Beating the diffraction limit
Physics in Action: May 2004
Negative-index materials are being used to make lenses with perfect image
In 1968 the Russian physicist Victor Veselago predicted the existence of a
material with a negative index of refraction, which he termed "left-handed."
He concluded that in the presence of such a negative-index material nearly
all known wave propagation and optical phenomena would be substantially
altered, although negative-index materials were not known to exist at the
More than 30 years later, negative-index phenomena are finally being
investigated. The reason for the intense activity in recent years is the
emergence of a new class of artificially structured materials called
metamaterials. The electromagnetic properties of metamaterials are governed
by elements that are patterned on a macroscopic scale and that take the
place of atoms or molecules in naturally occurring materials. They can
therefore be engineered so that they have a much wider range of
electromagnetic responses, including the elusive negative index.
Veselago predicted that certain optical phenomena would be completely
reversed in a negative-index material. Perhaps the most striking of these is
refraction, in which an electromagnetic wave is bent when it passes through
the interface between two different materials. Normally, the wave will
emerge on the opposite side of the line that runs perpendicular to the
interface (the "surface normal"). However, if one material has a positive
index and the other has a negative index, the wave will emerge on the same
side of the surface normal as the incident wave.
Many groups have demonstrated negative refraction in metamaterials,
confirming Veselago's early prediction (see "The reality of negative
refraction"). In particular, this initial work has demonstrated the enormous
potential for a new generation of lenses, which function, of course, by
refracting the rays of incident waves. Negative refraction implies that a
converging lens made from negative-index material should have a concave
surface rather than a convex one. While this change may not seem profound, a
negative-index lens has remarkably different properties from a
positive-index lens, stemming from an inherent asymmetry between the two.
For instance, air or a vacuum has a refractive index of n = +1, so a piece
of material with refractive index n = +1 does not refract rays, and thus
cannot form a lens, whereas a material with n = -1 refracts rays strongly.
Recently, Claudio Parazzoli, Robert Greegor and colleagues in the Phantom
Works division of Boeing have exploited this asymmetry to produce a
plano-concave metamaterial lens with a negative refractive index that has
unique advantages over equivalent positive-index lenses (Appl. Phys. Lett.
at press). What is intriguing, however, is that the n = -1 material can form
a lens without curved surfaces, as hypothesized by Veselago. The trajectory
of each ray that leaves a nearby source is exactly reversed as it enters an
n = -1 slab, such that all the rays are focused at the centre of the
material and then once again outside it (figure 1c). The question is, can a
negative-index lens produce an image that has a higher resolution than that
of a conventional lens?
Unlike the source depicted in figure 1c, a real electromagnetic source has
what are called near-field components in addition to the far-field, or
propagating, components shown. These quasistatic field components decay with
distance from the source, which means that the final image always contains
less information than is contained in the source. This diffraction limit -
which is associated with all positive-index optical components - means that
the best resolution that is possible corresponds to about half of the
incident wavelength of the light that is used to produce the image.
In 2000 John Pendry of Imperial College in the UK considered the
negative-index planar lens in more detail and reached a remarkable
conclusion. He found that in addition to refocusing the far-field
propagating components, such a lens could also refocus the near-field
components. In order to achieve this, however, the n = -1 lens would need to
amplify the near-field components, causing them to grow exponentially within
the slab. In principle, such a lens would provide perfect image
reconstruction, prompting Pendry to dub the n = -1 slab a "perfect lens".
Pendry's prediction proved unsettling for many, and sparked a vigorous
debate (see Physics World August 2002 pp8-9). Several researchers drew
attention to apparent conflicts with known physical limitations, such as
energy conservation or the uncertainty principle. As remarkable as Pendry's
prediction might seem, however, the prospect of a lens that can beat the
diffraction limit has survived these challenges.
As with most negative-index phenomena, the key to producing the near-field
refocusing effect is to develop the metamaterial. Intrigued by the prospect
of beating the diffraction limit, Anthony Grbic and George Eleftheriades of
the University of Toronto have formed an analogous metamaterial based on
electrical transmission lines. A standard transmission line consists of
repeated cells that contain inductors in series and capacitors in parallel,
so that it can support propagating electromagnetic waves with the same
dispersion characteristics (i.e. frequency versus wavelength) as a
By reversing the positions of the inductors and the capacitors, the
transmission line becomes the analogue of a negative-index medium. Grbic and
Eleftheriades created a circuit equivalent to a perfect lens by placing a
rectangular negative-index transmission-line between two positive-index
transmission lines. With this metamaterial, they have managed to refocus the
near-field components of a 1.057 GHz wave (Phys. Rev. Lett. at press).
To demonstrate this, the Toronto team placed an electromagnetic antenna (the
source) on one side of the negative-index region and mapped the
electromagnetic fields both within the slab and on the other side (the image
plane). They found that the recovered image does indeed have a resolution
that is better than that which the diffraction limit implies - in agreement
with Pendry's prediction (figure 2). However, the image is still broader
than the source, which means it is not perfect. This is due to material
losses in the transmission-line metamaterial, which place a limit on how
well the near-fields can be recovered; build a better metamaterial, and the
resolution will improve.
This latest round of experiments provides strong evidence that
negative-index metamaterials have an important future in imaging.
Negative-index lenses offer a new degree of flexibility that could lead to
more compact lenses with reduced aberration. Furthermore, the remarkable
phenomenon of near-field focusing demonstrated by Grbic and Eleftheriades
implies that the diffraction limit - which is the most fundamental
limitation to image resolution - may, in fact, be circumvented by
While the results reported so far have demonstrated negative refraction at
microwave frequencies, recent experiments and theoretical work suggest that
photonic crystals may enable these wonderful effects to be demonstrated at
David R Smith is in the Department of Physics at the University of
California, San Diego, CA, US