John Pendry receives a Royal Society Royal Medal for pioneering research on metamaterials

Descartes Prize

Some words from Professor Donal Bradley, Head of the Physics Department:

"I am sure that you would wish to join me in offering our heartiest congratulations to John Pendry on his receipt of a Royal Society Royal Medal for pioneering research on metamaterials. The Royal Medals are the most prestigious awards that the Royal Society bestows and represent a glowing endorsement of the standing of John's work. This is an outstanding achievement."

John Pendry works in the Condensed Matter Theory Group. In 2005, along with his research team, he won a Descartes Prize for creating and developing a new class of artificial materials: metamaterials with a negative refractive index. Here, we give an introduction to these topics, along with another possible application of metamaterials – an invisibility cloak!

A series of more formal papers can be found at the following web site:

http://www.cmth.ph.ic.ac.uk/photonics/references.html

Metamaterials, negative refraction and cloaking

The field of optics has been around for a long time. Newton wrote a famous treatise about it in 1704; the equations which govern the behaviour of light were assembled by Maxwell in 1864. However, recent technological advances have injected new life into the field, exposing a great deal of interesting physics and opening the door to a wealth of potential applications. One of the most exciting new developments is the invention of metamaterials.

Metamaterials

Light is a wave, made up of oscillating electric and magnetic fields. Inside a material, these fields push and pull electrons around, and this has an effect on the way the light behaves – for example, in glass, light slows down. The light wave doesn't “see” individual atoms and their associated electrons; instead, it sees the collective response of many thousands or millions. There are many different kinds of material, with different responses to light. However, until recently, producing materials with tailor-made optical properties was difficult, and limited to forming new chemical compounds. John Pendry's first insight was to realize that we could do better by building our own artificial “atoms”. Structures smaller than the wavelength of light would act like real atoms, except that we can design them to have the properties we need! Soon after this revelation, the first metamaterials were made by David Smith and Shelly Schultz at UCSD and by Mike Wiltshire at the Marconi Company. They were designed to work with microwaves, which have a longer wavelength than visible light; this means that the artificial structures do not have to be so small, and are more easily fabricated. The aim was to construct a material with a very interesting property not found in nature – a negative index of refraction.

Figure 1: Split-ring resonators as artificial atoms.

Figure 2: One of the first metamaterials, constructed by David Smith and Shelly Schultz.

Negative Refraction

The refractive index of a material describes how light behaves inside it. Air has a refractive index of 1, while that of water is around 1.34. This means that light travels more slowly in water; it also means that when light goes from air to water, or vice versa, it changes direction (see Figure 3). This is known as refraction, and explains why swimming pools look shallower than they really are.

All known naturally-occurring materials have a positive refractive index. The first person to explore the possibility of a negative refractive index was a Russian scientist called Victor Veselago.

Figure 3: Refraction. The red line shows what happens when light passes from glass to air: it changes direction. The blue line shows what would happen if the glass were replaced by a material with a negative refractive index (in this case, -1). The light would bend backwards!

Veselago showed that a negative-index material would have very interesting properties. To begin with, if we could fill a swimming pool with negative-index water, the bottom of the pool would appear to be above the surface! The Doppler effect would also be reversed, so that receding objects would be blue-shifted (rather than red-shifted), and Cherenkov radiation (emitted by a charged object moving faster than the local speed of light) would be emitted backwards instead of forwards. Another interesting consequence is that the phase and group velocities would be in opposite directions (see Figure 4). The phase velocity is the speed of the ripples in a wave, while the group velocity is the speed at which a pulse of light moves. Energy and information generally travels at the group velocity.

Figure 4: wave propagation in negative-index materials. The ripples in the wave (green) move to the left, while the overall “packet” (red) moves to the right.

Veselago provided a basic recipe for negative refraction. He showed that for the refractive index to be negative, two other quantities also had to be negative: the electrical permittivity, e, and the magnetic permeability, µ. Materials with negative e are easy to find: ordinary metals satisfy this requirement. However, negative µ is much harder to obtain, and Veselago was unable to realize his ideas, which were subsequently neglected. Only with the advent of metamaterials – which allow us to choose our own values of e and µ – were they revived.

At the physical level, a negative e or m implies that the electrons within the material move in a direction opposite to that of the force applied by the electric or the magnetic fields! John Pendry proposed that we could mimic this effect by using a metamaterial composed of split-ring resonators (SRR) in the magnetic case or a lattice of straight wires in the electrical case. Figure 2 shows a picture of a metamaterial made by the UCSD group that combines these properties to give negative refraction. Resonating rotating currents are induced by magnetic flux penetrating the split rings, analogous to conventional atomic magnetism in materials. By contrast, the back-and-forth resonating currents in the straight wires are induced by the application of an electric field, so that we can say wires are electric resonators. In this way, we introduce resonance in an artificial manner – and resonance is the key to obtaining a negative response. By applying a field above the resonant frequency, the lattice of wires can provide a negative electric response (e < 0) over some range of frequencies, while the split r ings can pro vide a negative magnetic response ( m < 0) over the same frequency band. The combined result is a negative-index metamaterial.

So what can we do with such a material? One possibility is to use it to make a new kind of lens. Conventional lenses, like those found in spectacles, microscopes and telescopes are rounded; this is what allows them to form an image. However, with a negative-index material, we can make a lens which is flat!

Figure 5: A rectangular slab of negative-index metamaterial acts as a lens. Negative refraction at the left-hand surface causes the light rays from the object to come together inside the metamaterial, forming a mirror image; the light rays are then refracted at the right-hand surface to form a second image outside the slab.

There is a limit to how much detail can be resolved by a traditional lens. Beyond a certain point, we can't keep magnifying any more. This is the well-known diffraction limit – in general, we can't see features on a scale significantly smaller than the wavelength of light we are using. The negative-index lens, on the other hand, is different. In principle, there is no limit on how much we can see! This is because the negative-index lens (or superlens ) is able to capture the near field of the object, whereas conventional lenses work only with the far field. The near field contains all the information about the fine details of the object (on a sub-wavelength scale), and decays very rapidly as we move away from the object.

The diffraction limit is not only a barrier in imaging. It is also an obstacle in optical lithography – used by the microchip industry – and in optical data storage (CDs and DVDs). The superlens may help us to fit more data onto optical disks (by allowing a smaller spot size) and to make microchips even smaller.

Cloaking

A negative index of refraction is only one example of a material property not found in nature that metamaterials can give us. Very recently, John Pendry proposed an idea for a metamaterial cloak which could be used to completely conceal an object!

We would like to bend space around the object so that light flows past, almost like a fluid. We can't bend space, but we can mimic the effect by manipulating e and µ. A coordinate transform process relates the “bending” we would like to achieve to the required metamaterial properties.

Figure 6: Cloaking. Objects within the inner sphere are hidden completely from the outside world. The blue annulus is the metamaterial cloak. Light rays enter the cloak on one side, are guided around the inner sphere, and emerge on the other side on their original trajectories.

This isn't quite the Invisibility Cloak of Harry Potter fame: no light enters the inner sphere, so anyone hiding inside would be unable to see the outside world!