# Focus: Left-Handed Materials Debate Heats Up

Published May 3, 2002  |  Phys. Rev. Focus 9, 23 (2002)  |  DOI: 10.1103/PhysRevFocus.9.23

#### Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous

P. M. Valanju, R. M. Walser, and A. P. Valanju

Published April 19, 2002

#### Left-Handed Materials Do Not Make a Perfect Lens

N. Garcia and M. Nieto-Vesperinas

Published May 3, 2002

Physicists learn early that light can bend only one way when it passes from vacuum into a material. Recent results, however, suggest that light bends the “wrong” way in so-called left-handed materials, which might be used to make perfectly focusing lenses. Now two groups, publishing in the 6 May and 20 May print issues of PRL, are stirring up more debate. One upholds the belief that light can only bend one way, period. The other claims that left-handed materials could never make a perfect lens anyway. These reports may be the opening shots in a new skirmish, say other experts.

Normally light waves carry energy in the same direction as they propagate, following what’s called a right-hand rule. But in 1968 Victor Veselago of the Lebedev Physics Institute in Moscow concluded that if you could tune the properties of a material just right, light would transmit energy one way while undulating in the other. Such a medium would, among other things, have a negative index of refraction: a straw in a glass of clear, left-handed liquid would appear bent backwards in a ”$<$” shape–the reverse of water’s behavior. A flat slab of the stuff would focus light, rather than dispersing it, as normal materials would.

Two years ago, John Pendry of Imperial College in London said this focusing by negative index materials should in fact be perfect [1]. The finest details of an optical image–those smaller than a wavelength of light–are carried by waves that die off rapidly as the light travels through a material. These “evanescent” waves can’t be focused, which leads to the so-called diffraction limitation on the sharpness of an image made with an ordinary lens. Pendry deduced that these decaying waves would actually grow as they pass through a left-handed material, making a perfect lens possible.

Some physicists pointed out what they saw as errors in short comments in PRL [2]. Now Nicolas Garcia and Manuel Nieto-Vesperinas, of the National Research Council of Spain in Madrid, dispute Pendry’s result in longer form. They first consider the component waves emanating from an object into an imaginary material that doesn’t absorb or disperse light’s energy. These waves would contain infinite energy, the researchers argue. For realistic media they say that even very small absorption will degrade the amplified waves, ruining the proposed benefit. The same effect should also ruin negative refraction, the team suggests in an upcoming Optics Letters paper [3].

Prashant Valanju and colleagues at the University of Texas at Austin say there’s a more fundamental problem. To transmit energy or a signal, the waves must come in a range of frequencies, which combine to form packets. The speed of each frequency component is called phase velocity, while the packet’s speed is called group velocity. A wave with just one frequency component could be bent the wrong way, but this is irrelevant because real light never has just one frequency, the researchers point out. If you look at several frequencies added together, they argue that the resulting packets bend and travel in the usual direction. As one consequence, even simple focusing by a slab is impossible. Normally the difference between phase and group velocity can be considered nil, they say, but not in this case. “Approximations physicists use to think about things fail absolutely” this time, Valanju says.

Both groups say the recent experimental results of negative refraction in a left-handed material [4] involve misinterpretations. Useful applications may well arise from these substances, they grant, but only after the physics is cleared up.

The other side is not throwing in the towel. Negative refraction is still possible, Pendry says, because the Texas group fails to consider a packet that doesn’t extend forever in both directions. Wave fronts of such a finite packet will indeed bend as they suggest, but will still propagate in the “wrong” direction, he says. As for lensing, he agrees that absorption does eventually kick in to limit the energy and resolution of a left-handed slab. But this limitation wouldn’t necessarily ruin “super” (if not perfect) focusing of features well below a wavelength.

The Texas group’s work points out the counter-intuitive nature of these strange new materials, says David R. Smith of the University of California, San Diego, a co-author on the paper documenting negative refraction. However, he adds, “the experimental and numerical evidence thus far indicates decisively that negative refraction is a reality.”

Ultimately, says Tomas Opatrny of Texas AampM University, the heat of this debate should generate some light. “People will want to show that they are right [and] this will stimulate nice experiments. I am looking forward to them.”

–JR Minkel

JR Minkel is a freelance science writer in New York City.

### References

1. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000).
2. G. W. ‘t Hooft, “Comment on “Negative Refraction Makes a Perfect Lens”,” Phys. Rev. Lett. 87, 249701 (2001); J. M. Williams, 87, 249703 (2001).
3. N. Garcia and M. Nieto-Vesperinas, “Is There an Experimental Verification of a Negative Index of Refraction Yet?” Opt. Lett. 27, 885 (2002).
4. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction,” Science 292, 77 (2001).