 Good evening everybody. Welcome. Thank you all for making the efforts in the the stormy weather which has probably disrupted your travel. One of the reasons for starting on time is that just in case it's difficult for some of you to get back home as it was to get here we're going to give you a little more time so we're going to try to keep to time fairly tightly and John our speaker is already aware of that so thank you again all of you who've made the effort to come this evening. I should explain who I am. I'm president elected of the Institute of Physics my name is Roy Sambles and I happen to be professor of physics at Exeter University and John and I have known each other for a very long time great privilege for me I'm not too sure it was for John but anyway John it goes back a few years. Can I remind you please to turn your mobile phones off could you do that now please because we don't really want any disruptions. In about 1704 Isaac Newton published his book on optics it's amazing treatise it's worth reading if you can get out of a copy not of the original but of the the paperback version it's well worth reading and he at that stage in his career was 62 and it rather denies the suggestion that by the time you're 35 everything you've done is over-industed. Well John likewise who had already established himself as a key figure in theory of certain services of semiconductors actually probably has done his most formative work somewhat later in life. He had an amazing purple patch from about 1996 to 2006 and I'm not sure it's quite over yet he's still very active in his research which took him to the forefront of theoretical research and electromagnetism. Electromagnetism of course for those of you who aren't experts is really how we function we're electromagnetic objects and it dictates much of our world around us. He did some key formative work in negative refraction which is a strange concept and he will explain it later on some really great ideas and transformation optics some really neat stuff in metamaterials. Metamaterials is burgeoned into a big area across the world, plasmonics and several other areas which he could mention I don't know what you're talking about tonight John. But he has galvanized the community across the world. If you look up the web of science you'll find that his papers have been cited about 40,000 times which is a staggering figure and the papers you published in your purple patch are all near enough not all of them but many of them cited over a thousand times some as much as four or five thousand the perfect lensing one I noticed is nearly five thousand citations so he has had an impact in science which is colossal one of the giants of British science to be honest with you and it's absolutely fitting because of what he's done and its impact on electromagnetism which optics was part of in which Newton in a sense stimulated back in 1660 something and then published his book on in 1704. It's absolutely fitting that someone of John Stature someone of rep repute across the world has been awarded by the Institute of Physics Newton medal and it's my pleasure and it really is a pleasure John to ask you to deliver your Newton medal lecture this evening. Thank you very much. Oh and by the way sorry questions after the lecture please so that we can do the video. Thank you John. Well thank you Roy for that by ears of red already. It is a great honor to give the Newton lecture named after our greatest perhaps the world's greatest physicist so it's a heavy burden indeed. I want to talk to you about some new ideas and electromagnetism. They have to do with new materials metamaterials they have to do with some new techniques which enable us to design these metamaterials and along the way there is there's some science which is very exciting and which has the great virtue that not all exciting science has that it can actually explain to school children and one of the happy things I've been doing in recent years has been doing some outreach to school children who of course I'm only part responsible for the fame of invisibility JK Rowling has a lot to answer for of course. So all these things I will mention but let's start with the way way back this isn't the beginning of optics by any means but it's where I'm going to start today. So Snell and day car actually had the same idea about the same time they told us how materials can be used to control light and they formulated this law of how light is refracted as an interface and we all know that lenses play a very important part in our lives cameras and microscopes telescopes and so on and Snell's law survives the day because it's great beauty is that you can think of light as just a stream of particles and once you know what's going to happen at an interface you can trace in your mind's eye how you might design some equipment before you even start putting the numbers in you don't have to ask computer for the answer until you want the details your imagination is free to roam courtesy of Snell's law but of course Snell's law was formulated well before our current rather complete understanding of electromagnetism light consists if you look on the microscopic scale of electric and magnetic fields intertwined with one another dancing from electrical form to magnetic form and this dance is described by Maxwell in these very famous equations here and although Snell's law is very intuitive and works at the everyday level once you get down to a length scale that is comparable with the wavelength of light then you really do have to switch to the ingredients of Maxwell's equations which are the electric and magnetic fields whose behavior he describes and to describe this we we introduced our aim was was of course Maxwell's equations do describe the behavior of light very accurately but I challenge you to stare at these equations and then ask how light would refracted an interface it's not obvious yes and it is true that you can give these equations to a computer and some boundary conditions they will tell you the answer but what it what they do not give immediately is an understanding of why that is so and so we wanted to formulate a way of looking at Maxwell's equations that was as intuitive as Snell's law and so we picked on the ingredients of Maxwell's equations which electric and magnetic fields and parody represented these by lines of force and so each field can be represented by a line which indicates the direction of the field and the density of lines which is not shown here but if you have many lines close together that means an intense field and that's a bit like rays except that you're now describing the accurate ingredients of Maxwell's equations the fields the electric and magnetic fields and what we realized was that if you imagine that these field lines are embedded in some sort of space and then you distort that space and think about a coordinate transformation then the field lines you imagine are moved with this rubber sheet which you're thinking of spaces being like and and so you can distort the passage of the line by distorting space and actually that's that's a way that Einstein taught of these these these things and from this distortion of space you can derive a formula for what the refractive index or if you would like to be precise epsilon mu should be to make these field lines go in this direction here and so that's the basis of transformation optics which is the design theory behind the concept of of metamaterials so this is the old Descartes-Snell law this must be a talk I gave in France because I call it a Descartes law and here's the the new law which applies not just to rays of light but applies to electric magnetic fields and if this matrix lambda is a matrix of the first derivative of that coordinate transformation this tells you how epsilon and mu change I don't have time to describe it here there is an intuitive way that you can actually crawl over this mesh and discover at each point how epsilon and mu change just just without doing any differentiation with a ruler so that's the design technology and the things we're designing are these things called metamaterials now it turns out that in electromagnetism generally and in optics in particular there are many material properties which you think might be allowed in terms of the laws of physics but you just can't find those properties in nature and and if you want to build some equipment or do something in optics you have to build it out of a material and if the material isn't there you can't do it and so we introduce this concept of a metamaterial now an order of material it responds to an electric field say and according to how the atoms and molecules polarize and its average response over many millions of molecules gives the electrical response of glass or water or whatever common material you're thinking of but in a metamaterial the atoms and molecules are replaced by slightly larger elements which have a physical structure they might be tiny metallic rings for example or holes in the structure they're very very simplest form and in these metamaterials these little units which are bigger than atoms and molecules but nevertheless small than the wavelength they act like rather big atoms and molecules and you by designing their structure you can design the properties of these metamaterials and because you're not limited by the periodic table by the chemistry you can add to the chemistry the flexibility of structure and in this way you can design into these materials properties which have never been seen before in material natural materials and I'm going to give you one or two examples of these materials the first ones were made to work at radar frequencies by Mike Wiltshire who was working at the Marconi company then this all originated from a consultancy I had with the Marconi company and here he's making a material to respond to 10 centimeter radar waves and these structures about five millimeters across much less than the wavelength of radar waves but still large enough that you can engineer them quite simply and you can see that they're in the form of a ring and so if you put a magnetic field normal to that ring it induces a current in the ring and that in turn produces a magnetic field in response so this is magnetism without magnets and if you start to do something slightly fancy like snip the rings off here so the ring isn't complete that makes a little resonant circuit and as you tune through the resonant frequency you get a whole spectrum of very different properties from this material the most striking of which is that at some frequencies the magnetic response come in the opposite direction from the magnetic applied magnetic field and that was one of the early fascinations of these structures negative magnetism and here's an exploitation of that made by David Smith who has been my very long-term collaborator and friend in all this David's both an experimentalist and a theorist and I'm just the theorist and he took this concept of metamaterials and he made these split ring structures which have been designed for the Marconi company and made them into this two-dimensional structure here and this wire is on the other side of the circuit so these rings give you negative magnetism and these wires give you negative electrical response now it turned out that that was the prescription given many years ago by a Russian scientist called Veselago and he said that if you could have negative electrical and magnetic response then something remarkable would happen but this material will become transparent to to electromagnetic waves and the refractive index would be negative the third negative and he had already explored theoretically what fascinating things you could do if you had a negative refractive index and this was the first structure ever that had a negative refractive index well it turned out the funding ran out for radar waves but there were some friendly MRI scientists willing to give us money at Marconi and this was a Swiss Roll structure which is a coil of insulated copper sheets wound round into a resonance structure and these were designed to have a resonance of 21 megahertz which is one of the frequencies used in in MRI equipment and the idea of this was to guide electromagnetic fields down the center of this this rod and i might come to that later in my lecture in terms of applications because there have been some applications of ideas related to that um yes so just very briefly explaining what negative refractive index is Victor Veselago's idea so this is what glass and water do and when light goes into glass or water it comes out this side of the normal but if it goes into a negative refractive medium it comes out the opposite side of the normal and so by this definition this angle is negative put it in here and you get a negative refractive index now stated so simply that seems really like a mathematical anomaly nothing very special we know about negative numbers but if my lecture runs to time i will tell you about some of the really remarkable consequences which follow from negative refraction and here are some of the structures which people are making to show negative refraction here's a metamaterial on a much finer scale here and these these this is a layered structure called the fishnet structure and the layers that have a thickness here 30 nanometers much much smaller structure this is designed to work at optical frequencies much shorter wavelength therefore the structures have to obey this law of being smaller than the wavelength so they're very small here's a micron and by layering silver and an insulator magnesium fluoride you can make this structure with a negative refractive index this work was done by Chang Sang's group at Berkeley California so that's a negative metamaterial working at optical frequencies so when we assemble these tools and we're very excited about them we ask ourselves how do we explain these to a wide audience and and show that audience that what we have is is profound and exciting as we believed it to be now i think you might not get terribly excited by that slide and in particular you might not have got very excited about these equations here but what we decided was to find something which you could do with these materials and with these equations which which hadn't been done before and which would surprise people make them wake up and perhaps pay attention to the less sensational things and the the target we chose was invisibility um now this is Peter Pan his statue in Kensington Gardens just north of my college and what this slide is is to show you is that um if you want to make something invisible it's not enough to make it black make it black and it's in a bright environment such as a squash court and a black squash ball you will be very much aware of it because what you'll be aware of is the shadow of that object and it's Peter Pan because he's a little boy who lost his shadow and when an object has lost its shadow it is truly invisible so how do you do that well the um idea is is quite simple to be stated so you want to take a region which you're going to hide so you can do anything in there that you like and you will not be seen um and the observer will not be aware that he's not seeing you and you're going to hide that region by means of a cloak which is going to be a finite extent and wrapped around this this hidden object and the function of the cloak is to grab the rays of light and steer them away from the hidden object so you never see it but also um return them to the path which they had before their path was uh disturbed so the observer standing here sees what's behind the object and is unaware of this deviation which has been made now i think you can see that this this technique of transformation optics which i outlined to you is ideally suited for this because here's a coordinate system and inside this cloak here i'm going to distort the coordinate system tear a hole in it and push the coordinate system out and taking with it the rays so the rays follow the distortion of a coordinate system and avoid the hidden space if you don't distort the coordinate system the rays don't move and you do not therefore change epsilon or mu the refractive index and so this technique is ideally suited to designing a cloak because if if you don't mess with the coordinate system then you don't disturb the ray so this ray stays where it was and this ray comes in as it did before and it's only in this region that you need uh tune the parameters and you go to the equations which are straight on manstein and uh there you have your cloak so here's the simplest possible cloak you tear a hole in the space and you squash all of this material inside this sphere or cylinder whatever your choice of cloak so that you now created a hole and compressed space and all the rays with it into this region here this simple algebraic formula tells you how you might do that there are many different ways you can compress space of course and when you have done that the rays will look like this and actually uh that idea once you have this notion of transformation optics that idea is so simple and easy that I thought it was a joke and I was invited to a DARPA meeting in San Antonio some years ago and they said your job is to ginger at the meeting so I blah blah blah metamaterials and I thought I'll finish with a joke I'll tell them how to design a cloak of invisibility and expecting a laugh and sit down and uh the joke fell rather flat everybody looked dead deadly serious and then they started muttering to one another I thought I've um trapped on some bad ground here and but it not so it turned out that they were very excited and certainly they offered me a lot of money after the meeting to do some research and if you think about it I mean this this idea is really really simple like you want to do this but the idea of invisibility is is something which we find magical children find it magical and that's because the notion of light traveling at a straight line is embedded in your brain and so when that notion is disrupted however simply we're surprised actually light doesn't always travel in a straight line this is a mirage in the desert and it comes about because of hot air on the desert surface which is less reflect refracting less dense and therefore less refracting the cool air above it and the gradient in refractive index means that the light travels uh in in not a straight line but a curved trajectory so it may reflect the light so that you appear to see the sky reflected in the desert here in the uk we're more familiar with these road mirages where hot asphalt seen in the distance appears even on a hot day to make the road seem wet so light is known to travel in a curved line and here's the first shot at making a cloak done in David Smith's laboratory in 2006 and there's an old slide it's not got the date on it and what he's done here is to use metamaterials to deflect radar waves the cloak for radar waves um my pointer isn't so good and this is the gradient in the refractive index of the cloak as you go from the outer the inner region and that's achieved by altering the physical structure of these little metamaterial elements here that's very easy to do and you don't even have to make these in your own laboratory because the elements of a printed circuit board so you design them on your computer you write off to a printed circuit company and back comes your metamaterial in the post and that gave the subject a flying star well that was the first cloak for radar waves i don't have time to show you the results of the rather old hat now anyway but then we had the thought that what people really want is a cloak for visible light and that's much harder because even with metamaterials to get the flexibility and the properties that you need to design a cloak is very difficult so we thought well how can we make the cloak easier to build and Jensen Lee my postdoc at the time from Hong Kong worked with me on on some new new ideas there and it's a matter of geometry so there are actually three ways you can imagine making a cloak so you can think of a cloak as a sort of lens now normally lenses have the task of making something appear bigger but you can also make lenses that make something smaller and if you made a lens that made something very very small that thing will be invisible so a cloak can be thought of as a lens which makes things inside it infinitely small now there are three ways you can do that you could have a vaguely spherical cloak and it can crush the contents of the cloak to a point or you could have a cylindrical structure and objects viewed through at the center of that cylindrical structure will be squeezed into a very very thin wire a point's invisible a very very thin wire is also invisible i think you catch my drift third way is to squash something really really flat now when you do that it becomes very very highly reflecting actually so what you have is a very very thin sheet and that isn't invisible only if you look at it edgeways on that's the only way it's invisible it's all two-dimensional but there is a way you can make it invisible um i've asked this question so many times in lecture i never get an answer where would you make a mirror invisible where would you put it to make it invisible obviously nobody's seen to this lecture before so the way you make it invisible is to put a mirror on another mirror okay so mirror plus mirror still a mirror and there are many situations particularly in radar where the ground is a good conductor a good reflector where you were working in an environment where you have a another mirror on which you could hide something which was a flat mirror and so this this was what we call the carpet cloak hiding under the carpet so what Jensen has done here is to take something which was flat and he's compressed space here and the various ways you can do this this is a quaysack conformal way in which the shirt this little cells retain their shape and and this region becomes more refracting as you you compress it and you can use the usual formula to tell what is the refractive index of that material there to make a cloak and this cloak was taken up by the Berkeley group here are some simulations of the cloak if you have a reflecting surface and then you just make a bump in that surface without cloaking it then that bump becomes very visible to a ray of light coming in because the facets on the cloak produce two reflections instead of a single reflection as will be the case for a flat mirror and here you put a cloak in place and you've still got this little bump down here but cloaked and you get a single reflection so the cloak has in fact made that a that bump appear so it's a perfectly flat than the mirror now this cloak was built at the Berkeley University of California Berkeley laboratories and what they did was to him this is a two-dimensional cloak again and here is a silicon slab acting as a wave guide and here's a piece of metal material where the refractive index is constant less than the surrounding and they've achieved that very simple mechanism they just drilled holes and it make it less refracting and then when you come to this region here which is the cloak the density of the holes becomes less so this region here is more refracting than this region out here and in just such a way as to reproduce the parameters of the cloak and so this this this mirror bump in the mirror here is hidden from view by this this this surrounding cloak and here's an electron micrograph of the cloak dimensions of one micron so it ain't a very big cloak but and the bump is about a micron across here are the parameters of the cloak and the data now i forget which is the theory which is the experiment here it doesn't matter of course agree with one of that i think this is the experiment so you have a flat mirror and of course it reflects a single beam so when you measure it you just see one Gaussian beam of light but if you put a bump on that surface with reflecting facets you get several reflect reflections from the bump and that's indeed what you see but finally if if you make a cloak in that silicon mirror and send the light in then you back to what appears to be a flat surface but it isn't it's a bump with a cloak all right so that proves the concept of optical frequencies but one of the things we're powered off with this design technique of transformation optics is that it's accurate not just at the level of the rays this cloak is big enough that you could have designed it with ray optics the transformation optics techniques also is accurate the level of field so you should be able to design a cloak where these lines represent not rays of light but the field lines of a magnet so here's a north pole of a magnet and here are the field lines coming out and you should be able to design a cloak which steers the field rounds around so that the the outside field is undisturbed and the bit in the middle is is cloaked so the fields never reach it now this is quite different from a shield and those of you who do experiments with magnetism know that there are things uh the materials called new metals which can wrap around an object and they will grab the field lines and steer them away so that there's no magnetic field inside that shield but the price you pay with these materials is that they also create outside the shield a very large dipole field and there's an enormous force in a strong magnetic field on the shield and at the same time there's huge disruption of the field itself outside but a cloak is quite different because a cloak does the shielding job but at the same time it leaves the field outside undisturbed so you cannot tell the cloak in place and therefore there is no mechanical force on this cloak and of course there's no disturbance to this field any experiments like an MRI experiment which rely on a uniform field is not disrupted and ben wood and I worked on the concept of this cloak in 2007 and the challenge was that the parameters of the cloak demand a material which is anisotropic and it demanded that if you put a field on in one direction you had a permeability greater than one a ferromagnetic material and if you put a magnetic field on in the other direction you wanted a permeability which was less than one now ferromagnetics are well known so that side of the problem is well addressed but although paramagnetism and not paramagnetism um um magnetism where mu is less than one is known that effect is very very weak in in all materials so if you had a material which is diamagnetic and its its mu was 0.95 that will be a really strong diamagnetic material but we're demanding diamagnets with mu of 0.5 and less unheard of until matter materials come along and this is the way you design that material so these are superconducting plates and superconductors expel magnetic fields magnetic fields penetrate only a very small distance into a superconductor so if you want to send a field in this direction it's got to squeeze its way through these very narrow gaps and that costs energy and that means that this material in this direction is acting like a diamagnetic the squeezing of the field lines creates a strong diamagnetic diamagnetic effect and so here's in some units the side of the plates and the number of layers of plates and the key thing is the spacing between the plates of course that determines how much the fields are pinched and as the spacing goes down the permeability decreases from 0.64, 0.23 and then eventually down to almost zero as the plates are pinched together these are numbers which you can never find in nature and our experimental group made this system they deposited lead on a microscope slide and then they scribed the lead so that it was in little squares lead is a superconductor if you cool it below helium temperatures and these are their measured permeabilities normal to the sheets and you see there's very good agreement so this metamaterial really does its stuff and without it you couldn't design this cloak so here's Ben's design for the cloak the paramagnetic stuff gives you a large permeability in this direction the sheets are thin so the field lines are unimpeded by the sheets traveling in this direction but if you take a field going in in the radial direction they have to squeeze through these little gaps and the mu in that direction is reduced now there the matter rested until a year or two ago and some guys in Harvard took this up these people here and they actually built this this cloak so here are the scribed sheets with the gaps between the superconducting plates and they didn't actually use a ferrite they used chromium to give you the mu greater than one and in this way they were able to build a cloak and and they tested the cloak by putting it in a magnetic field created by two coils okay so a magnetic field is traversing the cloak and then they did they sense the magnetic field they have many many sensors but i'm just going to show the data from two of their sensors this is a center inside the cloak which tells you whether or not the field has been removed there and this is a sensor outside the cloak which tests whether the field remains constant there and here are their data so this this is what you want to happen the cloak should grab the fields and just just as the original cloak did with rays of light transmit the fields the other side without any disturbance external to the cloak and here here are their data with no cloak so if you put no cloak there then the field ramps up uniformly with a current through the electromagnet um obviously but if you put a cloak in place the field inside the cloak remains zero whatever the current so it's doing the job of screening that internal region there now if you look at sensor two what you see is that for all the currents measured the magnetic field outside the cloak is exactly the same as it is inside and therefore the cloak is doing its job is screening the interior but outside you don't know that that's happening you just see a constant field of whatever's happening so that i think was a very nice confirmation for us that that the new technology which replaces Snell's law which only works for rays of light is is much more general and and operates at the level of the field lines in particular it can it can design a cloak for for magnetic fields and it can do much more than that that's just a demonstrate of what what it can do so in the last few minutes of my lecture last 20 minutes i want to return to this subject of negative refraction of course although it's not on the face of it is immediately sensational as a cloak and jk Rowling hasn't written any novels about negative refraction so it's something of a disadvantage there but to my mind it's the more remarkable effect of the two so why is it remarkable here is what the slago predictor for negative refraction and why should it matter that the light goes this way rather than that way why why is that so surprising well let me suggest you that you can actually use this effect to focus light so if if i got a point of light here radiating rays and they're bent back towards the axis of the lens then you can imagine they form an image here but they do it in a very curious way so if i have a source of light inside the material then this negative refraction will produce an image outside the material there so if i had a swimming pool full of negatively reflecting material then the contents of the pool would appear to be floating above the surface of the pool very strange health and safety mechanisms if your kids were in the pool you could actually see what they're up to floating above the surface of the pool so that that's one thing and now i want to combine this idea of negative refraction with transformation optics so you might think well that's really quite interesting but what else can we do here i mean that's that's a flat lens an object which is the same size as the image you might want a lens which make something bigger and transformation optics takes space transforms it bends it squeezes it so i could take that space and i could transform it so this flat slab of material became a cylinder or a shell of material and at the same time that will make the the image larger relative to the object because i'd be squeezing the lines in order to turn this into a shell or a cylinder and then you get a lens like this now i should explain that there's something else rather curious about this this lens and it's the following that if you um actually i i can best do that by snitching some slides from later on okay so here's here's a slab of negative refracting stuff acting as a lens and Veselago taught us that this this could happen that it does act like a lens but in the year 2000 i realized that this lens was rather special most lenses or all lenses that we know to that point were limited in the resolution by the wavelength of light that you use to to use them and that is about a micron and many things that you really really like to do to see in biology are below the micron length limit in size but it turns out when i look to the properties of this lens that um it it isn't limited by that law if you do the mathematics according to Maxwell's equations then it turns out that this focus providing you build the lens perfectly you build the lens perfectly the focus is perfect and that caused a lot of fuss at the time and now one way of understanding that is to go back to a statement i made at the beginning of the lecture and that is that Einstein said that when the coordinate system is distorted by a gravitational field for example then the metric changes so if you compress space the metric gets larger and that's just the measure is the metric of how much is squashed space and what's more i said that when you write Maxwell's equations in the notation that Einstein uses for general relativity you find that his metric comes in the same place as there's the refractive index so you don't have to find a neutron star you just have to find the right refractive index to change the metric as far as light's concerned but here's a paradox because um what if you make something with a negative metric and i'm pardon me whilst i do my origami here so many of you have seen you do this before so i'm going to make the simplest compression of space possible i'm going to take a little region of space like that i'm going to squash it and as i squash it the refractive index goes up of course the metric increases and i can squash it till you know the refractive index is infinite infinitely positive and then if i'm a mathematician i can squash it a bit more like that now that's a really weird space this space you can understand yes but this is really weird okay because if you've got something which is sitting here the light sees it once twice and three times so when you squash space like that you've actually created uh inserted into space three manifolds if you like the space is convoluted and it has these three values here and you do that by creating this region here where you compress space up to infinity and then down to minus infinity this is negative space optical antimatter it annihilates space which is next to it and so what you think the light is doing is going along here what the light thinks it's doing is going along this trajectory here and therefore this object is seen three times by the light now that description is accurate at the level of Maxwell's equations and so the seeing of this object is not an approximation in the ray approximation it's exact to the level of Maxwell's equations which knows nothing about the limitations of the focusing of light by the wavelength and therefore this this object this image is the object and is therefore perfect so this this lens is a perfect lens and that incidentally is why a negative refractive index is such a strange and mysterious thing on the face of it this way that way what does it matter but when you begin to look into the consequences that the consequences of that are quite profound so here we have the lens made into a magnifying glass it's a perfect magnifying glass and what it does it takes the contents of this inner region here and when you view them from outside through this now circular or spherical lens the contents appear to be contained within this larger sphere here and here's a bit of massacre with it if you're interested um so you can make a small object appear bigger than the lens uh itself magnified so it's bigger than the lens itself and uh why why is that strange well i normally have a glass of water uh have you ever noticed this if you look at a bottle of water the water appears to go right to the edge you can't see the glass and the reason for that is very simple that any ray of light which strikes this bottle must go through the water so if it were filled with milk it would be even more surprising the whites of the milk would go right to the edge of the glass and that's just a simple exercise in refraction very easily understood in ray tracing every ray passes through the water or the milk and therefore goes to the edge of the bottle but now what if this bottle was made not of glass but of this negative refracting stuff that i have here then the milk or the water would go not to the edge of the bottle but here it would appear as though the milk was in a very very large bottle like that which is very strange let me show you just how strange that is here i'm doing a ray tracing remember the ray approximation is an approximation okay so here i've got my a negative refraction lens the light goes through every ray of light which strikes this big circle according to Maxwell should be compressed into this inner circle here it's looking good they're all going in oops problem this ray of light doesn't hit the lens they're according to the laws of snell's law ray approximation how on earth can you capture this remote ray of light but here's a solution in Maxwell's equations and here the incident rays express a series of wave fronts and you can see that these wave fronts are grabbed and forced into the central region just as Maxwell as the theory says it should this is this is a solver computer solver for Maxwell's equations and so this this is a very strong statement of how transformation optics predicts things which are just not in the book of the ray approximation and demonstrates how very strange and remarkable the phenomena of negative refraction is so what can you do with this well there are devices in optics that only work if they're really big and one of them is a parasol a parasol creates a shadow to shade you from the sun and that works because the parasol creating the shadow is much bigger than the wavelength of the light if you try to make a really tiny parasol which was a micron across comparable with the wavelength of light it wouldn't create a shadow the waves would diffract around that object and rapidly fill in the electromagnetic field on the far side of the object you cannot create very very small shadows or you cannot create shadows very small objects however using this lens what you can do is to put a very very small parasol in here and make it appear like a really really big parasol much bigger than the original parasol much bigger than the lens itself and this big okay so you could make a parasol which appeared to be bigger than the wavelength if though it wasn't and this is a computer simulation which shows a black object inside a negatively refracting magnifying lens and so outside the blue stuff there's nothing and here you see a ray of light or hitting the object and it's actually creating a shadow which is much bigger than the original object than the cloak and as big as it's predicted to be by this guy in here so metamaterials transformation optics negative refraction some very surprising things some results which took me a long time to understand and which some people in the community have never accepted people still write papers saying negative refraction rubbish perfect lenses don't exist and so on i've got to the stage where i take it all on the chin but it was really rather hurtful when you wonder whether you were right or not in the beginning but at the end of the day you can have as much fun as you like with amusing mathematical theories but at the end of the day what matters in physics is if you first of all if your theories can be realized in experiment and then after that if the experiment can go to produce something which is useful for society and that takes a long time and the more profound the idea the longer it takes you only have to think of the laser what a profound idea that was and how long it took us to get to the state where we are today where the applications of lasers are so diverse and so very very imaginative um academically there's no doubt the metamaterials have taken off here's the somewhat rapid rise of metamaterials this is the items published in each year and the number of citations in each year 2013 obviously isn't completed yet so we don't have the citation data in full for that so there really are a lot of people working in this area and they're working on it because it's so exciting but also because it's now being seen to be very useful so I'll give you some instances now in my last couple of minutes of the applications so here is an outfit which gathers patterns intellectual ventures is based in Seattle it's owned by Nathan Mierwald ex scientific director of Microsoft and they hold most of the patterns on metamaterials and they are producing a company called chi meta which is just spun out with it's now capitalized to 50 million dollars I think and what they're doing is is is using metamaterials to create a phase array which is used to communicate with satellites for a sat comms phone and now people do that already but the kit they use is a dish which is about 30 centimeters in diameter in order to focus the beam on the satellite it has to be that big and it's mechanically steered to track the satellite it's expensive it's heavy it consumes quite a bit of power the metamaterials concept has no moving parts and it steers where the receiver points to electronically because the metamaterial can be tuned in a very cheap and simple way using a DC current and here's the prototype hotspot which they're they're creating which will look something like this 30 centimeters on its side the target price is under a thousand dollars it's very light it will plug into the usb port of your laptop and that you should be seeing those coming on the market quite soon this is again something which is is very simple this is a lens for focusing radar waves and instead of a big chunk of polythene which you'd normally use to focus radar waves 30 centimeters in diameter very heavy several kilograms you can do the same thing with a very thin sheet of metamaterials a graded index lens and and that will do the same job in fact it gives a better focal spot than the polymer lens and this is used in radar can be used in radar and Toyota are thinking about putting it in the collision avoidance radar to focus terahertz radiation um MRI um my colleague Richard Sims is working on a problem in MRI if you want a very accurate MRI scan of your heart or your liver what's what you do is is to put the pickup coil which senses the very tiny magnetic signals from the nuclei which which tell you what's going on there you want to put that coil very close to the heart or the liver and the way that's done is to make an incision in your vein down near your legs push that coil up the vein with a wires trailing behind and then it gets near to the heart and you can do a very precise MRI scan the problem with that is that you're turning the magnetic signal into an electrical signal which then travels down a metal wire which is about a meter long here to here and that's about the resonant length at the frequency that MRI scans are done inside the body and it can get hot if it gets too hot it sticks to the side of the vein and that's not nice as you may imagine so a more safe version would be to if you could define a designer wire which which instead of turning this magnetic signal into an electrical signal kept the magnetic signal and transferred the magnetism along the magnetic wire now this is exactly what Richard has done again it's you know it's not as impressive invisibility but this magnetic wire here which is consists of little metamaterial elements which which allow the magnetic field to hop along its length this is totally safe because it it is not an electrical conductor and it does not get hot when you put it in the RF field so that's another application Richard is trying to find a company to to to patent and sell that kit so i hope on this journey through metamaterials invisibility and transformation optics what i've shown you is that this ancient subject of optics is full of life and surprises even at this several thousand-year-old stage of its life and that as well as the things which which astonish scientists there are things which can astonish the general public even school children and at the same time these astonishing things are being turned into products which will help us in our everyday lives thank you very much for your attention