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SHAOUL EZEKIEL: The
light beam from a laser

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00:00:23,880 --> 00:00:28,260
is as close to an ideal
beam as one can get.

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00:00:28,260 --> 00:00:32,170
What I mean by that is that
the properties of this beam,

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00:00:32,170 --> 00:00:34,770
the propagation
properties, are limited

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00:00:34,770 --> 00:00:38,790
by fundamental laws of physics--

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00:00:38,790 --> 00:00:41,400
for example, loss
of diffraction--

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00:00:41,400 --> 00:00:45,870
and not by the properties
of the light source.

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00:00:45,870 --> 00:00:50,160
For example, a laser beam
from a well-behaved laser

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00:00:50,160 --> 00:00:59,190
can be collimated to
a very small angle.

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00:00:59,190 --> 00:01:01,740
This angle is
determined by, as I

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00:01:01,740 --> 00:01:03,570
said, the laws of
diffraction, which

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00:01:03,570 --> 00:01:06,030
is the wavelength
of the light divided

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00:01:06,030 --> 00:01:09,180
by the diameter of the beam.

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00:01:09,180 --> 00:01:12,570
And it doesn't say anything
about the size of the source

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00:01:12,570 --> 00:01:14,460
or the properties of
the source, and that

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00:01:14,460 --> 00:01:19,980
is the ideal collimation
limit on a beam.

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00:01:19,980 --> 00:01:22,500
At the same time,
a laser beam can be

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00:01:22,500 --> 00:01:25,260
focused to a very small spot.

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00:01:25,260 --> 00:01:28,980
The size of that spot
is, again, determined

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00:01:28,980 --> 00:01:33,720
by laws of diffraction, which
is the wavelength of the light

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00:01:33,720 --> 00:01:37,260
divided by the diameter
of the beam, multiplied

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00:01:37,260 --> 00:01:38,880
by the focal length of the lens.

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00:01:38,880 --> 00:01:41,130
And if we choose the
diameter of the beam

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00:01:41,130 --> 00:01:44,440
and the focal length of
the lens about equal,

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00:01:44,440 --> 00:01:46,810
then the spot size
would be of the order

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00:01:46,810 --> 00:01:48,030
of the wavelength of light.

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00:01:48,030 --> 00:01:49,830
And again, it
doesn't say anything

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00:01:49,830 --> 00:01:52,760
about the physical size
of the light source

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00:01:52,760 --> 00:01:57,720
or what have you, as we would
have in a case of an arc lamp

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00:01:57,720 --> 00:02:01,300
or any other kind
of light source.

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00:02:01,300 --> 00:02:03,580
Now, in these
demonstrations that follow,

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00:02:03,580 --> 00:02:07,650
we're going to illustrate
some of these basic properties

40
00:02:07,650 --> 00:02:11,550
of laser beams.

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00:02:11,550 --> 00:02:15,090
What we're going to start
with is this laser here,

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00:02:15,090 --> 00:02:17,490
which is a helium-neon
laser, and here

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00:02:17,490 --> 00:02:20,040
is the beam from the laser.

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00:02:20,040 --> 00:02:21,960
We're going to reflect
it by this mirror

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00:02:21,960 --> 00:02:25,920
here and then reflect
it again by this mirror

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00:02:25,920 --> 00:02:31,800
here and let the beam
fall on the screen.

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00:02:31,800 --> 00:02:36,180
Now, you might be able to get
a better feeling for the beam

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00:02:36,180 --> 00:02:39,210
if I use the black card.

49
00:02:39,210 --> 00:02:40,840
Maybe the colors
will come out better.

50
00:02:40,840 --> 00:02:44,700
So here is essentially the
beam coming out directly

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00:02:44,700 --> 00:02:48,390
from this laser.

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00:02:48,390 --> 00:02:52,080
And it's very difficult,
very difficult to tell

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00:02:52,080 --> 00:02:52,830
what's going on.

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00:02:52,830 --> 00:02:57,630
It looks pretty collimated.

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00:02:57,630 --> 00:03:02,790
Now, what the first thing I'm
going to do is expand the beam

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00:03:02,790 --> 00:03:04,740
and see what it looks like.

57
00:03:04,740 --> 00:03:07,800
So I'm going to take a
short focal-length lens

58
00:03:07,800 --> 00:03:11,550
and I'm going to place it
in the way of the beam,

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00:03:11,550 --> 00:03:21,850
and here on the screen now,
we see the expanded beam.

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00:03:21,850 --> 00:03:27,540
Now, if we go take a close-up,
we can see that it's got rings

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00:03:27,540 --> 00:03:28,500
and what have you.

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00:03:28,500 --> 00:03:33,060
Now, these rings that you
see or these fringes are

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00:03:33,060 --> 00:03:35,220
due to the fact that
the laser beam has

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00:03:35,220 --> 00:03:36,810
to go through
optical components,

65
00:03:36,810 --> 00:03:38,925
like the output
mirror of the laser,

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00:03:38,925 --> 00:03:41,880
it has to be reflected
by these mirrors

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00:03:41,880 --> 00:03:44,730
and then has to pass
through this lens over here,

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00:03:44,730 --> 00:03:48,240
and they all corrupt
the laser beam.

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00:03:48,240 --> 00:03:52,050
But we can easily get
rid of these effects

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00:03:52,050 --> 00:03:54,270
by placing a pinhole.

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00:03:54,270 --> 00:03:58,390
Here is the--
here's the pinhole.

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00:03:58,390 --> 00:04:00,630
And what I can do, I can
just place the pinhole

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00:04:00,630 --> 00:04:04,290
in front of this lens, where
the focus of this lens here,

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00:04:04,290 --> 00:04:08,610
and if I have my
adjustment right,

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00:04:08,610 --> 00:04:15,570
I have then so-called the
spatially filtered laser beam.

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00:04:15,570 --> 00:04:19,079
As you can see on the screen
now, we got rid of the--

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00:04:19,079 --> 00:04:23,040
all these rings, and this is
as close to an ideal laser beam

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00:04:23,040 --> 00:04:25,710
as one can get.

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00:04:25,710 --> 00:04:29,340
Now, what we see
here is the speckle.

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00:04:29,340 --> 00:04:31,530
So if I move the
screen a little bit,

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00:04:31,530 --> 00:04:33,670
you can see I can
wash out the speckle.

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00:04:33,670 --> 00:04:37,200
So when it's still, you can
see the speckled pattern

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00:04:37,200 --> 00:04:40,410
because the surface
is not smooth.

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00:04:40,410 --> 00:04:44,790
But otherwise, you don't
see any fringes on the beam.

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00:04:44,790 --> 00:04:48,900
And also there's an
intensely distribution,

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00:04:48,900 --> 00:04:51,870
which is essentially
Gaussian squared.

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00:04:51,870 --> 00:04:54,690
The field is Gaussian, but
the intensity distribution

88
00:04:54,690 --> 00:04:58,230
is Gaussian squared, so
that essentially drops off

89
00:04:58,230 --> 00:05:00,410
to zero in the wings.

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00:05:00,410 --> 00:05:04,880
All right, so this is a
so-called spatially filtered

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00:05:04,880 --> 00:05:06,470
laser beam, and for
some experiments,

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00:05:06,470 --> 00:05:10,640
it's very important to spatially
filter the beam, especially

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00:05:10,640 --> 00:05:14,490
in interferometry
and what have you.

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00:05:14,490 --> 00:05:16,770
Now I'm going to--

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00:05:16,770 --> 00:05:17,270
well, no.

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00:05:17,270 --> 00:05:18,770
Before I do anything
else, I'm going

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00:05:18,770 --> 00:05:26,480
to show you that the placing of
the pinhole is very critical.

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00:05:26,480 --> 00:05:30,430
If we can now take a
close-up of the spot--

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00:05:30,430 --> 00:05:32,960
now if I move the
pinhole slightly,

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00:05:32,960 --> 00:05:36,080
you can see that
first of all, the beam

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00:05:36,080 --> 00:05:38,450
disappears because
this pinhole is only

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00:05:38,450 --> 00:05:42,200
of the order of about
12 microns or so.

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00:05:42,200 --> 00:05:44,660
And another point that
one has to watch out

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00:05:44,660 --> 00:05:49,040
for when using such a
pinhole as a spatial filter

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00:05:49,040 --> 00:05:51,920
is that if the
pinhole interrupts

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00:05:51,920 --> 00:05:55,430
any part of the
laser beam, the--

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00:05:55,430 --> 00:05:58,700
now, let's look at
the insert again--

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00:05:58,700 --> 00:06:02,810
that this Gaussian
distribution in the beam gets

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00:06:02,810 --> 00:06:05,270
affected, and you
will start to see

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00:06:05,270 --> 00:06:08,060
all kinds of diffraction rings.

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00:06:08,060 --> 00:06:10,660
So again, for the
special filter to work,

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00:06:10,660 --> 00:06:19,220
the pinhole must not cut any of
the essential part of the laser

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00:06:19,220 --> 00:06:20,910
beam.

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00:06:20,910 --> 00:06:27,650
Now, what I'm going to do is
collimate this beam of light.

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00:06:27,650 --> 00:06:34,960
And here what I will use is
a simple two-lens collimator,

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00:06:34,960 --> 00:06:40,370
and I'll place it over here.

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00:06:40,370 --> 00:06:48,550
And here it is.

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00:06:48,550 --> 00:06:53,730
Here's the output from the
collimator on the black card

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00:06:53,730 --> 00:06:56,340
and see that--

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00:06:56,340 --> 00:06:58,620
obviously, you can't check
on the exact collimation,

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00:06:58,620 --> 00:07:06,270
but you can see that the beam
can be simply collimated.

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00:07:06,270 --> 00:07:06,930
All right.

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00:07:06,930 --> 00:07:10,340
Now, the next thing that
one sometime wants to do

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00:07:10,340 --> 00:07:12,660
is to focus the laser beam.

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00:07:12,660 --> 00:07:19,810
Again, if I take a simple lens
and again place it in the beam,

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00:07:19,810 --> 00:07:23,722
now I can focus.

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00:07:23,722 --> 00:07:24,930
Let's look at the beam again.

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00:07:24,930 --> 00:07:29,235
I can focus to a tiny
spot and back out again.

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00:07:29,235 --> 00:07:30,870
Here we are.

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00:07:30,870 --> 00:07:33,060
Focus to a small spot.

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00:07:33,060 --> 00:07:39,060
Now, it's very difficult
to see the size of the spot

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00:07:39,060 --> 00:07:45,462
or even the shape of this
focused Gaussian beam.

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00:07:45,462 --> 00:07:46,920
Remember, I said
before that it can

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00:07:46,920 --> 00:07:50,970
be focused to the spot size of
the order of the wavelengths

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00:07:50,970 --> 00:07:55,980
of light, and it's not so
easy to see it on this card.

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00:07:55,980 --> 00:07:59,320
So what we're going to
do when we come back,

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00:07:59,320 --> 00:08:04,020
we're going to get a
water tank and pass

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00:08:04,020 --> 00:08:07,830
the light beam, the focus
light beam-- laser beam

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00:08:07,830 --> 00:08:11,160
into the water tank, and we'll
add some scatterers to enhance

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00:08:11,160 --> 00:08:16,080
the scattering from the
laser beam by the water,

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00:08:16,080 --> 00:08:20,040
and then you'll see you get a
better picture for the focusing

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00:08:20,040 --> 00:08:23,130
of this Gaussian laser beam.

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00:08:23,130 --> 00:08:28,020
So when we come back, we'll
have that all ready for you.

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00:08:28,020 --> 00:08:30,570
We have now placed the
water tank in place

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00:08:30,570 --> 00:08:33,630
so that we can pass the
laser beam through it

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00:08:33,630 --> 00:08:40,620
and visualize the laser beam
as it passes through the water.

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00:08:40,620 --> 00:08:44,430
We've also-- here is the tank,
by the way-- and we've also

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00:08:44,430 --> 00:08:49,610
added a few drops of milk
to enhance the scattering,

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00:08:49,610 --> 00:08:52,980
and that's why the
water looks murky.

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00:08:52,980 --> 00:08:55,710
In addition, we've tilted
the tank a little bit

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00:08:55,710 --> 00:09:00,090
so that we can get a better
angle for the camera.

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00:09:00,090 --> 00:09:03,320
Now, the setup is just
like we had it before,

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00:09:03,320 --> 00:09:05,050
but let me remind you of it.

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00:09:05,050 --> 00:09:06,510
Here's the laser,
here's the beam

155
00:09:06,510 --> 00:09:09,690
from the laser reflected
by this mirror here.

156
00:09:09,690 --> 00:09:12,730
Then we pass it through
a polarization rotator

157
00:09:12,730 --> 00:09:15,600
here, so that we can
adjust the polarization

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00:09:15,600 --> 00:09:20,640
for maximum scattered
light for the camera.

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00:09:20,640 --> 00:09:24,360
And then the output after
the polarization rotates gets

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00:09:24,360 --> 00:09:27,000
reflected by this
mirror here into

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00:09:27,000 --> 00:09:30,930
this short focal-length lens,
the spatial filter we had

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00:09:30,930 --> 00:09:33,630
before and then the collimator.

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00:09:33,630 --> 00:09:36,540
The output of the
collimator is here

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00:09:36,540 --> 00:09:40,260
before it goes into the
tank and then out here

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00:09:40,260 --> 00:09:43,590
after it leaves the tank

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00:09:43,590 --> 00:09:45,930
Now, in order to
visualize the beam

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00:09:45,930 --> 00:09:48,390
as it propagates
in the water, we'll

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00:09:48,390 --> 00:09:51,480
have to turn the room lights
down, but let me tell you

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00:09:51,480 --> 00:09:55,740
what I'm going to do when
the room lights are down.

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00:09:55,740 --> 00:10:00,600
I'm going to first look at the
collimated beam in the water.

171
00:10:00,600 --> 00:10:03,510
And then I'm going to take
this lens and another lens

172
00:10:03,510 --> 00:10:09,610
like this, and I'm going
to place it over here,

173
00:10:09,610 --> 00:10:14,020
so that we can focus
the light into the tank.

174
00:10:14,020 --> 00:10:16,720
All right, and then we
can explore the region

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00:10:16,720 --> 00:10:18,850
around the focus.

176
00:10:18,850 --> 00:10:22,690
So now we're ready to turn
the room lights down and look

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00:10:22,690 --> 00:10:27,190
at the region around
the focus by simply

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00:10:27,190 --> 00:10:29,980
observing the scattered
light in the water.

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00:10:33,350 --> 00:10:36,770
Now that the room lights are
dim and the camera focused

180
00:10:36,770 --> 00:10:39,350
into the tank, the
first thing we see

181
00:10:39,350 --> 00:10:44,330
is the collimated beam or the
scattered light associated

182
00:10:44,330 --> 00:10:46,460
with the collimated beam.

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00:10:46,460 --> 00:10:51,470
There's not much I can
really say about that.

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00:10:51,470 --> 00:10:59,060
More interesting is when I
put a lens before the tank

185
00:10:59,060 --> 00:11:00,850
and look at the focal region.

186
00:11:04,770 --> 00:11:05,340
Here we are.

187
00:11:05,340 --> 00:11:07,230
I'm going to adjust the
position of the lens,

188
00:11:07,230 --> 00:11:12,630
so that the waist or the focused
region, the focal region,

189
00:11:12,630 --> 00:11:16,962
is in the center of your screen.

190
00:11:16,962 --> 00:11:18,420
Now, the thing that
you can observe

191
00:11:18,420 --> 00:11:22,110
is that laser beam coming
in from the left then

192
00:11:22,110 --> 00:11:28,150
is then focused to a region
where the spot is small,

193
00:11:28,150 --> 00:11:32,190
spot size is small,
and then expands again

194
00:11:32,190 --> 00:11:33,960
on the other side.

195
00:11:33,960 --> 00:11:39,780
Now, because of the limitation
of television recording,

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00:11:39,780 --> 00:11:43,210
especially recording of
color and especially red,

197
00:11:43,210 --> 00:11:45,270
you do better.

198
00:11:45,270 --> 00:11:47,640
If you want to see how
narrow that focal region is,

199
00:11:47,640 --> 00:11:51,120
you do better if you turn down
the color, turn off the color,

200
00:11:51,120 --> 00:11:54,270
and look at it in
black and white.

201
00:11:54,270 --> 00:11:59,310
If you do that, you'll see
that the focal region is now

202
00:11:59,310 --> 00:12:02,070
narrower than it
is when it's red.

203
00:12:04,970 --> 00:12:10,010
But in fact, the truth is that
you cannot really observe this

204
00:12:10,010 --> 00:12:20,420
way the true size of the focused
spot because that's only a few

205
00:12:20,420 --> 00:12:23,960
microns, and it's going to
be limited by television

206
00:12:23,960 --> 00:12:26,630
resolution in any case.

207
00:12:26,630 --> 00:12:29,180
But at least you get
a feel for the fact

208
00:12:29,180 --> 00:12:33,260
that the beam is pretty
narrow at the focus.

209
00:12:33,260 --> 00:12:35,030
Another thing you
want to observe

210
00:12:35,030 --> 00:12:39,650
is that the region
around the focus

211
00:12:39,650 --> 00:12:46,160
is reasonably
constant in diameter,

212
00:12:46,160 --> 00:12:48,460
and that's called the
Rayleigh region, where

213
00:12:48,460 --> 00:12:51,150
the expansion of the
beam is not so big.

214
00:12:51,150 --> 00:12:54,500
But after that, then the
beam expands one side

215
00:12:54,500 --> 00:12:58,520
and then symmetrically the
other side of the beam.

216
00:12:58,520 --> 00:13:01,700
The intensity distribution,
if you take a slice anywhere

217
00:13:01,700 --> 00:13:03,860
along the beam,
intensity distribution

218
00:13:03,860 --> 00:13:06,508
is still Gaussian
or Gaussian squared.

219
00:13:06,508 --> 00:13:07,925
The field distribution
is Gaussian

220
00:13:07,925 --> 00:13:10,460
and intensity is
Gaussian squared.

221
00:13:13,140 --> 00:13:20,040
The other thing to observe
is that the curvature.

222
00:13:20,040 --> 00:13:25,080
Now, at the focal at the
focus or at the middle

223
00:13:25,080 --> 00:13:27,950
of that Rayleigh range, what
we call the focus or the waist

224
00:13:27,950 --> 00:13:30,780
of the beam, the curvature is--

225
00:13:30,780 --> 00:13:33,490
the radius of
curvature is infinite,

226
00:13:33,490 --> 00:13:36,670
which means that we
have a plane wave.

227
00:13:36,670 --> 00:13:40,290
Now, it stays plane
within the Rayleigh region

228
00:13:40,290 --> 00:13:44,190
or close to plane, and then
we develop the coverage,

229
00:13:44,190 --> 00:13:45,930
so we have an expanding
beam on one side

230
00:13:45,930 --> 00:13:48,130
and expanding beam
on the other side.

231
00:13:48,130 --> 00:13:50,970
In fact, if we go far
away, the curvature,

232
00:13:50,970 --> 00:13:52,740
the radius of
curvature, is the same

233
00:13:52,740 --> 00:13:57,600
as if we had a spherical
wave starting at the waist.

234
00:13:57,600 --> 00:13:59,400
All, right that's
with this lens.

235
00:13:59,400 --> 00:14:03,240
Now I'm going to take
this lens off and place

236
00:14:03,240 --> 00:14:09,150
another lens that is a little
shorter in focal length.

237
00:14:13,690 --> 00:14:16,570
And here we are.

238
00:14:16,570 --> 00:14:22,570
Let me turn it around and
then let me again center it,

239
00:14:22,570 --> 00:14:25,500
so that the waist is the
middle of your screen,

240
00:14:25,500 --> 00:14:29,670
and see now the
divergence is different,

241
00:14:29,670 --> 00:14:32,940
showing that it's a shorter
focal length net and I find.

242
00:14:32,940 --> 00:14:35,490
Over to one side, you
can see that the beam

243
00:14:35,490 --> 00:14:38,760
gets quite big very
quickly and also the same

244
00:14:38,760 --> 00:14:40,650
to the other side.

245
00:14:40,650 --> 00:14:46,425
And then the other
thing you notice

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is that the Rayleigh range
or the region around focus

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now is smaller, so
it's a tighter focus

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than in the previous case.

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And as the focal length of the
lens gets bigger and bigger,

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then the Rayleigh region
gets bigger and bigger also.

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So here we are with a
shorter focal length.

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And again, if you want to see
a nice, small focal region,

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then you want to
turn down your color

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and look at it in
black and white.

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So in summary, we've illustrated
some of the basic properties

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associated with
the optics of laser

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beams, such as collimation,
focusing, and what have you.

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Also we've shown that the
use of a spatial filter

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can help clean up
the laser beam,

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and it looks very
beautiful after that.

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But in order to really measure
the properties of the laser

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beams and measure the
exact size of the focus

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and the exact collimation,
degree of collimation,

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one really needs to use
more precise methods,

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such as taking a tiny pinhole
of the order of 1 or 2 microns

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in diameter and then
scanning it across the beam

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at various locations.

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Otherwise, it's
only approximate.

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00:16:15,350 --> 00:16:19,760
But I think you'll get a feel
for these properties in these--

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of the laser beam in
these demonstrations.