Bending the rules. Light normally travels in straight lines, but with some clever pre-adjustment, it curves instead.

F. Courvoisier and J. M. Dudley

Light Bends by Itself

Any physics student knows that light travels in a straight line. But now researchers have shown that light can also travel in a curve, without any external influence. The effect is actually an optical illusion, although the researchers say it could have practical uses such as moving objects with light from afar.

It's well known that light bends. When light rays pass from air into water, for instance, they take a sharp turn; that's why a stick dipped in a pond appears to tilt toward the surface. Out in space, light rays passing near very massive objects such as stars are seen to travel in curves. In each instance, light-bending has an external cause: For water, it is a change in an optical property called the refractive index, and for stars, it is the warping nature of gravity.

For light to bend by itself, however, is unheard of—almost. In the late 1970s, physicists Michael Berry at the University of Bristol in the United Kingdom, and Nandor Balazs of the State University of New York, Stony Brook, discovered that a so-called Airy waveform, a wave describing how quantum particles move, can sometimes bend by a small amount. That work was largely ignored until 2007, when Demetri Christodoulides and other physicists at the University of Central Florida in Orlando generated optical versions of Airy waves by manipulating laser light, and found that the resultant beam curved slightly as it crossed a detector.

How did this self-bending work? Light is a jumble of waves, and their peaks and troughs can interfere with one another. For example, a peak passing a trough cancels each other out to create darkness; a peak passing another peak "interferes constructively" to create a bright spot. Now, imagine light emitted from a wide strip—perhaps a fluorescent tube or, better, a laser whose output has been expanded. By carefully controlling the initial position of the wave peaks—the phase of the waves—at every step along the strip, it is possible to make the light traveling outward interfere constructively at only points on a curve and cancel out everywhere else. The Airy function, which contains rapid but diminishing oscillations, proved an easy way to define those initial phases—except that the resultant light would bend only up to about 8°.

Now physicists Mordechai Segev and colleagues at Technion, Israel Institute of Technology, in Haifa say they have a recipe for making light self-bend through any angle, even through a complete circle. The problem with the Airy function, says Segev, is that the shape of its oscillations specify the right phases only at small angles; at angles much greater than 8°, the shape becomes a crude approximation. So his group turned to Maxwell's equations, the 150-year-old quartet of mathematical formulas that describe the propagation of electromagnetic waves such as light. After laborious mathematics and guesswork, the researchers found solutions to Maxwell's equations that precisely describe the initial phases required for truly self-bending light, as they report this week in Physical Review Letters.

"The Airy function is a solution for an approximate case," says Segev. "If you want [bending] to go to large angles, [the solution] must have the proper shape. People thought that there was no proper shape, that the solution would always fall apart—but we've shown that that is wrong."

The work of Segev's group might have remained theoretical, but by coincidence, a group led by John Dudley at the University of Franche-Comté in Besançon, France, has been performing its own experiments on self-bending light. By modifying the existing Airy function, Dudley's group managed to find initial phase values that match the Israeli group's solution, even though they were unaware of it. Using a device called a spatial light modulator to pre-adjust the phase of an expanded beam of laser light, the French group found that the resultant light self-bent by up to 60°, as it will report later this month in Optics Letters.

Self-bending light could put a neat twist on optical tweezers. These devices, which were developed in the 1980s, use the force created by intense laser light to hold microscopic objects in mid-air. Segev believes that by replacing the laser beams with self-bending light, researchers could force trapped objects to travel along complex paths without touching them. In doing so, the curved light could selectively move cells away from a biological sample—a boon for bioengineers.

Physicist Pavel Polynkin at the University of Arizona in Tucson suggests another application: -burning a curved hole through a material, which would be impossible with a regular laser. But despite such applications, he points out that the light itself doesn't actually curve, it only appears to, because of the way in which the interference bright-spots line up. In fact, he says, most of the light's power goes not toward the bright curve, but into the dim areas that have been cancelled out. "I am not disputing the scientific significance of the paper," he adds. "It reports an important contribution. … [But] no fundamental physics laws have been broken so far—and that is a good thing, in my opinion."