by Michio Kaku
Commenting on the importance of Maxwell’s equations, Einstein wrote that they are “the most profound and the most fruitful that physics has experienced since the time of Newton.”
(Tragically, Maxwell, one of the greatest physicists of the nineteenth century, died at the early age of forty-eight of stomach cancer, probably the very same disease that killed his mother at the same age. If he had lived longer, he might have discovered that his equations allowed for distortions of space-time that would lead directly to Einstein’s relativity theory. It is staggering to realize that relativity might possibly have been discovered at the time of the American Civil War had Maxwell lived longer.)
Maxwell’s theory of light and the atomic theory give simple explanations for optics and invisibility. In a solid, the atoms are tightly packed, while in a liquid or gas the molecules are spaced much farther apart. Most solids are opaque because light rays cannot pass through the dense matrix of atoms in a solid, which act like a brick wall. Many liquids and gases, by contrast, are transparent because light can pass more readily between the large spaces between their atoms, a space that is larger than the wavelength of visible light. For example, water, alcohol, ammonia, acetone, hydrogen peroxide, gasoline, and so forth are all transparent, as are gases such as oxygen, hydrogen, nitrogen, carbon dioxide, methane, and so on.
There are some important exceptions to this rule. Many crystals are both solid and transparent. But the atoms of a crystal are arranged in a precise lattice structure, stacked in regular rows, with regular spacing between them. Hence there are many pathways that a light beam may take through a crystalline lattice. Therefore, although a crystal is as tightly packed as any solid, light can still work its way through the crystal.
Under certain circumstances, a solid object may become transparent if the atoms are arranged randomly. This can be done by heating certain materials to a high temperature and then rapidly cooling them. Glass, for example, is a solid with many properties of a liquid because of the random arrangement of its atoms. Certain candies can become transparent via this method as well.
Clearly, invisibility is a property that arises at the atomic level, via Maxwell’s equations, and hence would be exceedingly difficult, if not impossible, to duplicate using ordinary means. To make Harry Potter invisible, one would have to liquefy him, boil him to create steam, crystallize him, heat him again, and then cool him, all of which would be quite difficult to accomplish, even for a wizard.
The military, unable to create invisible airplanes, has tried to do the next best thing: create stealth technology, which renders airplanes invisible to radar. Stealth technology relies on Maxwell’s equations to create a series of tricks. A stealth fighter jet is perfectly visible to the human eye, but its radar image on an enemy radar screen is only the size of a large bird. (Stealth technology is actually a hodgepodge of tricks. By changing the materials within the jet fighter, reducing its steel content and using plastics and resins instead, changing the angles of its fuselage, rearranging its exhaust pipes, and so on, one can make enemy radar beams hitting the craft disperse in all directions, so they never get back to the enemy radar screen. Even with stealth technology, a jet fighter is not totally invisible; rather, it has deflected and dispersed as much radar as is technically possible.)
METAMATERIALS AND INVISIBILITY
But perhaps the most promising new development involving invisibility is an exotic new material called a “metamaterial,” which may one day render objects truly invisible. Ironically, the creation of metamaterials was once thought to be impossible because they violated the laws of optics. But in 2006 researchers at Duke University in Durham, North Carolina, and Imperial College in London successfully defied conventional wisdom and used metamaterials to make an object invisible to microwave radiation. Although there are still many hurdles to overcome, for the first time in history we now have a blueprint to render ordinary objects invisible. (The Pentagon’s Defense Advanced Research Projects Agency [DARPA] funded this research.)
Nathan Myhrvold, former chief technology officer at Microsoft, says the revolutionary potential of metamaterials “will completely change the way we approach optics and nearly every aspect of electronics…Some of these metamaterials can perform feats that would have seemed miraculous a few decades ago.”
What are these metamaterials? They are substances that have optical properties not found in nature. Metamaterials are created by embedding tiny implants within a substance that force electromagnetic waves to bend in unorthodox ways. At Duke University, scientists embedded tiny electrical circuits within copper bands that are arranged in flat, concentric circles (somewhat resembling the coils of an electric oven). The result was a sophisticated mixture of ceramic, Teflon, fiber composites, and metal components. These tiny implants in the copper make it possible to bend and channel the path of microwave radiation in a specific way. Think about the way a river flows around a boulder. Because the water quickly wraps around the boulder, the presence of the boulder has been washed out downstream. Similarly, metamaterials can continuously alter and bend the path of microwaves so that they flow around a cylinder, for example, essentially making everything inside the cylinder invisible to microwaves. If the metamaterial can eliminate all reflection and shadows, then it can render an object totally invisible to that form of radiation.
Scientists successfully demonstrated this principle with a device made of ten fiberglass rings covered with copper elements. A copper ring inside the device was rendered nearly invisible to microwave radiation, casting only a minuscule shadow.
At the heart of metamaterials is their ability to manipulate something called the “index of refraction.” Refraction is the bending of light as it moves through transparent media. If you put your hand in water, or look through the lens of your glasses, you notice that water and glass distort and bend the path of ordinary light.
The reason that light bends in glass or water is that light slows down when it enters a dense, transparent medium. The speed of light in a pure vacuum always remains the same, but light traveling through glass or water must pass through trillions of atoms and hence slows down. (The speed of light divided by the slower speed of light inside the medium is called the index of refraction. Since light slows down in glass, the index of refraction is always greater than 1.0). For example, the index of refraction is 1.00 for a vacuum, 1.0003 for air, 1.5 for glass, and 2.4 for diamond. Usually, the denser the medium, the greater the degree of bending, and the greater the index of refraction.
A familiar example of the index of refraction is a mirage. If you are driving on a hot day and look straight toward the horizon, the road may seem to be shimmering, creating the illusion of a glistening lake. In the desert one can sometimes see the outlines of distant cities and mountains on the horizon. This is because hot air rising from the pavement or desert has a lower density than normal air, and hence a lower index of refraction than the surrounding, colder air, and therefore light from distant objects can be refracted off the pavement into your eye, giving you the illusion that you are seeing distant objects.
Usually, the index of refraction is a constant. A narrow beam of light is bent when it enters glass and then keeps going in a straight line. But assume for the moment that you could control the index of refraction at will, so that it could change continuously at every point in the glass. As light moved in this new material, light could bend and meander in new directions, creating a path that would wander throughout the substance like a snake.
If one could control the index of refraction inside a metamaterial so that light passed around an object, then the object would become invisible. To do this, this metamaterial must have a negative index of refraction, which every optics textbook says is impossible. (Metamaterials were first theorized in a paper by Soviet physicist Victor Veselago in 1967 and were shown to have weird optical properties, such as a negative refractive index and reversed Doppler effect. Metamaterials are so bizarre and preposterous that they were once thought
to be impossible to construct. But in the last few years, metamaterials have actually been manufactured in the laboratory, forcing reluctant physicists to rewrite all the textbooks on optics.)
Researchers in metamaterials are constantly pestered by journalists who wish to know when invisibility cloaks will hit the market. The answer is: not anytime soon.
David Smith of Duke University says, “Reporters, they call up and they just want you to say a number. Number of months, number of years. They push and push and push and you finally say, well, maybe fifteen years. Then you’ve got your headline, right? Fifteen years till Harry Potter’s cloak.” That’s why he now declines to give any specific timetable. Fans of Harry Potter or Star Trek may have to wait. While a true invisibility cloak is possible within the laws of physics, as most physicists will agree, formidable technical hurdles remain before this technology can be extended to work with visible light rather than just microwave radiation.
In general, the internal structures implanted inside the metamaterial must be smaller than the wavelength of the radiation. For example, microwaves can have a wavelength of about 3 centimeters, so for a metamaterial to bend the path of microwaves, it must have tiny implants embedded inside it that are smaller than 3 centimeters. But to make an object invisible to green light, with a wavelength of 500 nanometers (nm), the metamaterial must have structures embedded within it that are only about 50 nanometers long—and nanometers are atomic-length scales requiring nanotechnology. (One nanometer is a billionth of a meter in length. Approximately five atoms can fit within a single nanometer.) This is perhaps the key problem we face in our attempts to create a true invisibility cloak. The individual atoms inside a metamaterial would have to be modified to bend a light beam like a snake.
METAMATERIALS FOR VISIBLE LIGHT
The race is on.
Ever since the announcement that metamaterials have been fabricated in the laboratory there has been a stampede of activity in this area, with new insights and startling breakthroughs coming every few months. The goal is clear: to use nanotechnology to create metamaterials that can bend visible light, not just microwaves. Several approaches have been proposed, all of them quite promising.
One proposal is to use off-the-shelf technology, that is, to borrow known techniques from the semiconductor industry to create new metamaterials. A technique called “photolithography” lies at the heart of computer miniaturization and hence drives the computer revolution. This technology enables engineers to place hundreds of millions of tiny transistors onto a silicon wafer no bigger than your thumb.
The reason that computer power doubles every eighteen months (which is called Moore’s law) is because scientists use ultraviolet radiation to “etch” tinier and tinier components onto a silicon chip. This technique is very similar to the way in which stencils are used to create colorful T-shirts. (Computer engineers start with a thin wafer and then apply extremely thin coatings of various materials on top. A plastic mask is then placed over the wafer, which acts as a template. It contains the complex outlines of the wires, transistors, and computer components that are the basic skeleton of the circuitry. The wafer is then bathed in ultraviolet radiation, which has a very short wavelength, and that radiation imprints the pattern onto the photosensitive wafer. By treating the wafer with special gases and acids, the complex circuitry of the mask is etched onto the wafer where it was exposed to ultraviolet light. This process creates a wafer containing hundreds of millions of tiny grooves, which form the outlines of the transistors.) At present, the smallest components that one can create with this etching process are about 30 nm (or about 150 atoms across).
A milestone in the quest for invisibility came when this silicon wafer etching technology was used by a group of scientists to create the first metamaterial that operates in the visible range of light. Scientists in Germany and at the U.S. Department of Energy announced in early 2007 that, for the first time in history, they had fabricated a metamaterial that worked for red light. The “impossible” had been achieved in a remarkably short time.
Physicist Costas Soukoulis of the Ames Laboratory in Iowa, with Stefan Linden, Martin Wegener, and Gunnar Dolling of the University of Karlsruhe, Germany, were able to create a metamaterial that had an index of-.6 for red light, at a wavelength of 780 nm. (Previously, the world record for radiation bent by a metamaterial was 1,400 nm, which put it outside the range of visible light, in the range of infrared.)
The scientists first started with a glass sheet, and then deposited a thin coating of silver, magnesium fluoride, and then another layer of silver, forming a “sandwich” of fluoride that was only 100 nm thick. Then, using standard etching techniques, they created a large array of microscopic square holes in the sandwich, creating a grid pattern resembling a fishnet. (The holes are only 100 nm wide, much smaller than the wavelength of red light.) Then they passed a red light beam through the material and measured its index, which was-.6.
These physicists foresee many applications of this technology. Metamaterials “may one day lead to the development of a type of flat superlens that operates in the visible spectrum,” says Dr. Soukoulis. “Such a lens would offer superior resolution over conventional technology, capturing details much smaller than one wavelength of light.” The immediate application of such a “superlens” would be to photograph microscopic objects with unparalleled clarity, such as the inside of a living human cell, or to diagnose diseases in a baby inside the womb. Ideally one would be able to obtain photographs of the components of a DNA molecule without having to use clumsy X-ray crystallography.
So far these scientists have demonstrated a negative index of refraction only for red light. Their next step would be to use this technology to create a metamaterial that would bend red light entirely around an object, rendering it invisible to that light.
Future developments along these lines may occur in the area of “photonic crystals.” The goal of photonic crystal technology is to create a chip that uses light, rather than electricity, to process information. This entails using nanotechnology to etch tiny components onto a wafer, such that the index of refraction changes with each component. Transistors using light have several advantages over those using electricity. For example, there is much less heat loss for photonic crystals. (In advanced silicon chips, the heat generated is enough to fry an egg. Thus they must be continually cooled down or else they will fail, and keeping them cool is very costly.) Not surprisingly, the science of photonic crystals is ideally suited for metamaterials, since both technologies involve manipulating the index of refraction of light at the nanoscale.
INVISIBILITY VIA PLASMONICS
Not to be outdone, yet another group announced in mid-2007 that they have created a metamaterial that bends visible light using an entirely different technology, called “plasmonics.” Physicists Henri Lezec, Jennifer Dionne, and Harry Atwater at the California Institute of Technology announced that they had created a metamaterial that had a negative index for the more difficult blue-green region of the visible spectrum of light.
The goal of plasmonics is to “squeeze” light so that one can manipulate objects at the nanoscale, especially on the surface of metals. The reason metals conduct electricity is that electrons are loosely bound to metal atoms, so they can freely move along the surface of the metal lattice. The electricity flowing in the wires in your home represents the smooth flow of these loosely bound electrons on the metal surface. But under certain conditions, when a light beam collides with the metal surface, the electrons can vibrate in unison with the original light beam, creating wavelike motions of the electrons on the metal surface (called plasmons), and these wavelike motions beat in unison with the original light beam. More important, one can “squeeze” these plasmons so that they have the same frequency as the original beam (and hence carry the same information) but have a much smaller wavelength. In principle, one might then cram these squeezed waves onto nanowires. As with photonic crystals, the ultimate goal of plasmonics is to create co
mputer chips that compute using light, rather than electricity.
The Cal Tech group built their metamaterial out of two layers of silver, with a silicon-nitrogen insulator in between (with a thickness of only 50 nm), which acted as a “waveguide” that could shepherd the direction of the plasmonic waves. Laser light enters and exits the apparatus via two slits carved into the metamaterial. By analyzing the angles at which the laser light is bent as it passes through the metamaterial, one can then verify that the light is being bent via a negative index.
THE FUTURE OF METAMATERIALS
Progress in metamaterials will accelerate in the future for the simple reason that there is already intense interest in creating transistors that use light beams rather than electricity. Research in invisibility can therefore “piggyback” on the ongoing research in photonic crystals and plasmonics for creating replacements for the silicon chip. Already hundreds of millions of dollars are being invested in creating replacements for silicon technology, and research in metamaterials will benefit from these research efforts.
With breakthroughs occurring in this field every few months, it’s not surprising that some physicists see some sort of practical invisibility shield emerging out of the laboratory perhaps within a few decades. In the next few years, for example, scientists are confident that they will be able to create metamaterials that can render an object totally invisible for one frequency of visible light, at least in two dimensions. To do this would require embedding tiny nano implants not in regular arrays, but in sophisticated patterns so that light would bend smoothly around an object.
