By the way we've got to do.

There's a whole lot that I'm going to

give you know because it
was probably becoming

Why does he think it was
time that Washington.

Did he was going to go out there with

that first acknowledge these are real or

you know that's a little more I want

to listen to her on the I can't believe
a lot going on in the world somebody

or they are talking about the cost and
you got it going in your life.

I feel like I'm on the water.

I mean yes all the things in the city

and you know what do you want for
your children.

I want you to

do you want to get it working in

their offices because

they love you so

thank you very much very happy to
speak here in fact I'm gratified

to find a true large audience it's
been a long time since I've had so

many people who weren't worried about
what I was covering so that they would.

It's problems right on the quiz.

Right but I'm sure the pizza had
something to do with it right.

So anyway I'd like to tell
you a bit about some of

the recent research from my group on some.

Nanostructures composed of
metal nano particles and

I'm going to talk more about how
the structures work than any end

up with cations because in fact there
are some non obvious aspects of how these

structures function that suggests new and
different kinds of applications

that might not occur to one had
We're not delved into the details.

So let me just start out with a brief
outline of the rest of my talk.

I will spend two slides just giving you
a sampling of some other research my

group before I go on to talk about
the metal nanoparticle chains or

waveguides or arrays will see what
that means and then I'll conclude.

So broadly speaking the work in
my group really lies in areas

between are overlapping
nanostructures non-linear optics and

ultra fast phenomena in the frequency
domain Oktar fast phenomena

turns into terahertz more or less
depends upon how fast you think fast is.

So we're interested in
primarily very high speed and

non-linear effects in small structures.

Now those structures in some cases
are semiconductors in some cases metal

some cases of molecular structures and
just as a sampling of

one of our activities which is not the
core part of this talk we're interested in

the design of sources of
terrorists radiation So for

example on the left is shown
a piece of semi insulating gallium

arsenide with electrodes so
it's essentially an insulator.

However if we shine a short pulse of light

on that material whose center frequency is
above the bandgap of sort of silicon or.

Darshan edge.

One generates carriers that gives
rise to a current search and

that trends encouraged.

Current search produces a pulse
of terrorists radiation.

So there's a compact way of generating
post terrorists radiation and what

we're competing against and we're trying
to improve upon our other sorts of sources

such as a free electron laser large
facility based sources so what we want to

do is help design more efficient sources
that put terrorists on the table top.

OK So that's that's one of the sorts of
things we do another thing we do that

kind of couples nanostructures
with terror hurts and

nonlinear optics is to module eight.

For example the optical properties
of a semiconductor quantum well

with the terror field so think of this
is a very high speed optical modulator.

But if you module eight.

A semiconductor or
a modulator sufficiently fast

notice this is not a P.I.N. structure so
you don't have to worry about limitations

on modulation due to parasitics etc
There's an intrinsic structure.

If you module eight sufficiently fast you
have to analyze the situation in terms of

mixing different frequencies in
the context nonlinear optics.

So we're thinking ahead in terms of
optical modulators I can function

at extremely high speeds.

And other things as well so
that was just a couple of things.

So if you are interested in
anything related to that.

Let me know just wanted to give
an idea of some of the things we do.

At this point I want to go and talk
more about the core of the talk which is

the metal nanoparticle structures and to
start out I want to say that the idea of

metal nano particles and their interesting
optical properties is quite old.

So here is a Roman Cup that is doped.

It's glass.

It's coke with a small amount of gold.

Now the Romans didn't know that
the gold was aggregating to form the.

No particles but they did know that
it gave rise to intense colors.

So you can see that interest
in reflect in transmission.

We have a bright red color in reflection
of the scattered light is green.

OK and that color is due to
the fact that the gold is added.

Now gold as we all know doesn't look like
those colors so something's going on.

So let's see what's going
on really only emerged.

Perhaps in the last hundred or so

years with the understanding of me
scattering and surface platters Mons Let's

start out by looking at the system that
underlies these interesting properties.

So we're interested in primarily noble
metal nano particles gold silver.

OK there are cases were copper or
other metals may be of interest.

The nanoparticles may be from
a few nanometers in diameter.

Let's say a couple of hundred nanometers
and most of what I talk about today

involves feral nano particles but
other shapes have been made.

So what's going on.

Why do we see this bright color.

Well that bright color indicates optical
spectra that are associated with

natural peaks reasonably now.

So they have a well defined frequency.

What's going on is that if we
think about the charge within

the nanoparticle we can have collective
motion of the charge so that the charge

squashes back and forth so if we drag the
negative charge some of the free electrons

off their equilibrium position to
one side of the nanoparticle OK.

There will be a restoring force due to the
less screen positive charge on the other

side the electrons will move back to
overshoot their equilibrium position.

And then the leaf some months screen
positive charge on the bottom and

they'll oscillate back and forth.

Now this motion is a similar Torrie

in the frequency corresponds
to the colors we saw.

However it's.

We damped you only get a few oscillations

of those quick to bustle ations
of electrons before those

oscillations are damped out with
quality factors on the order of ten.

In other words if you look at the optical
spectra they're very broad OK.

They're not extremely narrow
they're they're broad They do have

the world defined frequency but
nonetheless are quite broadened.

So how can we get a better understanding
of what these planets Monsoor for

squares Manzanar what I want to do is just
start out with a different geometry just

planar geometry with a metal half space

above which is a dielectric
lossless dielectric So

I actually going through the exercise of
solving Maxwell's equations it's not hard.

What you do is you find that there
are modes electromagnetic modes

that are confined near that interface
those of the surface past months.

And one can ask the question What is the
frequency of those electromagnetic modes

as a function of wave vector in
the plane of that interface and

one finds a dispersion
relation shown here.

So what one sees is that
there's a region of the lower

ranch of the dispersion
curve that's fairly flat

which is essentially what's known as
the surface class month frequency.

And that frequency is sensitive to
the dielectric constant of the overlying

dielectric whether we're
treating We have air or

something else which is also very
interesting because the surface glass

Munns therefore are sensitive
to their environment.

So one can have some
interesting sensors now.

Does anyone know if this
has a laser pointer.

You have to turn it on yet.

And yeah.

There we go.

OK.

So we're not quite there yet.

We have nanoparticles as we
saw in the previous few graph.

The surface put us mon
actually forms a continuum.

So how do you get a discrete frequency.

Well if we imagine wrapping that surface.

Let's not think about a nanoparticle
sphere yet it's easy enough just to think

about a cylinder if we wrap that
metal surface around a cylinder.

Then we have these waves that go
around the cylinder but those waves

have to meet their tail in other words
the phase has to be the same when that

thing propagates around the circumference
of the cylinder that picks out certain way

vectors associated with surface clouds
Mons such is shown by the circles here.

Now the modes associated with those
waves these are waves of displacement or

excess electron charge
going around a cylinder

onesies there are different
modes of the lowest mode.

Is a dipole electric dipole mode.

That's the dominant That's in
terms of the optical properties of

the dominant mode that's the one
that you see most easily.

That's the most important
surface plasm on mode so

that gives rise to discrete frequency
which is more or less roughly speaking

picked off the surface class month
aspersion curve that fashion.

Now it's not quite true because
we have a finite Yama tree.

We're also dealing with the sphere cetera.

But that gives us a good semi quantitative
understanding of where the surface

class months come from how they
give rise to discrete resonances

in spherical or other nano particles.

So what of people done with these
well people can make various

sorts of structures.

Arrays of metal nano particles and
these metal metal particle rays

turns out we'll see the mechanism they can
basically serve to provide paths or guide.

Guiding structures for
like to propagate within them.

People have made very sorts of
structures that involve gaps

between arrays of nanoparticles and
under some circumstance.

As those can guide light
will also see that

chains of nanoparticles
themselves can guide light.

OK how do people make
structures like this.

Well.

Two main methods.

One is using E.B.M. lithography OK so

you can define a well defined array of
nanoparticles with the graphically it

turns out however that there's
enough disorder in that process that

the different nano particles are
sufficiently different that propagation

through that you know about genius
collection nanoparticles is not so great.

So there is more laborious technique that
involves more perfect nanoparticles and

that involves basically making one's
nanoparticles using what chemical

techniques so cool litle nanoparticle
growth and then picking out those nano

particles and manipulating them one by
one on a substrate with an A.F.M. tip.

OK So that gives rise to much
better quality structures.

However it's extremely laborious.

So I'm going to concentrate
more on structures of

this sorts of chains of nanoparticles
know as we'll see structures like

this can actually serve as
guiding as wave guides for light.

But here's the remarkable
aspect of these structures.

If we think of a conventional
dielectric waveguide.

The transverse dimension of the guiding
structure can typically be no less

than something like half
the wavelength of light.

OK.

You can't make things much smaller and
still guide the light.

Otherwise you're kind of weak out and
be gone.

If we look at these structures
the transverse dimension

of the metal nanoparticles maybe
in this case fifty nanometers

that's going to be we'll see much
much less and then go over to right.

So in other words one can potentially
make waveguides that have extremely small

transverse dimensions.

And therefore one can hope
to be able to address.

Optically dress nano nano devices
cane some sort of system.

Right.
So this has basically fuelled interest in

these structures for
Nanoscale optical interconnects and

other possible applications are using
structures like this to channel light into

nano scale objects so for instance suppose
you wish to deliver optical energy into

a very small structure within a cell but
you don't want to have collateral damage.

You don't want to deliver
light everywhere.

Well there are people interested
in structures of this sort to do

precisely that.

OK so what we want to do is understand
how these structures guide light.

So just to put some typical
parameters on what we talk about will

mostly be talking about gold nanoparticles
on the order of few tens of net meters in

radius these metal particles the center to
center space is more than the diameter so

they don't contact.

So there's no electrical conduction
path or no collective motion of

electrons that can move through
the entire structure of the electrons and

each Not a particle can
only talk to each other.

Let's say capacitively right.

They can't be transported from
one nanoparticle to another

and the sorts of problems
we're interested in

are to some extent typical problems that
one might be interested in waveguides.

OK if you have a bend in a waveguide.

What happens to signal that
propagates to through the bend.

Are there losses does
something else happen.

Are there eventually for
bed is very sharp you might have reflected

signals etc You might have distortions
different dispersion So if you're short

pulses they might get distorted
around a bend things of that sort.

If you have nearby waveguides
do they talk to each other.

OK so how can we understand CROSSTALK.

If you have defects which
are unavoidable let's say some

nano particles are smaller or
bigger than the others or absent.

OK how does that affect propagation.

So ultimately we want to address a number
of questions of this sort some of them.

We have some of them.

We have and.

OK.

In fact a lot of the understanding is
in a much more basic level even today.

So once again why metal
nanoparticle chains or

nano class monic waveguide same thing.

The potential is to fabricate optical
waveguides with lateral dimensions that

are far less than lambda OK so
certain that patients include nano optical

interconnects near field optical probes
nano scale lasers etc There are really two

challenges the main challenge the biggest
one is to control attenuation metals

as we all know are lossy conductors
right no matter what your favorite

metal is OK the dielectric function
has an imaginary part which

represents a loss those losses represent
translate into attenuation for

electromagnetic signals that
propagate down these waveguides.

So a very important thing is how to
control that attenuation those losses

are exactly what limits the Q. value or

the quality factor of the surface class my
motor nanoparticle to something like ten.

OK so how do we deal with that.

The other challenge which I didn't
write down here is that even

even though the look transverse dimension
may be very small the electromagnetic

field being dragged down here is
a propagates down can be very large right.

So and
that is what's going to produce CROSSTALK.

But it's not going to be the subject of
this talk we're also looking at some ways

of dealing of confining that
electromagnetic field bets that

propagates with surface class Mon are
the expectations along these waveguides.

How do we can find a further someone won't
have crosstalk event that's another talk.

OK once again to kind of
remind us where we are.

Silver or gold nanoparticles
few tens of nanometers and

radius center to center spacing
somewhat larger than the diameter.

Things to note we always have to remember
that broad resonance of the surface class

monitor single nanoparticle hate the fact
that these resonances are highly damped.

And what I want to show in a minute.

Is that what do we know experimentally
optical propagation of long chains

has kind of only indirectly been measured.

OK So unfortunately people have
not actually launched light at one

end of a chain watch to propagate
well they've done some of it.

Want to propagate down and
seem to come out the other side.

Most of the information is inferred from
other experiments which are shown here.

So here's some nanoparticle chains that

were fabricated in Herriot
what are scripted Cal-Tech.

OK they're gold medal particles fifteen
not a meter diameter seventy five

nanometer centered center spacing
these chains were fabricated using

manipulating the nano particles with an
A.F.M. tip on I believe a glass substrate.

And this data is optical extinction.

So what they've done is basically
they from the far field they shine

a light source narrowband light source or
broadband doesn't matter.

And then they spectral you analyze what
comes out from the other side see how much

light propagates through.

OK that like it doesn't propagate through
is the like that it was extinguished.

So depending upon the polarization of
that light if it's going to to move

polarized along the chain axis or
whether it's polar ice transversely.

Across the chain axis the optical
extinction is different it's peaked at

a different frequency and
on polar ice is just shown with you.

OK So the fact that the polarization
matters means that these

nanoparticles somehow
know about their G.M.'s.

Grangemouth there somehow
talking to each other.

OK And what underlies that is the fact
that actually one is essentially exciting.

The combination of modes
that involve coupled

coupled modes between all the various
nanoparticles on the chain.

Now people know this much better from
simulation So here's a Q. D.F.T. T.V.

calculation also from Atwater's group
of electromagnetic propagation down.

Well this isn't a nanoparticle chain
it's a chain of of Rod space coolly and

one can basically see that the light
is too large extent confined near

the chain right there is also damping seen
here what's shown here is the time domain.

What happens with the field as a function
of time you can see the damping

here is in the spec for
a transform spectrum.

It's broadened OK that's associated with
actually two things One is the imaginary

part of the of the dielectric
constant in the metal and

the other part of the broadening is due
to Frakt of losses so scattering losses.

OK The light is scattered
to the far field.

So how can we understand this problem.

K B F T T V calculation sure
one can go ahead and basically.

Plug in parameters into your favorite
F T T D code and let the thing run.

There's some big problems here.

First of all three D.F.T. T.D. for

a large structure is prohibitively
difficult in terms of time.

OK.

Number two.

When you have structures
that involve dielectrics and

metals F T T V is also
can be a bit problematic.

OK to do things accurately you often need
fairly fine mesh sizes and you have to be

very careful and the other thing is
because it's very long to do calculations.

It's often hard to
explore parameter space.

Right.
So you can only get a limited

understanding of why.

It's going on.

So you actually even if you could explore
parameter space you still may not know

what's really going on have a good
intuitive grasp of what's going on.

So sometimes it's better to look at
more analytic models of propagation and

such structures.

And shown here is the simplest
model you can imagine.

Each particle electrons are oscillating so

each nanoparticle is
an oscillating dipole.

So therefore it's a dipole So

the other dipoles nearby are couple
to it there's dipole dipole coupling.

So by considering a chain
of dipoles that are coupled

through nearest neighbor dipole dipole
coupling you could figure out that

really you don't just have individual nano
particles where the charge is oscillating.

But you have wave like
exit ations of the chain.

OK These are called
Class Mon pellagra times.

Know as we'll see this
model is really inadequate.

It's not just a bunch of static dipoles
interacting with their neighbors but

they're also waiting dipoles
interacting with all the other dipoles

nonetheless from such a simple model
you can learn something important.

You can learn.

You can learn that the positions of
longitudinal exit Taishan versus

transfer sex a Taishan give rise to
different frequencies and furthermore

the band that's formed of the different
wave like exit ations is different.

So it's hard to see but
the bandwidths are different here and

that because relate it back to what
comes out of a model of this sort.

So we want to look further we want
to look at more detailed aspects

of centrally exactly what's
going on in a simple model

that should be adequate
to describe the behavior.

So let me tell you about what we're doing.

OK Well let me tell you about what some
questions you can ask and then I'll tell

you what we're doing one thing you
might ask is What about higher mode.

He pulls a member we saw that there were
these different sorts of surface class

Monza nanoparticles and I just kind of
brushed aside those higher multi poles.

Well it turns out that the higher
Mulkey poles are not very important for

the optical properties and
furthermore there are a couple in

between different Moki poles
is not very important.

Once the distance between
the nanoparticles gets large enough and

we are more or less in the right regime.

OK so we can throw away the most people.

So that's that's actually well understood.

OK.

So we only keep
the electric dipole moment.

That's fine but what we do is we correctly
account for the retardation the fact that

when one dipole oscillate in the mix
electromagnetic field that field

propagates takes some time and there's
some phase change over the propagation

at the point that it interacts
with the other other dipoles.

Turns out that such a model gives
extremely good agreement with

you know more detail models
taking into account.

You know the finite size of the dipoles
the higher most people moments of cetera.

And there will be very few equations but
forgive me.

So our approach is really
purely analytic turns out

that we're fortunate that we can evaluate
everything in sight and literally and

what we're doing is we're driving
a relation that relates it gives us

the frequency of these waves as a function
of the wave vector of the waves.

OK So this is kind of the well omega of Q.

is what we're after Omega
subpoenas the surface

plasma resonance on a single nanoparticle
And then there's a factor here.

The Sigma which is called itself
energy somehow accounts for

the coupling between
the different nano particles.

So if we could evaluate this thing then
we have everything we need and in fact.

We can evaluate that C.Q. he.

Or is the exit Taishan way vector It's
the way vector along the chain and

it's related to the wavelength of
the waves along the chain lambda.

The nice thing one can learn immediately
from just finding the self energy is that

the real part of this quantity gives us
the frequency of the various mode for

a given cue looks here and

the imaginary part gives us the losses
the diffract of losses automatically.

OK so it all comes out in the wash
without any extra effort.

And what is the self energy.

It's simply the dynamical retarded
dipole dipole energy between two

oscillating dipoles So we have dipole one
it emits electromagnetic radiation which

is intercepted by dipole two and it turns
out if you look at the form of this

this whole expression is actually
symmetric in terms of dipoles one and

two K. so
it doesn't matter how we wrote it.

And we can evaluate we can write that down
just by going to a textbook looking for

the field of an oscillating dipole and
then when we have the entire chain.

We basically forty transform
the whole thing to vectors.

But before we forty transform
some point things to know

when the polarization is transverse or
perpendicular to the chain axis.

We have a near field.

I'm sorry near field term.

K. we have a far field field term and
some intermediate field term but

if the polarization is
along the chain axis that

that far field term is absent that
long range term rather is absent.

So in fact there is a very
different physics governing

the waves that propagate along these
chains depending upon the polarization.

So as I said we basically take
all that information we work

in terms of wave actors because these
are waves that propagate on the chain and

everything else will be given in
terms of dimensionless quantity so

instead of the actual
a vector along the chain Q..

You multiply Q.

by the distance between nanoparticles and
get some dimension this way vector of K..

The frequency is Omega instead
of working with the regular

frequency we convert that two dimensional
This way back to her as well.

Sorry about that probably
even I'll forget it.

By the next transparency.

I don't want to go into this too far but
what's shown here is just the real and

imaginary part of this self energy as
a function of wave factor and frequency.

This is exact we calculated in terms of
some special functions one can find so

in fact it's very efficient to
calculate the properties that

determine the dispersion of
exit ations on these chains.

OK so what you see just for those for the
fix you not know is out there you see this

line that runs through all these pictures
that's just a zone folded light line.

We have the light dispersion in free
space but we have a periodic structure.

So that's just the zone folded right line.

And interesting things
that you see here these

lower ones are the imaginary
part of the self energy.

You can see that if you're
below the light line

the imaginary part of
the self energy is zero.

In other words there's no rate of loss and
we'll talk a bit about that in a minute

let's start out with the dispersion we can
read the dispersion off such a view graph.

If we know this so these pictures
are universal for all parameters so

if we know the parameters
the surface Klansmen frequency and

the spacing between nanoparticles we can
read off the dispersion as a horizontal

squaddies here we have here is
the transverse mode of the distance so

this is the X.
Taishan wave vector This is frequency.

We get a shape like that for
the launch of Toodle mode.

It looks like that.

So we actually get we'll see about
a little more about this later.

This gives rise to negative group Losey.

So essentially what might be the.

Material the basis for left handed
materials based on some of the structures.

Likewise we can read off the radiative
losses the same way from the imaginary

parts of the rate of decay rate as a
function of way back to are shown here and

the important thing is that if the wave
vector is too large the extension wave

vector is too large.

There are no diffract of losses.

So there is no way to
find a far field photon

that can carry off the energy
of one of these acts to Taishan.

And conserve momentum
along the chain axis.

So if you can excite modes out here.

Then you can totally suppress at least
the diffract of contribution to attenuate.

Well the net result is that those
losses are pretty bad the diffracted

losses are bad and
homogeneous losses due to

the in homogeneous broadening
of the only Keating in the metal

as well as in homogeneous broadening due
to differences and then a particle sizes.

They are absolutely fatal for

making this work at least to
date in these simple chains.

OK people however of thought about ways
of fighting against that attenuation.

OK shown on the left is this is the use
of surface plasma in a laser or with

again medium here the point wasn't to use
the surface glass Monon to fight the ten

you ation here was actually to make a very
small laser cavity or confining structure.

So mid infrared foreign
Fred quantum cascade lasers

right as the wavelength gets
to be longer five microns.

You know one hundred microns or whatever.

What it means is if you want
to make a semiconductor laser

that has some confining
structure in normal conventional

dielectric confining structure you would
have to ask the M.B.E. or M.R. C.V.T.

grower to grow some enormous structure and
they tell you to get lost.

So as people went to longer and
longer wavelengths with these lasers

they realized they had to
come up with a new concept.

To confine the light in the plane
of the laser structure.

What they did was use
the centrally metallic structures

to confine the light basically does.

Form some sort of surface class Mon and
the field from the surface plasma on.

Penetrates into the gain medium.

Therefore one can one has gain and want
to make a laser out of this and works.

On the other hand people have looked more
to actually use the surface plasma and

as the key for there's a key part of
the functioning of some kind of structure.

This is work from home and screw up in
Amsterdam where they take a silver grating

they deposit glass on top where they're
it's erbium doped with in the grating and

the idea is to let the surface blast month
propagate along this grating kind of like

surface plasma class monthly or
times that he's changed and

to extract gain from the erbium ions and
then therefore make some kind of a laser.

So one idea that we've
come up with is actually

somewhat similar if you
put your surface put as

if you put your nanoparticle chain on top
of an optical gain medium or close by.

Can you as the surface class
Montclair Aton are those

expectations propagate in the waveguide
can they extract optical gain and

therefore can they fight
against that attenuation.

Now this is a much easier geometry we're
looking at nano particles out of substrate

it turns out it's a harder problem but
if we know how to do it.

It's easier to look at this if
they're embedded in the material

just as a model calculation.

In this case.

What might happen.

Well as we saw before there were there
were wave like exits Haitians or

guided waves in these structures that were
not really guided but could diffract away.

Right.
The small way vector X.

Taishan gave rise to diffract of
Wes's the long wave that directs

Haitians did not solve the short
wave vector X. Haitians.

Will propagate in the media but
they'll be scattered out and

they will they may undergo some gain but
they'll be lost.

Still still be lost but those surface
what are called surface plus Montclair

tonsils large way better extensions
will sense will be trapped

near the nano particles and will really
be able to benefit from the gain.

And in fact we could do similar
calculations what we saw before.

These are the centrally the radiative
loss as a function of wave vector for

perfect dielectric embedding in a perfect
dielectric medium a lossy medium and

again medium and
remember these are the last of

this mode here we see some negative
last negative losses gain.

So in fact the amount of
gain you get here is enough.

We predict a fight against the losses.

OK So we believe that there is a way of
dealing with these losses in these chains.

OK there are some costs however you'll
have a lot of losses and again medium

you probably have a lot of noise in the
signal but we haven't studied that yet.

A couple of other basic things study.

Well what we looked at were infinitely
long nanoparticle chains but

any practical device has ends.

OK you have to couple then
you have to couple out.

So how efficient is the coupling
into those structures.

How do you design the terminations so
that things work.

So we've just started working
on this kind of problem so for

example a very simple question to ask is
What if you eliminate a chain with and

then that's terminated from
the far field so plain waves.

What sort of exit Taishan can you
couple into you know how well you

couple in two X. a Taishan is in
the chain or guided waves in the chain.

Or if you have guided waves in the chain
and they reach the terminations

what happens when they reach
the end of a couple out very well.

OK so the easiest thing to do is just to
look at what happens in the far field.

Now that.

May not be what you really want
a couple to a nearby device but

that this is a start.

So we're going to look at
coupling to other structure soon.

So you have a chip.

Let's say seventy infinite chain of it.

Nanoparticles or a long chain how to treat
the end of such a structure is actually

a mathematically difficult problem
because you have to account for

all the coupling this is not just nearest
neighbor neighbor coupling right you just

put some boundary condition at the end
that doesn't work so it's a tough problem.

But there are ways of doing it
turns out semi analytically and

essentially exactly what's shown
here is the dipole moment induced

by a plane wave incident on
the terminations of a chain looking at

the dipole moment as a function of
nanoparticle away from the terminations.

So you see that there is
there is a real end effect.

OK within the first couple of
tens of nano particles and

eventually quiets down to an infinite
chain like behavior beyond.

So how many nano particles participate
here depends upon things like the distance

between the nano particles etc But this
is very useful information for us to know

what is a finite not a particle chain
kind of behave like an infinite chain.

When does it not.

And where does the action take
place in terms of coupling.

We can also calculate the scattered field.

For instance here this is in coupling
again this is a scattered field

these dash curves are the current
cop approximation that's just taking

the infinite nanoparticle chain
solution and truncating it and

looking at the rate radiation in
the solid curves of the exact solution.

You see that the exact solution
Akercocke solutions are quite different.

So Kirchhoff theory.

Perkoff approximation is pretty
lousy You could also get an idea.

So when as you shine
the light in the structure.

How much of it is scattered
back immediately if you.

Consider energy conservation you can see
how much of the energy actually ends up

in the nanoparticle chain.

OK so the these are fairly new things
we don't quite understand it so.

There's a lot more I can say
we also look at out coupling.

OK here we send a wave down the chain and
we look at what comes out or

is there any reflection in the chain.

OK So here once again you
see that all the action

near determination takes place in the
first couple of tens of nano particles.

And once again the kirk of cooked
up approximation is lousy again.

We don't quite know what all
this means it's pretty new.

But we get an idea of where the radiation
is going so at least in the far field you

see that some of the lights coming from
the right and going towards the left.

In fact you do have most of the light.

Is scattered forward which is good news.

Excuse me if you want to couple
that into another device.

We also look at near field exit Taishan So
this is starting to get into looking at

coupling to some other device and
we only did it in coupling.

And here we were focusing on
actually in the previous problem

the far field problems there
are similar things to look at here.

We want to look at again this idea of
the dispersion of the transverse modes has

this negative shape which basically is
associated with a left handed material or

with negative can be with
negative group philosophy.

So you see for the transverse polarization
there is this funny overall shape

that to the dispersion for
the longitudinal modes.

It has a more normal shape.

So here's the geometry we eliminated with
the near field tip near determination

of the nanoparticle Ray here we calculate
that the induced dipole moment.

Again.

Affects near the terminations
basically current or near.

The near field tip.

Well in this case it's actually more
than a few tens of nanoparticles

it extends fairly far
from the transverse mode.

Not sure why yet.

One of the neat things is if you
look at if you already analyze

the spatial frequencies along
the chain away from the terminations.

Here is the case for the logic to
model with normal dispersion so

we excite it with some in plain wave
that some projection of the wave vector.

Well essentially frequency
that will correspond to wave

that has some way vector positive K.Z.
or negative K.Z. for

the longitudinal model we just generate
positive K.Z. I know these aren't

labelled but what's indicated
here is the nanoparticle distance

from the terminations longest axis is
Casey and this is the local spectrum.

On the other hand for the transverse mode.

Even though you're exciting near the end
here exciting waves that are propagating

they have the phase with
the propagating towards the expectation

that doesn't violate energy
conservation because if you send

a wave packet it will propagate from
the X. Taishan point down the way.

Fak it but the underlying spectral
components underlying waves

are propagating towards
the expectation point and

that's indicated by these negative
values of the way vector.

So we're still interested in
seeing what one can do with it.

Well I'm just about done simply
want to give you an idea

of some of the other problems that we're
treating some we have partial results and

we have no results some we
have pretty complete results.

We're very interested in what
happens if you have disorder in

a chain the easiest thing to do is to
start out with a single defect you might

have a substitutional impurity a vacancy.

Turns out that these
are very similar problems.

Again the long range coupling means
that you introduce what's called Nanda

of the Sauder.

It's not a simple problem.

It turns out that the single impurity
problem is exactly solvable.

We can.

Exactly.

Calculate the scattering matrix for
this probably good.

I'm not sure what we want to do
with this but we can calculate it.

So we haven't published this stuff yet

we've looked at finite length chains
where you can directly diagonalize

a matrix that arises associated with all
the couplings and you can see what what

the modes on a finite chain look like and
how they converge to the infinite chain.

We've looked at rings rings are
interesting because they're kind of like

remind us of people made electron
carousal a kind of nano optical corrals

we want to make resonators and then when
tennis or perhaps nano optical tracks.

And again we can calculate
all of the modes.

Exactly.

Again we don't have to talk
about what it means but

we can get all the information we want.

So the interesting thing
is some modes are bright.

OK where when the dipole moments are all
in phase and these structures the total

size is less and Landover to that's
a bright mode for this polarization.

OK for out of plain polarization all of
the modes all the dipoles are oscillating

in phase so you see here the dipoles if we
think about going around with a sine wave.

This is what we can think of
give it a mode label any quiz

one because there's one node in the XA
Taishan here is the ne zero No there's

no face change going around
all the other modes are dark.

So those bright modes
might be of interest for

nano antennas they
radiate very efficiently.

Everything's radiating constructively.

For the dark modes.

It's also interesting because those modes
have interesting nodal structure and

I know structures which may provide
a way to trap another dipole

either nanoparticle or molecular molecule.

So this may form the basis
of nano optical traps.

So that's about it.

So I know this talk was kind
of all theory in physics but

the point I want to make is that
understanding these aspects is absolutely

crucial to seeing what what's going on
into making functioning structures.

OK So just some specific conclusions
the optical propagation nanoparticle

chains involves the interplay of long and

short range coupling polarization
effects rate of decay and

disorder many other things the specific
dielectric constant of the metals.

Each Anyway she is severe but
there might be strategies for

its management namely using
again medium near by a nascent

understanding of the inner now coupling to
and from nanoparticle chains is emerging.

So we have some preliminary results there.

Nanoparticle rings might form subway
links optical resonators and antennas.

OK which might have all sorts
of applications outside kind of

the optical interconnect field.

One thing I didn't talk about was that
these rings can also form nano scale

lasers actually much smaller
than the Nano lasers that people

talk about form from photon
of crystal cavities.

So this is a very rich field both
from the State of the science and

the applications and in between so.

I hope that I've given you
some idea of what I do.

I'd be very happy to talk to you
further any of this is of interest.

Just let me know.

Send me an email not to my office door and
we can talk about a more.

So thank you very much.

Yes

yes.

Yeah.

If if they're not up well there are a
couple of things that can give rise to

involve higher multipole moments.

If the nanoparticles are not spare
recall then you're likely to

involve higher multiple moments.

Also if the nanoparticles
are very close together.

OK We know that

if you solve basically Maxwell's equations
you know that there are some regions of

extreme the large electromagnetic
fields kind of at place that look like.

Geometric singularities right
to describe those huge fields as

huge field gradients you need higher
most peoples to construct those fields.

So if the nano particles are very close or
if they're not spherical then you might

have to worry about other
multiple coupling Yes.

Yeah.

OK.

Right.

Right.

Right.
The efficiency of the optical X.

Taishan I mean.

I wish I remember the numbers
the efficiencies are not very good of

the scheme that I showed So I mean you may
have micro lots of terrorists coming out.

Milli watts of light coming in.

If you're lucky.

I mean that's kind of the absolute
best case scenario so

far a couple things I think that.

In terms of well the couple of different

things one is a visit to generate
post terrorists radiation.

OK while the frequency
doubling is to produce E.W.

terrorists radiation narrowband.

So this produces broadband pulse radio.

Ation.

The frequency multiplying basically
produces narrow band terror hurts

the other issue is that most of the work
on the frequency multiplication

even though it's sold as terror hurts
a lot of it doesn't really reach

the terror hurts so much above.

So I mean it kind of falls off
at several hundred gigahertz

I mean this really produces terror hurts
you know between you know basically D.C.

and one hundred terrorists or ten.

We're not one hundred ten
ten thirty terrorists.

People have generated up to so
I mean there are some differences.

This is not cheap either.

At least today you need to tie sapphire
laser people are trying to basically put

a fast solid state lasers in a box with
a photo conductor to bring down costs so

there may be some promise to
bring down the cost to say I know

ten thousand dollars or
twenty thousand dollars for these sources.

Yes And then Kevin next right.

Yes.

Basically the.

If you.

You know look at the dispersion curves and

the dispersion is in those
in those gray scale plots

basically built into their the shape of
the dispersion curves are quite different.

For the longitudinal mode the dispersion
starts at a low energy and

goes to high energy and for
transverse and height from high to low.

Also the bandwidth is different and

the physics that underlies that if you
think about a bunch of parallel dipoles

wanted to do we polarized the low energy
orientation is when they're all aligned.

Once you start to flip
dipoles you raise the energy.

Well that's what it means to increase
the weight vector from zero and

for transverse polarized well
when they're all lined up.

That's a high energy
citrate situation where.

Start flip them.

You reduce the energy.

OK so the shape of the dispersion
curves is different.

What happens when the dispersion curve
crosses the white line is very different

because for the longitudinal modes.

When they cross they they actually cross
the light line because they're no longer

to no free space photons are fuel photons.

But the transverse modes do very funny
things when they bump into the right line.

If you're interested I can talk to you.

One about that later but
the short answer is yes there

are big differences in
the shape of the dispersion.

Yes.

Right.

Yes

right

right.

Well

we can get an idea from looking
at something like this.

So the when it looks the width of this

extinction spectrum or
that one that's basically the band with.

So these gold nanoparticle structures
actually are operating at around.

So this is in the frequency I
think is around two Evie So

this is not where you want probably to
operate your actual interconnects But

the important thing to note
is that the bandwidth.

May look broad OK but
it is not that broad from

I think the signal the point
of view of sending signals.

So it depends upon how fast your signals.

You know you're doing two things
you're increasing speed he so

you need more bandwidth and
you're also making things smaller.

OK so there may be some tradeoff
there actually OK we can talk

more about specifically what that
might be but there is a tradeoff.

Yes.

Well I mean this is all
classical physics there's

not no quantum mechanics up my sleeve.

You know there's all classical physics.

So the thing is these waves are a mixture
between electromagnetic fields and

squashing electrons that's I threw
around this word pellagra time

class Montclair Han that's basically
a hybrid mode that's partially right.

Partially electron squashing class moms.

Now how much of each is important.

Depends upon the weight vector
where you're operating at right.

So well again I can I don't want to find
it's quite but it varies but the whole

point is that these are hybrid modes
between light and surface class months.

Thank you.