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SHAOUL EZEKIEL: Now
we're ready to look

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at multiple beam
interference using

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a cavity with curved mirrors.

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The setup is here.

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We have the smaller laser.

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Because this laser can give
us single frequency operation.

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The beam from the laser
goes through this Bragg cell

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acting as an isolator.

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And the light, after the
Bragg cell, is over here.

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It gets reflected by this
mirror into a polarizer,

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which I'll explain the
reason for a little later.

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Here's the output
of the polarizer

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getting reflected by this
mirror here into the cavity.

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So let's look at the
cavity right now.

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It's made out of two
hefty mirror mounts.

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Because we need good stability.

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The mirrors have the same radius
of curvature of 25 centimeters.

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One of the mirrors is mounted
on a piezoelectric crystal

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over here.

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And the adjustment
to the mirror mounts

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are over here using
these knobs here.

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Now, if we come around
from the other side,

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we can see that we have a
differential screw over here

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that would enable us to adjust
the spacing between the two

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mirrors.

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00:01:50,380 --> 00:01:56,020
Right now, the spacing
is about 23 centimeters,

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00:01:56,020 --> 00:02:01,465
while the radius of curvature of
each mirror is 25 centimeters.

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00:02:04,760 --> 00:02:09,759
This laser is a special one.

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00:02:09,759 --> 00:02:11,245
We've used it before.

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It operates at two
frequencies, sometimes more.

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00:02:15,470 --> 00:02:19,660
But right now, let's look
at the two frequencies.

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00:02:19,660 --> 00:02:24,250
The two frequencies oscillate
with different polarizations,

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00:02:24,250 --> 00:02:29,950
orthogonal polarizations, so
that by using the polarizer

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over here we can select,
then, either one of the two

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frequencies so that
the output, then,

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00:02:39,160 --> 00:02:43,690
that we can inject into the
cavity can be single frequency.

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00:02:43,690 --> 00:02:45,370
If we want more
than one frequency,

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00:02:45,370 --> 00:02:50,180
then we just simply rotate
the polarizer by 45 degrees.

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00:02:50,180 --> 00:02:54,640
And then we can pick
off both frequencies.

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Now, the cavity, then,
the output of the cavity

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is over here.

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00:03:01,150 --> 00:03:04,400
And we're going to
expand it by the lens,

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00:03:04,400 --> 00:03:08,140
by this lens here, and
then onto the screen.

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00:03:08,140 --> 00:03:11,260
Now since the laser
is pretty weak,

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we're going to have
to dim the room

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lights to look at the output
transmitted through the cavity.

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So now we'll dim
the lights and see

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what we can see on the screen.

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And here we are on the screen.

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And what we can see is all
sorts of interesting patterns.

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They're going a
little fast right now.

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But I can slow them
down just a little bit.

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Here we are.

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These are the transverse
modes or radial

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modes of the resonator.

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What I'm doing now is changing
the horizontal alignment

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of the mirrors.

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And you can see the shapes of
the modes vary from a few spots

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to many spots.

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Here we are, some
very pretty patterns.

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And let me see if
I can scan by hand.

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Here we are.

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I'm scanning by hand,
holding the patterns

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for a little longer.

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There's a pretty
one, lots of spots.

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These are 0, 1,
or 1, 0, depending

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on how you read these modes.

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Let me bring it again, the
one with the two spots.

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Another one-- there's one.

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Now, what I'm going to do is
turn the scan back on again.

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00:05:18,400 --> 00:05:21,990
And then I'm going to
change the alignment so we

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can look at other patterns.

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Here we are, another set.

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Going to a vertical,
this alignment,

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now you see that the spots
are rearranged slightly.

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Let me separate them
a little bit more.

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00:05:49,050 --> 00:05:55,790
Again, let me switch off the
scan and scan by hand slowly.

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00:05:55,790 --> 00:05:59,740
Again, now, I see the two spots
have reoriented themselves

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with respect to the
vertical direction,

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00:06:02,340 --> 00:06:06,086
while before they were
in horizontal direction.

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00:06:06,086 --> 00:06:10,860
Now we get some other
interesting patterns.

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00:06:28,897 --> 00:06:29,980
Here's an interesting one.

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00:06:40,770 --> 00:06:45,270
I'm going to turn the
scan back on again.

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00:06:45,270 --> 00:06:47,990
And I'm going to
now align so that we

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can get the symmetrical
patterns, the patterns that

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look the same in both the
horizontal and vertical

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directions.

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Here we are.

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00:07:01,640 --> 00:07:07,930
I think I'm close to that.

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00:07:07,930 --> 00:07:12,400
Let me turn the scan off
and bring them in by hand.

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You can see now the
pattern is symmetric.

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There's one.

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There's another.

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00:07:27,598 --> 00:07:28,310
There's another.

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There's another lower one.

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00:07:40,580 --> 00:07:45,360
And here is the lowest order
mode, the so-called [? TN ?] 0,

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0 mode with a single spot.

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And here are the
higher order ones.

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00:08:02,790 --> 00:08:05,540
I'm going to put the
scan back on again

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and just adjust the
alignment and see what

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00:08:08,590 --> 00:08:10,600
we can get for different spots.

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00:08:20,980 --> 00:08:27,590
Let me separate the
modes some more.

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00:08:27,590 --> 00:08:32,360
And we can really get extremely
high order modes this way.

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Here we are.

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I'll turn the scan off,
bring them in by hand.

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00:09:21,830 --> 00:09:26,720
Well, I think we've seen
probably enough of these modes.

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00:09:26,720 --> 00:09:29,670
In the next part of
the demonstration,

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we're going to put
a photodetector

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00:09:34,040 --> 00:09:37,580
and look at the output
of the photodetector.

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And will see that the resonant
conditions for each high order

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mode is different.

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Just before, we saw the
modes on the screen,

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the modes of the resonator
with curved mirrors

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on the screen as a function of
the tuning of the resonator.

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00:10:04,390 --> 00:10:08,940
Now, we're going to look
at the output transmitted

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00:10:08,940 --> 00:10:12,030
through the cavity on
a photodetector that

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00:10:12,030 --> 00:10:15,900
is associated with the
different transverse modes

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00:10:15,900 --> 00:10:17,310
of the resonator.

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And the setup is here.

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The output of the
resonator, then,

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00:10:23,490 --> 00:10:27,600
is reflected by this mirror
onto a photodetector.

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00:10:27,600 --> 00:10:29,430
And the output of
the photodetector

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00:10:29,430 --> 00:10:34,090
is displayed on
the oscilloscope.

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So we're going to see both
the transmission associated

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with the transverse modes.

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And also, I'm going to adjust
the length of the resonator

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by means of this
translation stage driven

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00:10:51,960 --> 00:10:54,550
by this differential screw.

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So now, let's look at the--
let's look at the scope

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and see what we can see.

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On the scope, we
can see there are

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00:11:02,220 --> 00:11:05,490
lots of modes, lots of
resonances associated

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00:11:05,490 --> 00:11:09,060
with the transverse
modes of the resonator.

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00:11:09,060 --> 00:11:12,840
Also, we see that the
modes are shifting around.

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And a simple excuse
for the shifting

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around is due to the air
currents in the resonator.

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So I'm going to reduce this by
placing a tube over the light

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in the resonator.

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So here is a simple tube.

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And if I'm lucky, I
can do it on camera.

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00:11:34,260 --> 00:11:39,210
If I'm not, we'll have
to go back and fix it.

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Here is a tube, one end
of the tube, and here is--

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OK, now that I've got the
tube in place, let's go back

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and look at the oscilloscope.

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And you can see that the
modes are not moving around

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as much as before.

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00:12:04,790 --> 00:12:08,090
Let me just remind you that
the free spectral range

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00:12:08,090 --> 00:12:09,290
is from here to here.

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00:12:09,290 --> 00:12:12,455
The free spectral range of
the resonator is this much.

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The length of the cavity right
now is about 23 centimeters.

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And remember that the radius
of curvature of the mirror

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is 25 centimeters.

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So now what I'm going to do
is approach 25 centimeters.

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I want to change the spacing
now so that I can approach

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25 centimeters, which is
the radius of curvature

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of each mirror.

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And that's the
confocal condition.

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Now, as you can
see on the scope,

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the modes are now
blending into each other.

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In fact, you can't
even distinguish them.

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And as I keep going, as I
keep getting closer and closer

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to the--

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00:13:03,560 --> 00:13:10,420
let me make a DC adjustment
here on the scope.

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00:13:10,420 --> 00:13:12,440
As I get closer and
closer to confocal,

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they're really blending
into each other.

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And they're getting very big.

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And I have to reduce
the sensitivity.

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And as I approach the confocal,
the gain is saturating.

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So let me just do
one more adjustment.

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Here we are.

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We see that we get
only one resonance.

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00:13:41,310 --> 00:13:43,980
And don't forget that
the free spectral range

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00:13:43,980 --> 00:13:45,730
is from here to here.

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00:13:45,730 --> 00:13:47,550
So we get this
additional resonance

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in the middle of the free
spectral range, which

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00:13:49,770 --> 00:13:52,930
I leave to you to figure out.

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Now-- so when we
are confocal, then,

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00:13:56,220 --> 00:14:00,750
we have all the most coalescing.

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00:14:00,750 --> 00:14:03,630
And we also have the appearance
of an additional mode

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00:14:03,630 --> 00:14:05,670
in the middle of the
free spectral range.

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00:14:05,670 --> 00:14:10,350
And then if I go now and
make the cavity longer,

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00:14:10,350 --> 00:14:16,030
again, you see that as I go
away from the confocal condition

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00:14:16,030 --> 00:14:19,860
the other way, the--

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00:14:19,860 --> 00:14:21,590
let me bring up the sensitivity.

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00:14:21,590 --> 00:14:23,670
You can see now
that the modes start

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00:14:23,670 --> 00:14:32,690
to pile up on the other side
of the resonance as shown.

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00:14:32,690 --> 00:14:34,970
So what we've seen in
this little demonstration

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00:14:34,970 --> 00:14:41,570
is that the various radial modes
appear at different lengths

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00:14:41,570 --> 00:14:44,520
of the resonator.

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00:14:44,520 --> 00:14:48,020
And we saw that when we made
the length of the resonator

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00:14:48,020 --> 00:14:50,030
equal to the radius
of curvature,

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00:14:50,030 --> 00:14:53,690
which is the confocal
condition, we

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00:14:53,690 --> 00:15:00,890
saw that the modes
coalesced into two peaks.

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00:15:00,890 --> 00:15:04,610
And the spacing
between the peaks

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00:15:04,610 --> 00:15:07,790
is half the free spectral range.

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00:15:07,790 --> 00:15:10,880
And let's look at the scope.

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00:15:10,880 --> 00:15:11,390
Here we are.

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00:15:11,390 --> 00:15:13,710
This is the free spectral
range of the cavity.

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00:15:13,710 --> 00:15:19,070
And when we are at confocal,
we have the appearance

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00:15:19,070 --> 00:15:22,340
of this peak here, which
means that all the modes have

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00:15:22,340 --> 00:15:26,480
coalesced into just two peaks.

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00:15:26,480 --> 00:15:29,660
And we'll leave that
for you as an exercise

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00:15:29,660 --> 00:15:33,020
to explain why
this has happened.

211
00:15:33,020 --> 00:15:36,320
In the next
demonstration, we're going

212
00:15:36,320 --> 00:15:41,510
to show how a cavity like
this with curved mirrors

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00:15:41,510 --> 00:15:46,870
can be used to analyze the
spectrum of laser light.