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SHAOUL EZEKIEL: This
next demonstration

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00:00:23,220 --> 00:00:27,420
is about the laser line width or
the spectral width of the laser

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00:00:27,420 --> 00:00:29,110
radiation.

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00:00:29,110 --> 00:00:33,720
Now theory predicts that
the line width of a laser

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00:00:33,720 --> 00:00:38,460
should be very, very
narrow, much narrower then

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00:00:38,460 --> 00:00:41,910
a fraction of a Hertz, in
fact, of the order of 10

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00:00:41,910 --> 00:00:46,440
to the minus 3, 10 to the
minus 4 Hertz or even smaller.

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00:00:46,440 --> 00:00:48,690
In practice, we don't see that.

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00:00:48,690 --> 00:00:51,830
In practice, if you measure
the laser line width,

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00:00:51,830 --> 00:00:56,850
you find sometimes it's hundreds
of kilohertz, megahertz,

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00:00:56,850 --> 00:01:00,680
and even tens or
hundreds of megahertz.

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00:01:00,680 --> 00:01:03,030
So what is really
going on here, then?

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00:01:03,030 --> 00:01:08,000
What's the discrepancy
between theory and practice?

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00:01:08,000 --> 00:01:09,710
In order to explain
what's going on,

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00:01:09,710 --> 00:01:13,340
I'm going to review some
fundamentals about lasers.

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00:01:13,340 --> 00:01:18,170
Here is a laser, simple laser.

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00:01:18,170 --> 00:01:21,860
It's made up of a helium
neon discharge tube.

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00:01:21,860 --> 00:01:25,310
And the discharge tube is
terminated by two mirrors.

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00:01:25,310 --> 00:01:28,220
And there's nothing
else inside the cavity

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00:01:28,220 --> 00:01:34,250
besides the discharge
tube and the two mirrors.

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00:01:34,250 --> 00:01:38,900
Now the cavity resonance
associated with this length

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00:01:38,900 --> 00:01:41,240
cavity, then, is
certainly determined

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00:01:41,240 --> 00:01:46,490
by the length of the cavity
and the refractive index

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00:01:46,490 --> 00:01:52,010
of the medium between
the two mirrors

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00:01:52,010 --> 00:01:54,770
so that if we have
a cavity resonance

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00:01:54,770 --> 00:02:01,430
within the bandwidth of the
helium neon amplifier, then--

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00:02:01,430 --> 00:02:03,740
and then we have,
of course, gain

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00:02:03,740 --> 00:02:06,650
that's bigger than the
losses in the cavity--

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00:02:06,650 --> 00:02:10,100
then we'll have oscillation
at the cavity resonance.

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00:02:10,100 --> 00:02:12,020
So then the frequency
of the laser

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00:02:12,020 --> 00:02:14,660
is determined by
the cavity resonance

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00:02:14,660 --> 00:02:19,680
that is within the
bandwidth of the amplifier.

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00:02:19,680 --> 00:02:23,720
So the frequency,
then, will fluctuate

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00:02:23,720 --> 00:02:31,160
if the optical length of the
cavity will fluctuate due to,

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00:02:31,160 --> 00:02:35,620
let's say, due to
temperature, vibrations,

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00:02:35,620 --> 00:02:38,200
fluctuations in
the power supply,

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00:02:38,200 --> 00:02:41,510
that changes the
refractive index and so on.

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00:02:41,510 --> 00:02:44,500
So in practice, then,
the laser frequency

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00:02:44,500 --> 00:02:46,120
will just move
all over the place

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00:02:46,120 --> 00:02:51,460
depending on the mechanical
design of the laser.

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00:02:54,310 --> 00:02:57,870
So that if you want
to measure this line

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00:02:57,870 --> 00:03:00,847
width, this practical
line width of a laser,

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00:03:00,847 --> 00:03:02,430
then you would take--
one way of doing

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00:03:02,430 --> 00:03:05,880
it is to take two such
lasers oscillating

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00:03:05,880 --> 00:03:09,150
at a single frequency
in each one of them.

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00:03:09,150 --> 00:03:10,770
And then you beat them.

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00:03:10,770 --> 00:03:15,030
And you look at the beat on an
electronic spectrum analyzer.

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00:03:15,030 --> 00:03:18,160
And you'll find
that that beat is,

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00:03:18,160 --> 00:03:20,670
as I mentioned before, can
vary anywhere from hundreds

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00:03:20,670 --> 00:03:24,930
of megahertz down to a
few kilohertz depending,

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00:03:24,930 --> 00:03:28,680
again, on the
design of the laser.

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00:03:28,680 --> 00:03:34,200
In order to measure or observe
the intrinsic line width--

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00:03:34,200 --> 00:03:36,780
this is the line
width that's predicted

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by Shallon Town
many, many years ago,

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this line width is of the
order of, as I said before,

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10 to the minus 3,
10 the minus 4 Hertz

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00:03:46,690 --> 00:03:48,750
for a 1 milliwatt laser.

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00:03:51,290 --> 00:03:54,800
This width is due to
fundamental noise sources

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00:03:54,800 --> 00:03:56,900
such as spontaneous emission.

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00:03:56,900 --> 00:04:01,808
And it doesn't depend on
any length of the cavity

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00:04:01,808 --> 00:04:03,350
and the optical
length of the cavity.

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00:04:03,350 --> 00:04:06,070
Here, we assume that
everything else is fixed.

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00:04:06,070 --> 00:04:08,750
But only the
spontaneous emission

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00:04:08,750 --> 00:04:12,320
is giving us the
residual line width.

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00:04:12,320 --> 00:04:17,070
In order to measure this
fundamental line width,

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it's very difficult to do
it by using two lasers.

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00:04:23,000 --> 00:04:26,630
Because it's very difficult
to stabilize the length

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00:04:26,630 --> 00:04:30,460
of the cavities in each laser.

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00:04:30,460 --> 00:04:35,570
There are techniques using wide
band feedback stabilization

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loops to reduce the vibrations
and the drift of a laser

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00:04:40,940 --> 00:04:41,720
cavity.

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00:04:41,720 --> 00:04:44,900
But still, it still would
be difficult to reach

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00:04:44,900 --> 00:04:47,300
the fundamental line width.

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So in this demonstration,
we're going

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to give you a feel for how
small the laser line width can

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be using some simple concepts.

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Before I go on to describe
what we're going to do,

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I'm going to show you what
an ideal way of measuring

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00:05:04,130 --> 00:05:07,280
or observing the
laser line width is.

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00:05:07,280 --> 00:05:16,097
Here is a ring cavity
made up of three mirrors.

88
00:05:16,097 --> 00:05:18,180
Here's one mirror, another
mirror, another mirror.

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00:05:18,180 --> 00:05:20,520
It's a triangular cavity.

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00:05:20,520 --> 00:05:21,780
Here's the cathode.

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00:05:21,780 --> 00:05:26,290
And there are two anodes, one
over here and one over here.

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00:05:26,290 --> 00:05:29,010
So we have, say,
helium neon discharged

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00:05:29,010 --> 00:05:32,130
within the resonator.

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00:05:32,130 --> 00:05:36,390
Because it's a ring, we're going
to get two laser oscillations,

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00:05:36,390 --> 00:05:40,290
one in the clockwise
direction and the other one

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00:05:40,290 --> 00:05:43,270
in the counterclockwise
direction.

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00:05:43,270 --> 00:05:47,720
If we take the two
outputs and we beat them,

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00:05:47,720 --> 00:05:54,800
then the beat frequency will
give us essentially the sum

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00:05:54,800 --> 00:06:00,740
of the two individual spectral
widths of the two laser

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00:06:00,740 --> 00:06:01,640
frequencies.

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00:06:01,640 --> 00:06:04,830
Now, because the cavity
is common to both

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00:06:04,830 --> 00:06:07,130
and the refractive
index variations

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00:06:07,130 --> 00:06:09,500
are common to both
frequencies, then

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00:06:09,500 --> 00:06:12,320
this would give you probably
about the best measurement

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00:06:12,320 --> 00:06:15,950
of the true line width
or the intrinsic line

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00:06:15,950 --> 00:06:18,530
width of the laser.

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00:06:18,530 --> 00:06:22,700
But that's not what we're
going to demonstrate here.

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00:06:22,700 --> 00:06:24,200
What we're going
to use, we're going

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00:06:24,200 --> 00:06:28,340
to use our simple laser here.

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00:06:28,340 --> 00:06:33,620
And because of the
length of this cavity,

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00:06:33,620 --> 00:06:36,680
we get two modes,
two cavity modes

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00:06:36,680 --> 00:06:41,750
that are within the bandwidth
of the helium neon amplifier.

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00:06:41,750 --> 00:06:47,230
And since the cavity is
common to both modes,

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00:06:47,230 --> 00:06:51,680
except for the fact that they
are separated by c over 2L

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00:06:51,680 --> 00:06:54,920
where c is the velocity
of light and an L is

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00:06:54,920 --> 00:06:57,110
the optical length
of the cavity,

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00:06:57,110 --> 00:06:59,540
other than that,
the fluctuations

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00:06:59,540 --> 00:07:03,170
and the drift of the cavity
should be common to both.

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00:07:03,170 --> 00:07:07,520
So by then beating the
two outputs associated

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00:07:07,520 --> 00:07:13,640
with these two modes in this
laser on an electronic spectrum

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00:07:13,640 --> 00:07:17,195
analyzer, then the
line width that we'll

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00:07:17,195 --> 00:07:19,070
measure with the electronic
spectrum analyzer

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00:07:19,070 --> 00:07:25,160
will give us a measure of
how narrow the spectral width

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00:07:25,160 --> 00:07:28,060
of the individual laser is.

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00:07:28,060 --> 00:07:31,230
The set up we're going
to use is over here.

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00:07:31,230 --> 00:07:36,200
Now, in this box I have
a laser just like this.

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00:07:36,200 --> 00:07:38,000
The reason why we
use this box is

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00:07:38,000 --> 00:07:42,732
to keep the environment
at a constant temperature,

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00:07:42,732 --> 00:07:44,690
or as close to constant
temperature as possible

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00:07:44,690 --> 00:07:49,730
and also to isolate against
vibrations so that the laser

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00:07:49,730 --> 00:07:52,250
cavity is not shaking too much.

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00:07:52,250 --> 00:07:56,980
The output from the laser
goes through a polarizer.

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00:07:56,980 --> 00:08:05,140
Now, since this cavity is
made up of internal mirrors--

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00:08:05,140 --> 00:08:07,290
there's nothing else
between the two mirrors

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00:08:07,290 --> 00:08:09,390
except for the discharge tube--

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00:08:09,390 --> 00:08:11,860
the two modes that
will oscillate

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00:08:11,860 --> 00:08:15,750
will have orthogonal
polarization.

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00:08:15,750 --> 00:08:18,900
So that by using a
polarizer like this,

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00:08:18,900 --> 00:08:23,640
I can select either frequency.

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00:08:23,640 --> 00:08:26,730
Or, if I put it
45 degrees, I can

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00:08:26,730 --> 00:08:31,560
select both laser frequencies.

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00:08:31,560 --> 00:08:33,450
So after the polarizer,
then, I reflect

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00:08:33,450 --> 00:08:37,090
the light by this mirror,
and then this mirror,

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00:08:37,090 --> 00:08:41,162
onto an optical
spectrum analyzer,

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00:08:41,162 --> 00:08:43,120
which is a scanning
Fabry-Perot interferometer.

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00:08:43,120 --> 00:08:48,690
Now the length of this scanning
Fabry-Perot is about 10

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centimeters, which means that
the free spectral range is

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00:08:53,160 --> 00:08:56,680
about 1 1/2 gigahertz.

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00:08:56,680 --> 00:09:01,110
So now we are ready to look
at the output of this spectrum

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00:09:01,110 --> 00:09:05,010
analyzer on an
oscilloscope over here.

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00:09:05,010 --> 00:09:09,690
We see the output when we
have the polarizer adjusted

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00:09:09,690 --> 00:09:12,900
so that only one
laser frequency is

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00:09:12,900 --> 00:09:15,840
allowed to be observed by
the scanning Fabry-Perot

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00:09:15,840 --> 00:09:16,770
interferometer.

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00:09:16,770 --> 00:09:20,100
What we're seeing is the free
spectral range of the scanning

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00:09:20,100 --> 00:09:23,550
Fabry-Perot, which
is 1 1/2 gigahertz.

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00:09:23,550 --> 00:09:29,250
So, as you can see, eight big
boxes and corresponds to 1 1/2

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00:09:29,250 --> 00:09:30,150
gigahertz.

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00:09:30,150 --> 00:09:34,020
And the laser is oscillating
at a single frequency.

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00:09:34,020 --> 00:09:39,980
Now let me adjust the
polarizer so that I bring up

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00:09:39,980 --> 00:09:46,020
the other mode, as observed
by the scanning Fabry-Perot.

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00:09:46,020 --> 00:09:50,070
Now you can see that the other
laser frequency is about three

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00:09:50,070 --> 00:09:53,350
big boxes away from
here, from this mode,

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00:09:53,350 --> 00:09:57,150
which means that the separation
if you do your arithmetic,

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00:09:57,150 --> 00:10:00,170
since eight boxes corresponds
to 1 1/2 gigahertz,

166
00:10:00,170 --> 00:10:05,660
then three will correspond
to about 550 megahertz.

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00:10:05,660 --> 00:10:09,040
Now, if I rotate the
polarizer even more

168
00:10:09,040 --> 00:10:13,730
to block out the
first laser frequency

169
00:10:13,730 --> 00:10:21,040
I showed you before, I up
with only this frequency

170
00:10:21,040 --> 00:10:23,540
of the laser over here.

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00:10:23,540 --> 00:10:25,833
There we are.

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00:10:25,833 --> 00:10:27,250
So then, again,
just it's a matter

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00:10:27,250 --> 00:10:31,330
of adjusting then the polarizer
to have either one frequency go

174
00:10:31,330 --> 00:10:37,240
to the Fabry-Perot or the two
frequencies simultaneously.

175
00:10:37,240 --> 00:10:40,060
Right now we have both
of them simultaneously

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00:10:40,060 --> 00:10:42,380
incident on the
Fabry-Perot interferometer.

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00:10:42,380 --> 00:10:46,150
Again, as you can see, the
separation is 550 megahertz.

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00:10:46,150 --> 00:10:47,980
Now, the width
that you see here,

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00:10:47,980 --> 00:10:50,110
it has nothing to do with
the laser line width.

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00:10:50,110 --> 00:10:53,740
It is determined by the width
of the scanning Fabry-Perot

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00:10:53,740 --> 00:10:55,366
interferometer.

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00:10:55,366 --> 00:10:58,690
Of course, if the
laser jitters a lot,

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00:10:58,690 --> 00:11:01,840
then you would see the
width of the laser here.

184
00:11:01,840 --> 00:11:04,660
But right now, the width
of the scanning Fabry-Perot

185
00:11:04,660 --> 00:11:09,610
is much bigger than the
width of the individual laser

186
00:11:09,610 --> 00:11:10,811
oscillations.

187
00:11:13,970 --> 00:11:17,150
Now we're ready to look
at the beat frequency

188
00:11:17,150 --> 00:11:20,900
between these two modes.

189
00:11:20,900 --> 00:11:24,530
So we need-- for this, we
need a wide band detector that

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00:11:24,530 --> 00:11:30,920
can measure a beat note much
bigger than, or at least as big

191
00:11:30,920 --> 00:11:33,560
as 550 megahertz.

192
00:11:33,560 --> 00:11:36,890
The setup is over here.

193
00:11:36,890 --> 00:11:39,710
Here is the laser again.

194
00:11:39,710 --> 00:11:41,990
And the output of
the laser, again

195
00:11:41,990 --> 00:11:44,510
passes through the polarizer.

196
00:11:44,510 --> 00:11:47,420
And then we take a little bit
of the light through this beam

197
00:11:47,420 --> 00:11:52,730
splitter here and reflect it by
this mirror and onto this lens.

198
00:11:52,730 --> 00:11:54,830
And this lens here
will focus the light

199
00:11:54,830 --> 00:11:58,390
onto this fast detector.

200
00:11:58,390 --> 00:12:01,290
And that's how we're going
to measure the beat frequency

201
00:12:01,290 --> 00:12:03,810
between the two lasers.

202
00:12:03,810 --> 00:12:08,850
So now, let's look at the output
of the electronic spectrum

203
00:12:08,850 --> 00:12:12,630
analyzer here on the scope.

204
00:12:12,630 --> 00:12:15,360
Now, on your screen you see--

205
00:12:15,360 --> 00:12:16,860
in the lower part
of the screen, you

206
00:12:16,860 --> 00:12:20,050
see the output of the scanning
Fabry-Perot interferometer

207
00:12:20,050 --> 00:12:23,280
where we show you the two
frequencies of the laser

208
00:12:23,280 --> 00:12:26,220
separated by 550 megahertz.

209
00:12:26,220 --> 00:12:28,950
And in the upper
part is the output

210
00:12:28,950 --> 00:12:31,680
of the electronic
spectrum analyzer

211
00:12:31,680 --> 00:12:37,770
where the scale is
20 kilohertz per box.

212
00:12:37,770 --> 00:12:43,440
And the center frequency
over here is 557 megahertz,

213
00:12:43,440 --> 00:12:45,540
which is close to
what we estimated

214
00:12:45,540 --> 00:12:47,430
from the scanning Fabry-Perot.

215
00:12:47,430 --> 00:12:52,830
The resolution here
is three kilohertz.

216
00:12:52,830 --> 00:12:54,855
All right, so now what
I'm going to do, just

217
00:12:54,855 --> 00:12:58,200
to make sure that, indeed,
this beat output is coming

218
00:12:58,200 --> 00:13:00,000
from the laser, what
I'm going to do now

219
00:13:00,000 --> 00:13:04,320
is rotate the polarizer
to get only one frequency

220
00:13:04,320 --> 00:13:08,640
and see if we can
extinguish the beat.

221
00:13:08,640 --> 00:13:12,800
So, as you see on
this screen here,

222
00:13:12,800 --> 00:13:20,360
I'm going to be
then extinguishing

223
00:13:20,360 --> 00:13:24,260
one of the modes that enters
the fast detector and also

224
00:13:24,260 --> 00:13:25,820
the scanning Fabry-Perot.

225
00:13:25,820 --> 00:13:27,920
And as we watch
over here the output

226
00:13:27,920 --> 00:13:31,850
of the electronic
spectrum analyzer and see

227
00:13:31,850 --> 00:13:37,995
it gets smaller and smaller
until we have nothing at all.

228
00:13:37,995 --> 00:13:38,620
So here we are.

229
00:13:38,620 --> 00:13:41,020
There's only one frequency
oscillating in the laser.

230
00:13:41,020 --> 00:13:43,030
And there is no beat.

231
00:13:43,030 --> 00:13:49,090
All right, so now let me
bring up the other frequency.

232
00:13:49,090 --> 00:13:52,510
Now we have two of them,
then, going into the detector

233
00:13:52,510 --> 00:13:56,590
and into the
scanning Fabry-Perot.

234
00:13:56,590 --> 00:14:00,790
And we get back
our beat frequency

235
00:14:00,790 --> 00:14:06,810
centered on 557 megahertz.

236
00:14:06,810 --> 00:14:10,590
All right, now this resolution
is not so wonderful.

237
00:14:10,590 --> 00:14:13,920
And it's limited by
the setting that I

238
00:14:13,920 --> 00:14:17,800
have used on the electronic
spectrum analyzer.

239
00:14:17,800 --> 00:14:19,800
What I'm going to
do now is I'm going

240
00:14:19,800 --> 00:14:26,190
to change to our highest
resolution of 200 Hertz per box

241
00:14:26,190 --> 00:14:29,055
with a resolution
limit of 30 Hertz.

242
00:14:36,710 --> 00:14:37,760
Here we are.

243
00:14:37,760 --> 00:14:41,900
Now we have 200 Hertz per box
and a resolution of 30 Hertz,

244
00:14:41,900 --> 00:14:43,520
which I hope you can see.

245
00:14:43,520 --> 00:14:45,920
Now I'm going to
have single sweep

246
00:14:45,920 --> 00:14:51,650
scans to look at the spectral
width of the two lasers.

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So here we go.

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So here we are.

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We can see that, again with
a scale of 200 Hertz per box,

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and the resolution
is 30 Hertz, we

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see that the spectrum
that we can observe

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is indeed very close to
the instrumental line

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width of 30 Hertz.

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So we have demonstrated
that the intrinsic line

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width, the fundamental
line width of a laser

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must be pretty small, certainly
smaller, quite a bit smaller

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than 30 Hertz.

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So remember here is the beat
we looked at the spectral width

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of the beat note of two lasers.

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So each one must be quite a
bit smaller than 30 Hertz.

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If we had a better technique
for doing the spectrum analysis,

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we would have shown you an
even narrower spectral width.

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Now just as a footnote,
what I'd like to do

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is calibrate the electronic
spectrum analyzer for you

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by bringing in a good stable
oscillator around 557 megahertz

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or so and indeed demonstrate
that the 30 Hertz is really

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the resolution limit of the
electronic spectrum analyzer.

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So when you come back, we'll
have that set up for you.

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So here is the stable
oscillator over here.

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It's an HP stable oscillator.

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And the output at
557 megahertz or so,

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we're going to feed it into the
electronic spectrum analyzer

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to see what the width is.

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So here I pressed the
single sweep button.

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And here is the output.

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And you can see
that the width here

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is very similar to what we saw
for the beat between the two

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laser frequencies.

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And this shows that,
indeed, the resolution limit

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is 30 Hertz of the
electronic spectrum analyzer.

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So, in summary, the
laser spectral width

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depends on the stability
of the laser cavity.

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If the laser cavity
jitters and shakes,

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or the refractive
index fluctuates,

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then we would expect
that the laser spectral

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width would be quite broad.

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00:17:26,700 --> 00:17:29,280
So in order to reduce
the laser spectral width,

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we need to design a
stable laser cavity.

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00:17:34,560 --> 00:17:38,640
Now, in terms of typical
numbers, a simple helium neon

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laser like the one we used
in this demonstration,

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the line width would be
around 50 kilohertz or so.

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The recently developed
CW neodymium YAG lasers

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have a line width of the
order of 1 kilohertz.

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But other lasers like
semiconductor lasers, dilasers,

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and what have you can have line
widths of many, many megahertz.

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Now remember, the
intrinsic line width

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is only a small
fraction of a Hertz,

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or, as I mentioned before, of
the order 10 to the minus 3,

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10 to the minus 4
or even smaller.

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Now, there are not
many applications

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that require such narrow
line width, except one.

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And that is the
ring laser gyroscope

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that's used for navigation.

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Now, for this application,
the intrinsic line width

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of the laser is at
present the limit

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00:18:33,910 --> 00:18:38,200
on the ability of this device
to measure inertial rotation.

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00:18:38,200 --> 00:18:40,900
But many other
applications, at present,

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do not require that super
narrow spectral width

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that is inherent in the laser.