Antennas for light and their applications in classical optics, Dr Rupert Oulton, Imperial College

[MUSIC]>>Well, thank you
everybody for coming along to the latest talk in our Optics for the Cloud series
of public talks, and we’re very pleased to have Rupert Oulton with us today
from Imperial College and he graduated from Imperial with a PhD on
Optical [inaudible] Devices, and went on to research Plasmonics
and Meta materials at Berkeley. He’s back now at Imperial, and is particularly
interested in the Optics of metals and that’s what he’s
going to talk to us about today. So just to remind us that there’ll be a chance for Q and A
afterwards of course, and then please take this, you are going to have
external visitors, we will have a few bits to nibble, and maybe a glass of
something to drink. Please stay with us and enjoy a little post talk
discussions. Thank you.>>Good afternoon everyone.
Thank you for asking me to come along and talk about a little bit about the work
that I do at Imperial. I think it might come across as very researchy for the application driven science that you do here. Well, I hope that there’s
something that you can pick out of this that might be useful, or it might joke something an idea for future
collaboration and the like. So I have a lot of diverse interests. Research today is difficult to
get funding and you have to spread your wings and apply for
money in lots of different areas, and this is essentially
how the chips have fallen. When I was in the US I was
looking into Nano-Lasers, tiny lasers that potentially could be integrated on
chips for communications. But also how small
could you make a laser, and it turns out we can make lasers that are actually smaller
than the wavelength of light, which was a big surprise to us. Since then I’ve moved on to look at some more wider types of laser, Condensates of Light,
Lighting bosons, they can undergo
Bose-Einstein condensation. This is very new topical research, we just got a new
grant home recently. I’m going to talk in
this presentation today more about these other two topics
here, Nanophotonics, and Meta materials, and
Light-Matter Interactions between 2D materials Graphene and similar materials
with optical antennas. The theme of my talk, sorry,
acknowledgements first. So I work at Imperial College in the physics department in the Experimental Solid State,
physics group actually. But in our group we have a lot
of research on Optoelectronics, whether that be with Organic, or Inorganic Semiconductor materials. So anything to do
Light-Matter Interactions is covered by the experimental solid state physics
group at Imperial. We also have work going on with the photonic section at Imperial too, and the quantum optics
section as well. We interact with the materials
department as well at imperial, and we have long-standing
collaboration with King’s College London with
Anatoly Zayats there, and recently Stefan Maier who was also at Imperial just moved to
Ludwig Maximilian University, and we have strong ties
there as well. So these two faces here, these are the main
people who have done the work that I’m going
to talk about today. My students Michael is in Australia
now looking at Solar Cells, I think he found this work
a bit too [inaudible] and he wants to do something a bit more useful at least for the planet, and Viktoryia is currently in
Oxford researching 2D materials. So this is the outline of my talk. What is metal optics? You usually think about
metals as reflecting light, what else can they do? That’s what I’m essentially
going to show you today, and the examples are, I’m going to show you how
you can create an antenna, just like a radio antenna, but something that responds to
light at optical frequencies, and how this can then be turned into something called a Meta surface. All will be made clear
when I get there. I’m not going to talk
about a different aspect of these metal structures, and that is the capability
to squeeze light. In fact, any form of electromagnetic
radiation into a space that’s considerably smaller
than the wavelength of that excitation vacuum, and how this leads to extreme
Light-Matter Interactions. I’ll give you an example about a nonlinear process mainly
because it’s extremely weak, and we make it strong. But there are many other types of applications that
you could think of, anything to do with sensing would be the par for the course
for this study, or technology in the future. Finally, I’m going to talk about
Photodetectors because it’s quite interesting that if we play around with the
structure of metals, we can actually make physical things happen with the absorption
of light Photodetectors. So I’m going to show you
how the structuring of a material can lead to better absorption photodetection
rather than having to choose the material and the band gap of the material to create
that absorption. So what is the central theme
of metal optics? Well, it turns out that
diffraction limit, and if you think about the
Microscope Objective tried to focus light down to a smaller
points as possible, you can focus it down
to about lambda over twice the refractive index of
whatever is your imaging medium. Likewise, if you try to look at objects in the Focal Plane
of the microscope, this is about the scale to which
you can resolve those objects. But it turns out that this
is a consequence only of the fact that transparent media
have low refractive indices. So since Abbe came up with
this diffraction limit, it seems we’ve been tied to the
wavelength of light in optics, but we’ve had no reason
to be tied to that. So this is how it works. In fact, the only thing
that does not change for an electromagnetic because
of excitation is its frequency. So if I shine light through a medium
where I’ve changed the medium from refractive index 1 to
refractive index 2 and back to one, what happens is that the light slows down and it’s wavelength
gets shorter. They do this to compensate for the fact that your
frequency does not change. So the other thing is just
that we have these waves, they’ve got a certain wavelength, and if we want to focus light using a traditional
lens what we will do is we will shine lots and lots
of rays at different angles, and they interfere in
the Focal Plane of our lens. Essentially, if we, this
is the phase front of a wave traveling at an angle because it’s been
focused by this lens. Then the transverse wave number here, it can vary as a function of
angle and all these interfere, and if you add them all up you get
something that looks like this, and this represents the spread
function of our lens. That’s the smallest point, or smallest shape of field we
can generate with our lens, and you’ll find that this is about
lambda over n times Sine Alpha, that largest angle you used. So this is ingrained in history now. This is Ernst Abbe’s statue, which shows his
diffraction limit formula as I’ve expressed it
with an extra factor of two, but it’s counting. So of course, Abbe was
around in Indiana. This is Indiana. He was around at the same
time as Schott and Zeiss. Zeiss was the engineer, Schott was the material scientists, and Abbe was the physicist. They all got together and made the best microscopes and
lenses in the world. The point is, this is
only because we think of transparent materials with a
refractive index, that’s quite small. In fact, in the visible
and near infrared, the largest refractive index of any transparent material you
will find is about four, which is pretty bad. Go to microwave regime,
RF frequencies, you will get higher
refractive indices, but in optics, it’s about four. So why is this a ludicrous thing? Why are we not restricted
by the wavelength? While you’re doing some wavelength electromagnetism every single day, this is a plug obviously. Between about the centimeter
distance between these pins, we get very efficiently 50 hertz electrical signals and
they power our devices etc. But when you think about it, the wavelength of
50 hertz electromagnetic wave, well, it’s gigantic. So the British Isles is
Lambda by six, in this case. So we are definitely capable of
working below the wavelength. So what is it? This
is another example. This is our microchip. Two gigahertz is typical speed
from microchip these days. That’s a wavelength for
15 centimeters and yet, the little channels, the feature size in fact for
the transistor gates, it’s about 32 nanometers. These wires themselves that
joint transistors are a bit larger and this is now pretty much smaller since
the five years, I’ve had this slide. I think we’re a sub 10 nanometer now, in terms of transistor channel sizes. In a nutshell, you can do
the same thing with optics, but you have to use metals. But this is a structure which we
designed when I was at Berkeley. It’s got a metal substrate, it’s got some semiconductor
components on the top. The main point here
is that we launched light through the back here and it coupled into this funnel and they got slotted down
all the way to here. Then we brought in
this tip and this tip, we scan it over the
surface of our structure, and it scatters light out
where it’s strongest. We were able to show that really the light is trapped between
this yellow material and the silver. This is a semiconductor
and this is some metal. This is about 50 or
a 150 nanometers and it’s for a [inaudible] so this is
633 nanometers of wavelength, and the side of this picture is
pretty close to the wavelength. So it just shows that with optics, we could do the same thing
if we use metals. So the free electrons and metals, they interact really
strongly with light. There are free electrons, you shine light on them, they move. That’s why light is reflected
from a metal so easily. But more importantly, metals generate
optical excitations that are limited in principle only by our ability to fabricate
those structures. What the hell do I mean by this? In order to talk about this, I have to go into
a little bit of detail. The detail of concerns
these excitations that call surface plasmons. What’s the surface plasmon? Well, they are quite frankly, just natural solutions to
the wave equation when you look at the interface between
a metal and a dielectric. They are true surface waves. In fact, because they can
propagate in the plane, but the electromagnetic energy dissipates away or decays
away from the surface. So there’s no energy propagation
away from the surface, it’s only in the plane. So a general picture of this, what we can do is we can
represent these waves. Generally, when you want to look
at a new type of excitation, you look at its dispersion. That’s the plot of energy or
frequency versus its momentum. These are excitations that are
trapped to the metal surface, so they’re moving slower than any excitation in the eyes
of the air of the metal. So they’re trapped below what
we call the light line here. If you think about metal at
really long wavelengths, it becomes completely opaque. You get reflection from
light at long wavelengths, very conductive at those frequencies. So very little light
penetrates into the metal. It looks like a glancing angle wave that propagates along the surface. In fact, the Earth itself has a conductance which allows surface
waves to propagate over it. This is how radio waves propagate. But at high frequencies, the metal becomes more transparent. Eventually, when you read
the plasmon frequency, light will be able to
propagate through metal. But just before that, enough energy sits in the metal that the surface waves
can exist, but also, they take on a lot of
energy or a lot of momentum from the electrons that
are involved in the oscillations. This causes this turnaround, this increase in momentum
as you increase the energy. Eventually, you get to a place where surface plasmons
can no longer exist, and that’s about the UV,
about 350 nanometers. It changes four different metals, but that’s the region. So in order to understand
where confinement comes from, we have to look at what’s going
on at this metal surface. So in this next slide, I’ve just zoomed in on this wave. This is essentially, the plus minus, the change in polarity if
the wave as is propagating in space at a fixed point in time. If you look at what’s going
on in the metal here, I zoom in on what’s going on, within the metal, you can
think of electronic waves. They’re trying to move
electrons around, but as these electrons are moved, all the electrons around them, they move as well and
they try to screen any residual charge that may occur because you’ve
moved an electron. So within the metal, it remains essentially
charged neutral. It’s only at the
surface where there are no electrons in
the dielectric region. These cannot compensate for the
electrons that are being moved. So what you get is this very
thin layer of surface charge. This is the origin of
these field lines that define the field distribution
of your surface plasmon. So crucially, this turns out
to be about one angstrom. So it really is thinner than the interatomic
spacing, for instance. If you want to go
there, you have to go into quantum mechanics and
do some terrible things. I want to keep this as
a classical optics lecture. So we won’t go any further than that, although I’m happy to talk about
it later if you have questions. So can we make things that are
this smaller than the wavelength? Well, these are
colloidally, so chemically, sorry, synthesized gold nanowires. I don’t have a scale bar here, but the diameter of
these is below a micron. So if you think about
the cross-section, this is what a surface wave would look like traveling
along a nanowire. It looks pretty much like
the surface plasmons that propagate on the plane. It has a charge distribution. This charge distribution
changes polarity as the field propagates as
a wave into the plane, into the screen here
as it’s propagating. So the way to understand where
confinement comes from is to realize that while the plan on
surface has an exponential decay, when you curve this surface around, you can have a different
field distribution. If it’s a really small curvature, it will look just like
a plane wave, sorry, a plane surface plasmon if
the curvature is very large. But if the curvature is very small, you can imagine, for instance, that you’re trying to resolve something that moves
further and further away, this essentially looks just like a single positive charge or negative charge
depending on the phase. So eventually, it looks
like just a point charge. So we know that plasmons have an exponential decay that’s
tied to the wavelength. That a point charge has
a one over our decay. What that means is that
the field amplitude will decay by half in a distance that’s equivalent to the
radius of your wire. So what I mean to say
here is that the size of your field amplitude is now
not linked to wavelength, it’s linked to the size of the
structure that supports the wave. If we can make a smaller structure, we can make a smaller
more confined wave. So if you are mathematical, the mathematical
description of the light for a nanowire is
a modified Bessel function, this K function here. Doesn’t matter really
exactly what it is, it’s given by this black line. You can see that this black line at different length scales of distance, you have a one over r-squared decay and you have an exponential decay. What that means if
it’s a tiny nanowire, it’s like a one over our decay. If it’s a big nanowires, it’s exponential and linked
to the wavelength. So I have a movie here that
just shows you or illustrates, this is from a course
that I teach at Imperial, the effect of this confinement. So here’s the electric
field distribution from the nanowire plotted from, so actually, this point here is
near the center of the wire. So this is, zero point is the interface between the
metal and the dielectric, and this is the field decay of
the light away from the surface. This dotted line
represents what happens for essentially the infinite
radius of curvature. This is the starting
radius of curvature, which is radius of five microns. So as we decrease the size of
the nanowire, where’s my mouse? Is missing. There it is. It’s very simple plot.
Just to show you as you shrink the radius
of the nanowire, what happens is that the field
becomes more and more confined. So I haven’t changed the wavelength, all I’ve done is shrunk
the diameter of the nanowire. Here, we’ve got one over
[inaudible] for the small wire. Here, we’ve got something
linked to the wavelength. Interestingly enough, this
is purely geometrical. So before I showed you that
when surface plasmons are being confined or being operated
near ultraviolet waves, the momentum shoots up. Because more electrons are involved in the process of storing the energy. Here, this is the momentum here. The momentum is already increased
by less than five percent. So this is really to do with the geometrical electric field
pattern that a point charge has, a point line charge. All right. So now, imagine I’ve got this nanowire
and I truncate the ends. So now, I have something that
looks a bit like an antenna. So this antenna, if we change, if we have lots of different
frequencies, for instance here, you’ve got the wavelength
plotted from 400 nanometers, that’s blue light all the way
up to microns that’s already into the mid-IR against
the rod length. Each of these lines represents
a different diameter. As you change the diameter, you change the speed that
waves propagate along. So you change the condition when the phase is pi by two that allows
you to have a dipole antenna. Just like a radio
frequency antenna, but now, it’s four wavelengths approaching
the visible and near IR. So as you shrink down
this rod length, all of these conditions, essentially, the
resonant wavelength from the antennas is linked to
the length of the antenna. These linear relationships all basically converge
on one single point. At this point here,
at this wavelength, you cannot have a surface plasmon excitation for a small structure. In fact, if you make it smaller, you still have the excitation, it just doesn’t change wavelength. So this is, I’m sorry if
you’ve already seen this, but in our field, I suppose it’s a bit
of a running joke, but this always used
to be the thing people use to describe this condition
for small antennas. This is the Lycurgus
Cup British Museum. It’s quite interesting because
depending on how you look at it, where the light sources,
it looks different. So what you have essentially
is white-light shown from one end and inside this, the gloss of this cup
are metal particles. These metal particles are very
small and what you’ll notice from this plot here is that when you
make these gold wires smaller, and smaller, and smaller, they all converge on the same wavelength. So providing all the
particles are small enough, they will all have
a resonant wavelength at about 500 nanometers
which is green light. So here, we have all
these particles which is small enough so that they
all scatter green light. So if you look straight through, if you essentially have
a light source behind the cup, this is what you see, a nice red cup, light shining through it,
looks quite interesting. Pleasant to look at. What’s
happened here essentially, all the green light has been removed. It’s being scattered all the way
around in different directions. So if you now look at
the cup from the side, you should see it looks different, it looks green because the light that’s being
scattered is the green. So I’ve told you a little bit
about how metals can generate optical excitations that
are linked to their structure, their size and there’s many interesting consequences
because of that. The final thing is
about what happens, so my final thing is that
light-matter interactions can be greatly improved in strength
with this kind of optics. So electronic and optical
wave functions can be matched in scale to create
extremely fast optical processes. What do I mean by that? So we have to go back to
remarkably 1947 and 1946, where two different people had some very interesting ideas
about how antennas radiate and how the radiation
of an antenna can be improved. So the first one is
the Wheeler-Chu limit. So this is the paper from 1947. So this Jack was
an engineer and what he was doing was looking at
these little dipole antennas. But he said that these antennas, if they were smaller than
the wavelength, a lot smaller, there was a really simple
formula for telling you how quickly the radiation
could come off your antenna. Essentially, the radiation rate from the antenna. This is the formula. So this is the frequency at
which you are operating. This is the rate at which
light is being lost. This is some geometric factor
and this is nothing more than the ratio of the volume of your
antenna and the wavelength cubed. So the volume wavelength or
the volume of your antenna. What do they mean by
the volume of the antenna? Well, quite simply, if you
have an antenna, for instance, this little U-shaped antennas
commonly used in the literature. Its length-scale is
about 50 nanometers, if you draw a sphere that
encompasses it maximally. So the edge of
the antenna is touch it, this is what the volume
he was talking about. If you do the calculation, you find out that this antenna, being so big, about 50 nanometers
and scale is not that big as it. I’m going to show you some things
that smaller in a minute. This antenna has a radiative rate
of a 100 femtoseconds. So I designed this actually
for one micron wavelength. So this is just on the cusp of the near-infrared 300 terahertz and the optical period is
about half a femtosecond. So essentially, what
this means is that this antenna holds onto the radiation for about 200 cycles before it
dissipates it to the surroundings. So the atom is
an interesting situation. An atom is just an antenna, and it’s holding onto some radiation, and it’s going to radiate it. But it’s so small that the
radiation is very, very, very slow. In fact, at these
frequencies, most atoms, you have to look for atomic levels that have dipole moments on
the order of the Bohr radius, but if you plug the Bohr radius
into this equation, you come out with
millisecond timescales and that’s pretty
comparable to what you get. So now, an atom essentially
has a dipole that oscillates for millions
and millions of times before it can lose its energy. I always put this example up because
I’m a solid-state physicist, semiconductor materials
have things called excitons and these are
actually delocalized. So electrons and holes, they are whizzing
around each other like a hydrogen atom in a crystal. The length scale of those about a nanometer and that corresponds to the timescale that excitons
lift for about nanosecond. So what this means is that
most light emission processes, because you could think of them
as antennas, they radiate very, very weakly. Inherently slow. So now, I’m going to put you with the most exciting paragraph
of my field of nanophotonics. It’s probably the most highly
cited single paragraph in science, so I don’t know if
that’s true or not, but I reckon it is by how much it’s
been cited in our field alone. So this is Edward Purcell, got Nobel Prize for nuclear
magnetic resonance. He realized that the rate of
emission or the rate of transition of any process can be enhanced if you couple it
to a resonant circuit. He was using the example of nuclear magnetic states
inside like nuclear, he was looking at
nuclear magnetic states. Okay. I’m not going to go into it. Essentially, the nuclear
magnetic transition would take somewhere on the order
of 10 to the 21 seconds or the age of the universe
even longer to undergo a transition so it can
never be in thermal equilibrium. If you couple it to
a resonant circuit, he showed that this could
be done in minutes. So this is quite
remarkable because it’s a 20-order of magnitude change in the transition rate
of something and you can apply the same
principles to optics. Indeed, this is what people do. This is the formula that
Purcell came up with. He said you can change
the natural rate of emission. All you have to do is put it into a resonant cavity that has a size. So this is lambda cubed
over the volume now, not of the atom or the antenna, but of the optical resonator, that or radio resonate
or whatever it is. Then it’s modified again by
this thing called the Q factor. The Q factor is, once
you’ve got radiation held inside a cavity or
an object or an antenna, it resonates around for a little bit
before the energy is lost. This Q represents how
many times light’s bouncing around inside this
resonated before it dissipates. So people have used
photonic crystals to see enhancement factors
approaching a 100, but in metal optics, you can do better because
you can shrink down the size of your optical
modes dramatically. So in the photonic crystal case, you can get high Q factors, but you’re always limited by
diffraction or by the fact that refractive indices of
transparent materials have low refractive
indices, are very low. With this metal optics approach, you can do anything you
want with this volume while the Q factor doesn’t work so much
because metals dissipate energy, but this volume reduction gives
you a remarkable enhancement. This essentially,
this is the state of the art after a decade per
cell factors of a 100. This is the state of the art after perhaps five years with plasmonics
of Purcell factor of 1,000. So what I want to
illustrate here is if you take this idea of
Wheeler and Purcell, and put them together
because in effect, Wheeler was talking about
this parameter here. Purcell is talking about
the modification of that parameter. What you find is that
any interaction rate between light and matter is just linked to how big the antenna is
with respect to how big the optical mode is that
you’re using to access it. So the ratio, the volumes
of the materials state, and the optical state, and of course, modified also by the Q factor, how long the light hangs
around before it dissipates. So I’m going to skip that and I’m going to come
on to this point here. So what I really view is going on in plasmonics and metamaterials
or metal optics today. You’ve got light to
the diffraction limit up here. This is a micron length scales
for a wavelength of about a micron and you’ve got the characteristic length scales
of electronic states. In metamaterials, what you’re trying to do is you’re trying to make bigger antennas that
can interact better with light beams and full plasmonics. What you’re trying to
do is, you’re trying to shrink down the scale of light so it can interact better with very, very small things at the nanoscale.
I’m going to skip this. I’m going to skip this. These are just some examples I want to get on to what
I’m going to say here. So why metal optics? Well, it’s about decoupling the scale of optical devices
from the wavelength. You can strengthen
light-matter interactions with the plasmonic approach
making fields small. You can define new materials
that can mold the flow of light, that’s the metamaterials approach which we’ll talk about in a minute, and the Mantra, really, is
function through structure. I’m going to show you
a few examples now. One of the first questions that
I was asking when I joined this field is that how well can we interact with the single antenna? So these are two objectives confocal arrangement and we’ve got
a little disk antenna. So it’s not a bar
anymore, just a disk. Remarkably, this interaction
can be very strong. The reason it can be very strong is that if you think about this antenna, it’s like a dipole when it’s excited, and that means that it
radiates like a dipole. Dipole radiation looks like this. So its concentric waves coming
out from a point source. You also have to make
sure that you align your electric field along
the direction of the dipole, so it has a little bit of
missing here, but that’s okay. If you now think
about a focused wave, just shine a plane wave
onto an objective lens, it gets focused down,
what does that look like? It looks pretty much the same. Concentric waves in this case, for the focused wave, the lights coming in and out. For this case, the waves are
always leaving from the point. So this represents our antenna, this represents the excitation
wave, the plane wave. So actually, the overlap
is really good. This paper here, it showed that
if you had a perfect dipole, which didn’t lose any of its energy
and it just purely radiated, if you focused light down on this, it will give you 86 percent
reflection or something like that. So this guy is actually
working on trying to get 86 percent reflection
from a single atom inside a vacuum chamber for instance, quite a remarkable idea. So this shows you what happens if you illuminate with a focused beam, a single metal disc. This extinction represents one minus the transmission of the light
through the particles. So you can see that 60
percent of your light, you get a 60 percent drop
in transmission, for one of these particles. It also shows you that the
smaller your particle, the more weak the interaction is. This comes back to what
I was saying earlier. Actually, if you want
a strong interaction between light, the diffraction limit, just
conventional classical optical beams, you actually need antennas
that are quite big. You can also see here
that when you go from 60 nanometers to 110 here, the wavelengths doesn’t
change very much. Again, this comes back to
the point I was making. If the antenna is small,
it’s actually not, particularly, malleable in terms
of its ability to engineer it. It’s only the larger ones that show tunability and
this very high extinction. So when we were doing
these experiments, we were pretty shocked
about how sensitive the particle is to the focused beam. I’ve been telling you that you need a larger particle to be able to get good interaction between
light and the particle. But the problem is here. This is to show you that, actually, the particle is still very, very small and very sensitive
to its position in the beam. So we did this experiment. In fact, when we started doing this, we couldn’t understand our results, at all, for this very reason. It turns out the reason
we can’t understand it, is because of chromatic aberration. It’s so sensitive as
this technique is that it allows us to measure
the chromatic aberration of any optical imaging system. So chromatic aberration
is when any lens, they try to introduce
different glasses to compensate for
chromatic aberration. But inevitably, what happens is that red light and blue light come to
a focus at different positions. If I now drive my particle, which incidentally is
just 50 nanometers thick, through the focus here, what I will do is I will have a slightly different spectrum
of extinction because the blue, and the green light, and
the red light were all out of focus. So this would be the real
extinction of the particle. At different positions, I would
see a different extinction. So we did this experiment. So if you’re really cheap and you don’t want to spend
too much on a lens, you buy something called an Achromat, it’s corrected for two colors. So this is the true extinction
of our particle. These are real
experimental results now. This was the best position
where two colors were in focus, but all the other colors
were out of focus. If you spend more than £6,000, you can buy something
called an Apochromat, that is corrected at
three colors now. So this is the true extinction
of our different particle, what a different particle now
with a much broader response. But you can see that the three
colors are in focus together. But it’s pretty annoying
having to work with these things when different colors are in focus at different times. If you want to spend a lot of money, you can buy something
called a Superachromat, Apochromat and it’s in focus
at four different colors. Anyway, Nikon were pretty surprised when we showed
them these results. These are the positions of the
focus at different colors. So here, you can see
the slides here shows you that two colors were in focused for
this particular position of focus. This shows you that
three colors were in focus. They were surprised because
the best they’ve got, it takes them many days to measure this using interferometry
with lasers of all different colors so they
get points at different places. So they were pretty shocked
when we said it took us 10 seconds to do these
measurements in each cases. So nanoparticles are
pretty sensitive things. So this was a bit of
a hero result, the next one. I just really was interested in
whether we could do it or not. These antennas, they
extinguish light, but they also change
the phase of the light, because that’s exactly how extinction works. You’ve
got the Scatterer. It’s scattering light out
of phase with the light that’s exciting it and
that’s how it cancels out. We wanted to measure
this phase change. So what we did is we took light
on this beam splitter here. What the beam splitter
did is we put two beams in and two beams came out, and we tilted
the beam splitter so that these beams came at different angles
inside our objective. One beam gets focused
to a different point. So the change in angle shifts the point at which
it comes to a focus. What we did is we had a beam that was exposed to a particle
and a beam that was not. So all we did was we measured the phase difference between
these two light beams. When they come back through
the next objective, essentially, they come back and the beams were overlapped but have
a very small angle. When light is essentially
within the coherence length, when it’s a small angle, it will create interference fringes. So indeed, you get
interference fringes, we put it through a prism
and that results spectrum, and we’ve got
these really nice plots. So this is white light that’s being split into wavelengths
in one direction, but interfered with a reference beam
in the other direction. So you can see that
the spacing between these waves increases as
the wavelength increases. This was the residual phase. So these are flat to
within 0.1 of a radian, so it was a pretty nice technique. Anyway, the point is, is that this is the extension of this that I showed you from before. This now shows you the
phase of those disks. So why did I show you this? Well, the point was, to show you that you’re not
just cutting light out, you’re dynamically
changing or coherently changing the way this antenna
is interacting with the light. Where you’re shining a beam
on and then the antenna is then radiating that light with a different phase to
the light that’s coming in. This is key for the area
of metasurfaces. What is a metasurface? Well, all you do now is you make
an array of these antennas. So here, these are little gold antennas or
representations of them. What you can do is
you can change subtly the properties of each antenna and then it will scatter light at a phase that is dependent on
its position in the frame. So now, for instance, if I were to grade the phase
along here from linearly, what you would find if
you shine a plane wave on it would re-radiate and this light will be refracted as if this were a medium of
different refractive index. This is mimicking the effect
of an air glass interface but it’s essentially no thicker than
50 nanometers of gold. So this is the principle behind
the area of metasurfaces. So it is not a very good resolution
here but essentially, what metasurfaces plan to do is to take bulk glass optics
which are heavy, and thick, and non-compatible in terms of the portable
technology we love, and convert it into a very, very thin layer which can
be integrated on something flat and flexible and
whatever you want. So these are all the things that our people are
doing at [inaudible]. The field is so
saturated that there’s very little money available for this, so it’s not something that
I’m researching at the moment but it’s something that
I’m quite interested in. The other great thing
about this field is that, we don’t want small antennas. I just said that they
don’t radiate very well. So actually, we can get away
with dielectric antennas. So these structures here are just little blocks of
transparent material. They’re actually very big compared
to the wavelength but they allow you to do flat optics. The benefit of that is that all metals have
a little bit of absorption and the dielectric metal surfaces are pushing 80, 90 percent efficiency. So that it’s really possible to do optical components that are flat
and transmissive, pretty good. From optical antennas to metasurface, so large antennas interact
strongly with optical beams. Optical antennas with focus beams
are aberration sensors. This is very sensitive to position. But it tends to be that
people make arrays of particles now, and these arrays, because each antenna can radiate with a certain phase and that’s
controllable in space, you can make something
called a metasurface to guide and mold the flow of
light and do whatever you want. Since large antennas are required, dielectric structures with
low loss are possible. I’m doing okay for time. So something that really got me interested when I joined
this field in 2006, got me quite awhile, was a recent paper at the time
by a chap called Mark Stockman. Incidentally, Mark Stockman
also proposed that you can make tiny lasers so that was
another motivation for me. So what Mark Stockman proposed
is that you could taper metal structures in such a way to confine light to
infinitesimally small points. His proposal was, take that nanowire
example from the beginning. If you were to gradually shrink the nanowire diameter down and down and down as
light’s propagating along it, will it deliver
all the energy to the tip or will it scatter
the energy or whatever? Anyway, so what he did was a simple calculation and
he showed that, well, all the energy can be
transported to the tip without reflection or scattering and you can have this phenomenon
called nanofocusing, which he claimed incidentally. Nanofocusing is
perhaps a strange word because nano is only relevant
in the optical domain. If you were to do
this with microwaves, you could do subwavelength focusing just by making
these structures as well. But the point here is
to do it with optics. The only problem is
that he was really, really optimistic about
what we can make. He wanted a cone angle of one degree. He wanted the diameter to change from 50 nanometers down to one nanometer. Bear in mind that I think if we
make a 50 nanometer structure, we’re pretty happy with ourselves. This is actually very
challenging to achieve. What can you actually
do with this technique? So it wasn’t long after in 2007 where I got a bit
disappointed because people started reporting on this topic. This shows you a scanning
electron microscope image of one of these cones structures
that someone literally thought, “I’ll do exactly what
the theory said.” What he did, you see
these grooves here, they allow you to shine light
from them and launch waves, these plasmonic waves
along the nanowire, and they should be
focused to the tip. I thought this demonstration
really clearly showed the whole point
of nanofocusing. So what you see here is a schematic, and these position, one, two, three and four show you where the illumination was
put onto this tip. So firstly, we have illumination
right at the backend here, and you can see that
nothing much happens, it just illuminates
the nanowires you can see there. Next thing is they illuminate
the front of this grating. What you see is launching
of plasma and waves, and we see this tip lighting
up really brightly. So this, presumably, is
the nanofocusing effect. We’re able to cup a light
to this tip because we are launching the
waves that are creating the right conditions
to generate waves that go right to this tip using
this nanofocusing phenomenon. But they went further. They then focused the light a bit
closer to the tip. Well, in this region,
you don’t see much. Then they went straight
ahead and said, “Well, I can just illuminate the tip. Presumably, I’ll do
better.” But you don’t. The point is, when you
illuminate the tip, this is quite an expansive distribution
of light compared to this. Remember that this point source
here is diffraction limited. We can’t actually
see how small it is. But you can see here, this is definitely
a diffraction limited. Not a diffraction
limited point source. The energy is distributed
over a very large space. So these guys have done
fantastic scanning probe microscopies
using this technique. It really is quite nice. So I was more interested
in nanophotonics, and I think this is something
perhaps that you’re interested in here too
about how optical data communications can improve our data capacities and
energy efficiencies. So this work is from the [inaudible]
Group at the ETH in Zurich. This work is from
a Japanese group and I’m afraid, I think it’s an Atomic Group at NTT, which is a telecommunications
company out there. So what they’ve got are
simple standard silicon wave guides, and they taper them down and launch light into these metal
grooved structures. It works pretty well,
and what they’re doing here is they’re putting
a material inside this, and the lighter material
interact with each other and they apply bias. When they change the bias, they can modulate the light that
passes through this structure. So this is actually becoming
commercial technology now. People have always thought, put to one side the idea of using
metals because they’re so lossy. But [inaudible] is
pushing forward to this. These things, they only have 3dB Insertion Loss and they
can be extremely short. For instance, these modulators
are typically millimeters in length scale in
current optical devices, but these can be just micron. This is their wire result. This shows the ability
to couple 90 percent of their light from the silicon waveguard into
a ring resonator now, this gap ring resonator, and then they use
this as a modulator. So the reason I brought
up these examples is because they are
quite difficult to make. What we’ve been doing is coming up with a really simple technique that’s a test bed for all the things
that you can possibly do. So this was our demonstration. Essentially, because something
very similar to what the [inaudible] Group
and other groups have done with all this gap structure, this supports a very strongly
confined mode in the gap. In fact, this shows you
the field distribution that you would expect
for lighting this gap. Very high intensity here.
How does this work? Well, maybe this is beyond scope
actually and I will skip it. The main points about
this idea is that we don’t actually have to do
very much nanofabrication at all. We can just take, we can buy
off the shelf a silicon wafer. It’s got this thin silicon
layer sitting on silica, and then all we do is deposit
a little bit of silicon, and pattern on top of
it metal structures. This metal structure in
particular, this gap structure, is very interesting because
if you have a wide gap, the light sits in the silicon and
it propagates fairly low loss. If you now have a very narrow gap, the light gets pulled up into
the gap and gets focused down. So what we’ve essentially got here is a very simple way of
making a nanofocusing device. All we have to do is change one geometric parameter and we can use lithography,
very easy to do. Essentially, this is what we’ve done. These are all little waveguides
with incouplers and outcouplers, and you can see here
the little waveguide gap structures, and very little fabrication required. So how do we prove that we’ve
actually focused the light down? In fact, not many
demonstrations that can show this because the light really
is in such a small space, the only way to prove that it’s
actually doing anything or you’re actually getting focusing
is to look at some effect. So the [inaudible] Group makes a better modulator
because the gap is small. But no one’s really seen how
that light is strengthened. So this is one of the first
demonstrations to do this. What we did is we put light
emission centers inside this gap. So we’re getting through
remarkable distance scales here now. So this is the structure
as you see it on the SEM. If you zoom in, you can see that
there’s about a 25 nanometer gap, and in here, these little white dots, these are semiconductor quantum dots. They emit light in
the range 6-700 nanometers, so on the edge of the
visible towards the red end. What we do is we illuminate
this grating structure and we launch infrared light
at 1.5 microns now. We entice illumination
excitation and luminescence from the dots at the high frequency,
at 600 nanometers. So in order to do this, the Quantum Dot has to absorb
three photons and then emit them. So what you can see here, this is the one that I think is the most important one to show you. This shows you a scan or a line scan through this structure
that shows the focusing. So this here, this bump is the
illumination from the spot. So that shows essentially
three photon absorption and luminescence from
the dots from our input spot, and this shows the three
photon absorption and luminescence from the dots
that are in the gap. You can see that this enhancement intensities it’s quite staggering. So this is direct evidence
for a focusing effect. You can also see that this
excitation dies away quite quickly. This is the fact that
light waves inside are very confined metal structure are subject to losses
and they decay away. In this case though it’s three times shorter than the distance
they propagate because it’s a three
photon absorption effect, it scales with the
electric field to the power of six because of
the three photon absorption. This shows you a slightly wider gap. You still get the focusing
but in this case the excitation from the input beam
is a bit more prominent. So generally we can test
any structure before we make it using something called Finite
Difference Time Domain. So we essentially look at
electromagnetic problems, we divide space up into divisions in space and time and we let life
go into our structure and we can monitor how light
accumulates in various regions. This is just to show you that there’s a rigorous simulation
that shows how it works. So this is the silicon
structure here. So all of this is silicon, and this region here light is
pulled from the silicon as it propagates into the gap and you get this really nice
enhancement in the gap. These are cross-sections
through the structure here. Now you can see the light sits in the silicon wave-guide
modes pulled into the gap as it propagates along. So it’s very difficult to measure exactly what the
efficiencies are here, but if you shrink the gap down to about 20 nano meters which is the smallest size in this simulation, we end up with an 80 percent
coupling efficiency and literally last week we found an error and it’s 94 percent coupling efficiency. I pushed my students on it a lot because I thought
80 percent was a bit low, it’s 94 percent coupling efficiency. These things can be really, really useful I think. The other thing is that the
intensity is enhanced by 400 times, and this is not the intensity
relative to the input beam. This is the intensity relative
to the light that’s sitting in the silicon that you’ve
generated in the first place. So what’s the point of all this? Well, we want to generate really high intensity light because if you can
generate high-intensity light, you can get extreme interactions
between light and matter. When does a light field
become strong? Well, it will become
strong when you can ionize electrons from
the material and completely destroy it. All right? So that actually sets the limit because other than that there
are people who are going to intensities where you can basically separate electron-positron
pairs generated from vacuum and that would be so high intensity probably 30 orders of magnitude higher
than anything I consider here. But we’re considering material
damage to be the limit. So if you look at the Coulomb field, the electric field that
binds electrons in matter, you find out that this is
somewhere in the region of 10 to the 16 watts per square centimeter
in terms of intensity. People make lasers that got to 10_13 watts per
square centimeter these days. But we don’t necessarily
want complete ionization, it turns out that DC breakdown in the tunnel junction to be about
a volt per nano meter that’s corresponding to 10_12 watts per square centimeter and there’s
a phenomenon called High Harmonic Generation where essentially
non-linear optics become very strong. That happens around 10_12 watts
per square centimeter as well. So if we take the laser system
that sits in my lab, and we think about
the intensity enhancement we can get with what
I’ve just shown you, it turns out that we only need an average power of
about a 100 micro watts to create an intensity that
would destroy our material. Not quite destroy our material but would get very interesting effects. What is a 100 micro watts? Well, a laser pointer
is about a milliwatt. Now, the light here is pulsed so it’s actually squeezed in
time into higher intensity, but the average power, the average energy of the pulse
over a long period of time is no more than the power
you have in a laser pointer. So this means that
you can do portable really strong light-matter
interaction physics and that’s what’s
really exciting for us. So this is going probably
into a bit too much detail but we wanted to show
that not only can we see the focusing effect here
we can get a strong effect. So there’s a phenomenon
called Four Wave Mixing which is useful for
telecommunications instantly. It allows light signals
to talk to each other. Usually light just
interferes with itself. It doesn’t deflect itself or
change it’s direction or anything. But when you have
a very intense beam of light, the light will modify
the medium in which it propagates and then other beams
can be affected by that. This is called a
Four Wave Mixing process, and essentially you’ve got what
we call a virtual level diagram. What the material is doing is taking on the coherent oscillation from two pump photons and
then a third photon which we call or a third beam called the signal beam and it’s
generating a fourth beam, a new one completely. This is the mathematics for this process and it doesn’t really
matter exactly what this is. The electric field
forces the material, it has a linear response described here and this chi term
here, this chi one term. This typically is of order unity, and then this is the term that
generates this mixing process. So you’ve got this chi three term
because it’s mixing four waves. Three waves in, one wave out. This parameter here is small. It’s on the order of 10_minus 19
meters squared per volts squared. It’s really small parameter,
a weak effect. But the point is is that because
we can intensify this light in, the combined effect is
that this parameter now is getting close to
unity and it’s not quite. In fact if it got to unity everything would break down this whole analysis. It’s about 100th of the refractive
index, really strong effect. The nice thing is it’s
really easy to do. All we need to do is choose
a non-linear material and infiltrate it into the gap
and let’s have a look. So this is what we
did, shows nice SEMs. We’ve got two beams launched
onto this grating now, a pump beam and a signal beam and we generate
a third beam that comes out. This is just a nice image to show exactly how nice
this gap structure is. What we’ve done is measured
the efficiency of producing this idler at this point relative to the beams that
are injected at this point. So there’s a whole lot of
coupling and out coupling and propagation in and out that
we haven’t taken into account. We’re just looking at
the pure effect of creating this idler beam from the light that we get to
that point in the first place. There’s a bit of a caveat
to these efficiencies. So this is the main result. These are the two beams that going in at two different wavelengths. This is the pump, stronger beam,
and the signal beam. This is our idle beam and
you may be thinking well, that doesn’t look so efficient. It’s about one percent efficient. This is actually quite
amazingly efficient, because this structure is just two microns long and these
nonlinear effects, they take millimeters, centimeters, meters to accumulate in
most device technology today. When you account for the fact that we’re doing peak to peak efficiency, when you account for the whole power transport to this region it comes out near
a five percent efficiency. We made lots of different structures and each structure seems to be consistent in producing something that we can explain in
terms of the theory. So I just want to state here that the wave-guide length you would need to achieve a similar
efficiency in other technology. If you were to use an optical fiber, you’re going to need
10 centimeters to a meter of fiber to create
the same efficiency. If you are going to do this
in silicon technology, photonic technology you’ll need
a millimeter to a centimeter. We can do this in a micron. This is important. It’s a very subtle point but interaction distance actually
introduces limitations. If you have to accumulate an effect because it’s
very weak over a meter, the different colors you’re
trying to mix they’re all going to travel at
different speeds over a meter. They’re going to go out phase. If that happens,
the effect gets destroyed. So these devices here can
only convert or can only do this process over a very
restricted range of circumstances. Our technology completely
throws all this away. You can do these mixing processes under any conditions pretty much, over an octave of the spectrum.>>[inaudible] .>>Oh sorry, so they are shown here. So these are quite close to telecoms. This is down to about.
1450, 1480, yeah.>>You weight [inaudible] of the same order as the link
to this welcome thing.>>That’s right.
Exactly, two microns. In fact, when we made
all these devices, the two microns, I think
one micron was the smallest. But in all the new studies, two microns is the longest. We’re actually looking at
shorter and shorter structures. You can see here that the effect
accumulates up to two microns. But then if you have longer guides, the effect deteriorates
because the energy of the waves is lost because of
metallic losses, essentially. I don’t think I’ve got time
to go into the last part, Let me just summarize
this and perhaps just give you a taste of the next bit. We’ve got a very
straightforward approach to focusing light on a
silicon photonics platform. Really, it’s just one geometrical parameter that we have to change. It’s really reproducible and
we’re quite excited about it. This kind of idea is already
been commercialized for modulators or electric-optic effect
for silicon photonics. That’s the Swiss group,
Leuthold at ETH. We have the potential also to
get damaged level intensities. I say damage level. We could generate
higher intensities, potentially, it’s just there’s no point doing it because we would
destroy our material. But at these intensities, there’s all sorts of interesting
physics that can come out and it’s going to
be in portable devices. Another point is that really
strong nonlinearity can occur, and when non-linear processes can be similar in strength
to linear processes, I think that’s when
interesting things will happen in terms of the physics
and technology that you can do. So I will give you a one-minute
taster of the last part, and that is something
that we’ve been doing more recently, metals absorb. So we just saw that you get losses in these really
highly confined wave guides, metal surfaces that
I made out of metal, probably only 30,
40 percent efficient. Dielectric ones are much better. So very recently, perhaps
in the last five years, people are saying, “Well, can’t
we use this absorbed light?” It turns out that
the absorbed energy, it can be useful because it generates
things called hot electrons. There’s a series of papers in
Nature Nanotechnology from 2015 that talk about this topic. These are actually
all of them together. They’re all in
the same issue back to back, and I recommend that
you have a look at them if you’re interested in
this. What’s going on? Well, if you shine light on one of those disks that I’m saying
we had in the beginning, what you do is the absorption doesn’t just take energy away from the light field,
it gives off something. What happens is electrons get excited inside
the metal’s band structure. Then over a certain amount of time, they generate initially
a non-thermal population. Then they distribute
themselves into something that looks like electrons at
a very high temperature. Then gradually this energy is dissipated amongst the phonon
vibrations of the particle, and then you end up with the heat to being dissipated
into your material. So on these different timescales, on very, very fast timescales, what people are doing
is chemical reactions. If your electrons are
1,000 or 2,000 kelvin, it means they’ve got energy to activate reactions that
couldn’t occur before. People are doing water splitting, spatio reaction of making
methane from carbon dioxide. These are all really interesting
things that people are doing and you can do
this from sunlight too. Cancer treatment. So this is treating a mouse which was unfortunately
infected with cancer cells. What happens here is that over a long period of time
that it takes to dissipate the heat
from these particles, what they do is they
functionalize these particles that seek out cancer cells
and then they far laser beam at it and you only heat up the particles that are attached to the cancer cell and destroys it. We’re doing things with photo acoustics and people
also making photodetectors. The nice thing here is that if your electrons are
really, really hot, you can make a photo
detector that is not linked to the band gap of
the material you’re using. So this would be the last part of my talk which I’m not
going to go into. If you can use metal structures
to create photo absorption or photodetection to convert
optical energy into electrical energy without needing
a material with a band gap. I’m happy to talk about that later, but I should stop now in the interest of discussion. Thank
you for attention.>>Wonderful, thank you so much. I should [inaudible] look
good at metal samples the same way again. Any questions?>>For the last part that you
have a metal that you get, is this non-linear experiment in high temperatures or
quantum applications?>>High temperatures for?>>It’s cryo temperatures, I mean.>>No, these were conducted
at room temperature. So the limitations are damage. If you use too much laser intensity, it will destroy the material
that’s inside the gap. Unfortunately, we selected a number of materials which we thought
suitable but the one we ended up with which had the best
characteristics also happened to degrade in
ambient environment. But there are plenty of
materials that don’t. Essentially, there are not many real limitations to
using this in the future. The one thing that is
a problem is that the use of organic materials like this
in a fabrication environment, like a fab lab or foundry is not tested and that’s perhaps the only block I think
to getting this working. For instance, anything to do
with silicon, they hate gold. Actually all structures
are made out of gold. You’re going to have to change
that to make it work as well. Gold forms traps in silicon that
ruins electrical properties. But those are the only
limitations just in terms of technological limitations
of the materials. They’re all the materials
that we can use.>>Excellent work.
[inaudible] forward mixings. You have shown that
the conversion efficiency decreases with events
of your structure, and this is due to loss. Is this fundamental?
Can we evolve it? Because obviously you
said your size is much smaller compared to
the size of fibers or silicon and all these air
[inaudible] so long that you can have
kilometers [inaudible].>>Yeah. So you are right. When it comes to non-linear effects, distance, interaction distance
will always win. You can make a fiber a
kilometer and I mean, you can make it to be
100 percent efficient. Well, I don’t know quite 100 percent. But in doing that, you have to really play
carefully with the parameters because these waves
as they propagate, they’re all interacting with
each other and energy being transferred from one to the
other over long distances. So I’d say yes, you can get the efficiency
if you make it longer with any technology
apart from plasmonics, which you can’t make longer. The great thing here is
the flexibility that’s afforded by being
a broadband phenomenon. It’s not restricted to how fast the colors move with
respect to each other. I didn’t talk about it, but the colors go out of phase in this particular
experiment over 200 microns, whereas we’re working over two. We’re also looking at smaller
structures and not larger. We think that if we go to smaller
structures with smaller gaps, actually, the efficiencies
are going to be better. The point of this plot
here says that there is actually no point in working with a wave guide longer than two microns.>>That’s right.>>That all your effect
is coming from here and the modeling that we’re using is probably not good enough for
actually describing what’s going on. When we work in this regime here, it’s pretty much unknown
what’s going to happen. For instance, you can see here
that this point should be properly quite a lot
lower than it really is. This is a logarithmic scale. So something weird is going on here and so that’s
what we’re doing now. We’re working on really,
really small structures to see just how much we
can squeeze out of it.>>But the losses are fundamental.
You can’t do anything.>>The losses are fundamental. But remember that at this point
is really just 50 dB loss. This is equivalent to well, perhaps, a little bit more than that. This is about the propagation length. So just a bit more
than three dB loss, which for these kind of structures, I think is at least tolerable
for proof of principle. Yeah. I agree. I think that there’s a lot to be done before we can
really exploit this.>>[inaudible].>>We’re also interested by being unrestricted by this problem of the colors
propagating at the same speed. We reckon that in this case, these wavelengths are
chosen simply because the decoupling optics
have a limited bandwidth. In fact, we can’t go to 1,400 because this envelope is
where light actually, you can shine a beam, and
get it into the structure, and out of it as well. But with careful thought about how to do that in a much more
broad band nature, there’s no reason why we can’t start getting 1,500 nanometers
to talk to two microns, to talk to three microns. Now, when you’re doing that, eventually, all other
approaches dry up. You just can’t use anything else. So even though our efficiencies
may not quite be there, there are certainly things that
we can do that other techniques can’t and I think
that’s another reason, another way to push this.
Very good question.>>For the application
of the [inaudible] , I’m not sure how familiar
you are with it. Do you know how much
the functionalization changes the properties of particles?>>Yeah. So if you
put a shell of just really any dielectric material
in a shell around a particle, it will modify its resonance, but quite a small amount actually. A bigger problem may be
agglomeration of particles. So there are people that play
around with molecular rulers where they measure essentially the
average distance between particles, which can affect the resonances, but these are really,
really small effects. In terms of just delivering
heat to an object, I don’t think there’s any problem and this functionalization is designed. What they’ll do is they’ll
look at the cancer cell. They’ll look at the antibodies involved and then they will literally program that particle to
respond to that type of cell. So it’s really, really
specific as well. Then, the laser beam is
applied fairly locally. It’s not going to damage tissue
because the intensity is designed to heat the particles,
not the material. It’s the particles that
they heat the material. Yeah. I’m sorry. I didn’t
have time to go into that. I really, really wanted to.>>Any more questions?>>This ability to generate
such high intensity light. As I understand it, it
also to control it. You localize it very precisely. How would you see that being used to further our knowledge of the
interaction between light and matter?>>So by knowledge, I’m thinking physics and mathematics. If you think about it in that term, this equation here tells you
how a material polarizes. You usually think about
electrons sitting and we always think
about oscillators. So that’ll be some electron
that’s bound in a position, and when we shine light on it
will move around that position, and I know when I was doing A-levels, you just assume that everything is a harmonic potential like
a quadratic potential. So the restoring force is linear, but it turns out that what
I think can pretty much understand that electrons
when they’re in atoms, this potential is not quadratic, and that they can move, and have these higher-order terms. Usually, what you do because the electrons are
not driven too much, they’re just a little bit
beyond harmonic. You generate this perturbative
expansion it’s called. So there’s a K2 term, a K3, K4, K5, and these higher-order terms describe the potential landscape in
which the electron moves. This perturbation expansion
only works when the electrons still pretty much
confined to the potential. So these high order terms, they should die away quickly
if this analysis is valid. So there’s a whole area
of physics now, which I think is called
attosecond physics, and this revolves around the idea
that you’re driving electrons so far from their equilibrium positions that this perturbation
expansion breaks down. While he would expect each of the successive terms to
get successively smaller, what starts to happen is
these higher-order terms actually sustain themselves and
you get these plateaus where, for instance, people are generating the 111th harmonic
of an infrared beam. This means you can get
into the UV range with lasers and not only that, these processes because
they’re really broad band, and lots and lots of pulses
there are essentially in phase, these are also attosecond pulses. So attosecond physics is
all about vacuum chambers, and gases, and really
controlled environments, which require lab conditions. But very recently, perhaps
the last five years, people have been talking about solid-state high harmonic generation. I think it’s very open to think what we can do with
this kind of physics, but we’re talking about fast ranges
of wavelengths generation. So different light sources
with different colors, very, very fast processes, potentially doing new types of spectroscopy with
solid state devices, portable devices, so you can bring attosecond physics out of the lab
and into portable devices. So that’s one of the things
that I’m very interested in. So in terms of the science, you break down this
perturbative description and there may be some really nice
applications to come from that too.>>I’m sure you’ve got people
thinking about that in the context of what we’re
doing is. Thank you so much.>>Okay.>>Any last questions? Otherwise, we can go and see what the chatbot says. Okay. Let’s thank him once more.>>Thank you.

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