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METAMATERIALS

INSTANTEXPERT

7

John Pendry

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The Russian engineer Victor Veselago was one of thedriving forces behind the early development ofmetamaterials. In 1967, he predicted the possibility ofmaterials with a negative refractive index which wouldbend light the “wrong” way (see diagram, opposite).

All materials in nature have a positive refractiveindex. The refractive index is a measure of the

property that makes submerged objects appearcloser to the surface than they really are, andswimming pools shallow when they are not. Thegreater the refractive index of a material, thecloser to the surface an object within it appears.The logical consequence of this law is that a fish ina pond filled with a negatively refracting materialwould appear to have jumped right out of it (left).

Veselago’s argument that negative refraction

should be possible was complex. Light consistsof both electric and magnetic fields, with energyshared equally between the two. Light propagatesby tossing energy between the fields as if theelectric and magnetic components were ina dance. Atoms in a material with a positiverefractive index – water, glass or most other

transparent materials – respond by aligningtheir own electric and magnetic fields to theapplied fields so as to slow down the dance.

Veselago imagined a material that alignedits electric and magnetic fields in the oppositedirection to those in the light beam. This, hereasoned, would reverse the dance and create theeffect of negative refraction. His dream was onlyrealised with the advent of metamaterials.

NEW OPTICS, NEW THEORIES

The idea that a material’s internal structure couldinfluence its response to light has been debated sincebefore the time of James Clerk Maxwell, the 19th-century Scottish physicist who demonstrated howlight, magnetism and electricity are all aspects thesame phenomenon.

In the 1950s, researchers studying long-rangeradio communication built structures made from thinmetallic wires to simulate how Earth’s ionosphereinteracts with radio transmissions. But it wasn’t untilthe 1990s that we finally realised just how radicallya material’s structure could influence its properties.

I helped the GEC-Marconi company to produce aso-called split-ring structure. Manufactured byetching a copper circuit board with rings a fewmillimetres across, it had a particularly strongresponse to radar signals, which produced electriccurrents in the copper that in turn produced aninduced magnetic field (see image, above left).

This structure had another interesting property.Most magnetic materials align in the same directionas the applied field, like a compass needle pointing

north. In contrast, the new metamaterial aligned itsmagnetism in the opposite direction. In 2000, DavidSmith, then at the University of California, San Diego,took this split-ring structure and used it to make thefirst material capable of bending radiation in theopposite direction to normal materials such as glass.This was the negative refraction whose existence hadbeen predicted decades earlier by Victor Veselago.

A decade on, and we now have metamaterials withexquisitely intricate structures, like the onesfashioned from microscopic helices of gold by MartinWegener’s group at the Karlsruhe Institute ofTechnology in Germany (see image, bottom right).When light shines on the material, electric currents are

THE ROAD TOMETAMATERIALS

LIGHT REFRACTED BY MATERIAL WITHA NEGATIVE REFRACTIVE INDEX MAKES FISH

APPEAR AS IF IT’S OUT OF THE WATER

Metamaterials havebeen built for

radar waves (mainimage, and right, top)

and visible light(right, bottom)

ii | NewScientist

J O H N

P E N D R Y

induced in the helices. Interestingly,the size of the currents dependsstrongly on whether the light is leftor right-circularly polarised. Theresponse is stronger than even asolution of sugar, one of the most“optically active” natural substances.

This array of coppersplit rings was the firstmetamaterial to havenegative magnetism –meaning that its internalmagnetic field aligns inthe opposite direction toan applied magneticfield. It wasmanufactured at

GEC-Marconi in 1998 byMike Wiltshire and wasdesigned to respond tomicrowaves with awavelength of about3 centimetres. Thecopper rings areapproximately0.5 centimetres across

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David Smith was workingat the University ofCalifornia, San Diego,when he adapted thesplit-ring structure tocreate the firstmetamaterial with anegative refractive index(below, top). The copperloops change the magneticresponse, while thincopper wires on thesurface behind providethe required electricalresponse. Smith’s grouphas made extensivecontributions to thedevelopment ofmetamaterials, includingthe first working invisibilitycloak in 2006. It, too,operated at radarfrequencies

R A D I O

M I C R O W A V E

LIGHT REFRACTED BYA MATERIAL WITH ANEGATIVE REFRACTIVE INDEX

LIGHT REFRACTED BYA CONVENTIONAL MATERIAL

AN ENGINEERING CHALLENGE

The structures that make up metamaterials have to be smaller thanthe wavelength of the radiation to be manipulated

AMOUNT OF BENDING IS DETERMINEDBY A MATERIAL’S REFRACTIVE INDEX

S U B - M I L L I M E T R E

F A R I N F R A R E D

N E A R I N F R A R E D

V I S I B L E

U L T R A V I O L E T X - R A Y

G A M M A R A Y

10 2

(100m)10 0

(1m)10 -2

(1cm)10 -4

(100µm)10 -6

(1µm)10 -8

(10nm)10 -10

(100pm)10 -12

(1pm)

Wavelength (metres)

8 January 2011 | NewScientist | iii

How a material affects light falling upon it is dictated in part by itschemical composition, but its internal structure can have an evenstronger inuence. Silvered mirrors are highly reecting, but black-and-white photographs also owe their blackness to silver – billions of

nanometre-scale spheres of the metal embedded in the lm. Thisdramatic difference arises because the silver spheres are muchsmaller than the wavelength of light.

Metamaterials extend this concept with articial structures thatmight be nanometres across for visible light, or as large as a fewmillimetres for microwave radiation. Their properties are engineeredby manipulating their structure rather than their chemical composition.

The possibilities these materials open up are limited only by ourimagination, and not by the number of elements in the periodic table.As a result, metamaterials research has exploded during the past

decade. It has given us optical properties we once thought wereimpossible, including negative refraction never found in nature, andnovel devices such as invisibility cloaks.

HISTORY OF METAMATERIALS

J O N P E N D R Y P R O F E S S O R M A R T I N W E G E N E R U N I V E R S I T Y O F K A R L S R U H E

D U K E U N I V E R S I T Y

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A SLAB OF NEGATIVELY REFRACTINGMATERIAL CAN FOCUS DETAILS SMALLER

THAN THE WAVELENGTH OF LIGHT

iv | NewScientist

General relativity predicts that extremely massiveobjects will cause severe distortions to thesurrounding space. Perhaps the best known of these

objects are black holes – singularities in space-timefrom which even light cannot escape. Some peoplehave asked if metamaterials can be used to mimicblack holes, but this is not possible as metamaterialslack the built-in energy source required to producethe “Hawking radiation” that real black holes emit.

But there is something metamaterials can do thatis even more spectacular: they can create “negativeoptical space”. Think of space as a sheet of rubber thatcan be compressed. By pushing hard enough on thesheet, it should in principle be possible to fold spaceback on itself so that light moving in the folded spacepasses the same point three times. A fish swimmingin this space would come into focus three times, themiddle focus being inverted.

Transformation optics tells us that a portion of thefolded space must have a negative refractive index.This negative optical space has a remarkable property.Light leaving an object can be thought of as defocusingas it travels away in all directions. Negative opticalspace cancels out this effect. As a result, a lens madeof a metamaterial that creates negative optical spaceis optically perfect. It effectively eliminates the spaceseparating the object and image, so that the objectand image coincide.

Another limitation of ordinary lenses is that theycan never resolve details smaller than the wavelengthof the light being used. That’s because light diffractsor bends around objects of a similar size to its ownwavelength, so it can never be focused to a sharppoint. The lens is said to be “diffraction limited”.

When I calculated in 2000 that a negativelyrefracting lens breaks the diffraction limit, the resultcaused a furore, so entrenched was the notion thatlenses cannot be used to see anything smaller thanthe wavelength of light. Several experiments havesince shown my prediction to be correct. In particular,Nicholas Fang, working at the time with Xiang Zhangat the University of California, Berkeley, demonstrateda lens that could resolve details as small as one-sixththe wavelength of visible light. Subsequent work has

improved resolution to 1/20th of the wavelength.Such lenses are challenging to make, however,

because they are extremely sensitive to imperfections.

NEGATIVE SPACE ANDTHE PERFECT LENS

To be invisible seems somehow magical. Peoplehave dreamed of the possibility for centuries, butonly with the advent of transformation optics andmetamaterials has the dream of an “invisibility cloak”approached reality.

Such a cloak must have two properties. First,it must reflect no light and ensure that no light isreflected from the object it is cloaking. This isrelatively easy to achieve with a pot of black paint –or its equivalent for whatever wavelengths we wantto be invisible in. In essence, this is how the stealthtechnology used by the military operates.

Second, the hidden object must cast noshadow. Removing a shadow is a much greaterchallenge, but one that transformation optics

has successfully addressed.Our brains assume that light travels in a straight line

to reach our eyes, as if it travelled along a rigid rod.Now suppose that the rod were not rigid, but could bebent so that it curves around the object that we wantto hide. Our brains would be none the wiser becausethe light rays would reach our eyes exactly as beforewith no hint of the curved path that they had in facttaken. Metamaterials can make light flow like wateraround the hidden object, smoothly closing in behindthe object to leave no trace of its presence.

The eye is fooled in the same way by certain naturalphenomena that cause light to travel in a curve. Whenthe sun heats the desert sands, the air immediately

above the sand is also heated. Itbecomes less dense and thereforeless refracting. This effect tails offwith height, creating a gradient in theair’s refractive index. As a result, lightfrom the sky is bent so that it canappear to originate from the desertitself, as if part of the surface werecovered with water. Hence the

A CLOAK OF INVISIBILITY

J E R E M Y W O O D H O U S E / G E T T Y

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TRANSFORMATION OPT

NewScientist | v

We need a clever design tool to make the most of metamaterials’potential. In conventional optics, light travels in a straight line until ithits the boundary between two transparent materials, at which point itabruptly changes direction. Metamaterials are much more sophisticated.

They can force light to travel along a curved path, thereby opening upthe possibility of devices such as invisibility cloaks.The mathematical tool that tells us what kind of metamaterial will

bend light along the desired path is known as transformation optics.

TRANSFORMATION OPTICS

A remarkable experiment conducted during a solareclipse in 1919 showed that the sun acts like a giantlens, bending starlight that passes close to the sun’sdisc. It vindicated Albert Einstein’s prediction in hisgeneral theory of relativity that the sun’sgravitational field would distort space.

As far as light is concerned, the warped spacenear to the sun appears to have a large refractiveindex. Very helpfully for metamaterials, Einsteinproduced a formula relating the distortion ofspace to changes in effective refractive index.Furthermore, Einstein’s formula is an exacttransformation of Maxwell’s equations, whichgovern all electromagnetic phenomena.

What transformation optics seeks to achieveis to take a ray of light and distort its trajectoryin whatever way we please. We could do this bydistorting space itself using extremely massiveobjects, but thanks to Einstein’s insight this is notnecessary. Simply changing the refractive index willhave the same effect as far as light is concerned.

Transformation optics can be used to calculatethe required refractive indices. All that is thenneeded is to construct metamaterials that meet

these specifications.

A LITTLE HELPFROM EINSTEIN

x

y

x

y The wavering pathtaken by light from theroad makes it look wet

disappointment of a thirsty travellerwho thinks he has seen an oasis.Making an invisibility cloak thenbecomes a matter of devising asuitable refractive index gradient tobend light in precisely the right way.Transformation optics enables usto work out the exact properties ametamaterial would need to achieve

the required bending.It is a huge challenge to actually

build an invisibility cloak – particularlyat visible wavelengths where interestis naturally strongest. But at radarfrequencies, progress has been rapid.There have been more limitedsuccesses with visible light, withcloaks just a few wavelengths across.

”An invisibility cloakprevents reflectionsand shadows froman object”

A ray of lighttravelling throughspace behaves as ifit were “nailed” to thecoordinate system,even when spacebecomes warped. Tocontrol the ray in theway we want, all wehave to do is to warpthe coordinates .Einstein gave us aformula that letsus work out therefractive indices

that will do this

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vi | NewScientist

What if metamaterials could alter their propertiesin response to an electric current or a powerfullight source? Such “active” metamaterials, as theyare called, would be far more versatile than theirordinary counterparts.

For example, a metamaterial containing asemiconductor will conduct more electricity whenilluminated with light of the right frequency to excitecharge carriers in the semiconductor. This change inconductivity will, in turn, alter how the metamaterial

responds to a second light beam, providing a wayto modulate the intensity of the second beam oralter the direction in which it is bent.

The superior control provided by metamaterialsis making light almost as controllable as electronsin computer chips – a fact that could open the doorto faster telecommunications. At certain stages ina conventional fibre-optic network, the light signalhas to be converted to easy-to-manipulate electricalsignals and then back into light. Metamaterials willallow us to manipulate light signals without thistime-consuming and wasteful step.

However, metamaterials themselves can absorbenergy from light travelling through them, and this

ACTIVEMETAMATERIALS

N A N O S C A L E S C I E N C E A N D

E N G I N E E R I N G C E N T E R A T T H E U N I V E R S I T Y O F C A L I F O R N I A

, B E R K E L E Y

effect can greatly reduce theirusefulness, particularly as someof the more unusual propertiesof metamaterials, such as negative

refraction, require that light betrapped inside the material whileit is manipulated. For example,Xiang Zhang’s group at the Universityof California, Berkeley, has madea structure from alternating layersof silver and magnesium fluoridedesigned to have a negative refractiveindex for visible light (above left).Light is trapped between the layersof silver, but this also means it getsabsorbed over time.

To deal with such losses VladimirShalaev’s group at Purdue University

in West Lafayette, Indiana, introduceda dye into the structure. A powerfullight source pumps the dye moleculesinto an excited state, enabling them togive up their energy to a second lightbeam and amplify it. Here serendipityintervenes: the trapping effect thatmade the layered structure absorblight is now an advantage. The longerlight can remain in the structure, themore time it has to benefit from theamplification process.

This layeredmetamaterial worksat visible wavelengths

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NewScientist | vii

Metamaterials seemingly bend the rules of traditional optics, openingup a host of new applications and possibilities. Experimentalists areaugmenting their capabilities by using them in combination with otherexciting materials like quantum dots and dyes, while theorists are coming

up with novel ideas for metamaterials that are getting ever harder tomanufacture with the precision required.

FRONTIERS OF METAMATERIALS

”Metamaterials

make light almostas controllableas electrons incomputer chips”

SILVER SLAB

SILVERCRESCENT

SURFACE PLASMONS LIGHTSURFACE PLASMONS

SPREAD ENERGY OUTACROSS THE SURFACE

ENERGY IS FOCUSED ONPOINT OF CONTACT

Often we want to collect light and harness its energyto detect a molecule, switch a nanoscale electroniccircuit, or simply power a device. Nature has longused the feat of light harvesting in the process ofphotosynthesis: chlorophyll molecules in leavesabsorb light with a wavelength hundreds of timestheir size, and convert its electromagnetic energyinto chemical energy.

Transformation optics offers a systematic route tothis harvesting process. The strategy I favour is to startfrom a system that is well understood, yet doesn’t havethe desired properties, and then use transformationoptics to reshape it into something useful.

The starting point is an area of science calledplasmonics – the study of how electrons in a slab ofa metal such as silver wobble back and forth like jellyand create strong electric fields outside the slab.When these wobbles occur on the surface of the slab,they are called surface plasmons. It turns out we canuse them to harvest light.

Suppose light from an excited atom shines on aninfinite sheet of silver. Surface plasmons capture thelight and transport its energy away towards infinityalong the surface of the metal. This is a widely studied

HARVESTING LIGHTeffect, but it does not achieve ourgoal, as the harvested energy isdispersed to infinity.

What we want to achieve is thereverse: we want to capture light frominfinity and concentrate it to a point.A transformation known as aninversion shows us how to do this.It maps points at infinity to the origin,and the origin to infinity, with allpoints in between mapped intoreverse order (see diagram, below).So the source of light is now at infinity,and the surface plasmons are nowincoming waves focused on what wasthe origin. The silver slab becomesa crescent-shaped object whichgathers energy at its outer regionsand funnels it down to the cusp.In theory, a metal crescent of theorder of 100 nanometres in diametershould be an excellent light harvester.

However, transformation opticstells us more. As the light slows in its journey to the cusp, its energy densityis increasingly concentrated andwould reach infinite concentration atthe cusp were it not for losses in thesilver. Such theoretical studies show

that very large concentrations ofenergy should be possible.

Other structures can also harvestlight. Two metal spheres in contactwith each other will concentratelight at the point where they touch.As ever, the challenge is tomanufacture devices on a nanometrescale to the required precision.Several groups, including one ledby David Smith, who is now at DukeUniversity in Durham, North Carolina,have done this to develop effectiveharvesting structures.

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viii | NewScientist

is professor of physics atImperial College London.He works on the theory ofmetamaterials and otherproblems in electromagnetism

John Pendry NEXTINSTANTEXPERT

Dan HooperDARK

MATTER5 February

I M P E R I A L

THE BIG CHALLENGEREALISING OUR DREAMSThe advent of metamaterials has

inspired renewed interest in thefundamentals of electromagnetism.In part, our dreams of what can beachieved with these materials havebeen realised, but to some extent theyhave outrun our capacity to make themhappen. What are the stumbling blocks?

Fundamental to the metamaterialconcept is the ability to structurea material on a scale less than thewavelength of the radiation you wantto manipulate. This is not a problemwith the microwaves used for mobilephone signals, with a wavelength ofaround 30 centimetres, which is whymuch of the early experimental workwas with microwaves.

Visible light presents a greaterchallenge: whereas traditionaltechnologies used to manufacturemirrors and glass lenses have requiredtolerances of better that 1 micrometre,metamaterials have to be constructed

to nanometre-scale accuracy. Though

technologies such as ion beam etchingcan do this, they are expensive andhandle only small samples. Furtherprogress will require investment innano-manufacturing.

The performance of a metamaterialis ultimately determined by thecharacteristics of the ingredients fromwhich it is made. Metallic metamaterialsperform well at the frequencies usedby mobile phone networks but not atvisible wavelengths, where metalstend to absorb visible light.

One approach is to compensatefor such losses by introducing anamplifying medium, such as dyemolecules or an array of quantum dots.

What is not in doubt is the excitementcreated by the new metamaterial world,which has liberated theorists to dreamof things that were previously

thought impossible, and challengedexperimentalists to make them happen.

RECOMMENDED READINGA selection of articles at both advancedand popular level can be found atmy website (bit.ly/cBXmF4) andat David Smith’s site (bit.ly/bmFgh7)

Optical Metamaterials: Fundamentalsand applications by W. Cai andV. Shalaev (Springer)

Physics and Applications of NegativeRefractive Index Materialsby S. Anantha Ramakrishna andTomasz M. Grzegorczyk (CRC Press)

Cover imageDavid Schurig