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SHAOUL EZEKIEL: In
this demo, we're

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going to show how we can rotate
the plane of polarization

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of light using a
half-wave plate.

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We're going to use this setup.

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We have a helium neon laser.

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You can see the output
of the laser is here.

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And then we're going to reflect
the laser off this mirror

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and then reflect it
again off this mirror,

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pass it through this
polarizer here, and then let

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the light fall onto the screen.

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The polarizer here
establishes the state

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of polarization of
light, regardless

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of what the state was before.

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And the little arrow here is
the axis, the transmission axis,

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of the polarizer.

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So the light here is then--

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the polarization of it is
established by the transmission

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axis of this polarizer.

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Now, before we rotate the
plane of polarization,

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we want to first analyze
the state of polarization

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of the light.

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So we have a means of
checking on what we're doing

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to the state of polarization.

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We do this.

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We do this with this polarizer
acting so-called analyzer.

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Again, the arrow labels
the transmission axis

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of this polarizer.

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And, to establish that indeed
the polarization coming in

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of the light is
plane-polarized, we

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get a null when the arrow is in
the horizontal direction, which

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means that the light coming
in is plane-polarized

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and, also, that its axis,
its axis, polarization axis,

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is perpendicular to
the horizontal, which

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means it's along the vertical.

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So now, if we look
on the screen,

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we can get maximum
transmission around vertical

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and close to zero
around horizontal.

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So now we've established
the plane of polarization

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of the light here.

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Now we would like to rotate
the plane of polarization

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using a half-wave plate.

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Here is the half-wave
plate, which we now

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will place right in here.

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And, as we know, half-wave
plates have two principal axes.

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And, if the light propagates
along either principal axis,

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the polarization of the
light is unaffected.

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That means there's no rotation
of the plane of polarization.

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So let's check on that.

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Let's first place
this arrow, which

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is lined up with one
of the principal axes

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of the half-wave
plate, and let's check,

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indeed, with the analyzer that,
indeed, that the polarization

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is not rotated
when we are aligned

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along the principal axis.

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Again, let's rotate it to
find null, and here is null.

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And you can see
that null is, again,

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when the arrow of the
analyzer shows horizontal,

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which means that the
plane of polarization

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is really vertical.

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Now let's check--
while we're here,

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let's check on the
other propagation

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along the other principal
axis, which is 90 degrees away

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from this one.

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So let's go find horizontal.

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Let's say it's around here.

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Let's check again where null is.

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And you can see that null
is again in the same place

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when the analyzer is showing
horizontal, which again means

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that the plane of polarization
is in the vertical direction.

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All right, so we established
that there's no rotation

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when propagating along
the two principal axes

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of the half-wave plate.

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Now let's demonstrate rotation
of the polarization using

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this half-wave plate.

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So let me now set it at
let's say around 45 degrees

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or so with respect
to the vertical axis.

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Let's now go to the
analyzer and see

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what happened to the
state of polarization.

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Again, let's track the null.

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And I'll keep rotating the
analyzer until I find null.

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Here it is.

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Here it comes.

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Here's null.

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Now what does that mean?

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It means that the light here
after the half-wave plate

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is plane-polarized
and that, indeed,

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the plane of polarization is
along the horizontal direction

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because the block axis or
the null axis is vertical.

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So it means that we've rotated
the plane of polarization

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from the original one,
which was along here,

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to the horizontal one,
which means by 90 degrees,

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using the half-wave plate.

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So the thing that
you want to notice

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is that, when the half-wave
plate is rotated by 45 degrees,

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the polarization, the
state of polarization,

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is-- the plane of polarization
is rotated by twice that,

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by 90 degrees.

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And the interesting thing
about the half-wave plate,

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using a half-wave plate, is
that the peak intensity--

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and now let me get the
peak intensity here.

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The peak intensity does not drop
with rotation or polarization.

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For example, if I decide to
rotate by a smaller amount,

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like this, again,
let's establish

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the state of polarization.

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Again, null now is no
longer pointing below,

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but is pointing at
this angle here,

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which means that the plane
of polarization is different.

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And then we go see what the peak
value of the transmitted light

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is, which is around
here somewhere.

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And you can see that the
peak value has not dropped.

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So the conclusion of this
is that a half-wave plate

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or at least a good
half-wave plate

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can rotate the plane
of polarization

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from 0 to 90 degrees without
any loss of intensity.