So we're all familiar with the tools that we use to control light waves. A
great example of one is a magnifying glass - a lens like this. We also see those
lenses in eyeglasses like I'm wearing right here. And how those lenses work -
I'll sketch a shape of a lens here - many of us may remember from
high school physics how this lens works. When we think in terms of ray paths the
direction the light travels, and it's bent by the shape of the glass so that
on the other side, the light converges and creates a focus, or an
image, at this spot. From the perspective of how waves travel, there's an alternate
view of how lenses work. And what I'm sketching here are the individual peaks
and valleys. The wave fronts of the light waves that are traveling in this
direction and hitting the lens, and what happens is in the middle of the lens the
light is slowed down, while on the edges of the lens where the lens is thinner,
the light is slowed down less. And so what happens is the shape of the
wavefront as it emerges from the lens is now
curved - slowed down here or delayed, and least delayed here, and it creates a
converging wavefront that also creates a focus at this spot here. It's kind of the
opposite of what happens when you throw a rock in a pond, creating an expanding
wave. This is a converging wave to this image right here.
Conventional lenses work because of their specific shape. Remember that they
are curved in order that the incident light waves are slowed down in the
middle where the lens is thickest and slowed down the least at the edges where
the lens is thinnest. And that's what creates this converging wavefront and an
image. And the reason lenses are expensive and complicated is because
we're stuck with the material properties of glass, and the only way we can create
this spatially varying light propagation is with the shape of the lens.
And that lens shape has to be controlled very very precisely in
optical devices. But we could ask ourselves, what if we were no longer
stuck with material properties like glass that are fixed? If we had more
flexibility in the material properties, then we could imagine creating a lens
that has a much simpler shape, and we simply need different material
properties in the middle of the lens in order to slow down the light waves there
and allow the light waves to travel faster at the edges. And if we had the
ability to do that, we could create a lens that does exactly the same thing -
creates a converging wavefront and an image over here and yet has a much
simpler shape and actually could be much easier to manufacture. And the basic idea
of how can we control those light wave controlling material properties, that's
the basic idea of metamaterials. So what are the essential features of a wave? How
do we describe it? Well there are a couple of fundamental properties of waves.
One is the amplitude of the wave - how high it is from peak to valley, and
that's linked to how bright light is in a light wave or how loud sound is in a
sound wave. The more important feature for metamaterials is the wavelength,
which is the distance between one peak and the next peak. And that's tied to the
color of the light or the pitch of the sound wave. So how do we design
metamaterials? We start by looking at the wavelength we hope to control, and if the
wavelength is this size sketched here, then we need metamaterial structure that
is significantly smaller, or about the size I'm showing with my fingers. So we
then need to create an array or grid of metamaterial structures whose size is
that size or smaller. Now if we were creating something
with conventional materials like glass, we would be stuck with the same material
properties in each one of these squares. With metamaterials, we can put different
material properties in each one of those squares. That enables us to do things
like I sketched before - creating a flat lens where the wave travels slowly
through the middle of the structure and more quickly through the edges. But
what's really interesting with metamaterials is we can put anything at all
arbitrarily inside each one of these material building blocks. And when we do
something like that, we then have the ability to create wave
control that can take an input wave and not just create a converging wave on the
other side, but a completely arbitrarily complex wavefront. And that enables us to
do much more powerful wave processing with metamaterials.