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SHAOUL EZEKIEL: The
light beam from a laser

00:00:23.880 --> 00:00:28.260
is as close to an ideal
beam as one can get.

00:00:28.260 --> 00:00:32.170
What I mean by that is that
the properties of this beam,

00:00:32.170 --> 00:00:34.770
the propagation
properties, are limited

00:00:34.770 --> 00:00:38.790
by fundamental laws of physics--

00:00:38.790 --> 00:00:41.400
for example, loss
of diffraction--

00:00:41.400 --> 00:00:45.870
and not by the properties
of the light source.

00:00:45.870 --> 00:00:50.160
For example, a laser beam
from a well-behaved laser

00:00:50.160 --> 00:00:59.190
can be collimated to
a very small angle.

00:00:59.190 --> 00:01:01.740
This angle is
determined by, as I

00:01:01.740 --> 00:01:03.570
said, the laws of
diffraction, which

00:01:03.570 --> 00:01:06.030
is the wavelength
of the light divided

00:01:06.030 --> 00:01:09.180
by the diameter of the beam.

00:01:09.180 --> 00:01:12.570
And it doesn't say anything
about the size of the source

00:01:12.570 --> 00:01:14.460
or the properties of
the source, and that

00:01:14.460 --> 00:01:19.980
is the ideal collimation
limit on a beam.

00:01:19.980 --> 00:01:22.500
At the same time,
a laser beam can be

00:01:22.500 --> 00:01:25.260
focused to a very small spot.

00:01:25.260 --> 00:01:28.980
The size of that spot
is, again, determined

00:01:28.980 --> 00:01:33.720
by laws of diffraction, which
is the wavelength of the light

00:01:33.720 --> 00:01:37.260
divided by the diameter
of the beam, multiplied

00:01:37.260 --> 00:01:38.880
by the focal length of the lens.

00:01:38.880 --> 00:01:41.130
And if we choose the
diameter of the beam

00:01:41.130 --> 00:01:44.440
and the focal length of
the lens about equal,

00:01:44.440 --> 00:01:46.810
then the spot size
would be of the order

00:01:46.810 --> 00:01:48.030
of the wavelength of light.

00:01:48.030 --> 00:01:49.830
And again, it
doesn't say anything

00:01:49.830 --> 00:01:52.760
about the physical size
of the light source

00:01:52.760 --> 00:01:57.720
or what have you, as we would
have in a case of an arc lamp

00:01:57.720 --> 00:02:01.300
or any other kind
of light source.

00:02:01.300 --> 00:02:03.580
Now, in these
demonstrations that follow,

00:02:03.580 --> 00:02:07.650
we're going to illustrate
some of these basic properties

00:02:07.650 --> 00:02:11.550
of laser beams.

00:02:11.550 --> 00:02:15.090
What we're going to start
with is this laser here,

00:02:15.090 --> 00:02:17.490
which is a helium-neon
laser, and here

00:02:17.490 --> 00:02:20.040
is the beam from the laser.

00:02:20.040 --> 00:02:21.960
We're going to reflect
it by this mirror

00:02:21.960 --> 00:02:25.920
here and then reflect
it again by this mirror

00:02:25.920 --> 00:02:31.800
here and let the beam
fall on the screen.

00:02:31.800 --> 00:02:36.180
Now, you might be able to get
a better feeling for the beam

00:02:36.180 --> 00:02:39.210
if I use the black card.

00:02:39.210 --> 00:02:40.840
Maybe the colors
will come out better.

00:02:40.840 --> 00:02:44.700
So here is essentially the
beam coming out directly

00:02:44.700 --> 00:02:48.390
from this laser.

00:02:48.390 --> 00:02:52.080
And it's very difficult,
very difficult to tell

00:02:52.080 --> 00:02:52.830
what's going on.

00:02:52.830 --> 00:02:57.630
It looks pretty collimated.

00:02:57.630 --> 00:03:02.790
Now, what the first thing I'm
going to do is expand the beam

00:03:02.790 --> 00:03:04.740
and see what it looks like.

00:03:04.740 --> 00:03:07.800
So I'm going to take a
short focal-length lens

00:03:07.800 --> 00:03:11.550
and I'm going to place it
in the way of the beam,

00:03:11.550 --> 00:03:21.850
and here on the screen now,
we see the expanded beam.

00:03:21.850 --> 00:03:27.540
Now, if we go take a close-up,
we can see that it's got rings

00:03:27.540 --> 00:03:28.500
and what have you.

00:03:28.500 --> 00:03:33.060
Now, these rings that you
see or these fringes are

00:03:33.060 --> 00:03:35.220
due to the fact that
the laser beam has

00:03:35.220 --> 00:03:36.810
to go through
optical components,

00:03:36.810 --> 00:03:38.925
like the output
mirror of the laser,

00:03:38.925 --> 00:03:41.880
it has to be reflected
by these mirrors

00:03:41.880 --> 00:03:44.730
and then has to pass
through this lens over here,

00:03:44.730 --> 00:03:48.240
and they all corrupt
the laser beam.

00:03:48.240 --> 00:03:52.050
But we can easily get
rid of these effects

00:03:52.050 --> 00:03:54.270
by placing a pinhole.

00:03:54.270 --> 00:03:58.390
Here is the--
here's the pinhole.

00:03:58.390 --> 00:04:00.630
And what I can do, I can
just place the pinhole

00:04:00.630 --> 00:04:04.290
in front of this lens, where
the focus of this lens here,

00:04:04.290 --> 00:04:08.610
and if I have my
adjustment right,

00:04:08.610 --> 00:04:15.570
I have then so-called the
spatially filtered laser beam.

00:04:15.570 --> 00:04:19.079
As you can see on the screen
now, we got rid of the--

00:04:19.079 --> 00:04:23.040
all these rings, and this is
as close to an ideal laser beam

00:04:23.040 --> 00:04:25.710
as one can get.

00:04:25.710 --> 00:04:29.340
Now, what we see
here is the speckle.

00:04:29.340 --> 00:04:31.530
So if I move the
screen a little bit,

00:04:31.530 --> 00:04:33.670
you can see I can
wash out the speckle.

00:04:33.670 --> 00:04:37.200
So when it's still, you can
see the speckled pattern

00:04:37.200 --> 00:04:40.410
because the surface
is not smooth.

00:04:40.410 --> 00:04:44.790
But otherwise, you don't
see any fringes on the beam.

00:04:44.790 --> 00:04:48.900
And also there's an
intensely distribution,

00:04:48.900 --> 00:04:51.870
which is essentially
Gaussian squared.

00:04:51.870 --> 00:04:54.690
The field is Gaussian, but
the intensity distribution

00:04:54.690 --> 00:04:58.230
is Gaussian squared, so
that essentially drops off

00:04:58.230 --> 00:05:00.410
to zero in the wings.

00:05:00.410 --> 00:05:04.880
All right, so this is a
so-called spatially filtered

00:05:04.880 --> 00:05:06.470
laser beam, and for
some experiments,

00:05:06.470 --> 00:05:10.640
it's very important to spatially
filter the beam, especially

00:05:10.640 --> 00:05:14.490
in interferometry
and what have you.

00:05:14.490 --> 00:05:16.770
Now I'm going to--

00:05:16.770 --> 00:05:17.270
well, no.

00:05:17.270 --> 00:05:18.770
Before I do anything
else, I'm going

00:05:18.770 --> 00:05:26.480
to show you that the placing of
the pinhole is very critical.

00:05:26.480 --> 00:05:30.430
If we can now take a
close-up of the spot--

00:05:30.430 --> 00:05:32.960
now if I move the
pinhole slightly,

00:05:32.960 --> 00:05:36.080
you can see that
first of all, the beam

00:05:36.080 --> 00:05:38.450
disappears because
this pinhole is only

00:05:38.450 --> 00:05:42.200
of the order of about
12 microns or so.

00:05:42.200 --> 00:05:44.660
And another point that
one has to watch out

00:05:44.660 --> 00:05:49.040
for when using such a
pinhole as a spatial filter

00:05:49.040 --> 00:05:51.920
is that if the
pinhole interrupts

00:05:51.920 --> 00:05:55.430
any part of the
laser beam, the--

00:05:55.430 --> 00:05:58.700
now, let's look at
the insert again--

00:05:58.700 --> 00:06:02.810
that this Gaussian
distribution in the beam gets

00:06:02.810 --> 00:06:05.270
affected, and you
will start to see

00:06:05.270 --> 00:06:08.060
all kinds of diffraction rings.

00:06:08.060 --> 00:06:10.660
So again, for the
special filter to work,

00:06:10.660 --> 00:06:19.220
the pinhole must not cut any of
the essential part of the laser

00:06:19.220 --> 00:06:20.910
beam.

00:06:20.910 --> 00:06:27.650
Now, what I'm going to do is
collimate this beam of light.

00:06:27.650 --> 00:06:34.960
And here what I will use is
a simple two-lens collimator,

00:06:34.960 --> 00:06:40.370
and I'll place it over here.

00:06:40.370 --> 00:06:48.550
And here it is.

00:06:48.550 --> 00:06:53.730
Here's the output from the
collimator on the black card

00:06:53.730 --> 00:06:56.340
and see that--

00:06:56.340 --> 00:06:58.620
obviously, you can't check
on the exact collimation,

00:06:58.620 --> 00:07:06.270
but you can see that the beam
can be simply collimated.

00:07:06.270 --> 00:07:06.930
All right.

00:07:06.930 --> 00:07:10.340
Now, the next thing that
one sometime wants to do

00:07:10.340 --> 00:07:12.660
is to focus the laser beam.

00:07:12.660 --> 00:07:19.810
Again, if I take a simple lens
and again place it in the beam,

00:07:19.810 --> 00:07:23.722
now I can focus.

00:07:23.722 --> 00:07:24.930
Let's look at the beam again.

00:07:24.930 --> 00:07:29.235
I can focus to a tiny
spot and back out again.

00:07:29.235 --> 00:07:30.870
Here we are.

00:07:30.870 --> 00:07:33.060
Focus to a small spot.

00:07:33.060 --> 00:07:39.060
Now, it's very difficult
to see the size of the spot

00:07:39.060 --> 00:07:45.462
or even the shape of this
focused Gaussian beam.

00:07:45.462 --> 00:07:46.920
Remember, I said
before that it can

00:07:46.920 --> 00:07:50.970
be focused to the spot size of
the order of the wavelengths

00:07:50.970 --> 00:07:55.980
of light, and it's not so
easy to see it on this card.

00:07:55.980 --> 00:07:59.320
So what we're going to
do when we come back,

00:07:59.320 --> 00:08:04.020
we're going to get a
water tank and pass

00:08:04.020 --> 00:08:07.830
the light beam, the focus
light beam-- laser beam

00:08:07.830 --> 00:08:11.160
into the water tank, and we'll
add some scatterers to enhance

00:08:11.160 --> 00:08:16.080
the scattering from the
laser beam by the water,

00:08:16.080 --> 00:08:20.040
and then you'll see you get a
better picture for the focusing

00:08:20.040 --> 00:08:23.130
of this Gaussian laser beam.

00:08:23.130 --> 00:08:28.020
So when we come back, we'll
have that all ready for you.

00:08:28.020 --> 00:08:30.570
We have now placed the
water tank in place

00:08:30.570 --> 00:08:33.630
so that we can pass the
laser beam through it

00:08:33.630 --> 00:08:40.620
and visualize the laser beam
as it passes through the water.

00:08:40.620 --> 00:08:44.430
We've also-- here is the tank,
by the way-- and we've also

00:08:44.430 --> 00:08:49.610
added a few drops of milk
to enhance the scattering,

00:08:49.610 --> 00:08:52.980
and that's why the
water looks murky.

00:08:52.980 --> 00:08:55.710
In addition, we've tilted
the tank a little bit

00:08:55.710 --> 00:09:00.090
so that we can get a better
angle for the camera.

00:09:00.090 --> 00:09:03.320
Now, the setup is just
like we had it before,

00:09:03.320 --> 00:09:05.050
but let me remind you of it.

00:09:05.050 --> 00:09:06.510
Here's the laser,
here's the beam

00:09:06.510 --> 00:09:09.690
from the laser reflected
by this mirror here.

00:09:09.690 --> 00:09:12.730
Then we pass it through
a polarization rotator

00:09:12.730 --> 00:09:15.600
here, so that we can
adjust the polarization

00:09:15.600 --> 00:09:20.640
for maximum scattered
light for the camera.

00:09:20.640 --> 00:09:24.360
And then the output after
the polarization rotates gets

00:09:24.360 --> 00:09:27.000
reflected by this
mirror here into

00:09:27.000 --> 00:09:30.930
this short focal-length lens,
the spatial filter we had

00:09:30.930 --> 00:09:33.630
before and then the collimator.

00:09:33.630 --> 00:09:36.540
The output of the
collimator is here

00:09:36.540 --> 00:09:40.260
before it goes into the
tank and then out here

00:09:40.260 --> 00:09:43.590
after it leaves the tank

00:09:43.590 --> 00:09:45.930
Now, in order to
visualize the beam

00:09:45.930 --> 00:09:48.390
as it propagates
in the water, we'll

00:09:48.390 --> 00:09:51.480
have to turn the room lights
down, but let me tell you

00:09:51.480 --> 00:09:55.740
what I'm going to do when
the room lights are down.

00:09:55.740 --> 00:10:00.600
I'm going to first look at the
collimated beam in the water.

00:10:00.600 --> 00:10:03.510
And then I'm going to take
this lens and another lens

00:10:03.510 --> 00:10:09.610
like this, and I'm going
to place it over here,

00:10:09.610 --> 00:10:14.020
so that we can focus
the light into the tank.

00:10:14.020 --> 00:10:16.720
All right, and then we
can explore the region

00:10:16.720 --> 00:10:18.850
around the focus.

00:10:18.850 --> 00:10:22.690
So now we're ready to turn
the room lights down and look

00:10:22.690 --> 00:10:27.190
at the region around
the focus by simply

00:10:27.190 --> 00:10:29.980
observing the scattered
light in the water.

00:10:33.350 --> 00:10:36.770
Now that the room lights are
dim and the camera focused

00:10:36.770 --> 00:10:39.350
into the tank, the
first thing we see

00:10:39.350 --> 00:10:44.330
is the collimated beam or the
scattered light associated

00:10:44.330 --> 00:10:46.460
with the collimated beam.

00:10:46.460 --> 00:10:51.470
There's not much I can
really say about that.

00:10:51.470 --> 00:10:59.060
More interesting is when I
put a lens before the tank

00:10:59.060 --> 00:11:00.850
and look at the focal region.

00:11:04.770 --> 00:11:05.340
Here we are.

00:11:05.340 --> 00:11:07.230
I'm going to adjust the
position of the lens,

00:11:07.230 --> 00:11:12.630
so that the waist or the focused
region, the focal region,

00:11:12.630 --> 00:11:16.962
is in the center of your screen.

00:11:16.962 --> 00:11:18.420
Now, the thing that
you can observe

00:11:18.420 --> 00:11:22.110
is that laser beam coming
in from the left then

00:11:22.110 --> 00:11:28.150
is then focused to a region
where the spot is small,

00:11:28.150 --> 00:11:32.190
spot size is small,
and then expands again

00:11:32.190 --> 00:11:33.960
on the other side.

00:11:33.960 --> 00:11:39.780
Now, because of the limitation
of television recording,

00:11:39.780 --> 00:11:43.210
especially recording of
color and especially red,

00:11:43.210 --> 00:11:45.270
you do better.

00:11:45.270 --> 00:11:47.640
If you want to see how
narrow that focal region is,

00:11:47.640 --> 00:11:51.120
you do better if you turn down
the color, turn off the color,

00:11:51.120 --> 00:11:54.270
and look at it in
black and white.

00:11:54.270 --> 00:11:59.310
If you do that, you'll see
that the focal region is now

00:11:59.310 --> 00:12:02.070
narrower than it
is when it's red.

00:12:04.970 --> 00:12:10.010
But in fact, the truth is that
you cannot really observe this

00:12:10.010 --> 00:12:20.420
way the true size of the focused
spot because that's only a few

00:12:20.420 --> 00:12:23.960
microns, and it's going to
be limited by television

00:12:23.960 --> 00:12:26.630
resolution in any case.

00:12:26.630 --> 00:12:29.180
But at least you get
a feel for the fact

00:12:29.180 --> 00:12:33.260
that the beam is pretty
narrow at the focus.

00:12:33.260 --> 00:12:35.030
Another thing you
want to observe

00:12:35.030 --> 00:12:39.650
is that the region
around the focus

00:12:39.650 --> 00:12:46.160
is reasonably
constant in diameter,

00:12:46.160 --> 00:12:48.460
and that's called the
Rayleigh region, where

00:12:48.460 --> 00:12:51.150
the expansion of the
beam is not so big.

00:12:51.150 --> 00:12:54.500
But after that, then the
beam expands one side

00:12:54.500 --> 00:12:58.520
and then symmetrically the
other side of the beam.

00:12:58.520 --> 00:13:01.700
The intensity distribution,
if you take a slice anywhere

00:13:01.700 --> 00:13:03.860
along the beam,
intensity distribution

00:13:03.860 --> 00:13:06.508
is still Gaussian
or Gaussian squared.

00:13:06.508 --> 00:13:07.925
The field distribution
is Gaussian

00:13:07.925 --> 00:13:10.460
and intensity is
Gaussian squared.

00:13:13.140 --> 00:13:20.040
The other thing to observe
is that the curvature.

00:13:20.040 --> 00:13:25.080
Now, at the focal at the
focus or at the middle

00:13:25.080 --> 00:13:27.950
of that Rayleigh range, what
we call the focus or the waist

00:13:27.950 --> 00:13:30.780
of the beam, the curvature is--

00:13:30.780 --> 00:13:33.490
the radius of
curvature is infinite,

00:13:33.490 --> 00:13:36.670
which means that we
have a plane wave.

00:13:36.670 --> 00:13:40.290
Now, it stays plane
within the Rayleigh region

00:13:40.290 --> 00:13:44.190
or close to plane, and then
we develop the coverage,

00:13:44.190 --> 00:13:45.930
so we have an expanding
beam on one side

00:13:45.930 --> 00:13:48.130
and expanding beam
on the other side.

00:13:48.130 --> 00:13:50.970
In fact, if we go far
away, the curvature,

00:13:50.970 --> 00:13:52.740
the radius of
curvature, is the same

00:13:52.740 --> 00:13:57.600
as if we had a spherical
wave starting at the waist.

00:13:57.600 --> 00:13:59.400
All, right that's
with this lens.

00:13:59.400 --> 00:14:03.240
Now I'm going to take
this lens off and place

00:14:03.240 --> 00:14:09.150
another lens that is a little
shorter in focal length.

00:14:13.690 --> 00:14:16.570
And here we are.

00:14:16.570 --> 00:14:22.570
Let me turn it around and
then let me again center it,

00:14:22.570 --> 00:14:25.500
so that the waist is the
middle of your screen,

00:14:25.500 --> 00:14:29.670
and see now the
divergence is different,

00:14:29.670 --> 00:14:32.940
showing that it's a shorter
focal length net and I find.

00:14:32.940 --> 00:14:35.490
Over to one side, you
can see that the beam

00:14:35.490 --> 00:14:38.760
gets quite big very
quickly and also the same

00:14:38.760 --> 00:14:40.650
to the other side.

00:14:40.650 --> 00:14:46.425
And then the other
thing you notice

00:14:46.425 --> 00:14:49.440
is that the Rayleigh range
or the region around focus

00:14:49.440 --> 00:14:53.130
now is smaller, so
it's a tighter focus

00:14:53.130 --> 00:14:54.960
than in the previous case.

00:14:54.960 --> 00:15:00.060
And as the focal length of the
lens gets bigger and bigger,

00:15:00.060 --> 00:15:04.450
then the Rayleigh region
gets bigger and bigger also.

00:15:04.450 --> 00:15:07.750
So here we are with a
shorter focal length.

00:15:07.750 --> 00:15:13.050
And again, if you want to see
a nice, small focal region,

00:15:13.050 --> 00:15:15.120
then you want to
turn down your color

00:15:15.120 --> 00:15:20.340
and look at it in
black and white.

00:15:20.340 --> 00:15:24.740
So in summary, we've illustrated
some of the basic properties

00:15:24.740 --> 00:15:27.140
associated with
the optics of laser

00:15:27.140 --> 00:15:32.570
beams, such as collimation,
focusing, and what have you.

00:15:32.570 --> 00:15:37.220
Also we've shown that the
use of a spatial filter

00:15:37.220 --> 00:15:40.190
can help clean up
the laser beam,

00:15:40.190 --> 00:15:45.390
and it looks very
beautiful after that.

00:15:45.390 --> 00:15:50.900
But in order to really measure
the properties of the laser

00:15:50.900 --> 00:15:55.700
beams and measure the
exact size of the focus

00:15:55.700 --> 00:15:58.310
and the exact collimation,
degree of collimation,

00:15:58.310 --> 00:16:01.940
one really needs to use
more precise methods,

00:16:01.940 --> 00:16:06.200
such as taking a tiny pinhole
of the order of 1 or 2 microns

00:16:06.200 --> 00:16:09.500
in diameter and then
scanning it across the beam

00:16:09.500 --> 00:16:12.080
at various locations.

00:16:12.080 --> 00:16:15.350
Otherwise, it's
only approximate.

00:16:15.350 --> 00:16:19.760
But I think you'll get a feel
for these properties in these--

00:16:19.760 --> 00:16:22.960
of the laser beam in
these demonstrations.