Okay Welcome to intro to photonics last week
we had been looking at ways of manipulating
light and with respect to that we started
with how does light propagate through a medium
and then went on to look at the using light
polarization manipulating light polarization
can we let us say for example change the intensity
of light and so that what looking at last
week and we said we can change the intensity
we can actually change the polarization of
light using anisotropic medium and while talking
about those.
we came up with this specific thing about
quarter wave plates and half wave plates and
I made a mistake hear I just pointed out by
the TA at the end of the last session, so
I said we are actually going to go through
a rotation this way but what will happen here
is you know we talked about the incident polarization
being like this into on and half-way plate
by theta but while propagating that through
the half way plate we said the EY component
is getting flipped.
So the EY component will you know show up
once it is flipped that the actual polarization
will show up here and this is basically 2
theta, so that is what we wanted to convey
but you know I did the mistake there in the
in the last session, so far we have been looking
at either extinguishing a polarization using
a polarizer or rotating the polarization or
changing the polarization state using a half
wave plate or a quarter wave plate there is
actually one more important application that
I want to touch upon before.
We move forward and that application is what
is called optical isolator, so question is
when you send light from a source let us say
laser you send this light and it gets into
some other components over here okay but some
of that light could actually get reflected
by those components and that reflected light
can potentially go into the source, so now
we have a cavity a laser cavity let us say
that is based on two mirrors and light is
going out of that cavity it hits some component
and then the reflection is coming back and
it gets coupled into the laser again.
So this is like an external cavity that is
getting developed, so now the properties of
the laser is only dependent on this cavity
but also what is happening you know outside
based on this reflection and that can change
a lot of things that can changes of course
the power that is emitted that can fluctuate
but it can also mean that there is fluctuation
in the wavelength at which light is emitted,
so this back reflection is back reflection
typically leads to power as well as spectral
instability of the laser.
So you need to essentially introduce a component
the output of your source such that it allows
light to get transmitted in one direction
but it should not allow light to comeback
so whatever component here it should block
whatever component coming back you know it
should block that, so that essentially means
that this component which will call as an
isolator will need to exhibit a non-reciprocal
response, so before we talk about on-reciprocal
response.
Let us just understand what reciprocity means
reciprocity means that you go from left to
right you have a certain response from this
component and that response should be the
same if you go from right to left the opposite
direction that is you are flipping the input
and output right flipping the input and output
if the responses is the same then you say
that component is reciprocal but that is not
what we want, we want to go from left to right
but we should not have light going from right
to left, so we need a non-reciprocal response.
So how can you achieve a non-reciprocal response
one way of achieving that is through what
is called the Faraday effect clearly it is
named after Michael Faraday who has a lot
of you know brilliant observations this is
one of those observations where in what he
observed is that when you look at response
of certain medium we try to characterize the
response of the medium based on your permittivity
that is what we are looking at last week in
the last weeks lecture but it so happens that
there is also a response in terms of changing
the polarization of light in the existence
of external magnetic field that response is
given by J epsilon naught gamma B cross E,
where B corresponds to the magnetic field
this case represented by the magnetic flux
density along the axis of the material.
So through this magneto gyration coefficient
this gamma is called 
the magneto gyration coefficient you have
a gyration of the light polarization in other
word if you have light polarization let us
say linear and going through this material
that polarization will be rotated by an angle
corresponding to theta and where theta is
given by minus pi times gamma over lambda
not N not B times L where B corresponds to
the magnitude of your magnetic flux density
along the axis of this material and L corresponds
to the length of this material itself.
So in the presence essentially what we are
saying in the presence of an external magnetic
field your light polarization which corresponds
to the electric field of your wave that polarization
is going to get rotated and how much it rotates
depends on the strength of the magnetic field
or the extent of the interaction length, now
this factor over here is denoted by what is
called the verdict constant, so it is theta
is just given by V multiplied by B multiplied
by L where we corresponds to the verdict constant
yes, so yeah so what is the significance of
this being imaginary thing it is basically
saying it is phase shift involved.
So that corresponds to E power J pi sort of
factor yeah, so this is in this case we are
assuming that the B is constant, so you can
assume or you can actually this would be a
good idea if B is not constant then you are
talking about possibly modulating that polarization
coming out of this material, so by modulating
B you can achieve modulation of the polarization
state I and it is also dependent on the sine
if B, so if the B is the opposite direction
the rotation will be in the opposite direction
so the question is can this be correspond
to another electromagnetic wave possibly you
can say I mean this just says that B cross.
So that other B can correspond to another
electromagnetic wave however the rate at which
this change happens the response of the medium
would tend to be much muted right, so the
we are not talking about the response time
it is highly unlikely that this will respond
to another electromagnetic wave at optical
frequencies that is was your question whether
it can respond to that and basically sorry,
so we are not actually quantifying the response
time corresponding to gamma, so that actually
is medium dependent, so I do not know of existence
of a material that responses optical frequencies
that does not mean that there is an end but
you know as far as I know it does not sorry
and I do not understand the question.
So the question is whether this can happen
in vacuum and answer is no this is actually
based on interaction with a material and that
material having a magnetic addition coefficient
corresponding to gamma and gamma is different
for different material jus the same way as
your relative permittivity is different for
different material gamma is different for
different material and a suspect gamma is
also dependent on frequency but the point
I want to make is that you could achieve this
now if this material was a black box you could
when you say your polarization is getting
rotated what could be in that black box what
else can you imagine can give you a rotation
of your polarization half wave plate.
A half wave plate could do that rotation but
in a half wave plate if you had done this
rotation and you flip which is the input and
output or rather you come back with this polarization
as the input you come in with this polarization
angle theta as input from the right side it
would have gone back to this linear polarization
in other word the half wave plate would have
been completely reciprocal in nature nut this
faraday effect is not reciprocal why because
the sine depends on which way the rotation
happens depends on B cross E in one case B
is oriented along the direction of propagation
the other case of B is oriented at you know
against the direction of propagation.
So the rotation would have been in the other
direction then what happening in there, so
in this case for faraday effect in the this
magnetic gyration effect you would have gone
out if you came in with that polarization
you would have gone out with two theta as
your polarization of light that is going in
this toward the left direction, so this is
actually the because of the non-reciprocal
nature of this faraday effect yes that is
a question sorry if we put right-right that
direction is, so the question is if we had
another rod like this after this output after
it is rotated by theta it would have gone
to theta again.
So that is right so it is going two theta
in this case we are looking at it from a perspective
of building an isolator, so the question is
can we use this we are not talking about just
getting rotation if you want to get just rotation
theta to theta whatever you would have young
usually just used a half wave plate and achieve
that rotation orientation of the magnetic
field with respect to the electric field yes
so if I had another crystal after this and
in that crystal let us say the B is in the
opposite direction and of the same magnitude
both the crystal are you know the same material
in the same length then it would have gone
back to the original polarization exactly
but now we are talking about the reflected
light.
So reflected light going from right to left
that reflected light would have gone to two
theta because of this non reciprocal nature
if it was a reciprocal deice it would have
gone back to the original polarization itself,
so how would you build an isolator based on
this effect that is simple right so you can
basically put a polarizer which allows only
this polarization, so that is how you got
this output polarization like this but that
polarizer if the theta, so if this theta is
45 degrees so you have rotated you r polarization
by 45 degrees going from left to right but
coming back it would have rotated 90 degrees,
90 degrees with respect to the original polarization
and then when that goes into the polarizer
what happens that would have been absorbed.
So you would not have any light going in this
direction, so you had light going this way
go through that you material go through theta
equals to 45 degrees and go through any back
reflection but that back reflection while
going back would have been rotated such that
two theta is 90 degrees and then it is going
across this polarizer which would polarizer
would have blocked that orthogonal polarizer,
so this entire device now consisting of a
polarizer followed by this faraday material
or a material which has this gamma the magnetic
gyration that would have together work like
an isolator.
So the question is yes the would this would
work only if theta is 45 degree yes to get
maximum isolation you need to have theta set
at 45 degree and there is there is something
very important about this we go back and look
at the verdict constant, the verdict constant
is inversely proportional to lambda the wavelength
of the light that is going through, so the
faraday isolator this that is what this device
would be called faraday isolator for a one
wavelength will not provide the same isolation
at some other wavelength because for some
wavelength theta would not be 45 degrees and
you would have to go through Malice law essentially
to determine how much light is actually going
through.
So it would not work as perfect isolator now
this isolator typically provides you isolation
of up to 25 30 DB with the typical number
meaning only 0.1 percent of the light that
is going in the forward direction is going
back into the going back in the reverse direction
that is good for most cases but if you have
a high power source let us say you know 100
watt source under what source 0.1 percent
of it still 100 milliwatts, so 100 milliwatts
may be lot of power to you know handle at
your original source so certain application
require you to have 50 or 60 DB isolation.
So what would you do you can cascade to two
of these things and of course when you cascaded
you have to be careful that the polarization
alignment is taken care of the second polarizer
is alignment at 45 degrees it is a question
there yeah, so the reflection that is true
the assumption here is that the reflection
is not changing the polarization state right
but normally it does not but yeah if you have
some anisotropic response on the other side
then this will not work however in those sort
of conditions I did not mean to talk about
this very much but since there is a question
I will just mention this.
So this a principle for what is called a polarization
sensitive isolator it is called polarization
sensitive also because of the fact that only
if you have polarize light you have maximum
throughput right only a polarize light matching
the input polarizer then you have maximum
throughput if you put circular polarization
for example coming in that polarizer right
up front would have taken out one of the polarization
components, so half the power would be lost
right at the polarizer the front end itself.
So then that sort of thing would be lossy
so what you would need in that case is a polarization
insensitive isolator I did not actually expects
so many questions in this topic I am glad
I am getting those many question because that
means that you guys are really getting into
this topic of showing interest in this talk
so keep them coming, so you could have a polarization
insensitive isolator which basically says
okay I will spit my polarization such that
my vertical polarization goes that way my
horizontal polarization goes this way and
then I would have a mirror here and then go
through this then I go through my faraday
rotation material and then I go through.
So this is my FR material which is rotating
this polarization by 45 degrees and then I
would go through a half way plate the half
way plate would rotate the input polarization
it set such that rotating the input polarization
by further 90 degrees why that is needed is
because of this particular configuration that
we have, so you put another polarization splitter
here so the polarization splitter what it
does is it any horizontal polarization it
reflects any vertical polarization it transmits,
so both these polarization will go together
the same.
So here my input can be any arbitrary polarization
consisting of booth X and Y components that
polarization will be preserved as it propagates
through this structure and similarly any arbitrary
polarization coming back is going to go through
this polarization you know this what is called
the polarization diversity configuration because
it separate out the two orthogonal polarization
the part for the two orthogonal polarization
but it effectively will end up blocking the
wave just as we talked about.
So in this case you could have some other
arbitrary polarization coming in as well but
you know you could find a way of you know
extinguishing that providing isolation for
that so that is a polarization insensitive
isolator, so just to give you a clearer picture
here so this is 45 degrees but after going
through the half wave plate it would have
been this horizontal polarization so vertical
is becoming horizontal and when you trace
your way back this horizontal would have gone
back to 45 but after going through the faraday
rotation it would have been 90 degree at 90
degrees this polarization beam splitter will
reflect we get the beam splitter is such that
it is reflecting horizontal polarization.
So when coming back it would have been 90
degrees and that would have been reflected
over there, so it is not going back to the
source, so some of you may not be following
this polarization insensitive scheme and I
can questions on that separately but it is
okay if you do not follow that if you understand
this polarization sensitive isolator that
is all I wanted to convey to you today that
is right, so it is actually so look at it
this way normally if it is a reciprocal device
it would have gone back to the original polarization
and in this case it is non-reciprocal that
means it is going in the opposite direction
because of the orientation of the magnetic
field with respect to the incoming polarization.
The magnetic field is reversed yes okay do
not go so much into the orientation yes but
just think about it as this way right so in
one case if it was reciprocal it would have
actually given you the original polarization
itself and in this case because the magnetic
field is opposite because my electric field
are the incoming wave is in this direction
but magnetic field is in this direction because
of that it is going in the opposite direction
the polarization is that is essentially the
non-reciprocal effect there is a very fine
point over here when we talk about a polarization
insensitive isolator we are talking about
light not going back towards the source.
So we are blocking this light but we are actually
having light go into that other direction,
so there is an opportunity to pick up that
light and use it also or in other words maybe
your intention is to go from port 1 to port
2 but anything from port 2 you actually want
to extract from port 3 does that remind you
of something that you have come across that
is the functionality of a circulator, so a
polarization insensitive isolator can actually
be modified to provide you the circulator
functionality as well so you can extract a
light coming back from the other direction
so you can do one to two but anything coming
from two goes into three.
So already out of time I actually wanted to
go into different topic but that is fine we
can meet on Wednesday and then we will talk
about, so where we are going with this so
far all this is still very much linear response
from the material but what we will deal with
in the next lecture is what if the material
responds in a nonlinear fashion one key point
there is as long as you have linear response
whatever your incoming frequency is the same
frequency will go out okay for any linear
respond material whatever is the excitation
frequency the output frequency will be the
same but when we go to nonlinear response
you have an opportunity of changing that frequency
so the outgoing frequency may not be the same
as incoming frequency, so those aspects we
will discuss in more detail in the next lecture.
