The Science Fact and Fiction of Invisibility

There is undeniably a link between science fact and the ideas that emerge in science fiction and fantasy. Science fiction authors are inspired by actual scientific and technological discoveries, but allow themselves the freedom to project the possible future course of these discoveries and their potential impact on society, perhaps remaining only weakly tethered to the facts. And, when faced with obstacles presented by the realities of actual technology, authors of fiction can break free from the tethers entirely, inventing completely imaginary technologies to move their storyline forward. However, the most skilled practitioners of the genre create compelling stories by having the fictional technology maintain some connection to either existing or at least projected technologies.

Scientists, in turn, often derive inspiration from the imaginative possibilities that exist in fictional worlds, but are constrained to follow the laws of nature that apply in this world. The inventions in fictional worlds seldom transition to the real world,--at least not in the way they are first imagined. But it does happen. Jules Verne wrote about space ships and submarines before either were demonstrated. Planet colonization and terraforming, space elevators and "bionic" replacement limbs are science fiction concepts that have not yet fully materialized into reality, but that are taken seriously by researchers and are very active research topics. The idea of semi-intelligent servant robots, once restricted entirely to the realm of fiction, is now actively being pursued by both academic and corporate researchers. Already, we can buy Roombas and Robovacs to tidy up around the house!

While the science in fiction seeks and achieves the same broad goals as actual science seeks, it differs from actual science in that the details are left out. Science reality is driven by a massive collection of small details, mostly too difficult to describe easily except to other experts in the field. To achieve the really big, exciting results, scientists devote most of their time to what might seem like small and even insignificant minutiae. Everyone can understand what a cell phone is and what it does--conveying voice and other information across space wirelessly--but only experts and the most devoted enthusiasts really understand the underlying technologies such as electromagnetic wave propagation or digital communication theory. As in any technology, the details of wireless communication comprise volumes of technical material representing decades of development.

So, the science in fiction necessarily short-cuts the scientific process, providing largely only the "big" results. Of course, it has to be this way, because a science fiction story is foremost a story, with characters and a plot and all of the other things common to all stories. The science, even if crucial to the plot, is secondary. If a technology is introduced in a science fiction story, its purpose must be easily understood by technical and non-technical readers alike. If we know nothing else, we can understand that Death Star in the Star Wars universe is a collosal weapon that has to be stopped; the warp drive in the Star Trek universe enables faster-than-light travel, so the Enterprise can zip around between galaxies in days rather than the eternity it would take given our actual technology; an advanced artificial intelligence computer chip enables the Terminator robot to think and act in a nearly human way. In reality, scientists work on topics that are nowhere near as easily conveyed to a non-technical audience. It is especially difficult to communicate ideas originating in the mathematical and physical sciences to non-experts, since most concepts are conveyed using a language that amounts to a steady stream of equations and formulas.

Our group studies the interesting electromagnetic properties of artificially structured materials, or metamaterials. As remarkable--sometimes even science-fiction like--as these metamaterials are, we usually run into the problem that it is difficult to convey their importance to non-experts. However, we have recently had the opportunity to study a new type of electromagnetic metamaterial that has a function easily understood by all. In a recent paper published in the journal Science, we have outlined a theoretical method to design a material that would render objects invisible. This topic has raised an enormous amount of interest worldwide, and with that interest inevitably comes rampant speculation about what might be possible with this new paradigm. With all the speculation it can become easy to blur the line between what is science fact and what remains science fiction! So, we thought we'd describe here, in a non-technical way, our view on the prospects of invisibility, and try to sort out the fact from the fiction.

Invisibility in Science Fiction

Invisibility is a common theme in tales from science fiction, fantasy, fables and mythology. If we exclude magic and supernatural mechanisms for invisibility--sorry, but this includes Harry Potter's cape and Platform Nine and Three Quarters at King's Crossing for the moment--then we are left with a few more "scientific" routes to invisibility that have been postulated in the science fiction genre. In H. G. Well's Invisible Man, a series of chemical experiments renders a man invisible. Although the process is never fully described, one would speculate that biochemistry has altered the invisible man's molecules so as to be inert to light passing by.

A chemical route to invisibility is pretty unlikely. The complex molecules that make up human beings do absorb and scatter light, and these interactions are often tied to other important biological functions that would probably stop working if we tried to tinker too much at the molecular level.

But, even the fictional invisible man suggests some of the issues that would arise if invisibility were ever developed. For example, the invisible man has the advantage only when his adversaries are not expecting him to be there. If, on the other hand, we suspect an invisible man is in our presence, we can simply toss paint or powder everywhere randomly to reveal him!

In another fictional invisibility approach, mysterious "fields" are created that can render people and objects undetectable, perhaps routing the rays of light around the object to be concealed. Examples of this sort of invisibility can easily be found science fiction: both Susan Storm of the Fantastic Four as well as the Romulans in the Star Trek universe are able to produce fields that can cloak people and other objects. In both of these embodiments of cloaking, energy is required to create the fields, which forms an important limitation of the technology. The Romulans can shield themselves from detection, but at the cost of not being able to utilize their power hungry weapons. And Storm can vanish and make other objects invisible, but often not at the same time as when she exercises some of her other "psionic" powers.

The speculative mechanisms of invisibility conjured up in Star Trek and in the Fantastic Four contain a glimmer of reality within them. Normally, of course, light travels in a straight path. According to Fermat's Principle, the reason light travels in a straight line is because that is the shortest distance between two points. However, it is known from Einstein's theory of general relativity that an object--any object--warps the very fabric of space-time around it. If space itself is curved, then the shortest distance between two points in that space can become a curve instead of a line. So, the trajectory of light that passes near very massive objects, like suns or black holes, is actually bent, often resulting in lensing and mirage-like optical effects. Unfortunately, Einstein's theory of general relativity requires enormously massive, stellar-sized objects to provide a noticeable warping of space. We also have no way to control this effect: there is no "on" or "off" switch! So, while the bending of light rays due to distorting the fabric of space is science fact, the control of this distortion remains firmly the domain of science fiction.

Approaching Reality

Although far-fetched, Storm's invisibility is worth considering in a bit more detail. What if one could really warp space at will?

The animation below shows a lattice representing space. One could imagine the lines as interwoven threads in a fabric. A beam of light that starts out traveling along one of the lines is constrained to stay on that line, in accordance with Fermat's Principle. Now, imagine that there exists another space. Every point in this new space can be related to a point in the first space by a mathematical function or transformation. The important point is that we don't need to maintain the same density of space--we can squeeze and expand different volumes of this new space so as to open up voids. The animation below depicts a possible transformation from our space to a new space in which a void appears. Our lattice has been warped in this new space, with light still constrained to follow the now-curved lines. Light that is incident on the void is actually swept around the void, in the same way that the threads of a fabric would be pushed around if you tried to create a hole in a fabric without breaking any of the threads. Light now circulates around the void--like water flowing past a rock in a stream. We have mapped to a space where a particular region just does not exist! Light can't illuminate nor be scattered by this region, because it is outside of the space where light can even exist.

All of this warped space is compelling and great for science fiction. But, unless we can somehow carry black holes around, it's not likely we will be able to alter the flow of light in any signficant way. Susan Storm's route to invisibility is thus not likely; one shouldn't pay very much to obtain the secrets of Romulan cloaking technology, either.

But this is where things start to become interesting! When space is warped by a massive object, all physical phenomena are likewise modified in the new distorted space. But, if we are concerned with just modifying electromagnetism and electromagnetic fields, then we can restrict ourselves to Maxwell's equations--the equations that govern how electric and magnetic fields behave. And here we're in luck, because unlike many other equations of physics, Maxwell's equations have parameters that enter that can easily be modified: the electric and magnetic material parameters.

What does this mean for invisibility? We've decided that making people or other objects invisible by chemically altering their constituent molecules won't work. Nor is there any reasonable hope that we will be able to shield objects from detection by curving space. This leaves our third and most viable option for invisibility--and one familiar to Harry Potter fans--creating a cloak using some sort of material whose parameters have been suitably chosen. But we don't need to attend Hogwarts School of Witchcraft and Wizardry to conjure such a cloak; we can combine the idea of transforming space with Maxwell's equations, which will reveal precisely the necessary material properties for our invisibility cloak.

Here is how it works. We start by transforming space in a desired manner. To achieve invisibility, for example, we would like to push space outward creating a nice concealment volume, as in the animation above. Now, we can't actually transform space, but in Maxwell's equations the material properties enter in such a way that we can achieve the same effect by transforming the material properties. We thus replace the space outside the concealment volume by a material--a cloak--in which light rays travel the exact same paths they would have travelled in the warped space. When the dust has settled, we arrive at a set of material properties. The resulting material parameters for our invisibility cloak will be complicated, of course, but will be fully consistent with the known laws of physics.

In our recent Science paper, we have presented a mathematical approach that provides us with the expected material parameters needed to make a cloak. Does it work? We can test out the idea by a variety of different methods. One method, used by lens designers, is called ray-tracing. Starting with a bunch of rays that represent light, the path of each ray can be traced as it passes through an object made of any material. Ray tracing provides a good test as to whether or not the mathematical transformation has predicted the right set of material parameters. The figure to the right shows the result of a ray-trace performed on a set of rays that pass through a spherical cloak. The objects to be concealed are assumed to lie within the inner sphere, while the cloak occupies the region between the inner and outer spheres. If one knew nothing about the method that was used to design the material, the conclusion based on ray-tracing alone would be that a cloak had indeed been found.

The Reality of Cloaking

We have now succeeded in taking the prospect of invisibility from the realm of science fiction and fantasy to reality, providing what amounts to a blueprint for a cloaking device. It is now fair to ask, as with any technology, what are the limitations? The capabilities and limitations of cloaking will continue to be sorted out in the coming months and years, but there are some issues that are clear from the outset.

The cloak is a complicated structure. Not just complicated, but one that requires materials that are not known to exist! This appears to be one difficulty we can surmount by the use of artificial micro- and nano-structures that can substitute for the lack of conventional materials having the right properties. And while the cloaking structures are complex as materials go, they are nevertheless easily fabricated using available technologies.

There is an inherent limitation in bandwidth. This is actually clear from the ray tracing figure above; note that rays that would normally impinge on the cloaked sphere must instead be swept around the sphere, essentially traversing a longer distance than they would have had they passed directly through a volume of space. For all the rays to arrive in step after swirling around the sphere, they must travel faster than the speed of light in vacuum while in the cloak. This isn't quite as bad as it sounds. Without going into the details, it is possible for electromagnetic waves to exceed the speed of light within a material, but only at a particular wavelength (or, equivalently, frequency). Thus, the material of which the cloak is made must disperse with frequency--that is, our cloak can be designed to work optimally at a targeted wavelength or bandwidth, but its performance will degrade sharply away from the optimal bandwidth.

An ideal cloak would absorb no light whatsoever, since whatever amount light is not transmitted by an object can be a signature that the object is present. The artificial materials that we can currently imagine using tend to absorb a significant amount of light that passes through them, and this presents a very serious limitation that will ultimately set the size of any object to be cloaked. At the moment, we have a few strategies in mind that might help to soften the blow we sustain from absorption in the material, but it is a problem we will have to grapple with as we pursue cloaking.

Conclusions

We've provided a brief summary of the facts and fiction associated with cloaking, but we've neglected an important point. While it would be great if we could make things vanish entirely, a cloak needn't accomplish complete invisbility to be potentially useful. Remember how easy it is to defeat the invisible man? Being invisible is only of fleeting value at best if your adversary knows that you are there. The advantage of invisibility comes about when your adversary has no idea that you're there. That is, invisibility is probably best thought of as being a really good form of camouflage: it doesn't have to be perfect to work.

In perhaps one of the most realistic portrayels of invisibility, the alien in the movie Predator possesses a cloaking device that renders it nearly invisible. When

cloaked, the predator is mostly transparent, but there is a noticeable distortion of the transmitted light that just vaguely outlines the shape of the predator. As depicted in the movie, it is difficult to perceive the presence of the alien unless you know it's there and it's in motion. Otherwise, the imperfect cloaking does a pretty good job of keeping the alien well hidden. Although the underlying fictional technology is not described in the movie, the cloaking effect appears to be related to the alien's armor, which would make it more akin to the material cloak that we think might be possible.

Along the lines of advanced camouflage, we should not overlook the solutions that nature has provided. An object is invisible if it is indistinguishable --or at least hard to distinguish--from its surrounding environment. Many animals and insects have evolved in form to blend into their enviornment, making it harder for predators (animal, not alien) to find them. But some creatures, like chamelians and cuttlefish, can change there appearance dynamically, virtually being able to disappear in changing environments. This type of camouflage/invisibility is similar to an optical device, invented by Japanese scientist Susumi Tachi, that can provide a transparency effect to people or objects.

Invisibility of any sort will be a very difficult achievement, one that will involve much more complication than we have even begun to delve into here. As a result of the publication of our paper and several others on the same topic, there have been reports in the media of Harry Potter's cape being "five to ten years off"; but those reports have to be treated with some amount of realism. The physics of cloaking, as we have outlined, is sound, and cloaks may be fabricated using the artificial materials that have been introduced over the past several years. But, as we have also described, there are serious and seemingly unavoidable limitations on cloaking that will impair the performance of any structure we can currently envision making. So, when we ourselves project a demonstration will be possible, what we have in mind initially is a very specific sort of structure that will most likely be useable (but not necessarily useful!) at very long wavelengths in the electromagnetic spectrum--radio frequencies for example, where wavelengths are on the order of many centimeters to meters. It may not be quite as exciting as making objects visibly disappear, but it will be an important step. How much further might we go beyond this initial demonstration is an open question, but given the tremendous interest in the area, we can say for certain that the scientific community will do its best!

One last point to consider is that the entire design paradigm that leads to the cloak--starting by transforming space and then determining the equivalent electromagnetic material--represents a new approach to optics. Just five years ago this idea of transform optics might have been abandoned because the resulting material requirements would have been considered impractical. With the advent of metamaterials, that conclusion has now changed, and we can envision entirely new classes of optical devices, invisibility cloaks being just one example. So, while we have been inspired by the invisibility of fictional worlds, perhaps the discoveries that might follow from transformation optics will in turn have an impact in fictional worlds--as well as in the actual world.