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SHAOUL EZEKIEL: In
previous demonstrations,

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we showed the laser beam
to be a very simple beam

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00:00:27,110 --> 00:00:31,690
with a single spot in
the transverse direction.

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00:00:31,690 --> 00:00:35,020
Now, most lasers actually
put out a beam like that--

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00:00:35,020 --> 00:00:37,780
just one spot in the
transverse direction,

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and the intense
distribution is Gaussian.

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00:00:43,500 --> 00:00:45,210
It has very nice
properties, and that's

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00:00:45,210 --> 00:00:50,030
why it's a very popular
beam from a laser.

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00:00:50,030 --> 00:00:54,270
Now, a laser can also put out
other intense distributions

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00:00:54,270 --> 00:00:58,170
because of the existence
of transverse modes,

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00:00:58,170 --> 00:01:03,960
which means that the beam
would look very spotty.

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00:01:03,960 --> 00:01:06,780
Sometimes it can
look like a doughnut

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00:01:06,780 --> 00:01:09,610
with darkness in the center.

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00:01:09,610 --> 00:01:12,560
You can also make it look
like two spots, three spots--

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00:01:12,560 --> 00:01:14,820
you can make it look
like a flower and so

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00:01:14,820 --> 00:01:19,730
on, all because of the
existence of transverse modes.

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00:01:19,730 --> 00:01:21,760
Now, in this
demonstration, we've

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got a special laser
for you that can

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00:01:24,550 --> 00:01:27,790
exhibit these transverse modes.

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00:01:27,790 --> 00:01:31,030
And the setup is here.

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00:01:31,030 --> 00:01:33,970
We have our usual
discharge tube.

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00:01:33,970 --> 00:01:37,360
Except in this case,
the bore diameter

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00:01:37,360 --> 00:01:41,020
is a little bit bigger than
in previous demonstrations.

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00:01:43,530 --> 00:01:47,370
The diameter here is of the
order of 2 millimeters--

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00:01:47,370 --> 00:01:49,320
2 and 1/2 millimeters or so.

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00:01:49,320 --> 00:01:53,820
While before, the bore
diameter was about 1 and 1/2

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00:01:53,820 --> 00:01:56,200
millimeters.

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00:01:56,200 --> 00:02:00,880
One mirror is attached to
the discharge tube over here.

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00:02:03,570 --> 00:02:05,760
And the other end of
the discharge tube

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00:02:05,760 --> 00:02:09,660
has a Brewster window
so that we can place

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00:02:09,660 --> 00:02:11,810
the second mirror over here.

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00:02:14,960 --> 00:02:19,810
This mirror here is curved
about 60 centimeters

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00:02:19,810 --> 00:02:24,920
of a radius of curvature, and
the mirror here is a flat one.

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00:02:24,920 --> 00:02:29,010
The transmission of the
mirrors is very small, and so

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00:02:29,010 --> 00:02:31,020
that the output light
is not going to be

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00:02:31,020 --> 00:02:32,610
as bright as we would like it.

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00:02:32,610 --> 00:02:38,050
But hopefully, we'll be able
to see the transverse modes.

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00:02:38,050 --> 00:02:42,450
The beam, then, from the
laser will come out over here.

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00:02:42,450 --> 00:02:45,060
And then we'll reflected
by this mirror,

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00:02:45,060 --> 00:02:48,120
and then this
mirror into a lens.

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00:02:48,120 --> 00:02:49,770
Here, we expand the beam.

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00:02:49,770 --> 00:02:51,570
And then the expanded
beam then will

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00:02:51,570 --> 00:02:56,290
fall onto the screen over here.

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00:02:56,290 --> 00:03:00,230
So now, let me
turn on the laser.

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00:03:00,230 --> 00:03:03,550
And then we count up to
7 or 8 seconds or so,

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00:03:03,550 --> 00:03:06,150
and here is this laser on.

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00:03:06,150 --> 00:03:10,950
And the output, then, from
the laser is weak, I know,

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00:03:10,950 --> 00:03:12,970
but you might be able to see it.

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00:03:12,970 --> 00:03:14,670
Here's the output
from the laser.

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00:03:14,670 --> 00:03:16,128
And then we're
going to reflect it,

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00:03:16,128 --> 00:03:18,330
as I said before, by
this mirror, this mirror,

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00:03:18,330 --> 00:03:21,540
to the lens, and
then onto the screen.

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00:03:21,540 --> 00:03:24,450
And now we'll have one
camera look at the screen

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so we can look at
the transverse modes,

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and another camera can
look at my hands adjusting

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one of the mirrors to
change the number of modes

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and the intensity
distribution that you

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00:03:37,502 --> 00:03:38,460
will see on the screen.

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Now here, as you can see, the
beam looks like a doughnut mode

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with no field in the center.

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00:03:52,150 --> 00:03:55,540
And my hand, you can see in
the lower right-hand corner,

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00:03:55,540 --> 00:03:58,390
adjusting the mirror mount.

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Now here, I'm going to
start now adjusting.

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And then you can see that the
intense distribution varies--

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00:04:05,825 --> 00:04:07,300
varies quite a bit.

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00:04:07,300 --> 00:04:07,900
Here we are.

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00:04:07,900 --> 00:04:10,390
Here you can see a very
complicated kind of pattern.

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00:04:10,390 --> 00:04:13,300
Here's another one
with two dark spots--

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00:04:13,300 --> 00:04:16,220
single dark spot.

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00:04:16,220 --> 00:04:19,660
And here it looks like a flower.

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00:04:19,660 --> 00:04:21,040
Nice, pretty little patterns.

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00:04:21,040 --> 00:04:24,340
And these are all due to
these transverse modes.

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00:04:24,340 --> 00:04:27,790
Now, what you're seeing here is
a mixture of transverse modes.

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00:04:27,790 --> 00:04:29,590
They're not
necessarily pure ones.

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That means just a single
transverse mode by itself.

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Now here, if I'm misaligned
too much and get rid of most

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of them, here is our
lowest-order mode,

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00:04:42,980 --> 00:04:46,730
which is called the 00 mode.

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Now, here is the normal
kind of laser beam.

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00:04:49,390 --> 00:04:52,030
But in this particular
laser setup,

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00:04:52,030 --> 00:04:58,120
I can generate all kinds of
other intense distributions,

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00:04:58,120 --> 00:05:02,110
due to the other
transverse modes that

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00:05:02,110 --> 00:05:05,910
can be generated in
this kind of setup

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00:05:05,910 --> 00:05:09,330
with a larger bore in
the discharge tube.

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00:05:09,330 --> 00:05:16,280
It's very pretty,
as you can see.

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00:05:16,280 --> 00:05:21,370
Now, as I mentioned
before, in most lasers,

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00:05:21,370 --> 00:05:26,050
one wants to get rid of these
transverse modes so that we can

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00:05:26,050 --> 00:05:28,870
only have the 00 mode.

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00:05:28,870 --> 00:05:30,790
And when we come
back, we're going

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00:05:30,790 --> 00:05:35,860
to show a method of
eliminating the lasing

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00:05:35,860 --> 00:05:39,190
of these transverse modes,
other than the lowest-order one.

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00:05:39,190 --> 00:05:42,990
We're going to do this
by placing an aperture--

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00:05:42,990 --> 00:05:46,560
a small iris inside
the laser cavity.

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We have now placed an aperture
inside the laser cavity,

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00:05:54,460 --> 00:05:58,870
so as to get rid of all
transverse modes except

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00:05:58,870 --> 00:06:01,720
the lowest-order
one-- the 00 mode.

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00:06:01,720 --> 00:06:04,660
The aperture is over here.

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00:06:04,660 --> 00:06:07,720
When we're placing it in the
space between the Brewster

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00:06:07,720 --> 00:06:10,900
window and the second mirror.

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00:06:10,900 --> 00:06:12,160
So here's the aperture.

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00:06:12,160 --> 00:06:17,560
And then by adjusting
this knob here,

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I can then change the
size of the aperture.

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00:06:22,120 --> 00:06:25,570
In the meantime, we've
also covered the laser tube

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00:06:25,570 --> 00:06:31,090
here with some white paper so
that we don't have too much

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00:06:31,090 --> 00:06:33,250
light to burn the camera.

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00:06:33,250 --> 00:06:35,050
So in case you don't
see the discharge tube

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00:06:35,050 --> 00:06:38,170
so well as before, it's
because we've covered it up.

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00:06:38,170 --> 00:06:43,020
So now let's look
at the screen now

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00:06:43,020 --> 00:06:48,820
to see the transverse modes
without the aperture stopped

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00:06:48,820 --> 00:06:49,720
down.

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00:06:49,720 --> 00:06:52,030
Here we are.

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00:06:52,030 --> 00:06:55,540
We see those transverse modes or
mixture of transverse moles now

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00:06:55,540 --> 00:06:58,150
what I'm going to do is
I'm going to now reduce

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00:06:58,150 --> 00:07:00,370
the size of the aperture.

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00:07:00,370 --> 00:07:02,000
And let's see what happens.

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00:07:02,000 --> 00:07:05,600
Here I am reducing it.

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00:07:05,600 --> 00:07:07,700
And you can see as we
go back a little bit,

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00:07:07,700 --> 00:07:08,710
here's some other modes.

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00:07:08,710 --> 00:07:12,190
And then when I stop it, way
down to about a millimeter

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00:07:12,190 --> 00:07:15,230
or so, you can see that I have
now the lowest-order mode--

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00:07:15,230 --> 00:07:17,380
the 00 mode.

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00:07:17,380 --> 00:07:18,200
Let's do it again.

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00:07:18,200 --> 00:07:19,240
Let me open it up again.

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00:07:19,240 --> 00:07:24,250
Here is the transverse mode,
and then I stop it down.

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00:07:24,250 --> 00:07:28,460
I get rid of all transverse
modes except the lowest order.

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00:07:28,460 --> 00:07:31,420
In fact, now I can
even adjust the mirror.

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00:07:31,420 --> 00:07:34,240
I can adjust the
mirror, and indeed, I

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can't move the
spot around, but I

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00:07:36,670 --> 00:07:42,460
don't get any transverse
modes showing up.

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00:07:42,460 --> 00:07:47,650
So in summary, then by putting a
small aperture inside the laser

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00:07:47,650 --> 00:07:52,150
cavity and choosing the
diameter appropriately,

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00:07:52,150 --> 00:07:55,480
we can get rid of all
transverse modes except

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00:07:55,480 --> 00:07:58,690
for the lowest-order mode.

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00:07:58,690 --> 00:08:01,780
Now, most commercial
lasers either

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00:08:01,780 --> 00:08:04,870
have an aperture like that
inside the laser cavity,

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00:08:04,870 --> 00:08:11,650
or have the bore size of the
laser amplifier so chosen

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00:08:11,650 --> 00:08:14,620
so that only the
lowest-order mode would lase,

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00:08:14,620 --> 00:08:17,440
and would by very difficult
to have the other transverse

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00:08:17,440 --> 00:08:18,720
modes lase also.

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00:08:18,720 --> 00:08:21,460
And that's why most
commercial lasers put out

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00:08:21,460 --> 00:08:25,870
that lovely single-spot beam.

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00:08:25,870 --> 00:08:29,350
Now, another interesting
thing about transverse modes

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00:08:29,350 --> 00:08:34,539
is that their frequencies are
different from one another.

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00:08:34,539 --> 00:08:38,650
And that depends on, again,
the length of the cavity

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and the curvature
of the mirrors.

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So when we come
back, we're going

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00:08:43,580 --> 00:08:47,170
to have the spectrum
analyzer set up

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00:08:47,170 --> 00:08:50,050
so we can look at
the frequencies

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00:08:50,050 --> 00:08:52,000
of the various transverse modes.

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00:08:56,120 --> 00:09:00,440
We're now ready to look at the
frequencies, or the spectrum,

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00:09:00,440 --> 00:09:04,760
of the transverse modes of
this laser using a scanning

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00:09:04,760 --> 00:09:08,480
Fabry-Pérot interferometer
acting as an optical spectrum

160
00:09:08,480 --> 00:09:09,350
analyzer.

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00:09:09,350 --> 00:09:10,655
And here is the set up.

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00:09:10,655 --> 00:09:13,280
The output of the laser-- now we
take the output from the other

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00:09:13,280 --> 00:09:14,000
end--

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00:09:14,000 --> 00:09:15,260
from the other mirror.

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00:09:15,260 --> 00:09:17,240
We're going to reflect
it by this mirror here,

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00:09:17,240 --> 00:09:19,970
this mirror here, onto
this scanning Fabry-Pérot

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00:09:19,970 --> 00:09:21,590
interferometer.

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00:09:21,590 --> 00:09:25,190
The length of the cavity
is about 10 centimeters,

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00:09:25,190 --> 00:09:27,440
which means that the
free spectral range will

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00:09:27,440 --> 00:09:30,300
be about 1 and 1/2 gigahertz.

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00:09:30,300 --> 00:09:32,990
The output of the scanning
Fabry-Pérot interferometer then

172
00:09:32,990 --> 00:09:41,940
goes onto the scope to display
the frequencies of the laser.

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00:09:41,940 --> 00:09:46,860
Now we're going to look at
the intensity of the beam,

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00:09:46,860 --> 00:09:49,910
or the transverse intensity
distribution of the beam

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00:09:49,910 --> 00:09:51,740
showing the various
transverse modes.

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00:09:51,740 --> 00:09:55,280
And at the same time, we're
going to look at the spectrum

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00:09:55,280 --> 00:09:59,810
of the laser light as measured
by the scanning Fabry-Pérot

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00:09:59,810 --> 00:10:00,774
interferometer.

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00:10:03,680 --> 00:10:07,380
Now, here on the
screen now we see--

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00:10:07,380 --> 00:10:12,030
on top, we see the intense
distribution of the laser--

181
00:10:12,030 --> 00:10:13,650
the transverse
intensive distribution.

182
00:10:13,650 --> 00:10:18,330
And below, we see the
corresponding spectrum.

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00:10:18,330 --> 00:10:21,600
What I've done here is I've
stopped down the aperture

184
00:10:21,600 --> 00:10:23,640
so that we only have
the lowest-order mode--

185
00:10:23,640 --> 00:10:27,330
the 00 mode oscillate.

186
00:10:27,330 --> 00:10:32,310
And on the scope, we
see three or four modes

187
00:10:32,310 --> 00:10:38,302
due to the longitudinal modes
oscillating in the laser.

188
00:10:38,302 --> 00:10:40,260
And of course, the number
of longitudinal modes

189
00:10:40,260 --> 00:10:43,590
will depend on the width
of the gain medium.

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00:10:43,590 --> 00:10:47,340
The laser is about
40 centimeters long,

191
00:10:47,340 --> 00:10:51,470
which means that the
mode spacings are

192
00:10:51,470 --> 00:10:53,550
about 375 megahertz.

193
00:10:53,550 --> 00:10:55,350
And that's why we get
three and sometimes

194
00:10:55,350 --> 00:11:00,370
four modes oscillating within
the bandwidth of the amplifier,

195
00:11:00,370 --> 00:11:02,070
which is 1 and 1/2 gigahertz.

196
00:11:02,070 --> 00:11:05,670
And just for fun, what I'm
going to do is tap on the mirror

197
00:11:05,670 --> 00:11:07,400
gently to shake the cavity.

198
00:11:07,400 --> 00:11:14,675
And you can see the contour of
the bandwidth of the amplifier,

199
00:11:14,675 --> 00:11:16,050
which is about,
as I said before,

200
00:11:16,050 --> 00:11:18,520
around 1 and 1/2 gigahertz.

201
00:11:18,520 --> 00:11:20,640
So when I'm not shaking
the cavity too much,

202
00:11:20,640 --> 00:11:29,400
then we see the longitudinal
modes stable and quite clearly.

203
00:11:29,400 --> 00:11:33,630
So now what I'm going to do
is open up the aperture--

204
00:11:33,630 --> 00:11:35,190
introduce some high auto modes.

205
00:11:35,190 --> 00:11:39,970
So what I'd like you to do--
look at the picture above.

206
00:11:39,970 --> 00:11:41,970
And then at the same time,
look at the spectrum.

207
00:11:41,970 --> 00:11:45,760
So I'm just slowly
going to bring in--

208
00:11:45,760 --> 00:11:48,390
Now you can see already here,
even though it still looks

209
00:11:48,390 --> 00:11:50,758
like-- it appears to be
just the lowest-order mode,

210
00:11:50,758 --> 00:11:51,300
but it isn't.

211
00:11:51,300 --> 00:11:52,860
Because if you look
at the spectrum,

212
00:11:52,860 --> 00:11:56,480
you see that we have introduced
some new frequencies.

213
00:11:56,480 --> 00:11:59,070
And these new frequencies
are associated

214
00:11:59,070 --> 00:12:02,380
with the transverse modes
that are now oscillating.

215
00:12:02,380 --> 00:12:06,780
And I can go further now and
open up the aperture some more.

216
00:12:06,780 --> 00:12:07,690
Here we are.

217
00:12:07,690 --> 00:12:11,910
So now, you can definitely see
a number of high-order modes.

218
00:12:11,910 --> 00:12:13,320
And look at the frequencies now.

219
00:12:13,320 --> 00:12:14,550
There's lots of them.

220
00:12:14,550 --> 00:12:18,720
And again, they're within the
bandwidth of the amplifier.

221
00:12:18,720 --> 00:12:20,220
There's one thing
nice about having

222
00:12:20,220 --> 00:12:22,770
a lot of transverse
modes is that you

223
00:12:22,770 --> 00:12:25,800
can have a lot more power
coming out from the laser,

224
00:12:25,800 --> 00:12:28,740
because you have more
modes oscillating.

225
00:12:28,740 --> 00:12:29,970
So here, I'll do it again.

226
00:12:29,970 --> 00:12:34,800
I'm going to reduce the
aperture size and to get

227
00:12:34,800 --> 00:12:37,920
the lowest-order mode
oscillating-- see again,

228
00:12:37,920 --> 00:12:42,360
they just get the longitudinal
modes of the 00 mode.

229
00:12:42,360 --> 00:12:48,790
And now I will introduce
the transverse modes again,

230
00:12:48,790 --> 00:12:50,490
to show that they have--

231
00:12:50,490 --> 00:12:54,210
their longitudinal mode
frequencies are different from

232
00:12:54,210 --> 00:12:56,700
the 00 mode.

233
00:12:56,700 --> 00:13:00,180
So far, I've only
been able to show you

234
00:13:00,180 --> 00:13:02,350
a mixture of transverse modes.

235
00:13:02,350 --> 00:13:05,940
In fact, the only isolated mode
that I was able to show you was

236
00:13:05,940 --> 00:13:09,480
the lowest-order one,
the 00 mode, by itself.

237
00:13:09,480 --> 00:13:14,520
And then I showed you a
mixture of transverse modes.

238
00:13:14,520 --> 00:13:16,860
Now, in the next
demonstration, I'm

239
00:13:16,860 --> 00:13:19,800
going to use a little
trick to isolate

240
00:13:19,800 --> 00:13:24,270
a single higher-order transverse
mode so that we can look at it,

241
00:13:24,270 --> 00:13:27,000
and then we can also
look at its spectrum.

242
00:13:31,360 --> 00:13:37,330
Now, in order to isolate one
high-order transverse mode,

243
00:13:37,330 --> 00:13:41,230
I'm going to use
a very thin wire.

244
00:13:41,230 --> 00:13:45,010
The wire, we'll place along
the vertical direction

245
00:13:45,010 --> 00:13:47,270
inside the laser cavity.

246
00:13:47,270 --> 00:13:51,760
And in this way, we'll be able
to prevent the lowest-order

247
00:13:51,760 --> 00:13:54,580
mode, the 00 mode,
from oscillating,

248
00:13:54,580 --> 00:13:57,910
because we'll place the wire
right in the center of the 00

249
00:13:57,910 --> 00:14:00,940
mode, so it's providing a lot
of diffraction loss for it.

250
00:14:00,940 --> 00:14:05,620
But for the next high-order
mode, the two-spot mode,

251
00:14:05,620 --> 00:14:09,770
so-called 1 0, 01, depending
on how you count these modes,

252
00:14:09,770 --> 00:14:13,210
then one will be able to
oscillate if the wire's thin

253
00:14:13,210 --> 00:14:16,960
enough, because this wire is
going to be placed right where

254
00:14:16,960 --> 00:14:19,150
the field is 0.

255
00:14:19,150 --> 00:14:22,440
Now, to make that clearer,
I'm going to show it

256
00:14:22,440 --> 00:14:23,800
to you on the screen.

257
00:14:23,800 --> 00:14:27,190
Before I do this, I want to show
you where the wire is placed.

258
00:14:27,190 --> 00:14:29,800
The wire is placed
in a holder here,

259
00:14:29,800 --> 00:14:32,890
and the wire is about
50 microns wide.

260
00:14:32,890 --> 00:14:37,810
And you place it vertically
inside the laser cavity.

261
00:14:37,810 --> 00:14:39,010
I have an adjustment here.

262
00:14:39,010 --> 00:14:42,730
I can move the wire in and
out in a horizontal direction.

263
00:14:42,730 --> 00:14:44,950
And also, I have
another adjustment here

264
00:14:44,950 --> 00:14:48,580
that rotates the orientation
of the wire from,

265
00:14:48,580 --> 00:14:51,940
let's say, vertical
to horizontal.

266
00:14:51,940 --> 00:14:55,240
Now let's go look at
the screen and see

267
00:14:55,240 --> 00:15:00,730
what sort of transverse mode
I've been able to isolate.

268
00:15:00,730 --> 00:15:05,120
Now, here on the screen,
you see that I've isolated

269
00:15:05,120 --> 00:15:07,650
the next transverse mode.

270
00:15:07,650 --> 00:15:11,730
It's called either 01 or 1
0, depending on how you count

271
00:15:11,730 --> 00:15:13,540
these modes.

272
00:15:13,540 --> 00:15:17,100
And this consists of
essentially two spots

273
00:15:17,100 --> 00:15:21,650
with 0 field in between.

274
00:15:21,650 --> 00:15:24,810
And remember, I used
a vertical wire right

275
00:15:24,810 --> 00:15:29,910
in the center of the mode so
that this particular transverse

276
00:15:29,910 --> 00:15:34,020
mode doesn't need any
gain in the middle,

277
00:15:34,020 --> 00:15:38,730
and therefore can oscillate
with the wire in place.

278
00:15:38,730 --> 00:15:41,940
But most of the other modes,
like the lowest-order mode

279
00:15:41,940 --> 00:15:44,550
and so on, cannot oscillate
with this wire in there,

280
00:15:44,550 --> 00:15:47,990
because that provides too
much diffraction loss.

281
00:15:47,990 --> 00:15:51,120
And that's why we've been
able to isolate this one

282
00:15:51,120 --> 00:15:53,920
particular mode like this.

283
00:15:53,920 --> 00:15:58,550
Now, if we look on the output
of the spectrum analyzer,

284
00:15:58,550 --> 00:16:01,440
as shown on the
oscilloscope below,

285
00:16:01,440 --> 00:16:08,700
you can see that we have two
and sometimes three modes that

286
00:16:08,700 --> 00:16:11,680
correspond to the longitudinal
frequencies of this transverse

287
00:16:11,680 --> 00:16:16,440
mode, just like in the
case of the 00 mode--

288
00:16:16,440 --> 00:16:20,370
just clean, single
transverse mode.

289
00:16:20,370 --> 00:16:24,660
Now, what I'm going to do
now is adjust the wire,

290
00:16:24,660 --> 00:16:27,060
or translate it
horizontally so that I

291
00:16:27,060 --> 00:16:30,840
can bring in other modes.

292
00:16:30,840 --> 00:16:36,870
So now, I'm going to
move it a little bit.

293
00:16:36,870 --> 00:16:42,380
Now you can see I brought
what we call the 02 mode.

294
00:16:42,380 --> 00:16:47,070
It's a little faint, but that's
what I'm able to do right now.

295
00:16:47,070 --> 00:16:51,000
And you can see on the scope
below that, again, it's

296
00:16:51,000 --> 00:16:52,050
clean mode.

297
00:16:52,050 --> 00:16:55,890
But of course, the
intensity is weak.

298
00:16:55,890 --> 00:16:59,220
Now let me go in the other
direction, back again.

299
00:16:59,220 --> 00:17:01,260
Here we bring in the 01 mode.

300
00:17:01,260 --> 00:17:03,300
And now let me go further--

301
00:17:03,300 --> 00:17:08,030
get the wire out of
the way of the cavity.

302
00:17:08,030 --> 00:17:13,920
And now you can see that I'm
bringing in other transverse

303
00:17:13,920 --> 00:17:14,430
modes.

304
00:17:14,430 --> 00:17:16,349
Difficult to tell from the
intensity distribution--

305
00:17:16,349 --> 00:17:17,490
just looks like a blob.

306
00:17:17,490 --> 00:17:20,400
But below, the frequencies--
you can see I'm

307
00:17:20,400 --> 00:17:25,140
bringing in other modes.

308
00:17:25,140 --> 00:17:27,069
And here I go further.

309
00:17:27,069 --> 00:17:28,380
And that's what it is.

310
00:17:28,380 --> 00:17:34,435
Now let me go back
to the 1 0 mode.

311
00:17:40,280 --> 00:17:41,720
Here I am--

312
00:17:41,720 --> 00:17:43,520
1 0 mode.

313
00:17:43,520 --> 00:17:50,570
And then over here, which is
the 2 0, or 02, depending,

314
00:17:50,570 --> 00:17:53,540
as I say, how you count them.

315
00:17:53,540 --> 00:18:00,550
And now I'm back to the
mixture of transverse modes.

316
00:18:00,550 --> 00:18:03,730
Now, the frequencies
of the transverse modes

317
00:18:03,730 --> 00:18:06,730
depend on the
length of the cavity

318
00:18:06,730 --> 00:18:08,890
and the curvature
of the mirrors.

319
00:18:08,890 --> 00:18:11,360
And under certain
conditions-- for example,

320
00:18:11,360 --> 00:18:16,390
in the case of a confocal cavity
where the rays of curvature

321
00:18:16,390 --> 00:18:19,830
of the mirrors are identical
and equal to the spacing

322
00:18:19,830 --> 00:18:30,210
in the cavity, you can get all
the even modes under the 00

323
00:18:30,210 --> 00:18:35,670
mode, and all the odd
modes halfway in between.

324
00:18:35,670 --> 00:18:36,790
And for a plane--

325
00:18:36,790 --> 00:18:40,950
another example is for
a plane mirror cavity,

326
00:18:40,950 --> 00:18:43,080
the frequencies of
all transverse modes

327
00:18:43,080 --> 00:18:45,540
are degenerate-- are identical.

328
00:18:45,540 --> 00:18:49,980
But if you're not confocal
and you're not plain plane,

329
00:18:49,980 --> 00:18:55,910
then you can expect transverse
modes all over the place.

330
00:18:55,910 --> 00:19:01,590
So so far, I've shown you that
by using a simple thin wire

331
00:19:01,590 --> 00:19:04,620
placed in a vertical direction
inside a laser cavity,

332
00:19:04,620 --> 00:19:09,270
we were able to isolate one
of the transverse modes--

333
00:19:09,270 --> 00:19:12,330
the 01 or 1 0 mode.

334
00:19:12,330 --> 00:19:16,430
That's the one with the
two spots side by side.

335
00:19:16,430 --> 00:19:19,310
Now, if I took this
wire and I placed it

336
00:19:19,310 --> 00:19:22,130
along the horizontal
direction inside the cavity,

337
00:19:22,130 --> 00:19:26,870
I would be able to isolate
the other transverse

338
00:19:26,870 --> 00:19:31,640
mode that has the two spots,
one on top of the other.

339
00:19:31,640 --> 00:19:34,870
Similarly, if I place
the wire at 45 degrees,

340
00:19:34,870 --> 00:19:39,020
I would have the two spots
inclined at 45 degrees.

341
00:19:39,020 --> 00:19:40,610
Just in case you
don't believe me,

342
00:19:40,610 --> 00:19:43,740
I'm going to do this right now.

343
00:19:43,740 --> 00:19:47,090
So let's look at
the screen while I

344
00:19:47,090 --> 00:19:53,630
rotate the wire by a
few degrees at a time,

345
00:19:53,630 --> 00:19:56,060
and then pick it up--

346
00:19:56,060 --> 00:19:58,730
pick up the horizontal
position of the wire.

347
00:19:58,730 --> 00:20:04,146
As you can see, the two modes
are beginning to get inclined.

348
00:20:04,146 --> 00:20:06,620
I'll do some more.

349
00:20:06,620 --> 00:20:07,230
Here we are.

350
00:20:07,230 --> 00:20:11,990
It's almost 45 degrees
or so, following

351
00:20:11,990 --> 00:20:15,860
the orientation of the wire.

352
00:20:15,860 --> 00:20:16,610
So here we are.

353
00:20:16,610 --> 00:20:21,140
We see the two modes now are
inclined at an angle close

354
00:20:21,140 --> 00:20:23,310
to 45 degrees.

355
00:20:23,310 --> 00:20:24,080
Now let me see.

356
00:20:24,080 --> 00:20:29,820
If I adjust the translational
position of the wire,

357
00:20:29,820 --> 00:20:32,450
let's see what happens to the
next high-order mode, where

358
00:20:32,450 --> 00:20:33,870
here we are.

359
00:20:33,870 --> 00:20:38,930
The 02 or 2 0-- you can see
that that one is also inclined

360
00:20:38,930 --> 00:20:43,282
at the same angle
as the 01 mode.

361
00:20:43,282 --> 00:20:52,880
Now let me go back to that
one and back to this one.

362
00:20:52,880 --> 00:20:55,310
And indeed, you can see
that I have a pure mode,

363
00:20:55,310 --> 00:20:59,090
because the spectrum
below shows that I

364
00:20:59,090 --> 00:21:05,990
have only the longitudinal modes
associated with one transverse

365
00:21:05,990 --> 00:21:08,530
mode.

366
00:21:08,530 --> 00:21:13,150
Now, in practice, I could
place all kinds of structures

367
00:21:13,150 --> 00:21:17,170
inside the laser cavity
and isolate almost

368
00:21:17,170 --> 00:21:19,360
any transverse mode I want.

369
00:21:19,360 --> 00:21:23,770
May get complicated, but in
principle, it can be done.

370
00:21:27,650 --> 00:21:31,900
Now, in this next demonstration,
we're going to have some fun.

371
00:21:31,900 --> 00:21:35,940
We're going to start with the
laser oscillating in the 01

372
00:21:35,940 --> 00:21:38,460
or 1 0 transverse mode.

373
00:21:38,460 --> 00:21:44,010
Then, I'm going to take a
knife edge or a razor blade,

374
00:21:44,010 --> 00:21:47,220
like this, and I'm
going to place it

375
00:21:47,220 --> 00:21:53,880
inside the laser cavity to
block only one of the spots--

376
00:21:53,880 --> 00:21:56,490
one of the lobes of
this transverse mode--

377
00:21:56,490 --> 00:22:01,740
and see if the laser can
still oscillate on one lobe.

378
00:22:01,740 --> 00:22:02,400
All right?

379
00:22:02,400 --> 00:22:04,560
So I'm going to take this,
then-- this knife edge,

380
00:22:04,560 --> 00:22:10,600
and I'm going to place it
here inside the laser cavity.

381
00:22:10,600 --> 00:22:14,325
And as I'm doing it, maybe
we can look at the screen.

382
00:22:17,570 --> 00:22:18,290
And here we are.

383
00:22:18,290 --> 00:22:22,440
We have the 1 0 or 01 mode.

384
00:22:22,440 --> 00:22:29,050
Then I'm going to bring
this knife edge up close.

385
00:22:29,050 --> 00:22:30,230
Here we are.

386
00:22:30,230 --> 00:22:32,110
And now, it's not
interrupting anything.

387
00:22:32,110 --> 00:22:38,552
But now, I'm going to move it
in to cut one of the lobes out.

388
00:22:38,552 --> 00:22:39,760
So I'm going to do it slowly.

389
00:22:46,530 --> 00:22:47,030
Oops.

390
00:22:47,030 --> 00:22:47,680
Too fast.

391
00:22:47,680 --> 00:22:48,950
Now I'm going to start again.

392
00:22:48,950 --> 00:22:54,380
Now you can see that as soon
as I get close to these lobes,

393
00:22:54,380 --> 00:22:59,030
the entire mode drops
out or stops lasing.

394
00:22:59,030 --> 00:23:02,958
I cannot just have the
laser oscillate only in one

395
00:23:02,958 --> 00:23:03,500
of the lobes.

396
00:23:03,500 --> 00:23:08,225
And this shows that indeed,
this is a transverse mode

397
00:23:08,225 --> 00:23:11,630
of the laser, because
I cannot separate them.

398
00:23:11,630 --> 00:23:13,580
They go together.

399
00:23:13,580 --> 00:23:18,840
I cannot just have
one and not the other.

400
00:23:18,840 --> 00:23:23,660
Now, what's going to happen
if I take this knife edge

401
00:23:23,660 --> 00:23:27,450
and place it outside
the laser cavity

402
00:23:27,450 --> 00:23:30,150
and try to block
one of the modes

403
00:23:30,150 --> 00:23:33,322
when the mode has
already left the cavity?

404
00:23:33,322 --> 00:23:34,780
So this is an
interesting question.

405
00:23:34,780 --> 00:23:36,930
So I'm going to take
it out from here,

406
00:23:36,930 --> 00:23:40,860
and then I'll place it
outside the laser cavity.

407
00:23:40,860 --> 00:23:42,630
And then we'll see
what happens then.

408
00:23:42,630 --> 00:23:45,720
Here we are outside
the laser cavity.

409
00:23:45,720 --> 00:23:49,470
Now I'm going to put the
knife edge over here.

410
00:23:49,470 --> 00:23:52,740
Let me first adjust it
so I'm close to the beam.

411
00:23:55,780 --> 00:23:56,980
Oh, right about here.

412
00:23:59,610 --> 00:24:02,670
Now let's look at
the transverse mode.

413
00:24:02,670 --> 00:24:08,570
As I cut with this knife edge,
I cut into the transverse mode.

414
00:24:08,570 --> 00:24:09,320
So here we are.

415
00:24:09,320 --> 00:24:10,740
You see above the
transverse mode.

416
00:24:10,740 --> 00:24:15,060
Now let me start coming
in with a knife edge,

417
00:24:15,060 --> 00:24:17,340
and let's see what happens.

418
00:24:17,340 --> 00:24:21,050
So what you see happens is
that we get rid of one lobe,

419
00:24:21,050 --> 00:24:23,300
and the other lobe is there.

420
00:24:23,300 --> 00:24:27,000
If I cut in some
more, you see the--

421
00:24:27,000 --> 00:24:29,950
starts to distort a little
bit, starts to get bigger.

422
00:24:29,950 --> 00:24:31,912
And then we go back.

423
00:24:31,912 --> 00:24:34,160
Here it is by itself.

424
00:24:34,160 --> 00:24:41,380
And then here is with the
knife edge outside the beam

425
00:24:41,380 --> 00:24:42,400
altogether.

426
00:24:42,400 --> 00:24:47,470
And we have the
transverse mode by itself.

427
00:24:47,470 --> 00:24:48,925
Again-- let's do it again.

428
00:24:48,925 --> 00:24:49,870
I come in.

429
00:24:49,870 --> 00:24:54,742
I can cut one side lobe, and
it still is an intensity left.

430
00:24:54,742 --> 00:24:56,200
And then as I cut
in some more, you

431
00:24:56,200 --> 00:25:00,370
can see that the
other lobe gets wider.

432
00:25:00,370 --> 00:25:02,500
So that's very,
very interesting.

433
00:25:02,500 --> 00:25:08,340
When I did it inside
the cavity, the mode

434
00:25:08,340 --> 00:25:09,700
actually just got extinguished.

435
00:25:09,700 --> 00:25:11,380
It could not lase.

436
00:25:11,380 --> 00:25:13,420
But when I did it
outside, I still

437
00:25:13,420 --> 00:25:19,360
have light propagating, even
though I cut one of the lobes

438
00:25:19,360 --> 00:25:19,960
out.

439
00:25:19,960 --> 00:25:25,900
Now, to actually
calculate what happens

440
00:25:25,900 --> 00:25:28,610
to the intensity distribution,
or the field distribution

441
00:25:28,610 --> 00:25:32,320
When I do that, is a
little complicated,

442
00:25:32,320 --> 00:25:35,640
because it's not just that
I remove one of the lobes.

443
00:25:35,640 --> 00:25:38,790
It's a lot of diffraction
issues that one has to consider.

444
00:25:38,790 --> 00:25:41,820
And just like any
complicated problem,

445
00:25:41,820 --> 00:25:45,480
we leave it as an
exercise to the viewer

446
00:25:45,480 --> 00:25:48,300
to calculate what actually
happens to the field

447
00:25:48,300 --> 00:25:52,950
distribution when I place
a knife edge in the beam

448
00:25:52,950 --> 00:25:55,940
when it's outside
the laser cavity.