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A 3D printed metamaterial.
It has been a long time since I've been
grabbed by a metamaterial. For those of you who don't know or remember
what metamaterials are, they are the things that make invisibility
cloaks work. Unfortunately, I got tired of writing about incrementally
better invisibility cloaks and stopped paying attention.
So it was with a glorious sense of
anticipation that I attended the opening talk at the Physics@FOM 2017
conference. Martin Wegener, who delivered it, hails from Karlsruhe
Institute of Technology in Germany. Wegener has quite a reputation in
the field of optics, but for this talk, he took a kind of scattered
approach to show how the ideas behind metamaterials apply everywhere and
can be used to design entirely new functions into simple
materials—materials that may find their way into almost every aspect of
your life one day.
What are metamaterials?
A metamaterial is both a very simple and a very complex object to describe. The simple level is very simple:
mix two materials to obtain a new material with distinct properties.
But, to borrow Wegener's analogy, imagine that we take two materials,
one very dense, like lead, and the other less dense, like air. I can mix
the two by drilling holes in a bar of lead. At the end of the process,
the density of my new material lies somewhere between the density of air
and lead. But, with a metamaterial, this combination can result in
strange properties—the equivalent of a density that is larger than that
of lead or less than that of air.
This is where the complexity comes in. No
simple combination of materials will do anything like that. Instead, you
have to consider the scale of the phenomena you are interested in. In
our density example, we might care about density for the sake of the
propagation of sound waves. To create a specialized material for sound,
we need to combine our lead and air in a controlled fashion on length
scales that are much smaller than the wavelength of sound that we care
about.
That much has been known for a long time, but
in recent years, the field of metamaterials has really exploded, thanks
to two ideas.
Bend your space
The first idea comes from general relativity.
In general relativity, we consider space to be curved, and its curvature
is increased by massive objects. As I fly through space, I fly in
straight lines, but thanks to the curvature of space, I trace out some
complicated path as I go past a more massive object. To put it
differently: I always take the shortest path between two locations. On a
plane, that's a straight line; in curved space, it's a curved
trajectory.
How does this help? Well imagine that I want
to create some invisible area in space. To prevent light from
interacting with the object, I have to make sure that all paths curve
around that volume so that it looks like no hidden volume exists.
General relativity can tell us what the shape of such a surface looks
like. And (remarkably) a link between the equations of electromagnetism
and general relativity tell us what the material properties need to be
at each point in space to create the equivalent of curvature.
So, in principle, all sorts of previously unimaginable optics can be created, among them invisibility cloaks.
Tomography doesn’t work (but don’t tell your doctor)
The second idea comes from tomography. Any
time you get a 3D image from ultrasound, the image is reconstructed from
sound waves that are detected outside of the volume being imaged.
According to Wegener, a long-standing question in tomography was "is the
reconstruction unique?"
Now, since it works, you, I, and Wegener all
believed that yes, it probably is. But a couple of years ago,
mathematicians proved that this was absolutely not the case. The heart
of the proof was the idea that a particular form of equation maintained a
type of invariance, no matter how space was curved or stretched. That
means that tomographic reconstructions can be fooled by hidden volumes.
The critical equation occurs everywhere: it
applies to sound waves, heat propagation, light, and quantum mechanics.
You name the physics, and Wegener can probably show you how that type of
equation appears. Suddenly, it became very simple to take the idea of
stretching space and apply it to the creation of desirable properties in
almost any domain—light, sound, or whatever. You could then use this
equivalence to determine how the properties of the material needed to
vary in order to obtain the intended behavior.
A tour of hidden objects
Since that revelation, Wegener has taken to
hiding things in all manner of ways, with a huge amount of success. Not
just success in the "hey, that's pretty cool" way. But in the "can you
scale that up and put it on my device?" way.
There were many striking examples, and I don't
want to turn this into a listicle, so let me discuss just three.
Wegener showed how to prevent heat from moving into a volume. Now you
might think this is just insulation, but it's not. At the border of an
insulated volume, you have a temperature gradient. These gradients then
distort the temperature field around the object in a way that, if you
were to measure the temperature, you would know there had to be an
object in the center.
The metamaterial, which consists of rings of
copper (high thermal conductivity) and plastic (low thermal
conductivity), guides the energy flow around the hidden volume in such a
way that on all sides, the temperature gradient looks exactly as if
there was no object between a heat source and the cold sink.
You might think that this doesn't have much
use, but there are many cases in which some critical component that
can't be allowed to get too hot has to be located somewhere near a heat
source. For the lifetime of the heat source, good thermal conductivity
is required to clear the heat away. This metamaterial goes some way to
achieving that goal. It allows heat to flow around it undisturbed and
doesn't allow the heat into the center volume.
Another example does the same thing with
light. In this case, the shells consist of highly scattering and highly
transparent materials. Think of layers of paint sandwiched
between layers of glass, but on a scale of just a few nanometers. This
structure will guide light around the volume encased in the shell. This
technology is so robust that it has been scaled up to objects that you
can hold in your hand, and Wegener showed a picture of this working in
non-laboratory settings. However, that demonstration involved placing
the object in a translucent medium (think a partially opaque bathroom
window) as well. So, it worked there, but I don't think it would work in
a clear window.
(Mind you, how would you know... and come to
think of it, once they put their device on the lab bench, how do they
find it again?)
On the other hand, this already works well
enough that it would be useful for covering conducting electrodes that
go on the front of solar panels, to give one example. And, in complex
optical environments, like the front face of a large OLED screen, it
would probably work as well, provided the electrodes weren't that big.
Sound waves are a bit more challenging. This
is because solid materials support three types of sound waves:
longitudinal waves, where material moves forward and backward (these are
the sort that travel through air), and two types of shear wave where
the material moves from side-to-side. These can only travel through
solids. The issue is that you can create a structure that works for one
type of wave, but it won't work for the other two. Critically, if a
longitudinal wave approaches at a glancing angle, it looks like both a
shear wave and a longitudinal wave from the perspective of anyone
watching. So any material has to work for all these waves.
To get something to work for sound waves,
Wegener had to create a solid material that didn't support shear waves.
It turns out that you can do this by joining needles together at the
points to create a lattice. You can't just put the needles together any
old way—they have to have a specific structure (diamond-like). The
result is surprisingly strong and can transmit longitudinal waves. The
points where the needles connect, however, don't resist sideways motion,
so shear waves die out very quickly. So, the shear wave components that
are created at boundaries and at imperfections are absorbed by the
structure.
This material also has to be structured to
guide the remaining longitudinal waves. In the end, you need a
metamaterial of a metamaterial. The result is that a volume is shielded
from both longitudinal and shear waves, where the longitudinal waves
pass around the object as if it weren't there.
Thinking big
At the end of his talk, Wegener outlined some
work that I've written about before: using giant metamaterials to guide
surface waves from earthquakes. Apparently, that work is still in
progress and is looking hopeful. At the time, I was pretty skeptical.
But, given the advances presented here and the fact that these are now
devices that are not at the limits of fabrication, I'm starting to
become a believer.
This talk was presented at Physics@FOM, Veldhoven, 2017
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