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Practical applications for metamaterials beyond the invisibility cloak

In the late 1960s, Russian physicist Victor Veselago pondered whether two key electromagnetic properties could ever be negative. In conventional materials, permeability and permittivity are always positive. But he proposed that if both permeability and permittivity were negative, so too would the refractive index of that medium.

This demanded a new look at some of the equations that determine electromagnetic behaviour and opened up intriguing possibilities for materials that might have negative refractive indices.

One result was the prediction that a light ray entering a transparent material with negative refractive index would bend the 'wrong' way relative to the surface normal. The reason behind this change lies in the group and phase velocities of a wave. Refractive index is a ratio of phase velocities. So, the phase velocity of a light wave has to turn negative when the wave encounters a medium with a negative refractive index, while its group velocity can remain positive.

As no real world bulk materials have negative permeability or permittivity, interest waned for 30 years until, in 2000, Professor Sir John Pendry and colleagues from Imperial College and the University of California at San Diego showed it was, indeed, possible to build an artificial material with negative permittivity.

Negative permittivity can be encountered naturally under certain circumstances. A metal below the plasma frequency – the point at which it becomes transparent to light – shows the effect and it comes from free electrons in the metal that act to screen out external electromagnetic radiation. Metal gratings show the same kind of effect, but it was only once work started on attempts to combine negative permeability and permittivity that the effect was reinvestigated.

The plasma frequency depends on the density of carriers and their effective mass. In a wire lattice, the geometry controls both parameters – by making the wires thinner, it is possible to increase the effective mass of the charge carrier which, in turn, reduces the effective plasma frequency. In principle, it is possible to achieve negative permittivities using wire meshes or gratings all the way from the low radio frequency to the optical region of the spectrum.

Prof Pendry's team proposed a structure for negative permeability. The split ring resonator – which, as the name suggests, is an almost complete circle of metal – behaves like the inductive-capacitance (LC) resonator of an electrical filter circuit. When the resonator sits in a magnetic field that changes with time, charge builds up across the gap in the ring. At low frequencies, the currents that oscillate within the resonator stay in phase with the driving field. But at higher frequencies, the currents start to lag, generating an out of phase response – which produces the effect of negative permeability at those higher frequencies.

The next step was a composite material that could exhibit negative permeability and permittivity, albeit over a narrow frequency range where effective range of the resonators and wire gratings overlap. This step was taken by researchers at the University of California at San Diego. They demonstrated a negative refractive index, as predicted by Veselago, and the idea of a 'left handed' material became a reality.

Applying a negative refractive index to waves of a certain frequency range was only the starting point to explore the kinds of manipulations made possible by carefully designed surfaces. Earlier this year, Professor Bumki Min and colleagues at the Korean Advanced Institute for Science and Technology built a structure that demonstrated, for terahertz waves at least, the highest value for positive refractive index ever recorded. This peaked at 38.6, more than an order of magnitude greater than that of diamond.



The structure in this case was a polymer film that carried a pattern of gold or aluminium H-shapes, depending on the target wavelength. These were arranged into square unit cells that sat close to each other, but were not allowed to touch. The shapes were designed to keep permeability at normal levels, but to boost the permittivity artificially by using linearly polarised light to create electric fields between the metal shapes. At resonant frequencies, the electric field increased and boosted the refractive index to its maximum.

To overcome the innate electromagnetic parameters of a bulk material, the surface features need to be smaller than the wavelength of light they are expected to affect – in principle. In terms of electromagnetic interactions, the wavelength determines whether a collection of surface features can be considered a material. If they can be grouped together and treated as bulk properties, then the features become, in effect, artificial atoms. As Prof Pendry explained in a 2004 review paper in Science, together with other metamaterial pioneers David Smith and Mike
Wiltshire: "Although such an inhomogeneous collection may not satisfy our intuitive definition of a material, an electromagnetic wave passing through the structure cannot tell the difference. From the electromagnetic point of view, we have created an artificial material or metamaterial."

A left handed material that bends light the wrong way or, at extreme angles, the right way is interesting intellectually, but does not immediately suggest an application. But such control over light has potential benefits.

Normally, refraction through a solid causes light to disperse at each interface, according to Snell's Law (see fig 1). A material with a negative refractive index can refocus the light rays, making new types of lenses possible (see fig 2). Using these metamaterials, a diverging lens can be turned into a converging lens, or vice versa.

Potentially more usefully, Prof Pendry showed, in another experiment in 2000, that a material with a negative refractive index could focus an image beyond the conventional diffraction limit. Normally, diffraction limits the resolution of an image focused by a lens to double the wavelength of light used. Semiconductor companies have struggled with this problem for more than a decade (see feature on p??). But negative refractive index materials can recover the information lost by conventional lenses, allowing subwavelength focusing.

Prof Pendry and his colleagues argued the term 'lens' is a misnomer when dealing with these metamaterials. "A more accurate description of a negative index material is negative space … it is as if [a slab of material] had grabbed an equal thickness of empty space next to it and annihilated it."

This effective destruction of space opens up the possibility of the metamaterial's more unusual applications: for example, a Harry Potter style invisibility cloak. If a cloak can remove space, then one that is thick enough could remove an entire object from view, when illuminated with light of the right wavelength. In practice, a broadband cloak is likely to remain the stuff of fantasy for many years. And conventional camouflage may be just as effective and lighter.

The most offbeat use so far is as a demonstration of the impossibility of time travel. Using a metamaterial intended to model some of the conditions present shortly after the Big Bang, Igor Smolyaninov and Yu-Ju Hung of the University of Maryland claimed in April 2011 to have shown that time travel can never be possible. They built a metamaterial in which one of the spatial coordinates could be considered to have 'timelike' behaviour, based on a rewriting of some key equations. The pattern of light within the metamaterial when illuminated by a laser could then be considered to be its 'history' within its confines: a 2D+1 'toy' representation of spacetime.



Originally, the researchers had attempted to use the metamaterial to create closed timelike curves – circular paths in spacetime that allow particles to return to where they started and allowed by one solution to the equations of general relativity. The reason for attempting to model the universe was to achieve a model of the highly curved spacetime that existed in the initial moments of the Big Bang. But they found restrictions on the way that light rays can move through a metamaterial and, although some could return to their starting point, they did not perceive the supposedly timelike variable as truly timelike: they were behaving as ordinary rays in space.

One of the first real world applications for metamaterials has been the artificial magnet. Researchers realised that turning a non magnetic material into an artificial magnet could provide a new way of building magnetic resonance imaging (MRI) scanners.

MRI scanners work by bathing the body in a strong magnetic field that oscillates at radio frequencies. This changing field causes the nuclei of hydrogen atoms to resonate and generate their own, much weaker field in response. Electron shielding changes the resonance frequency, revealing detail about the molecular environment of each hydrogen atom. The scanner picks up on this change in resonance by sweeping the source field through a range of frequencies. Computer processing then reassembles the incoming data into an image.

In practice, it is hard to generate a strong magnetic field that oscillates at high frequency. Instead, MRI scanners use a strong – of the order of 1Tesla – to make the body's nuclei align. Then a weaker radio frequency electromagnetic pulse excites them enough to precess around the main field. A material to focus the RF field or transport weak magnetic flux to a detector helps, but only if it does not perturb the stronger field, which enables the high resolution of a body scanner.

If an artificial magnet can be made to only respond to a time varying field, but to be effectively invisible to the static field, it becomes much easier to focus the RF field without disrupting the resulting image. In MRI scanners, the wavelengths are so long that only the effective permeability of the metamaterial matters. This can be controlled using a structure known as the Swiss roll – an insulated metal sheet wrapped around a cylinder. Around 10 turns on a 1cm diameter cylinder brings the resonant frequency in the range of an MRI pulse. The resulting metamaterial is an array of these rolls.

At the resonant frequency, the slab of Swiss rolls behaves like an array of magnetic wires. A magnetic field that hits one side of the slab is conveyed to the other side, where it can be picked up by a detector. Using a metamaterial for its negative refractive index can also be used to focus and shift the RF field.

In 2008, researchers from the University of Seville found that negative refractive index can extend the range of a scanner's receiving coil by effectively shifting the magnetic field inside a patient to the outside – taking advantage of its 'negative space' property. Without the metamaterial, an MRI scanner could yield a usable image from one knee. WIth a slab of metamaterial sandwiched between the knees, usable images were captured from both knees. In principle, this allows deep, high resolution images to be generated without having to increase the strength of the static field, which run of risk of creating hotspots in the patient's body.

One problem is that a metamaterial designed to focus the RF field can distort the very weak signal generated by the hydrogen nuclei. Further work at Seville has resulted in a tunable metamaterial. The team used split ring resonators with a twist – putting diodes into the ring so that when a strong field hits them, they 'short out' and become invisible. The weaker response fields do not close the circuits and are focused by the resonators.

There are other ways to tune a metamaterial. One technique is to excite photocarriers in a gallium arsenide substrate on which is printed an array of split ring resonators. These charges remain for around 1ns and shift the frequency resonance of the metamaterial temporarily. With shorter lived photocarriers, it becomes theoretically possible to build switches that operate in the terahertz regime and this opens the prospect of purely optical computers that can be microfabricated in a similar way to conventional electronic integrated circuits.

Nader Engheta of the University of Pennsylvania and Andrea Alù of the University of Texas believe metamaterials research makes it possible to go further and design and build optical circuits using techniques similar to those used today to develop RF electrical circuitry. Instead of trying to build what looks like a bulk material to photons in the target frequency range, they would use different types of nanoparticles to create analogues of capacitors, resistors and inductors (see fig 3).



In principle, the techniques used to design RF circuits – such as simplifying the circuit into a collection of lumped elements – apply to optical frequencies as much as the lower frequencies of light. Unfortunately, the material properties of metals do not scale so well. Materials that are simply conductive at RF and microwave frequencies shift into plasmonic resonance at optical wavelengths – where the optical signals couple with conduction electrons at the metal's surfaces.

These 'metananocircuit' elements themselves are much more leaky than those found in microwave circuits: where dielectric materials can isolate components such as resistors and capacitors. The biggest issue remains one of manufacture. The individual component shapes need to have overall dimensions of just tens of nanometres: at the limit of current fabrication techniques.

The work may lead to low power interconnects for cross chip communication. Alù and Engheta have proposed the use of nanoantennas for optical frequency photons could be more efficient than conventional waveguides and offer a free space alternative in which multiple signals could be received and multiplexed by a single antenna from a number of sources.

Metamaterial construction techniques may not even be needed for some applications. In March 2011, scientists at the Lawrence Berkeley National Laboratory in California demonstrated 'superlenses' that could demonstrate the subwavelength focusing properties of negative refractive index materials using the crystal structure of perovskite materials, rather than synthetic metamaterials.

Unlike the metamaterial lenses, the perovskite coated structure does not work with propagating waves but reconstructs the evanescent waves that are normally lost by conventional lenses. Potentially, the superlensing activity can be turned on and off electrically, thanks to the ferromagnetic nature of the perovskite crystals.

In just 40 years, an intellectual exercise has led to the development of a new family of techniques for handling electromagnetic properties – potentially opening up new applications for machines that full use of the interactions between photons and electrons.

Author
Chris Edwards

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