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SHAOUL EZEKIEL: In this demo, we're
going to show how we can rotate the plane of polarization
of light using a half-wave plate.
We're going to use this setup.
We have a helium neon laser.
You can see the output of the laser is here.
And then we're going to reflect the laser off this mirror
and then reflect it again off this mirror,
pass it through this polarizer here, and then let
the light fall onto the screen.
The polarizer here establishes the state
of polarization of light, regardless
of what the state was before.
And the little arrow here is the axis, the transmission axis,
of the polarizer.
So the light here is then--
the polarization of it is established by the transmission
axis of this polarizer.
Now, before we rotate the plane of polarization,
we want to first analyze the state of polarization
of the light.
So we have a means of checking on what we're doing
to the state of polarization.
We do this.
We do this with this polarizer acting so-called analyzer.
Again, the arrow labels the transmission axis
of this polarizer.
And, to establish that indeed the polarization coming in
of the light is plane-polarized, we
get a null when the arrow is in the horizontal direction, which
means that the light coming in is plane-polarized
and, also, that its axis, its axis, polarization axis,
is perpendicular to the horizontal, which
means it's along the vertical.
So now, if we look on the screen,
we can get maximum transmission around vertical
and close to zero around horizontal.
So now we've established the plane of polarization
of the light here.
Now we would like to rotate the plane of polarization
using a half-wave plate.
Here is the half-wave plate, which we now
will place right in here.
And, as we know, half-wave plates have two principal axes.
And, if the light propagates along either principal axis,
the polarization of the light is unaffected.
That means there's no rotation of the plane of polarization.
So let's check on that.
Let's first place this arrow, which
is lined up with one of the principal axes
of the half-wave plate, and let's check,
indeed, with the analyzer that, indeed, that the polarization
is not rotated when we are aligned
along the principal axis.
Again, let's rotate it to find null, and here is null.
And you can see that null is, again,
when the arrow of the analyzer shows horizontal,
which means that the plane of polarization
is really vertical.
Now let's check-- while we're here,
let's check on the other propagation
along the other principal axis, which is 90 degrees away
from this one.
So let's go find horizontal.
Let's say it's around here.
Let's check again where null is.
And you can see that null is again in the same place
when the analyzer is showing horizontal, which again means
that the plane of polarization is in the vertical direction.
All right, so we established that there's no rotation
when propagating along the two principal axes
of the half-wave plate.
Now let's demonstrate rotation of the polarization using
this half-wave plate.
So let me now set it at let's say around 45 degrees
or so with respect to the vertical axis.
Let's now go to the analyzer and see
what happened to the state of polarization.
Again, let's track the null.
And I'll keep rotating the analyzer until I find null.
Here it is.
Here it comes.
Here's null.
Now what does that mean?
It means that the light here after the half-wave plate
is plane-polarized and that, indeed,
the plane of polarization is along the horizontal direction
because the block axis or the null axis is vertical.
So it means that we've rotated the plane of polarization
from the original one, which was along here,
to the horizontal one, which means by 90 degrees,
using the half-wave plate.
So the thing that you want to notice
is that, when the half-wave plate is rotated by 45 degrees,
the polarization, the state of polarization,
is-- the plane of polarization is rotated by twice that,
by 90 degrees.
And the interesting thing about the half-wave plate,
using a half-wave plate, is that the peak intensity--
and now let me get the peak intensity here.
The peak intensity does not drop with rotation or polarization.
For example, if I decide to rotate by a smaller amount,
like this, again, let's establish
the state of polarization.
Again, null now is no longer pointing below,
but is pointing at this angle here,
which means that the plane of polarization is different.
And then we go see what the peak value of the transmitted light
is, which is around here somewhere.
And you can see that the peak value has not dropped.
So the conclusion of this is that a half-wave plate
or at least a good half-wave plate
can rotate the plane of polarization
from 0 to 90 degrees without any loss of intensity.