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SHAOUL EZEKIEL: Now we're ready to look
at the state of polarization of the transmitted
and reflected beams on a glass-air interface
as a function of the input polarization of the light
and also as a function of the input angle of incidence.
The setup is here is the laser.
The laser beam we reflected by this mirror
into this quarter-wave plate.
So we have here, we have circularly polarized light.
Then we pass it through the polarizer here.
So in this region, we have plane polarized light.
And the polarization is set by the transmission
axis of this polarizer.
Here's our prism.
Here is the transmitted beam over here.
And here is the reflected beam over here.
Now, just to make sure that, indeed, in this region here
we have plane polarized light incident at the prism,
we will take this polarizer and test that, indeed, the light is
plane polarized in this region.
In a way, we're checking on this polarizer.
So let me put a screen over here so we can see the light.
So now, if indeed the light is plane polarized,
then I should be able to extinguish it
by simply rotating the transmission
axis of the polarizer here.
And here, indeed, you can see that I
can extinguish the light.
So indeed, the light is plane polarized.
I now will change the transmission axis
of this polarizer, let's say, to some angle here
and then again check that, indeed, I can extinguish
the light again at this angle.
Let me go back over here.
And yes, indeed, I can extinguish it
And you can see that there is 90 degrees between this polarizer
and this polarizer.
So now we're happy that the light is, indeed,
plane polarized in this region regardless
of where I set the transmission axis of the polarizer.
Let me put it back to vertical.
We'll take this polarizer out, take the screen.
Now we're ready to study the state of polarization
of the transmitted beam and the reflected beam.
First, we start with the transmitted beam.
So I'm going to place the polarizer
in the way of the transmitted beam like this.
And with the state of polarization coming in
along the vertical plane, as shown here,
I'm now going to demonstrate that the light transmitted
is indeed plane polarized.
And, as you can see, I can extinguish it
with this polarizer here, which means the state of polarization
is linear and also perpendicular to this horizontal axis.
Now I will change the state of polarization of the input beam,
let's say to some angle like this.
And now let me see if I can extinguish it again.
Yes indeed, I can extinguish it again.
And you also notice that the angle here is
orthogonal to the angle here.
So we've shown that the state of polarization
of the transmitted beam is indeed
plane polarized regardless of the orientation
of the transmission axis of the polarizer here.
Now we're going to look at the state of polarization
of the reflected beam.
So now I'll put the polarizer here
in the way of the reflected beam then adjust the reflected beam
to go through the polarizer.
And let's see again with the polarization at this angle,
with the input polarization at this angle.
Let me now rotate the analyzing polarizer here
to see whether, indeed, I can--
first let me transmit the maximum amount of light.
Let me see now if I can extinguish it.
And indeed, I can, which shows that for this orientation
of the transmission axis of the input polarizer, indeed
I have plane polarized light.
Let me check it for vertical polarization.
And indeed, I can extinguish it here too.
And I'll do one more of the horizontal polarization,
about so.
And let me see if I extinguish that.
And indeed, I can extinguish the light.
So again, we've shown that the state of polarization
of the reflected beam is plane polarized, again regardless
of the orientation of the transmission
axis of this polarizer.
Now we're ready to look at the state of polarization
of the reflected beam after the critical angle or the totally
internally reflected beam.
But first, I'd like to convince you
that we are looking at the totally internally reflected
beam.
So let's look at the setup again.
This is the transmitted beam.
And this is the reflected beam for any angle of incidence
below the critical angle.
So as I increase the angle of incidence
until I reach the critical angle,
you can see that the transmitted beam is extinguished.
And all we have left is the reflected beam.
So from here on, this is the totally internally
reflected beam.
So I'm going to now adjust the angle of incidence
to about 50 degrees or so this direction.
And now I'll place the polarizer in the way
to analyze the state of polarization of the totally
internally reflected beam.
Now, the input polarization is--
p polarization, or polarization in the horizontal plane,
is set by this polarizer.
Let's see what the state of polarization
is of the totally internally reflected beam.
And you can see that, indeed, I can extinguish the light, which
means that for p polarization input,
the polarization of the reflected beam or the totally
internally reflected beam is plane polarized,
and indeed, also p polarization.
Now let's go to s polarization.
It means polarization in the vertical plane.
So we are here about vertical.
Let me now adjust the analyzer here
to see whether I can extinguish the beam again.
Let me do a little more tweaking.
Just a little bit more, and indeed, you
can see that I can extinguish the beam again.
This again says that for polarization
in the vertical plane or s polarization, the polarization
of the totally internally reflected beam is also s
polarization, also linear polarized and s polarization.
Now let me go away from s or p polarization
by changing the angle of the transmission
axis of the polarizer, which means what I'm doing
is changing the orientation of the plane of polarization
of the input b.
Now let's see if we can extinguish the beam.
As you can see, the intensity varies
as I rotate the polarizer.
But I cannot extinguish it like I did before.
This implies that there is a phase shift between the s and p
polarizations in the totally internally reflected beam.
In fact, let me change the input orientation
to about 45 degrees.
And indeed, again, I cannot extinguish the beam.
And this, again, implies that the state of polarization
of the totally internally reflected beam
for this kind of orientation of the polarization of the input
beam, that indeed, the totally internally
reflected beam is elliptically polarized.
And this elliptical polarization can be made use of.
For example, for a 50 degree angle of incidence,
one can get a phase difference between s
and p polarization of about 50 degrees.
This phase shift, then, is very interesting
and has been exploited for the construction
of quarter-wave plates and half-wave plates
simply by taking advantage of this phase shift
on reflection on a glass-air interface.
For example, a quarter-wave plate
requires two such reflections to make up 90 degrees.
And a half-wave plate requires four such reflections.