Given a provisional field density of 10³⁵ surfaces per unit centimeter volume (cm³), the path density around the circumference of the chamber can be pragmatically set at 1/3 the field density, or 3 x 10³⁴ surfaces per centimeter linear circumference.

The idea of this experiment is to move these surfaces around the circumference sufficiently to cause a detectable change in weight of a mass inside the chamber, such as a lead pellet.  Since scales able to measure only 1/500,000 (5 x 10^-5) change in weight are readily procurable, we will set this as our modest goal;  a greater proportional change in weight requiring more time.

This proportional change in weight (DW) directly relates to the angular change of surfaces (presumably caused by photon impact, which is the investigative purpose of this experiment), which is distance each surface is pushed around the chamber's circumference by photon bombardment. In other words, as photons stream around the circumference of the chamber, they push all surfaces by the amount DC, where DC/C : DW/W.

In order to accelerate noticeable change, the chamber should be as small as possible, though a large chamber would be more useful.  Let's start with a chamber large enough to build without the utilization of microtechnology, a chamber in the order of 4mm diameter.  With this chamber in operation, one should be able to insert inside of it a small (1-2 mm) lead pellet to weigh.  Given these parameters, the chamber's circumference will be:  C = pD = p4mm = 4p mm = 4p x 10^-1 cm.

Setting W to unity, the proportionality expression becomes:  DC / 4p x 10^-1 cm = (5 x 10^-5) / 1.

Solving for DC: DC = (5 x 10^-5) x (4p x 10^-1) = 6.28 x 10^-5 cm.

This value is the distance all surfaces must be pushed the photon stream, where each photon impact only moves surfaces a distance equivalent to the reciprocal of the path density (3 x 10³⁴), or 3.3 x 10^-35  cm.  Thus to move surfaces the distance DC, the number of photons required would be,
6.28 x 10^-5 cm / 3.3 x 10^-35  cm = 1.9 x 10³⁰ photons.

Now the question is, how long and how much energy would be required to produce this many photons?

There is a relationship between electrical power and photon generation, where in one second 1.5 x 10¹⁸ photons per watt can be generated using an ordinary flashlight.  This is of course the total photon generation, non-directed.  Given that lasers follow the same general parameters, but are directed (highly collimated), one can expect all photon production to pass through a narrow (around 2 mm) photon stream.

By dividing the total photon production required (1.9 x 10³⁰) by their rate of production per watt, in this example 1.5 x 10¹⁸, 7.89 x 10¹¹ seconds will be needed to cause a 1/500,000 weight change.

Given a 50 watt laser, 1.58 x 10¹⁰ seconds will be needed.

Given that there are 3.11 x 10⁷ seconds in one year, 5 x 10² years would be required to reach this stage using a 50 watt laser continuous duty cycle!

The adjoining illustration shows a prototype chamber whose aperture allows the entrance of a beam of light.  This beam is directed just to the above of center and upon striking the far wall of the circular chamber, it returns just below center.  Upon striking the wall near the original entrance aperture, it is again reflected just above center.  In this way all photons associated with all directed beams go in a clockwise direction around the central chamber, thus causing the field to twist clockwise.  Because the wall consists of a multilayer Bragg effect mirror, all reflection is in phase, in essence, becoming a photonic trap.

If the perfect Bragg effect mirror lives up to its expectation in providing 100% reflection without loss, the internal beam power will continue to increase, decreasing the time of completion of this experiment by 1/2, or 250 years.

If a known mass is introduced into the center of the chamber as shown, its weight should decrease by 1/500,000 parts.

If all said is true, a wheel whose rim is allowed to rotate through the chamber should be able to produce work, silently and without waste product because of the differential in the weight of the wheel's rim inside and outside the chamber, causing it to continually spin.  As the beam power continues to increase, the wheel will turn faster, until eventually, all its mass inside the chamber falls upward, but of course downward outside the chamber.

One obvious problem is light returning out through the entrance aperture.  One possible fix is to place the laser light source directly at the aperture so that its face is in line to the circular mirror and then tuning it so as to be in constructive phase with the exiting beam.  This may minimize losses.

For more information about photonic band gap:

William Vos (wvos@science.uva.nl), University of Amsterdam;  Ronald Walsworth (rwalsworth@cfa), Harvard-Smithsonian Center for Astro Physics; Lene Hau, Harvard;  Susamu Noda, Kyoto University;  Axel Scherer, Caltech; Philip Russell, University of Bath, (Blaze Photonics);  Joel Fink, MIT (Omni Guide Comm);  Sajeen John, University of Toronto, (Bell Communications Research);  Eli Yablonovitch, (Bell Communications, Red Bank Research, N.J.);  Philip Anderson, Princeton;  Dederik Wiersma, (European Lab for NL Spectroscopy, Florence);  Ad Lagendijk, University of Amsterdam;  Kai-Ming Ho, Iowa State University;  and Discover Magazine (Trapping Light by Robert Kunzig, April 2001).

Trapping Light
This is the future, and it moves at 186,000 miles per second
By Robert Kunzig
Photo illustrations by Jana León

A face-centered cubic, above, is the ideal crystal for capturing light. But it took scientists 14 years to make one that worked. Photo illustration by Jana León

One day in the spring of 1987, Eli Yablonovitch and Sajeev John got together for a lunch they both remember well. The two researchers had never met. They got in touch after discovering that each had submitted a paper to Physical Review Letters based on the same novel idea— an idea now considered groundbreaking.

Yablonovitch was an electrical engineer at Bell Communications Research, or Bellcore, in Red Bank, New Jersey. He was already known for his work refining a laser that would become a mainstay of fiber-optic communications. John was a promising theoretical physicist; he had recently joined the faculty at Princeton University. When they sat down together, in the civilized surroundings of a Princeton dining hall, the sociobiological dynamic was that of two large dogs sniffing each other.

"The conversation was lively," recalls John.

"The meeting was lively, but it was also a little tense," Yablonovitch says. Both men knew they were onto something big, though each concluded his paper with only modest predictions. Yablonovitch said the idea "may someday have a role to play in the study of semiconductor lasers." John's paper said only that it "may lead to a number of useful device applications." Both conclusions now look like massive understatements. These days hundreds of papers come out of dozens of labs all over the world citing those 1987 papers. Back then, however, Yablonovitch and John were alone. Being a lone genius can be gratifying. But having a rival can be reassuring: It suggests you're not a crazy lone genius.

The two men finished lunch on amicable terms. They also agreed on a name for their idea: It should be called a photonic band gap. Their idea has since been realized in the form of photonic crystals, which could prove as far-reaching an innovation as semiconductors. Photonic crystals have the regular lattice structure of natural crystals. They look a bit like cages, and that's just what they are. They're cages that trap photons— particles of light that move at 186,000 miles per second— like fireflies in a jar.

Physicist Sajeev John, above, holding a photonic microchip, says that "the Internet is the biggest driver of this technology."  Photo shot at Max-Planck-Institute of Microstructure Physics	"Everything we've done with semiconductors will be done with light," says Eli Yablonovitch, who has pioneered photonic crystals. Photo shot at Max-Planck-Institute of Microstructure Physics

To stop light without absorbing it, which just destroys it, to trap light while keeping it intact and useful— that is a neat trick. Anybody can stop light by absorbing it; each of us stops trillions of photons a second. The trick is not to kill the photons but to tame them. Once they're in a cage you can find a way to let the light out when you want. You can channel it so that it flows only where you want it to. You can control light the way we already control electrons in microchips, or integrated circuits.

Microchips are made of semiconductors, and the hallmark of a semiconductor is a band gap. In any solid material, electrons exist only in discrete energy bands, just as they orbit an individual atom at discrete energy levels. But in a semiconductor, there is a large gap between the band of atom-bound electrons and the livelier band of electrons that conduct electric currents. That band gap makes it possible to control the flow of electricity in a chip. In a pure crystal of silicon, electrons can't exist at band-gap energies at all. But if you dope the crystal with impurities— a few ions of arsenic, for instance— you can inject the number of mobile electrons you want. That's the basic principle of integrated circuits.

If we could do the same with light, in photonic integrated circuits, information would flow more rapidly and copiously than it does today— much more rapidly. An optical computer that processed information as light rather than as electricity could process trillions of bits per second. That's thousands of times faster than the one-gigahertz microprocessors in the most advanced computers today. And long before we have optical computers, photonic integrated circuits could dramatically speed up the Internet. Right now an e-mail message leaves your computer as an electronic signal, gets converted to light wherever it reaches a fiber-optic trunk line— and then gets converted back and forth again many times as it gets routed through the network. If the Net used photonic microchips, its speed and capacity could increase at least a hundredfold.

To make light chips, you need the photonic equivalent of silicon: a material that can trap light. The exotic gases that have recently been used to do the trick (see "Stoplight on the Road to Quantum Computers," below) aren't much help: The equipment involved fills laboratories. You might think optical fibers, the backbone of the Internet and the telephone network, would be good candidates. After all, light remains confined in their glass cores for thousands of miles, as it ricochets off the glass cladding. But if the light strikes the cladding at anything steeper than a grazing angle, it leaves the fiber— which means it could never negotiate the sharp-cornered circuits on a microchip. "You need a way of trapping the light so there are no escape channels," says John, who is now at the University of Toronto.

When John first started thinking about trapping light in the early 1980s, visions of photonic microchips were far from his mind. He was a graduate student at Harvard, working on a thesis inspired by Philip Anderson of Princeton. In a famous 1958 paper, Anderson showed that electrons could be trapped in a disordered material— one in which the atoms are arrayed randomly. If the material is random enough, an electron collides with atoms so often that it keeps getting bounced back to where it started. John's thesis considered whether that could be done with photons. "I was just asking a fundamental question of nature," he says.

His answer was yes, light could be localized— but it wouldn't be easy. Not until 1997 did European investigators succeed in trapping light in a random material. Diederik Wiersma and his colleagues from the European Laboratory for Non-linear Spectroscopy in Florence and Ad Lagendijk of the University of Amsterdam used a powder of gallium arsenide, ground so fine that the grains were smaller than the wavelength of light. They showed that a laser beam couldn't penetrate a layer of the powder even when the layer was less than a hundredth of an inch thick. The light just bounced around among the grains on looping paths, without finding an exit. It was the first time anyone had trapped light. But microchips can't be made out of powder.

By 1986, when John joined Anderson at Princeton, he had started wondering if there might be a systematic way to trap light. Maybe an orderly crystal would work, he decided; maybe you could build a crystalline cage for light. For John, it was still a question of pure physics.

Bragg's Rules Each plane of a crystal reflects part of a light beam and transmits the rest. If the spacing between the planes is half the wavelength, the reflected waves line up and interfere constructively, intensifying the reflection. With enough planes the crystal can reflect all the light of a certain wavelength, which is why an opal, for instance, glints green or red. Graphics by Matt Zang

Eli Yablonovitch's job at bellcore was not to ask fundamental questions of nature. It was to make better lasers. In 1986, the conversion from copper to fiber-optic telephone cables was just beginning, and semiconductor lasers that could transmit signals without wasting gobs of light were a high priority. The biggest waste came from something called spontaneous emission. Before the stack of semiconductor layers at the heart of a laser begins lasing— sending out a tight beam of photons— it spews a tremendous number at random. If those photons could be trapped in the semiconductor, they would add to the laser pulse, but most of them just squirted out the sides of the stack. "I was trying to make a trap in all three dimensions that wouldn't have any leakage," says Yablonovitch, now at the University of California at Los Angeles.

One day in October 1986, as Yablonovitch sat doodling in his office, "I started drawing crisscrossing lines, and everywhere the lines crossed I put a heavier mark. Before I knew it I had drawn a checkerboard. And then I said, 'Well, I might as well do it in three dimensions.' " Later, pondering that 3-D checkerboard, Yablonovitch had his eureka moment.

What he had drawn, he realized, was a crystal structure that might trap light through interference. Interference happens when two light waves of the same wavelength meet. If their crests line up, they interfere constructively: The light is intensified. If the crest on one wave lines up with a trough on the other, destructive interference dims the light.

Light traveling through a crystal, hitting one lattice plane after another, can interfere in a peculiar way. Each plane reflects some light but transmits the rest. Now consider what happens if the spacing between those parallel planes happens to equal the distance from one light-wave crest to the neighboring trough— or half the wavelength (see the diagram, above). A light wave that passes through one plane but is reflected back by the next plane will, on reaching the first plane again, have traveled exactly one full wavelength farther than a light wave that is reflected by the first plane. The crests of the two reflected waves will line up— and they will also line up with all the waves bouncing back from other planes, because each of them will have traveled an exact multiple of one wavelength farther. All those waves will interfere constructively, intensifying the reflected light. With enough planes, a crystal could reflect all light that struck it, which is known as Bragg reflection.

Yablonovitch saw that if you could design a crystal that Bragg-reflected light no matter which direction it was coming from, you would have built a trap. Whichever way the light tried to enter the crystal from the outside, it would be repelled; whichever way it tried to escape, if it were already inside the crystal, it would be reflected back. This would only work for light in a narrow range of wavelengths— a particular photonic band gap, as Yablonovitch and John would later describe it. And even for those wavelengths it would be hard to do: You would only get that critical interference in all directions if the spacing of the lattice planes were roughly the same in all directions.

Now look around your flat-walled room, and ask yourself whether it's possible for you to be the exact same distance from every point on every wall— or even one wall. It's not possible unless the room is a sphere, nor is it possible for a photon in a crystal made of flat lattice planes. The crystal would need to be made of spherical shells, and even then it would only work for one photon at the center. That's what Yablonovitch's eureka moment was all about. He saw which crystal structure would come closest to the spherical ideal— and it is called a face-centered cubic.

How to Build a Better Light Trap  One kind of light cage is an inverse opal, which mimics the latticed structure of real opals. Sajeev John's group makes this type of photonic crystal by arranging glass spheres a few hundred nanometers in diameter in a face-centered cubic, a configuration that resembles stacked oranges.  A vapor of the semiconductor silicon is inserted between the spheres. The glass is then etched away with hydrofluoric acid. The result: a latticework of semiconductor surrounding spheres of air. Graphics by Matt Zang

A face-centered cubic is the crystal structure of many natural materials. In one unit cube there are atoms at each corner and in the center of the six faces— hence the name. It's the pattern of oranges when stacked on a fruit stand. It's also what you get when you draw a checkerboard and then extend it vertically, stacking black cubes on red and vice versa. A perfectly common structure, but until Yablonovitch did his doodle, no one had recognized its light-trapping potential. And yet John reached the same conclusion at about the same time, although he came to it by a more mathematical route. When they met for lunch in 1987, the two men convinced themselves they were onto "a very, very sweet idea," as Yablonovitch puts it. But their peers weren't immediately persuaded. "It took off very slowly," says Yablonovitch. "A lot of people didn't get it at first."

What people might have noticed in those early days was that Yablonovitch was having a hard time producing a photonic crystal. He couldn't use just an ordinary face-centered cubic crystal. The wavelength of visible light is between 400 and 700 nanometers, but the distance between planes of atoms in natural crystals is only a few nanometers— much less than half the wavelength. (A nanometer is a billionth of a meter.) To reflect visible light, a photonic crystal would have to be an engineered, crystallike structure assembled from elements much larger than atoms but still only a few hundred nanometers across.

In 1987, this was difficult to do. Nor was it even clear what raw material to start with— only that the structure would have to alternate pockets of air with some much denser but still translucent material. The denser the material, the slower it transmits light, and the more it refracts or reflects light. This is measured as a material's refractive index, which is simply the speed of light in a vacuum divided by the speed of light in the material. Air has a refractive index of 1, glass 1.5 (meaning it transmits light two thirds as fast as air), and silicon or gallium arsenide, 3.6. The strongest reflection occurs at the boundary between two highly contrasting materials— such as air and silicon. In principle, a crystal made of such materials could create Bragg reflection strong enough to block some band of wavelengths in all directions— the requirement for a photonic band gap— even though the crystal couldn't possibly have perfect half-wavelength spacing in all directions. That, anyway, was Yablonovitch's optimistic plan. "Although I had the concept, there was no evidence at all that it could be done," he says. "Maybe it would have required a refractive index of a hundred— well, there's nothing in nature with a refractive index of a hundred! But we just went ahead and made a couple. And guess what? They didn't work!"

Yablonovitch wasn't even trying to trap visible light; to prove the principle, he was trying to trap microwaves, which have a wavelength 100,000 times longer. His first attempt was a piece of Plexiglas 16 inches on each side, into which he drilled a bunch of airholes. Later he had it framed; it hangs in his office at UCLA. The label reads, "The first unsuccessful photonic crystal." Many more failures followed. "This went on for four years," says Yablonovitch. "At that point there had already been a huge commitment of money and time and effort. We were running on hope." Finally he got some help from Kai-Ming Ho, a theorist at Iowa State University. Ho and his colleagues calculated that the best kind of crystal for trapping light (or microwaves) was a particular kind of face-centered cubic: the diamond. Yablonovitch approximated it by drilling three sets of slanted columns through a piece of plastic, such that the columns crossed inside to form an interlocking grid of airholes.

That piece of plastic, he found in 1991, stopped microwaves from all angles: It was the first three-dimensional photonic band gap. But it wasn't good for much— it couldn't stop the photons you see, nor could it stop the near-infrared kind that transmit phone calls and e-mail. Trapping these photons is what researchers all over the world have been racing to accomplish for a decade.

Photo illustration by Jana León

In Willem Vos's office at the University of Amsterdam, white neon light is scattering off a drum set— Vos's hobby— which stands in the middle of the room. Light is scattering whitely, too, off Vos's fashionably shaved head. But it is interacting differently with the opal he holds in his raised hand. As Vos slowly twists the opal, it glints first green, then red. Those are the colors that couldn't penetrate the gem at those particular angles. "That's the opalescence," says Vos. "Opalescence is really Bragg reflection."

An opal, he explains, is a special kind of crystal in which the layers are not made of atoms but of minute glass beads. Along certain paths through the opal, the layer spacing is half the wavelength of green light; when white light comes from those directions, the opal reflects its green component. In other directions the spacing is half the wavelength of red light, and the opal reflects red. There is no wavelength it reflects from all directions. It is not a true cage for light. Nothing in nature is.

Some of the most successful recent attempts to build such a cage have been inspired not by nature but by the microchip industry, with its elaborate procedures for etching patterns in semiconductor wafers. The basic approach is to approximate a diamond crystal structure with a "woodpile" of semiconductor "logs" stacked in a crosshatch pattern, with air between the logs. The strongest results so far were reported last year by Susumu Noda and his colleagues at Kyoto University: Their woodpile, made of gallium arsenide logs just .7 micrometer across (a micrometer is one millionth of a meter), blocked 99.99 percent of the near-infrared light they shone on it.

But Vos believes the future lies with a different and cheaper approach, inspired by opals. He holds up a vial filled with a milky liquid that contains polystyrene spheres, each less than a micrometer across. Suspended in water, the spheres scatter white light randomly. Slowly, though, they settle out of suspension, and as they do they stack up like oranges: A face-centered cubic crystal assembles itself at the bottom of the vial. It glints green and red as Vos twists it in the light.

A photonic-band-gap material would glint one color all the time, no matter the angle of the incident light. To achieve that, Vos needs a much larger contrast in refractive index than the one between polystyrene and water. Once he has dried the crystal, he fills the air gaps between the polystyrene spheres with a highly refractive material, such as gallium arsenide. Then he heats the crystal, evaporating the polystyrene. Instead of a stack of solid spheres with air-filled interstices, he now has a latticework of semiconductor surrounding spheres of air: an "inverse opal."

Inverse opals have been popping up in labs all over. Last year a team led by Sajeev John fashioned one out of silicon. "The point of our work," John says, "is that you don't need all that complicated and laborious microlithography, which costs a tremendous amount. You can do it with self-assembly." John's team claimed its material showed "a complete three-dimensional photonic band gap" in the near-infrared.

Opinions differ about whether John, Noda, or anyone else has built a leakproof light trap. The real proof, Vos thinks, will come when someone puts a microscopic light source inside a photonic crystal and finds that the light cannot escape. His own crystals are not quite there yet, but he says "we are tantalizingly close."

For those interested in creating photonic circuits, that's close enough— especially given the Internet's insatiable need for communications capacity. "It's like the early days in semiconductor physics," says John. "The first challenge is: Can you synthesize materials with the required specifications? We're just now overcoming that bottleneck. That's why the field is exploding."

Light Cages Shown in the micrographs below is the template of an inverse opal. Visible in this cross-sectional view is an arrangement of glass spheres, each several hundred billionths of a meter in diameter. Silicon is added to produce a photonic crystal. Courtesy of Instituto de Ciencia de Materiales de Madrid (cisc) (2)

Technically, no one wants a perfect photonic crystal. A perfect crystal would be a dark and empty cage, locked from the outside. Just as semiconductors must be doped with impurities to make them useful, a photonic crystal will be doped with carefully chosen defects— breaks in the crystal palisade that allow light of the forbidden wavelength to penetrate at those points only. A single defect allows light into the cage; a series of defects can channel it around once it's inside. "You create a material in which you eliminate all the pathways for light," explains John, "and then you selectively put in the pathways you want by introducing defects. You're basically writing a circuit path for the light to follow."

A practical photonic crystal might be imperfect in another way: It might have a band gap in only two dimensions. A two-dimensional photonic crystal is a thin film of semiconductor affixed to a substrate and perforated by a regular array of holes. Bragg reflection from the holes keeps light from wandering around horizontally inside the film; ordinary reflection off the surrounding air keeps most of the light from escaping in the third, vertical direction. If you plug one of the holes, you create a light-trapping defect in which photons can rattle around and stimulate atoms to emit more photons— the nucleus of a laser. A team led by Axel Scherer at the California Institute of Technology recently used this effect to create the world's smallest laser, just a few hundred nanometers across. It radiates in the near-infrared, and something like it may one day see action in photonic circuits.

If you plug not just one hole but a line of holes in your 2-D crystal, you create a waveguide that channels the light, even around sharp corners. If you then enlarge a hole to one side of the waveguide by a certain amount, you create an escape route for light of a certain wavelength; Noda's group at Kyoto demonstrated this effect last year. With a series of holes enlarged by different amounts, they showed, you have the rudiments of a device that could sort individual conversations, each encoded as a distinct wavelength, out of the hundreds that now travel simultaneously down an optical fiber. Today that is done by large devices that first convert all the optical signals to electronic ones.

By making communications devices smaller, photonic crystals will make them cheaper. "All the basic components of the telecommunications network will be affected by this," says John.

That includes even the backbone— the long-distance optical fibers. Their inability to take sharp corners is not their only limitation; the bigger problem is simply that glass does bad things to light. It absorbs light, weakening the signal; it disperses different wavelengths in a single pulse, causing the pulse to spread out and overlap its neighbor. Phone companies spend a lot to correct these problems— for instance, installing amplifiers every 50 miles or so along a cable, even on the seafloor.

But if the light could just be sent through air, down a hollow fiber, the problems would go away. That's the promise of photonic-band-gap fibers. Philip Russell and his colleagues at the University of Bath in England have made a hollow fiber whose wall consists of several hundred glass capillaries, stretched long and thin like taffy. The tiny airholes in the capillaries form a crystal pattern that confines light to the hollow core by Bragg reflection. A team at the Massachusetts Institute of Technology has tried a different approach: a coaxial fiber in which the light travels down the air space between two concentric, Bragg-reflecting cylinders. Either approach could make it possible to transmit higher-power light with a wider band of wavelengths, thereby radically increasing a fiber's capacity. You could then rescue the public from Internet traffic jams.

Photo illustration by Jana León

Just as in 1960, when no one could have predicted the present reach of semiconductors, it's difficult now to foresee all the ways photonic-band-gap materials might eventually be used.

Fourteen years ago Yablonovitch and John met for lunch and named a field of physics research; now they're naming companies, and this time they're not alone. Yablonovitch's start-up, called ethertronics, will use photonic crystals to redirect the microwaves that cell phones send and receive, making them more efficient. Philip Russell says he was forced to start a company, though his heart is in academia, by the tremendous interest in his photonic-crystal fibers; it's called Blaze Photonics. "One of the things that's fascinating about this whole field," says Yoel Fink of MIT, Russell's rival, "is that there's a closed and short loop going between basic research and commercialization." Fink's company is called OmniGuide Communications. "Starting companies is really popular right now," says researcher David Norris, who works for NEC, the communications giant, "because people see that they can one, become personally very wealthy, and two, advance their research."

John is also starting his own company. He hopes to be producing various devices for telecommunications within two to three years and eventually to go into optical computing. "I think we can be the first mover in this field in a big way," he says. But he only just recently came up with a name: KeraLight Technologies. "It's hard to come up with a name for a photonics company," John says. "Anything with photonic in it has probably already been taken."

This past January, two teams of Harvard physicists demonstrated that there's more than one way to catch a light beam. Working independently, the two groups caged light for the first time inside a cloud of atoms, braking it from its normal speed of 186,000 miles per second down to a skidding standstill. The work could someday pave the way for ultrafast and unhackable quantum computers.

Physicist Ronald Walsworth of the Harvard-Smithsonian Center for Astrophysics and his colleagues created their light trap out of a warm vapor of rubidium atoms housed inside a small glass cell. (Harvard physicist Lene Hau and her group used superchilled sodium atoms.) Normally, rubidium atoms absorb light, just like blacktop. Walsworth's team zapped them with a control beam of light, which made the rubidium vapor transparent. The control beam also prepared the atoms to couple with individual photons of light. Next, the treated atoms were zapped with a second pulse of light 20 milliseconds long. The photons in that pulse linked with the rubidium atoms, and the pulse slowed down dramatically. After the second beam was safely nestled within the glass cell, the control beam was shut off. The rubidium gas was no longer transparent; the light signal was trapped. It seemed to disappear.

Walsworth and his team were then able to reanimate the light pulse. Through a quirk of quantum mechanics, the pulse's information gets imprinted into the gas atoms in a form known as their "spin state." When the control beam is turned back on, that information is released by the atoms and transformed back into the original pulse of light. "This coupling between light and matter is exactly what you need to build a quantum computer," says Walsworth. Of course, he adds, "we won't know for a very long time if any of this will ever work."
— Kathy A. Svitil

 Sajeev John and Eli Yablonovitch, the groundbreaking scientists at the forefront of this field, each have extensive Web sites. Yablonovitch's page is www.ee.ucla.edu/labs/photon; John's can be found at www.physics.utoronto.ca/~john.

Researcher Philip Russell also has a site, jdj.mit.edu/photons/index.html, as does Willem Vos: www.thephotonicbandgaps.com. Nature has recently published several articles on photonic physics, including John's letter in Vol. 405 (May 25, 2000, p. 437) and Yablonovitch's article in Vol. 401 (October 7, 1999, p. 539).

For more about the alternative approach to stopping photons described in the sidebar: "Storage of Light in Atomic Vapor," D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Physical Review Letters, Vol. 86, Number 5, January 29, 2001, pp. 783-786. "Observation of Coherent Optical Information Storage in an Atomic Medium Using Halted Light Pulses," Chien Liu, Zachary Dutton, Cyrus H. Behroozi, and Lene Vestergaard Hau, Nature, Vol. 409, January 25, 2001, pp. 490-493. Also visit the Walsworth group's site: cfa-www.harvard.edu/Walsworth.
What is Bragg's Law and Why is it Important?

Bragg's Law refers to the simple equation:

nl = 2d sinq (1)

derived by the English physicists Sir W.H. Bragg and his son Sir W.L. Bragg in 1913 to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (theta, q). The variable d is the distance between atomic layers in a crystal, and the variable lambda l is the wavelength of the incident X-ray beam (see applet); n is an integer

This observation is an example of X-ray wave interference (Roentgenstrahlinterferenzen), commonly known as X-ray diffraction (XRD), and was direct evidence for the periodic atomic structure of crystals postulated for several centuries. The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS and diamond. Although Bragg's law was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons, with a wavelength similar to the distance between the atomic or molecular structures of interest.

The applet shows two rays incident on two atomic layers of a crystal, e.g., atoms, ions, and molecules, separated by the distance d. The layers look like rows because the layers are projected onto two dimensions and your view is parallel to the layers. The applet begins with the scattered rays in phase and interferring constructively. Bragg's Law is satisfied and diffraction is occurring. The meter indicates how well the phases of the two rays match. The small light on the meter is green when Bragg's equation is satisfied and red when it is not satisfied.

The meter can be observed while the three variables in Bragg's are changed by clicking on the scroll-bar arrows and by typing the values in the boxes. The d and q variables can be changed by dragging on the arrows provided on the crystal layers and scattered beam, respectively.

Bragg's Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle. The rays of the incident beam are always in phase and parallel up to the point at which the top beam strikes the top layer at atom z (Fig. 1). The second beam continues to the next layer where it is scattered by atom B. The second beam must travel the extra distance AB + BC if the two beams are to continue traveling adjacent and parallel. This extra distance must be an integral (n) multiple of the wavelength (l) for the phases of the two beams to be the same:

nl = AB +BC (2).

Fig. 1 Deriving Bragg's Law using the reflection geometry and applying trigonometry. The lower beam must travel the extra distance (AB + BC) to continue traveling parallel and adjacent to the top beam.

Recognizing d as the hypotenuse of the right triangle Abz, we can use trigonometry to relate d and q to the distance (AB + BC). The distance AB is opposite q so,

AB = d sinq (3).

Because AB = BC eq. (2) becomes,

nl = 2AB (4)

Substituting eq. (3) in eq. (4) we have,

nl = 2 d sinq, (1)

and Bragg's Law has been derived. The location of the surface does not change the derivation of Bragg's Law.

The following figures show experimental x-ray diffraction patterns of cubic SiC using synchrotron radiation. 

Players in the Discovery of X-ray Diffraction

Friedrich and Knipping first observed Roentgenstrahlinterferenzen in 1912 after a hint from their research advisor, Max von Laue, at the University of Munich. Bragg's Law greatly simplified von Laue's description of X-ray interference. The Braggs used crystals in the reflection geometry to analyze the intensity and wavelengths of X-rays (spectra) generated by different materials. Their apparatus for characterizing X-ray spectra was the Bragg spectrometer.

Laue knew that X-rays had wavelengths on the order of 1 Å. After learning that Paul Ewald's optical theories had approximated the distance between atoms in a crystal by the same length, Laue postulated that X-rays would diffract, by analogy to the diffraction of light from small periodic scratches drawn on a solid surface (an optical diffraction grating). In 1918 Ewald constructed a theory, in a form similar to his optical theory, quantitatively explaining the fundamental physical interactions associated with XRD. Elements of Ewald's eloquent theory continue to be useful for many applications in physics.

If we use X-rays with a wavelength (l) of 1.54Å, and we have diamonds in the material we are testing, we will find peaks on our X-ray pattern at q values that correspond to each of the d-spacings that characterize diamond. These d-spacings are 1.075Å, 1.261Å, and 2.06Å. To discover where to expect peaks if diamond is present, you can set l to 1.54Å in the applet, and set distance to one of the d-spacings. Then start with q at 6 degrees, and vary it until you find a Bragg's condition. Do the same with each of the remaining d-spacings. Remember that in the applet, you are varying q, while on the X-ray pattern printout, the angles are given as 2q. Consequently, when the applet indicates a Bragg's condition at a particular angle, you must multiply that angle by 2 to locate the angle on the X-ray pattern printout where you would expect a peak.

Text written by Paul J. Schields
Center for High Pressure Research
Department of Earth & Space Sciences
State University of New York at Stony Brook