 Helo, Rwy'n gweithio i chi ddweud o ymwneud mewn material mewn yma, a'r taito'r ymwneud ymwneud material, mewn material mewn ymwneud. Yn ymwneud, yma ymwneud o ffnwneud ymwneud, ychydig mae'r angen, ychydig ymwneud a'r angen i'w gweithio ymwneud. Yn ymwneud it starts with Einstein's theory of general relativity so basically that's a sort of loose mathematical framework where space and time is distorted by matter so we've got an example of a gravitational lens there where the galaxy is distorted by the black hole in the centre Lenders go back a long time from the start of civilisation where they first discovered lenses in 2000 BC. Black holes also result from a singularity. This is all relevant because this is the mathematical framework behind transformation optics, which is an offshoot of metamaterials. So, what is transformation optics? Basically, I've mentioned astronomy, and you have thermal cloaking. So, one of the applications is cloaking. So, you can have thermal cloaks, cloaking for sound waves, cloaking for matter, where you use the equations to cloak electrons going around a hidden insulating shell. So, there's a picture of one there. So, it's a nice programme to use, finite difference time domain. You use it in MATLAB to simulate electromagnetic waves. So, I've got some equations on the right. So, on the left is the ray, and on the right is the distorted ray. So, I can just show away a bit of code. So, this is a simulation of the cloak. You've got an electromagnetic pulse from the left. Cloaking takes place there in the cylindrical region. So, in theory, you could cloak anything. You've got different methods. You can cloak tanks in the infrared. Some people have tried to use projectors on a screen that they're wearing to project the image behind them. So, basically, invisible to human eye. So, what gives these cloaks their interesting properties? Things called metamaterials. So, these are electrical structures, combinations of capacitors and inductors. They're usually sort of split rings. And here, you've got an example there. So, cloaking is invisible. I've mentioned some sort of applications and stuff already. So, an innovation in the cloaking field, I suppose, which I've done my PhD on and stuff, is to cloak something underneath a carpet effectively. It's called like hiding something under a carpet. So, this is possible using an all dielectric implementation. So, instead of using anisotropic materials, you would use isotropic materials made of a single block of dielectric. So, this technology is basically, I mean, it's got some interesting applications there. But, basically, it's going to revolutionise satellite communications. So, currently, you've got antenna dishes. They're sort of parabolic and you can create sort of flat dishes. So, you're saving space and cost and things. So, I've showed the video. It's something fun to play around. I mean, you need MATLAB to run the codes. Another interesting feature is negative refraction. So, conventionally, in a lens, you would have refraction. In a negative index material, you would have negative refraction. So, you have negative Cherencroff radiation, which is the radiation from nuclear reactors. It glows blue. So, I wasn't able to show you the code, which is quite interesting. So, I've mentioned it's got lots of applications. So, you can design thermal cloaks where you're cloaking something from heat, basically. You can have mechanical cloaks, so you have negative compressibility. So, it's basically sort of covering lots of aspects, really. So, I've mentioned satellite communications. You can transform parabolic dishes to flat dishes. You can also do that with lenses. So, you can transform curved lenses to flat lenses, saving space and cost for optical engineers. So, you can do some fun sort of Fourier optics and calculate the reduction in the wavefront in sort of transformation optics lenses. And I think that's it. Are there any questions? Well, it mostly works on microwaves, so a lot of experiments are done sort of at eight gigs. When you're getting sort of optical frequencies, it's more difficult, and people tend to use silver. Yes, yes. I mean, that's why the sort of methodologies moved away from metamaterials, which have negative effraction, to transformation optics, where you're kind of having anisotropic material. So, you could do a similar lens, but it would be anisotropic. You can use silver. I mean, it's quite lossy. Like I say, I mean, it's easier to replace them with transformation optics media, which is kind of like anisotropic. And you could do that with something like, there's a foam called baryon titanate foam. So, you sort of, it's a foam, and then, you know, you have a distribution of particles in the foam, which gives it the variation of permittivity. Well, it's generally blocks. I mean, you discretise the map, and so you've got blocks of single permittivity materials. Yeah, I mean, as long as it's smaller than the wavelength. You have a question, Liz? So, basically it's made from, it's a resonant phenomenon. Basically, you've got the permittivity and permeability, which combined gives you the negative refraction. So, by using a split ring resonator, you, at the resonance frequency, you get a narrow band region where, you know, you've got negative permittivity. So, yes, I mean, that's... Is there another question, or shall we just wrap up at this point?