Here's an experiment whose importance actually depends on how you slice it. Physicists in the Netherlands say they have discovered a new twist on diffraction—the phenomenon in which an array of objects such as atoms in a crystal redirects light in certain directions. The new effect would seem to side step a fundamental limit set by the century-old textbook theory of diffraction. But the apparent contradiction may arise merely from how the researchers view their crystal-like structure, others say.
The disagreement all comes down to interpreting a simple formula found in virtually every physics textbook known as Bragg's law. Willem Vos, a physicist at the University of Twente in the Netherlands, says he's "humbled" to think that he and his team may have found a new phenomenon that provides an exception to that rule. "I still wonder every once in a while, 'Okay, what are we doing wrong.' " Others say nothing, except stretching the interpretation of the experiment too far. "The way the work is presented is maybe pushing it a little harder than it should have been," says Steven Johnson, a theorist at the Massachusetts Institute of Technology in Cambridge.
Diffraction occurs when light rays like x-rays scatter off a regular array of objects such as atoms in a crystal. Such an array can be thought of as a set of parallel planes, and when light waves reflect off neighboring planes at certain angles, they can reinforce one another to produce an especially strong flow of light. That choiring radiation occurs only if the wavelength of the light, the spacing of the planes, and the angle at which the light strikes them are tuned just right, according to a simple formula in Bragg's law.
That's why scientists can deduce the structure of a crystal by rotating it through all orientations in a beam of x-rays of fixed wavelength and observing the directions in which the x-rays are scattered. For decades, such x-ray crystallography has been an indispensable tool of scientists of all stripes, enabling, for example, biologists to determine the structures of tens of thousands of proteins. But Bragg's law predicts that the wavelength of the light has to be shorter than twice the distance between neighboring planes—hence the need for x-rays with sub-nanometer wavelengths to probe real crystals. Now, however, Vos and his colleagues at the University of Twente have found a way to side step that limit, as they report in a paper in press at Physical Review Letters.
Instead of working with a real crystal and x-rays, the physicists worked with a so-called photonic crystal, a plate of silicon with a two-dimensional rectangular array of 155 nanometer holes in it, and longer-wavelength near-infrared light. They shined the light in through the edge of the plate, perpendicular to the rows of holes, and expected the light to diffract straight back out if its wavelength was twice the rows' 347-nanometer spacing. Instead, longer wavelength light diffracted back out. The observation of that phenomenon—which the researchers dub "sub-Bragg diffraction"—came in 2007. "We were mulling it over for a long time," Vos says.
In the new paper, the researchers explain what's going on. The key is that the crystal can be sliced not only into horizontal rows of holes but also as diagonal rows. In fact, it can be sliced in diagonal planes in two different ways (see figure). The light diffracts off both sets of planes simultaneously in a process known as multiple diffraction, sending two waves rippling almost sideways through the crystal. But those two waves overlap and interfere with each other to produce a total flow of light straight back out of the crystal. What's more, because the distance between the diagonal planes is larger than the distance between the horizontal planes, the diffraction occurs even though the wavelength of the light is longer than twice the distance between the horizontal planes.
Thus, multiple diffraction produces a reflected beam at a wavelength longer than the angle of reflection and the spacing of the horizontal planes should allow when Bragg's law is applied to them. That's new, Vos says. "We couldn't find anybody who had observed this before," he says. Previously, multiple diffraction had been seen only at wavelengths shorter than the Bragg's law limit, Vos says.
But is the new result really surprising? The light is actually diffracting off the two sets of diagonal planes. And everybody agrees that for those interactions, Bragg's formula holds just fine. In fact, the reflection appears to occur at an unexpectedly long wavelength only if one uses the smaller spacing of the horizontal planes to predict the wavelength. As that's not the spacing of the relevant planes, the name sub-Bragg diffractions is a bit of a misnomer, Johnson says.
The interference does send the light in an odd direction, but unusual effects often pop up when there are multiple diffracted waves, says J. Friso van der Veen, an x-ray physicist at the Paul Scherrer Institute in Villigen, Switzerland. "It is a bit of a surprise that the wave is sent back along the direction that it came, but these things happen with multiple diffraction," he says.
So is sub-Bragg diffraction really something new? More data won't decide the case, as everybody already agrees on what's going on inside the experiment. It's purely a matter of interpretation—is it really novel to show that multiple diffraction from certain planes appears to violate Bragg's law when it's applied to different planes? Maybe it's time to bring in the lawyers.
*The story has been corrected 31 January to reflect that Bragg's law has not been violated per se, but that researchers have observed a new phenomenon that gives the appearance of violating Bragg's law.