Positive thinking

Tomáš Tyc

In 2000, Pendry showed1 that a slab of material that bends light at a negative angle can work as a lens with the ability to resolve details much smaller than the wavelength of light. This is due to the fact that, unlike conventional lenses, which refract light at a positive angle (Fig. 1), this device transfers not only the propagating (long-range) waves of light from an object to its image, but also the object's evanescent waves — short-range light that carries smallest-scale information about the object. However, such a perfect lens, although based on a neat idea, has some serious drawbacks. For example, it turns out2 that, for fundamental reasons, negative refraction is always connected with light absorption, and such absorption destroys the super-resolution ability of the lens. More over, perfect lenses based on negative refraction are difficult to manufacture and can work only in narrow bands of the electromagnetic spectrum.

Figure 1: Positive versus negative refraction.
figure 1

Unlike conventional materials, which refract incident light at a positive angle, artificially engineered materials that have a negative refractive index bend light at a negative angle.

Full size image

A natural question to ask, therefore, is whether super-resolution lenses could be achieved by using materials that have a purely positive refractive index. In my opinion, the answer is definitely yes. As Leonhardt has shown3 by analytical calculations, Maxwell's fish eye4 — a prototype of a positively refracting perfect lens — can provide imaging that has, in principle, unlimited resolution. This theoretical prediction was confirmed experimentally by Ma, Leonhardt and colleagues5, who showed that images of two sources of microwave radiation (used instead of light), separated by one-fifth of the radiation's wavelength, could be clearly distinguished.

However, to achieve such super-resolution by Maxwell's fish eye, an outlet (drain) is required so that the radiation reaching the point of image formation can be absorbed or otherwise extracted. And it is this feature that is at the root of the controversy surrounding the issue of using positive refraction to make perfect lenses. Using a drain is not a problem, however, because the very reason for imaging is to record the image on some photosensitive medium, which naturally provides the outlet.

There are some similarities between imaging by Maxwell's fish eye and by time-reversal mirrors6,7. In both cases, the object's electromagnetic waves converge at the image point from all directions to create a subwavelength-resolution image. To produce a time-reversal mirror, the electromagnetic field must be recorded, inverted in time and then re-emitted using a complicated set-up involving active elements (additional sources of radiation). By contrast, Maxwell's fish eye and other positively refracting perfect lenses form the converging waves naturally, without the need for active elements or field recording.

Although the theoretical3 and experimental results5 are promising, there are still many unresolved challenges relating to super-resolution with positive refraction. Probably the most exciting one is how to apply Maxwell's fish eye and other perfect lenses in microscopy or nanolithography — the two fields that these devices are most likely to revolutionize.

No drain, no gain

Xiang Zhang

I take issue with Leonhardt and colleagues' claim3,5 that Maxwell's fish eye is a perfect lens. Maxwell's fish eye, proposed4 more than 150 years ago, is subject to a diffraction limit: it cannot resolve any feature smaller than a fraction of the wavelength of the light being used.

Over the past decade, negative-index metamaterials, which are made of artificially structured composites, have been used as a means to overcome the diffraction limit and to make a perfect lens by focusing all wave components of light emitted or scattered from the object1,8. The key to such a perfect lens is its very ability to restore the smallest features of the object by enhancing the evanescent waves, which often decay in space.

Leonhardt and colleagues argued3,5 that a metal-coated Maxwell's fish eye, which is made of a positive-index material, can also act as a perfect lens by collecting all wave components. Their trick for attaining a perfect lens was to place an additional optical active element (the drain) exactly where the object's image is formed.

The problem with this approach lies in the physical interpretation of the imaging resolution beyond the diffraction limit. An image formed using the drain-assisted fish-eye system involves electromagnetic waves not only from the object but also from a new source — the drain. The image is therefore no longer an intrinsic property of the fish eye itself. It was shown9,10 that removal of the drain destroys the sub-diffractional object details, resulting in a diffraction-limited image. It is therefore not justified to claim that a general positive-refracting material can make a perfect lens.

Placing the drain at the image position supplies, through an electromagnetic field induced in the fish eye, the time-reversed form of the object's electromagnetic waves, and the superposition of the time-reversed waves yields an apparently perfect image. The device thus falls within well-known super-resolution image schemes based on time reversal7.

The drain-assisted perfect lens is, however, an interesting use of Maxwell's fish eye, and it may offer opportunities from operations known as non-Euclidean optical transformations. Conventionally, the lens is an independent device that is separated from the object and its image. By contrast, with the fish-eye lens, both the object and image are embedded in it. How the embedded object and image affect the lens and its functions remains to be investigated. For example, displacement of the space inside the lens by an object of finite size can significantly alter how the refractive index varies across the lens and therefore the lens's optical functions. What's more, detecting the image from inside the fish eye can be a challenge for practical applications. Nevertheless, the 'entangled' or integrated approach of an object–lens–image with a drain is an idea worth exploring.