Saturday, September 17, 2022

The New Meta-Materials for Superlenses and Invisibility Cloaks

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

Meta is the Greek prefix for “after” and Aristotle used the phrase “metaphysics” for the stuff in his writing that came literally “after” he was done with the physics. Metaphysics is concerned with some of the most important questions we face at this critical moment in human history. Questions like whether the holes in cheese exist, whether cheese exists, or whether only the atoms that make up the cheese exist.

But this is not what we’ll talk about today. This video is about metamaterials which, I assure you, have nothing to do with cheese. Though, maybe, a little bit. Metamaterials are the next technological stage “after” materials. It’s a research area that has progressed incredibly quickly in the past decade, and that includes superlenses, invisibility cloaks, earthquake protection, and also chocolate. What are metamaterials, and what are they good for? That’s what we’ll talk about today.

First things first, what are metamaterials? A linguistic approach might lead you to think a metamaterial is what comes after the material, so I guess, that’d be the bill. But that’s not quite right. A metamaterial has custom-designed micro-structures which give a material new properties. These micro-structures are typically arrays that resonate at specific frequencies, and that interact either with acoustic waves or with electromagnetic waves. This way, metamaterials can be used to control sound, heat, light, and even earthquakes.

This sounds pretty abstract, so let us start with a concrete example, the superlens.

When you take an image of an object, with your eyes or with a camera, you collect light that reflects off the surface of an object with a lens. Lenses work by “refraction” which means they change the angle at which the light travels. If an object is too close to the lens, the refraction can no longer converge the light. For this reason, you can’t take images of things that are too close to the lens.

But not all the light that reflects from an object gets away. The part that gets away is called the far field, but there is another part of the light called the near field, which stays near the surface of the object. The electromagnetic waves in the near field are oscillating like usual, but they don’t travel into the distance, they decay exponentially. It’s also called an “evanescent wave”.

This figure shows how waves enter a medium at a surface, which is the red line. The top image is a normal, refracted wave, which continues traveling through space but the angle changes when it enters the medium. The bottom image shows an evanescent wave, which decays with distance from the surface. The evanescent waves contain tiny details of the structure of the object, but since they don’t reach the camera, those details are lost. And you can’t get the camera arbitrarily close to the object, because then you couldn’t refocus the light. And that’s a shame because you might not be able to count the hairs in my eyebrows after all.

But in 2000, the British physicist Sir John Pendry of Imperial College in London found a way to use the information in the near field. He said, it’s easy enough, you just use a material that has a negative refractive index.

What does it mean for a material to have a negative refractive index? Normal materials don’t have this, but metamaterials can. When a ray of light enters a medium, then the refractive indexes of the two media relate the angles. This is called Snell’s law. If the refractive index of the medium is negative, then this means the continuation of the ray in the medium is also reflected from the normal to the surface. So, it goes back into the direction it comes from. How would that look like?

Well, as I said, stuff that we normally encounter in daily life doesn’t have a negative refractive index, so I can’t show you a photo. But we can illustrate what it would look like. You probably remember the “broken pencil” illusion. If you put a pencil half into a glass of water, then the part in the water appears shifted to the side. It’s because the light is refracted in the water but the brain interprets the visual input as if the light travels in straight lines. If the water had a negative refraction index, then the lower part of the pencil wouldn’t just seem shifted, it’d also be reflected to the other side.

Aaron Danner had the great idea to use a raytracer to create a 3-d image of a pool filled with water that has a negative refraction index. Here is the image of the pool with normal water. And here is the image with the negative refractive index. The thing to pay attention to are those three black lines, which indicate the corner of the pool. You’d normally expect this to be out of sight, but since this strange water mixes refraction with reflection, you can now see it. If there were fish in the pool they’d appear to be floating on top of the water. Which, I don't know if you know this, but it’s not what a fish is supposed to do.

What’s this got to do with lenses? Well remember that you need lenses to collect rays of light. But if you put a sheet of a medium with negative refractive index between two with normal refractive index, that’ll basically turn the light rays around and effectively focus them. It acts like a lens. And, here comes the important bit, this also works for evanescent waves which usually get lost. They get focused too, and are prevented from decaying. This is why metamaterials with a negative refraction image can reach a resolution that’s impossible to reach with normal lenses.

A superlens was built for the first time in 2005 by researchers at UC Berkeley. Their lens was made of a silver sheet that was merely 35 nanometers thick. In this case, the structure of the material comes from oscillations in the electron density in the silver which amplifies the evanescent waves coming from the object. You have to put the object directly into contact with the silver surface for that to work.

This image (A) is a lithograph taken with a focused ion beam, so this is the control image. This image (C) is the optical control without superlens. And this one (B) is the superlens image. You can clearly see that the superlens image has a higher resolution. This graph D shows the difference in accuracy between imaging with the superlens, that’s the blue curve, compared to imaging without the superlens, that’s the red curve.

Though this jump in resolution might sound good, these lenses are rather impractical. You have to put the metamaterial directly into contact with whatever you want to image and then your camera on top. So it does away with selfie sticks, but unfortunately also ruins your makeup. This is why, last year, a group of researchers from Iran and Switzerland published a paper in Scientific Reports, in which they propose to use a metamaterial to turn the near field into a far field, so you can put your camera elsewhere.

They call this device a “hyperlens” which to me sounds like it’s a superlens that’s had too much coffee, but they mean a grid of aluminum nanorods that resonate at wavelengths in the visible part of the spectrum. For now, this is just a computer simulation, but the idea is that the resonance converts the evanescent modes into propagating modes, so then you can capture them elsewhere. The researchers claim that at least in their numerical simulations this structure can image biological tissues with a resolution of a tenth of the wave-length of the light. The resolution limit of conventional lenses is about a quarter of a wave-length.

Let’s then talk about what’s the probably best known application of metamaterials, the invisibility cloak. You may have read the headlines a few years ago about this. Metamaterials make invisibility cloaks possible because with a negative refraction index you can bend light in the opposite direction to what normal materials do. This means that, at least in theory, with the right combination of materials and metamaterials, you can bend light around an object. This appears to us as if the object isn’t there, again because the brains assume that light travels in straight lines.

This sounds pretty cool, and indeed scientists have some things to show, or maybe in this case it’s better to say *not show. Early experiments in the mid-2000’s mainly used microwaves. But in 2015, a team of researchers from China made an invisibility cloak that works in the infrared. In this Figure (Figure 1f) you see how the light is redirected. They used several triangles of germanium and put them in a very precise geometric configuration so that it creates a hidden area inside. You might say that this isn’t much of a metamaterial, but it’s the same idea: you custom-design structures to redirect waves as you want. Into this hidden region they put a mouse. (Figure 2b). Then they took an image with and without the cloak (Figure 4a and 4b). Half of the mouse is gone!

Invisibility cloaks in the visible part of the spectrum haven’t yet been made, but some semi-invisibility shields exist, for example this one from a company named Hyperstealth Corp. These don’t work by bending the light around objects, but by spreading the light in the horizontal plane. If you have a narrow object, then its image will be overpowered by the light coming from the sides of the object which blurs out what is behind. This works particularly well when the background is uniform. However, it’s not really an invisibility shield. Easiest way to build an invisibility shield is put a camera behind you and project that on a screen in front of you.

You can also use metamaterials to manipulate electromagnetic fields that are not in the optical range. For example, as I explained in this earlier video, the main problem with wireless power transfer is that power decreases with very rapidly with distance from the sender. A “magnetic superlens”, however, could extend this reach.

That this works was shown in a paper by a group of American researchers in 2014. This figure shows the difference between wireless power transfer using a magnetic superlens compared to wireless power transfer through free space. On the y-axis, we have wireless power transfer efficiency, and on the x-axis, we have distance in meters. The solid black line represents wireless power transfer through free space, which drops quickly to near-zero values as distance increases.

The colored lines represent wireless power transfer with the use of a magnetic superlens made up of metamaterials. You see that at best you can extend the reach by a few centimeters. And notice that the efficiency is in all cases in the single digits. So, nice idea, but in practice it doesn’t make much of a difference.

Another type of wave you can manipulate are acoustic waves. Acoustic metamaterials aren’t really a new thing. Sound absorption foam like this one uses basically the same idea. It has a lot of tiny holes. So you see, it’s kind of like cheese. The holes make it very difficult for sound waves in certain frequencies to bounce back which basically kills echo. If I wrap this around my head, you’ll hear the difference. Wrapping your head into one of those will generally improve your experience of the world, highly recommended.

Metamaterials are more sophisticated versions of this. You can for example design them so that they only absorb particular frequencies, this is called a sonic or phononic crystal. Another thing you can do is to reflect the signal back without spreading it out. This was done by a team of researchers from China and the USA in 2018. The material they used was just a plastic dish with a spiral structure that effectively changes the refractive index. They say an application could be to make vehicles easier to detect. Though I suspect that their metamaterial would sell better if it made a car less easy to detect.

You can also use acoustic metamaterials to build an acoustic type of superlens, which has been done for ultrasound, but it’s the kind of solution still looking for a problem. And, as you can guess, they are trying to build acoustic invisibility shields. This has been done for example underwater with ultrasound which is great if you want to hide from dolphins. And in 2014, a group from Duke University used a pyramid with a special surface structure that makes it reflect sound as if it was an empty plane. Here is how this pyramid would look looks like if you could see sound. The pyramid is hollow, so you can hide stuff inside. Maybe they’ve finally figured out what the Egyptians were up to?

Another application of metamaterials is earthquake protection. Like you can use structures in materials to change how light and sound propagates, you can change the properties of the ground to change how seismic waves propagate. For this you embed structures around or under buildings so that seismic waves are diverted around the building. You basically make the building invisible to earthquakes.

For example, a group at MIT’s Lincoln lab use arrays of boreholes that are either filled or empty to redirect seismic waves. They haven’t actually build a real world example, but they have made measurements on downscaled physical models and they have done computer simulations.

This image is an illustration for how seismic barriers could work in theory. The green squiggly lines are the surface waves, the blue squiggly lines are P-waves, and the black arrows are the S-waves. All these waves get partly redirected and diffused.

At least in a computer simulation, the cloaking effect is quite impressive as you can see in this image from a 2017 paper. For this, they used data from a real earthquake, the Hector Mine earthquake that happened in Southern California in 1999. It had a magnitude of 7.1. The metamaterial barriers effectively reduced it to an earthquake of magnitude 4.5. And just a few months ago, a group from China proposed another metamaterial to dampen seismic waves. They want to use steel embedded with cylinders of foam.

Image A of this figure shows an aerial view of a seismic wave moving through unprotected soil – without protection, the wave moves without losing energy, exposing any infrastructure atop the soil to the full power of the seismic wave. In Image B, the metamaterial array effectively neutralizes the wave. Here you see the effectiveness of the metamaterial array from a side view – in Image A, the seismic wave travels across the surface uninterrupted, while in Image B, the metamaterial array dissipates the wave at Line C. The authors claim that their system can dampen seismic surface waves in the range of 0 point 1 to 20 Hertz with up to 85 percent efficiency.

And as promised, a tasty example to finish. A team of researchers from the Netherlands have created an edible metamaterial. It’s made of chocolate in multiple s-shaped pieces that makes the chocolate more or less crunchy, depending on the direction you chew it. And if you think about it YouTubers do this too when they cut breaths out of their videos and zoom back and forth in every other sentence. This structural changes affects how you travel through a video. So we’re really doing meta-videos.

Metamaterials have opened a whole new dimension to material design, and as you can see, they are well on the way to application already. We will certainly come back to this topic in the future, so if you want to stay up to date, don’t forget to subscribe.

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