electrical and magnetic fields of electromagnetic radiation. Changes in these values can make light slow down, speed up and thus refract, or bend. (Wave fronts swerve when one portion slows compared with the others.) While other qualities determine how transparent a material is to a given wavelength, e and m work pretty much the same at all wavelengths. They are the components of the refractive index.
And metamaterials, whose refractive index can be engineered far more flexibly than can natural substances (even to the point of a negative index that bends light more than halfway back on its original direction), are the medium of choice.
Unlike the atoms and molecules that nature provides, which are limited in the combinations of electrical and magnetic permittivity and permeability, the novel metamaterials can mix and match e and m to provide exactly the radical refractive index variations that make light do loop-de-loops around a cloaked void, while obeying rules that would otherwise produce a straight route.
The shorter the wavelength passing through, the tinier must be the bits of matter whose combined optical behavior yields a metamaterial. So it is no surprise that the first working cloak, about the diameter of a CD but much thicker, functioned only with microwaves at wavelengths of about an inch in air. The device, made by Smith’s group at Duke in 2006, has antenna-like copper wires embedded in concentric rings of fiberglass easily visible to the eye (SN: 10/21/06, p. 261).
Earlier this year, Zhang’s lab at Berkeley steered infrared waves, which have much shorter wavelengths, around a hiding place. Grad student Valentine and colleagues used a focused beam of ions to drill varying arrays of holes in silicon-based semiconductors to make the carpet cloak. Similarly, delicately patterned forests of tiny pegs, planted on a silicon wafer by Lipson’s team at Cornell, altered the electrical permittivity so that infrared waves bouncing off a mirrored surface didn’t notice a lump. They reflected as though the surface were flat — the lump and anything beneath were cloaked.
“It’s not good for anything, now,” says Valentine of the carpet cloak. For one thing, it works only in two dimensions. And for another, it has a special but not very useful geometry that lets the researchers manipulate permittivity, e, alone, allowing use of ordinary materials that are poor conductors but are friendly to electric fields. The holes and pegs simply change the material’s gross density, hence its electrical response. “But it works, and that’s a start.” And it works at a broad range of infrared wavelengths, from about 1,400 to 1,800 nanometers. The scheme will not work, however, at visible wavelengths, which range from 700 down to 400 nanometers, at least not with any fabrication method clear to the researchers. And wavelengths shorter than that — from ultraviolet to X-rays and below —remain pure science fiction for now.
Asked how to make metamaterials whose simulated “atoms” of unnatural material are small enough to smoothly steer visible light, Valentine’s boss Zhang is a bit evasive. He and several teams, he says, have something in mind. What is it? “I cannot tell you,” he says. “It will take more work.” Until it is tested and published, Zhang will say no more.
Remarkably, the mathematics of metamaterials and transformation optics have led researchers to think freshly about other ways to manipulate electromagnetic radiation. At Purdue University, for example, a group led by Shalaev has found that the equations for how light is channeled down a waveguide —basically a mirrored conduit — are similar to those that describe how variable refractive indices smoothly steer light’s path. It turns out that when such a waveguide gets so narrow that its walls are about as far apart as the wavelength of radiation between them, the radiation slows down. If the conduit is too tight, then the radiation can go no further. But if a path just a little wider is available, the radiation swerves down that. Shalaev has come up with a system of gold-plated convex mirrors stacked with similarly mirrored flat, gold-plated sheets. As radiation enters from the side, the gaps between the gently curved surfaces and flat sheets squeeze down. When the gap between the central portion of the convex mirror and the flat sheet becomes too small for the light to pass through, it scoots around the protruding dome of the mirror, converges on the opposite side and keeps going. In May in Physical Review Letters, Shalaev and colleagues report that a one-layer cloak of this tapered waveguide device shielded a tiny area about 50 micrometers across. As he said: “I can cloak a human hair. It’s a good start. If I could answer how to cloak a human, I have Nobel Prize.”
For all the excitement now, says Smith, “the basic ideas behind this have been around a long time, some of them from Maxwell’s time.” A paper written in 1961 in an obscure, Russian journal by an optics specialist named Lev Dolin used almost the exact same manipulation of Maxwell’s equations, coordinate transformations and alterations of permeability and permittivity that Pendry and Leonhardt have been using within the last decade.
But whether cloaking in the sense of science fiction’s dreams ever occurs or not, the dam has burst. New ways to focus and project light and other radiation seem certain. “There is a whole new class of optics waiting for us,” Smith says.
Nobody expects cloaking to make things invisible to all detectors. But even here, fiction has anticipated things with a spooky parallel. Recall the Romulan warships? Their cloaking didn’t work perfectly either — and the Enterprise crew learned to track them, cloaked or not.
And one more thing to remember. If a cloak were to make an object fully invisible to the outside world, then the outside world would be invisible to the object within the cloak. A thing (or person) inside a perfect cloak is not only invisible. It is blind.
Charles Petit is a freelance writer based in Berkeley, Calif.
