Ok, welcome to yet another session of introduction
to photonics during the last couple of sessions
we would been trying to get into this learning
outcome of identifying the fundamental principles
of photon optics and quantifying photon properties
and to understand that it was essential that
we introduce light as electromagnetic waves.
So if I go back and look at where we all where
we started this all you know ray optics, wave
optics and last couple of lectures we have
been looking at light propagation as electromagnetic
waves.
Now what we will do for today is session is
actually consider light to be propagating
as particles, ok these quantized electromagnetic
waves that are known as photons, ok.
So let us try to see what this is all about,
the basis for a lot of this discussion came
about when Max Planck was conducting his research
that was to solve this problem of blackbody
radiation when I say blackbody radiation what
comes to your mind? What is blackbody radiation?
Can you give any example of blackbody radiation?
Student is answering: (())(01:54)
The black holes more simply the light from
the stars, closest star that we have?
Student is answering: Sun
Sun, so when we are looking at Suns radiation
we can consider that as blackbody radiation.
So Planck was actually looking at blackbody
radiation and around 1900 when he was trying
to explain blackbody radiation, he figured
that light must be emitted as or this blackbody
radiation must be coming out as quantized
electromagnetic waves. So essentially he was
figuring that light is emitted when an atom
or more specifically an electron actually
jumps from a higher energy level to a lower
energy level when that happens he said you
have this quantized electromagnetic wave packets
that are emitted, ok.
So this electromagnetic wave packet he said
this is one of those fundamental you know
explanation for how we view blackbody radiation,
so as you know blackbody radiation is something
that could be spread over a spectrum, right
and one of the simplest things of explaining
that is by considering an hot object, so when
an object is heated to very high temperatures
it could emit light where do we use this principle
for our lamps, incandescent lamps you know
the light bulbs we do not see those light
bulbs anymore, it used to be like a tungsten
filament that is when you pass current through
that it gets really hot and when you heat
it up we know that we can get light, right
from that.
So to explain some of those things Planck
actually came up with this suggestion that
there is there this emission is actually quantized,
right. So quantized wave packets and Einstein
followed it up, right so he is actually trying
to piece together another puzzle which was
quite you know it was attracting lot of attention
at that time. Einstein was trying to explain
photoelectric emission, right so what is photoelectric
emission? Know somebody had projected that
when light actually falls on some material
consisting of all these atoms molecules, right.
And if you have in light of a certain kind,
right for example if you have ultraviolet
light the observation was that with that sort
of light you could get electrons emitted from
this material, ok. So that is what is called
photo electric emission and so that was an
unsolved puzzle at that particular time and
Einstein looked at this and said as that is
quite amazing actually 1905 it is a really
famous year because Einstein came up with
this for papers which spew out for different
areas of research, ok.
So this is one of those for the photoelectric
emission equal to m c square that came out
of that year theory of relativity came out
of one of those papers that year and explanation
of Brownian motion was also or done in another
paper that, yes. So four papers and you know
decades of research following those papers,
so that is just amazing, right. So that is
why we worship Einstein when we think about
scientists but this was one of those things
and what he basically said was that if this
was happening he pieced together what Planck
had already said it is happening in a quantized
manner.
So he said this has to be light must have
quantized energy wave packets with E equal
to h nu where h quite rightly he called it
as a Planck is constant because without Planck
coming up with that previous observation he
could not have possibly come up with this
and new corresponds to the frequency of light,
ok. So now the entire scenario changes quite
a bit now so far you know I want you to think
about this as if you are in around 1900 all
you know about light is that light travels
as waves, right and of course Maxwell came
up with this fantastic observation that light
can travel as electromagnetic waves, right.
And that is what people knew off and then
Einstein came up and says no light actually
travels as photons, ok so that was like completely
disrupting the entire picture and then people
are really stunned right and they are wondering
this guy is pulling a fast one on us, right
this cannot be true can it explain this can
it explain that and so on, right so many of
those questions were raised and as we know
now most of those questions have been answered
and this hypothesis at that time is now something
that we consider as you know is a real thing
but just to illustrate one of those you know
answering one of those questions let us go
back and look at this video, ok.
Let us observe this video for a while and
then we will go back and replay that and try
to see this in a little more detail, let us
see this video. So first we are considering
a particle we are not telling what sort of
particle it is, it is just some small balls
that are bouncing around and they bounce around
this interface and then you saw that picture
what it creates and now it is a wave, right
and this is the you can say is the Young’s
double slit experiment we know what is supposed
to happen, right so it's supposed to create
these interference fringes.
And now we are looking at a quantized object,
so it can be looked upon as a particle but
it has wave like properties, right so when
you observe it is a (pro) particle but this
particle actually is exhibiting wave-like
property. So let us go back and look at that
once more. So when you observe that is observation
screen you observe it as a particle but if
you have multiple observations quite interestingly
all these particles start making a pattern,
it is a very fairly well defined pattern,
just as the case of the wave, ok.
So what else what exactly is happening if
I go back and look at this picture, right
it is emitted as a quantum particle, ok but
see how it is that quantum particle has got
a certain wave associated with it from electromagnetic
Theory you can think of this as some electric
and magnetic field is carrying it is going
as an electromagnetic wave, ok. It is a particle
but it is got this electromagnetic wave that
is associated with this propagation and because
of that now you are seeing you know this interference
effects because when you put a slit when you
put a couple of slits between them then the
secondary wave fronts now start interacting
with each other and then it gives rise to
this you know interference pattern which actually
shows up as bunch of particles falling in
different places, ok.
Now this is actually an advanced topic but
just to complete the video let us go ahead
and try to do this, ok. So what we have here
is this person that is observing this wave
like property, right. So there that eye is
the eye of the observer, in this case it could
be a camera, right that is trying to observe
what is happening 
and so what do we see there no interference
pattern, no wave like property.
So why is that happening the process of observation?
What does that mean? If I am observing something
an event related to light I am observing a
photon, right so if I am observing a photon,
if I am detecting a photon then it (exen)
essentially collapses this particle nature
of light rather it loses it is wave nature
of light, right and then (bef) from that point
onwards it is actually just propagating as
a particle.
If I am observing I am actually intercepting,
intercepting the photon, ok. So of course
you would ask that if I am intercepting the
photon then that photon cannot go past that
slit, right so that is what is that so that
particular photon is lost, it is already collapsed
in that observation process, ok but the you
know principle that is explained beyond that
is that photon might have collapsed but other
photons are coming up, right but just the
fact that you have an observation and that
observation is loaded on one side, right.
So it is actually starting to disturb this
wave function that corresponds to the photon,
right once is disturbed that wave function
then it cannot proceed further with a wave
like property, ok. So then it just goes has
some random particle that is bouncing around,
ok. So of course this is a fairly like I said
the advanced concept that I do not expect
most of you to get right away but nevertheless
I think that the takeaway point from here
is more of this, right.
So you can have emission of photons coming
up and this emission if we go back and look
at the case of an incandescent lamp right
we know you heat up that filament, it emits
photons ok and what Planck said was that is
actually quantized particles that is not just
some wave that is generated, right it is actually
quantized particles that I emitted and quite
interestingly depending upon the temperature
of that blackbody it can emit multiple colours
of photons, nu is not specific to one transition
you could have multiple transitions if we
go back and look at this picture that we have
here this could be multiple transitions, right
so you could have multiple energy levels and
you could have multiple transitions of different
colours with different energies, right.
So that is what we were seeing there and said
that explains why an incandescent lamp looks
yellowish, ok but it has got yellow, orange,
red, spectral colours, a little bit of green
also maybe, right. If you heat it up further
so we are not able to heat it up normal in
you know tungsten filament much more we not
allowed to heat it up but if you heat it up
further can you imagine what is happening
what colour would it look like? Would it still
remain yellow or would it be some other colour?
So you would have maybe more number of colours
but would it look a yellowish or would it
look something else?
So what are you doing when you are heating
up and a material you are building thermal
energy, right? Thermal energy 
is quantified by K b T where K b is the Boltz,
Boltzmann constant, right multiplied by T.
So when you have higher temperatures you have
higher thermal energies and because of that
what happens you have building up of electrons
at higher energy levels, ok and due to which
what sort of photons do you emit? If my energy
gap is really large, you can now have higher
energy photons, higher energy means higher
frequency and higher frequency mean is what
is what in wavelength.
Student is answering: Shorter wavelength.
Shorter wavelength, so if it is a yellowish
at a particular temperature if I increase
the temperature what is it going to look like?
Student is answering: Closer towards the blue
Closer towards the blue, right maybe it will
start looking greenish and then bluish and
so on, right so that is what we are talking
about here. So key thing is you know Einstein
actually took something that Planck had done
and then applied it to some other long standing
problem and then said you know light consists
of photons, ok. So light can be characterized
like propagation can be characterized as you
know as propagation of these particles known
as photons but the key thing that we realized
through this you know just this video that
we saw what is it show? It basically says
light or these photons exhibit wave particle
(dude) duality, right.
So it can be thinking it can be characterized
from the emission perspective it can be characterized
as emission between two energy levels, right
and so a mission of quantized electromagnetic
wave packet which we are calling as a photon
but that photon has wave like properties just
because that electromagnetic feels that correspond
to that photon are extending in the transverse
direction, ok. So with this sort of a picture
let us now see what should be the properties
of the photon, ok.
So let us go ahead and try to look at this
in a little more detail, so we said E equals
to h nu, so to really understand what this
means let us actually draw the electromagnetic
spectrum and see how energy frequency and
wavelength because if E is equal to h nu this
can be right written as h c over lambda, right
where c is the velocity of light in vacuum
and if conversely if you are trying to find
value of wavelength, wavelength in say in
micrometer lambda can be written as since
h and c are constants, h corresponds to a
value of 6 point 6 3 into 10 power minus 34
joule seconds and c corresponds to 3 into
10 power 8 approximately 3 into 10 power 8
meters per second, the actual values to 2
point 999 and 8 something, ok but we approximated
3 into 10 power 8.
So since those are constants lambda can be
expressed as 1 point 24 over the energy when
the energy is expressed in electron volts,
ok. So as far as the Planck constant is concerned
we are using unit of joule seconds, so we
are clearly the energy is expressed in terms
of joules and here we are expressing energy
in electron volts, so what does one electron
volt correspond to?
Student is answering: 1 point 602
1 point 602 and 10 power minus 19 joules,
right. So just make sure you are comfortable
with these different units, ok. So let us
look at how these what these correspond to
let us say this is new it is in frequency
in Hertz, so we are going from 10 power 15
to 10 power 14, 10 power 13, 10 power 12,
11 power 10, 10 power 9, 10 power 9 is what
we typically deal with, right. What is happening
around 10 power 9 hertz around a gigahertz,
your mobile communication right that has a
carrier frequency of 10 power 9 hertz but
yes you know expanding the scale all the way
to 10 power 15 and let us actually also represent
the wavelength lambda, right.
So this corresponds to it is point one micron
or hundred nanometers and somewhere over here
it is one micron here is 10 micron, 100 and
then we get to the millimeter waves, one millimetre,
10 millimeter and 100 millimeter and then
if we look at energy scale of course that
is also going this way that is E expressed
in electron volts, so 10 power 15 would correspond
to a boat or one actually the scale is like
this one micron, let us say is our reference
one micron corresponds to roughly about one
electron volt, right.
So if lambda equal to 1 micron then that corresponds
to 1 point 24 electron volt, so one is somewhere
over here so this is going towards 10 electron
volt and so on, so one and then this is point
1, this is point 01 this corresponds to point
001 and so on, right. So in energy we are
going down in energy as we go down in terms
of frequency clearly, right. So to give you
a feel for what we are dealing with normally
we have basically blue happening over here
and red happening over here, so blue wavelength
around you know point 45 less than point 5
microns and red greater than point 6 microns,
ok.
So the visible region happens over here and
in the visible region the corresponding frequency
is in the order of 10 power 15 hertz or hundreds
of terahertz and the corresponding energy
is you know going towards as we go to ultraviolet
region you have higher and higher energy lower
wavelength but higher energy so it is not
surprising that when in the photoelectric
effect was first looked upon they used ultraviolet
radiation and they were able to see these
electrons coming off, right. So clearly that
radiation corresponds to fairly high energy,
ok.
So we understand photon energy, ok so while
we look at it what about photon momentum?
What about what are the mass? Let us the photon
have a mass associated with this, it is an
electromagnetic wave, ok. So photons have
zero rest mass, so you cannot like catch a
photon and weigh it, right so photons have
zero rest mass but it does carry momentum
so when we look at photon momentum so that
is going to be equal to is given by energy
over c which can be written as h over sorry
h over lambda and that can be written as h
cross multiplied by k, right k is the is the
wave vector 2 pi over wave number, 2 pi over
lambda and h cross is nothing but h over 2
pi, right.
So photons have zero rest mass but it can
carry momentum in other words if a bunch of
photons are illuminating a surface you could
have certain energy imparted on the surface,
ok so that is what we call as radiation pressure,
we will not go into the details right now
but basic point is that the photon can carry
momentum. We will come back and qualify this
in a little more detail in a few minutes but
let us just move on with this picture for
now, ok.
And then there is this question of probability
of finding a photon, so you know we say that
photons can be emitted at different time scales
and in different directions and so on, so
what is the probability of finding a photon?
So photon probability is such that if you
say probability of finding a photon at a particular
location are, right so p 
of r over some unit area is actually proportional
to the intensity of light in that location,
ok.
So essentially it says that if you have higher
intensity then there is a you know higher
probability of finding a photon there. So
let me just explain that insert a new page,
ok.
So let us just look at this, so in our previous
lecture we looked at Gaussian beams, right.
So you have laser, right which is emitting
it is a plane waves and we said when we look
at the intensity in the transverse direction
that is the transverse plane, transverse to
the direction of propagation that intensity
was 
you know for a perfect light source with only
the fundamental transverse mode operating,
so that would have looked like a Gaussian
function, right.
Now in terms of photon probabilities what
are we saying? We are saying that the intensity
is high than this corresponds to a high probability
of finding a photon and similarly this region
represents a low probability of finding a
photon, ok. So that actually explains some
of the randomness associated with light, now
we are starting to talk about finding a photon
in terms of probabilities, ok.
So the classical measure of light has been
the light intensity, so now what we are saying
is based on that measure if you look at you
know the photons we will find that certain
regions where there is high larger intensity
of light you have better probability of finding
a photon and if you extend that to something
that we did earlier into a Young’s double
slit experiment and we said, ok the Young's
double-slit experiment what we expect to see
in the far field is some intensity pattern
like this of constructive and destructive
interference over there and what we are saying
here is this high intensity, if you say that
the intensity is increasing this way manner
here we have a high probability of finding
a photon, ok and similarly this is indicative
of low probability of finding a photon, right.
So that actually you know reverts back to
this picture over here so clearly we see that
in this picture you have certain regions where
you can the photons are denser, you know when
you and you have large number of observations
of course if you make much many more number
of observations you will find that these bands
are very (niar nea) nicely formed but that
just corresponds to the fact that you have
high probability of finding a photon, you
have low probability of finding a photon in
other areas and there is it is not like there
is zero probability, right.
So you always say high and low but you could
always find one of these photons showing up
in the so called dark band so unless it is
absolute zero intensity you cannot rule out
the possibility probability of finding a photon
there. So the question is you know the total
probability does it correspond to one, so
we will just go back and look at the issue
of what you already experienced previously
which is 50, 50 beam splitter, so 50 percent
of the light goes here, 50 percent of the
light goes here and what we are saying is
in terms of photon probabilities if you have
one photon 50 percent, we are not splitting
a photon by the way, ok it is got 50 percent
probability of going one way and 50 percent
the other way, right.
So what that means is if you have multiple
observations you will find 50 percent of the
photons have ended up there, 50 percent of
photon other, 50 percent has ended up here.
So the question is if the total intensity
is so it is, so first of all we are saying
that probability is proportional to that intensity,
if the total intensity is not conserved is
the photon probability conserved actually
that is a hypothetical situation because the
intensity if you have a certain intensity
you either have reflection, refraction, scattering,
absorption but you have to account for all
that intensity, right.
So as long as energy is conserved we are saying,
ok the photon probabilities need to be adding
up to 1, right so we are not introducing anything
new here, ok. So in terms of finding a photon
we are saying that it is a probabilistic event
and from that perspective this actually leads
to this other principle which is called photon
uncertainty, ok just like in quantum mechanics
you have an uncertainty principle what is
the uncertainty principle?
Student is answering: (())(40:52)
Heisenberg’s uncertainty principle which
states that the error the uncertainty in finding
the momentum multiplied by the uncertainty
in finding the position is at least h bar
over 2, right. So similarly the photons have
an uncertainty associated with them that is
the r m s error the root mean square error
in finding an a energy of the photon multiplied
by the r m s error in determining the time
at which photons there at a particular point
that is got to be greater than h bar h cross
over 2, h crosses basically h over 2 pi, right.
So what does this mean? What is the implication
of this? And this is something that we have
already in certain ways seen also, ok. So
what is this photon uncertainty mean? Lake
let us take the example of 
a single frequency, so monochromatic source,
ok. So you have a if you have a monochromatic
source let us call this new, right. so it
has it is a single frequency source, so if
there is something called a single frequency
source the uncertainty associated with determining
that frequency goes to zero, ok.
But in time what is this represent? When can
you tell through observation in time that
you have a monochromatic source? if you are
observing it with time, so if it is characterized
by a periodic waveform then you say that is
monochromatic but to absolutely say this sources
monochromatic at all times you essentially
have to make an infinite observation, in this
case unless you can go to an infinite observation
you cannot characterize this as a monochromatic
source, right.
So if your uncertainty in frequency goes to
zero the uncertainty in time goes to infinity,
ok so that is what we are talking about as
far as the photon uncertainty is concerned,
of course you can play the other way also
you could have a source which actually exhibits
you know polychromatism and then you essentially
take a sample of that and you look at it in
frequency space you would find that it has
got multiple frequencies, ok which is something
that we already saw from perspective of this
Wiener-Khinchin theorem, we were saying that
you know we were saying there we were saying
in more in terms of the power spectral density
and an autocorrelation but here what we are
saying is for a for a polychromatic source
if you take a sample of that wave front and
look at it in some sample of that wave in
time and we look at the frequency content
it will have multiple frequency content, right.
So this photon uncertainty is once again saying
that, ok what we are dealing with is a quantum
particle, right. So it exhibits all this quantum
natures that you associate as we have seen
in quantum mechanics, ok but here we are talking
more in terms of energy and time determination,
ok. Where of course energy is related to frequency
so it is basically frequency and time relationship
and what we are looking at talking of time
I think we run out of time now so let us stop
here and we will continue from this in the
next lecture.
