[MUSIC]
Hi.
Welcome to Nanotechnology: The Basics.
This is week 4, lecture 5.
And I'm Daniel Middleton.
In our previous lectures this week, we
have been
talking about the interaction of light
with semiconductor nanostructures, and
how that interaction is really mediated by
quantum confinement
- the quantum effects of squeezing exitons
on the Nanoscale.
In this lecture, I'm going to switch gears
a little bit, and talk about the
interaction
of light with metal nanostructures.
And what we're going to see is, that this
also has important implications.
Making things nano changes their
interaction with light in important ways.
But the mechanism is really completely
different.
It's not a quantum mechanical mechanism at
all.
It's based on plasmons.
So today we want to talk about what's a
plasmon.
And what are some of the implications of
their existence.
So let's start with a thought experiment.
This is a simple idea.
Imagine we could do this experiment and
let's see what happens.
So let's have we, suppose we have a sheet
of metal.
Which is opaque.
And we put a bunch of holes in it.
Okay, as, as illustrated here, each of the
holes has a certain radius, and
there's a certain number of them, and we
shine light on them from one side.
And we ask, what fraction of that light
makes it to the other side, okay?
So let's make this a little easier and say
that the light uniformly illuminates
the metal surface and just say how much
light gets to the other side?
Simple question, right?
So a simple question
of course is going to have a simple
answer, right?
The total area of the metal sheet,
including the holes Will be that.
And the total area covered by just the
holes is that.
It's the number of holes times pi R
squared.
Right?
And that ratio of the area covered by the
holes divided by the total area,
which is obviously a ratio that is less
than one would be the fraction
transmitted, right?
The light that falls on a hole is going to
go through.
The light that misses a hole and falls on
a metal is
not going to go through.
That's the simple way to think about it.
It would be very strange if we ever saw
a fraction transmitted that was greater
than that ratio.
That would be a strange result.
So now let's see what happens when we make
the hole smaller, right?
We're going to start with big holes and
we'll start making them
smaller and smaller and smaller until we
get into the nano range.
Well, before we get there obviously since
this ratio is
proportional to the square of the radius
we can imagine
that the fraction transmitted is also
going to decrease
in proportion to the square of the radius.
In other words, we're making the area of
the hole smaller so less light will get
through.
No surprise there, right?
So what's the interesting thing that
happens?
Well, there are really two interesting
things that happen.
Number one is what happens when you
decrease the size of the holes to
the point where you reach a size equal to
the wavelength of the light.
Well at that point, the amount of
light transmitted continues to decrease,
but even faster,
okay?
And this is an effect that's been
understood for decades.
For quite some time.
And it has to do with the fact that
light has a characteristic length scale,
which is its wavelength.
And if you try to shove light of a
given wavelength through a hole that's
smaller than that.
It gets harder and harder to do.
Light does not like to propagate through
sub wavelength holes.
And so, the fraction transmitted starts to
drop much
more rapidly as you get down below the
wavelength.
That's maybe a little surprising, but not
shocking.
The shocking thing is number two here.
So under certain special circumstances,
what we can see.
Is that the light transmitted through the
holes actually
skyrockets and becomes enormous, okay, so
that's really surprising.
So here's an example, this has been done a
number of times.
This is one example that I'm illustrating
here, and
this shows you that the holes cover about
you
know, a certain percentage of the area of
the
film, shown here, but at a, at a certain
wavelength,
the transmitted light is actually way up
here in percentage.
And that's kind of very surprising.
It's sort of as surprising as if you saw
this happen, right?
Something big being shoved into a really
little hole.
Doesn't seem like it ought to be possible.
And yet, here it is, there's experimental
data.
So, how can we understand this?
This is, I mean this is really worth
stopping and scratching your head and
saying what?
What did you just say?
In that previous example the holes covered
only
about 28% of the area, but 78% of the
incident
light reaches the other side of the, of
the metal screen.
How is that possible?
In other words, the amount of, the
fraction transmitted is
greater than that area ratio that we
started this discussion with.
In fact it's about 2.8 times.
So, it gets even stranger.
Here's another example of an experiment
that has been
done recently, and if you do things just
right.
You can actually see that the transmitted
fraction can actually approach 100%.
So, in this example here,
the holes cover about 30% of the area, but
100% of the light gets through at a
certain frequency.
Notice that this is strongly
frequency-dependent, right?
At one particular frequency, you see 100%
of the light getting through.
So, clearly something very interesting is
going on here.
So, the key to it all is plasmons, and so
what's going on is, let's imagine an
incoming light wave.
This is a sort of a cartoon explanation.
incident on our piece of metal,
which is shown here.
With a bunch of holes in it.
Well, some of the light is going to hit a
hole, right?
And that light'll go straight through.
But some of the light is going to hit the
metal surface.
And what can happen is, a fraction of the
energy of that light wave
can convert into plasmons, which are
surface
waves that propagate along the metal
surface.
And when those plasmons reach the holes,
they can funnel through the holes, and
so you can get light propagating through
the holes that didn't actually hit a hole.
So you can get transmission that is
greater than that area ratio.
Those surface waves are known as surface
plasmons, and they are
the key to understanding this phenomena
of extraordinary transmission through
small holes.
So, the reason we know this is happening.
Well, there's a bunch of experiments and
theories and things, but
this is an experiment which nicely
illustrates how we know this.
This is an experiment which shows only a
single hole, not a bunch of holes.
So, it's just one hole and that hole is
surrounded by a groove.
That's what this circle is.
This is a groove in the metal that doesn't
go all the way through.
It's just a, a groove.
So, here's a cross section which shows the
groove.
And what we see is, that there's two
transmissions
of light as a function of time.
First what you see is the light that gets
directly transmitted through.
That's that big red pulse.
And then at a delayed time, you see the
light that was transmitted through by
plasma unassisted transmission.
In other words, the light that hits the
groove,
excited a plasmon which then propogates
into the center.
And then follows through.
And it comes out later in time because
it's gotta do that extra stuff, which
takes time.
So we can, if we can resolve things in the
time domain we can really see these two
separate transmission phenomena and that's
a really nice illustration of
how we know why this is working the way
it's working.
So I want to make a little bit of an aside
and point out that in that
previous example I just showed you, the
hole
was almost a half a millimeter in
diameter.
So, is this really nano-optics?
Well, I think it is.
sometimes I refer to it as kilo
nano-optics,
which is a little bit of a joke.
but the point is a serious point.
And that is that in plasmonics,
the study of plasmons, often, the size of
the hole is not the important number.
What's the important number is the size of
the
hole in ratio to the wavelength of the
light.
So this ratio is the number that matters.
And so for nano-optics you might say the
wavelength is 500
nanometers and we're talking about 115
nanometer hole or something like that.
In the previous example, the size of the
hole was
half a millimeter but the wavelength was
three millimeters, right?
So that ratio is the same And so
in many cases, the physics is the,
depending only on that ratio.
So you can scale up the size of your
holes, or your
plasmonic structures, and also scale the
wavelength, and get the same physics.
And in many cases, that's an easier way to
do the experiment.
So it's an easier platform with which we
can use to study the physics of plasmonic
phenomena.
And so, this idea of scaling is really
important in electromagnetics.
So, now, let's get back to a more rigorous
definition of what's
a plasmon?
A plasmon is an oscillation of all the
electrons in a metal.
Or a large number of electrons in the
metal.
Earlier in week two, we talked about how
current is the flow
of electrons and we made an analogy to
water in a pipe.
Well, that analogy sort of works here too,
because
all of the electrons sort of behave like a
fluid.
And they are an incompressible fluid and
they will
move collectively, just like waves on the
surface of water.
So a plasmon is, is a wave in the, in the
electron density.
You get a bunch of electrons, then not so
many, then a bunch, then not so many.
And that will move, right.
And so that's what a plasmon is.
So a way to picture this is imagine you
have thin metal film.
Imagine you take all the electrons in that
film and displace them up by a small
amount.
Now you have a little bit of a negative
charge on top and a
little bit of residual positive charge on
the bottom where the electrons have been
removed.
And those will attract each other and so
that whole block of fluid will slosh.
And oscillate back and forth.
So, that's a plasmon in this metal film.
Now, the, what a plasmon looks like will
depend on the geometry of the metal.
So, for example, if you have a, a metal
surface, you
can have a plasmon wave that will
propagate along that metal surface.
And this is an illustration of what that
looks like.
The red arrows show the electric field,
which
is the electromagnetic field which is
propagating along.
And associated with that is an increase in
electron density, and then
a decrease, and then an increase, and then
a decrease.
So, you have an electron density wave and
an
electromagnetic wave propagating together
across the surface of the metal.
And that's really a plasmon on the
surface.
What are some special things about
plasmons?
Well, first of all, they are a coupled
excitation, as I've said.
You have to have the electrons oscillating
as a, a collective group.
And you also have an electromagnetic wave
oscillating back and forth.
at the same frequency.
So, in phase with it, right?
So, those two things are grouped.
You can't have one or, and not the other.
You have to have both.
The second thing about plasmons is, unlike
light
waves in empty space, they're not limited
by diffraction.
So, if you take a plasmonic structure and
taper it down.
And then have a plasmon propagating along,
it may taper, too,
and become much, much smaller than the
wavelength of the light.
So,
[INAUDIBLE]
can be used to beat the diffraction limit
in some sense.
You can make electromagnetic energy
localized
in a sub-wavelength volume using plasmonic
structures.
And the third thing is that plasmons live
very close to metal surfaces.
Which has two important consequences.
Number one is that the electromagnetic
field near the surface can be really big.
Much bigger than the electromagnetic field
intensity
that you used to excite the thing.
And number two, they're very sensitive to
what's happening near the surface, which
enables
some really sensitive sensing
applications, that
we will discuss in a subsequent lecture.
So the ideas here, are that plasmons
are an oscillation of the electron fluid,
right?
And coupled to that is an oscillation of
the electromagnetic wave.
So they're a coupled oscillation.
They can be localized on a nano-structure.
Or they can propagate across a surface for
long distances.
and one surprising consequence of
plasmons, that we discussed here, is this
efficient funneling of light through
nano-holes, which
leads to this phenomena of extraordinary
optical transmission.
Which I think is a really in, great
illustration of how plasmons can lead
to counter intuitive behavior of the way
light waves interact with metal nano
structures.
Thanks for listening.