1
00:00:00,118 --> 00:00:09,744
[MUSIC]

2
00:00:09,744 --> 00:00:12,260
Hi.
Welcome to Nanotechnology: The Basics.

3
00:00:12,260 --> 00:00:14,570
This is week 4, lecture 5.

4
00:00:14,570 --> 00:00:16,170
And I'm Daniel Middleton.

5
00:00:16,170 --> 00:00:17,950
In our previous lectures this week, we
have been

6
00:00:17,950 --> 00:00:23,170
talking about the interaction of light
with semiconductor nanostructures, and

7
00:00:23,170 --> 00:00:26,705
how that interaction is really mediated by
quantum confinement

8
00:00:26,705 --> 00:00:31,530
- the quantum effects of squeezing exitons
on the Nanoscale.

9
00:00:31,530 --> 00:00:32,700
In this lecture, I'm going to switch gears

10
00:00:32,700 --> 00:00:35,220
a little bit, and talk about the
interaction

11
00:00:35,220 --> 00:00:37,330
of light with metal nanostructures.

12
00:00:37,330 --> 00:00:42,000
And what we're going to see is, that this
also has important implications.

13
00:00:42,000 --> 00:00:45,570
Making things nano changes their
interaction with light in important ways.

14
00:00:45,570 --> 00:00:47,180
But the mechanism is really completely
different.

15
00:00:47,180 --> 00:00:49,170
It's not a quantum mechanical mechanism at
all.

16
00:00:49,170 --> 00:00:51,010
It's based on plasmons.

17
00:00:51,010 --> 00:00:52,850
So today we want to talk about what's a
plasmon.

18
00:00:52,850 --> 00:00:55,730
And what are some of the implications of
their existence.

19
00:00:55,730 --> 00:00:57,510
So let's start with a thought experiment.

20
00:00:57,510 --> 00:01:00,840
This is a simple idea.
Imagine we could do this experiment and

21
00:01:00,840 --> 00:01:02,150
let's see what happens.

22
00:01:02,150 --> 00:01:03,780
So let's have we, suppose we have a sheet
of metal.

23
00:01:03,780 --> 00:01:04,770
Which is opaque.

24
00:01:04,770 --> 00:01:06,170
And we put a bunch of holes in it.

25
00:01:06,170 --> 00:01:09,660
Okay, as, as illustrated here, each of the
holes has a certain radius, and

26
00:01:09,660 --> 00:01:12,980
there's a certain number of them, and we
shine light on them from one side.

27
00:01:12,980 --> 00:01:16,780
And we ask, what fraction of that light
makes it to the other side, okay?

28
00:01:16,780 --> 00:01:20,532
So let's make this a little easier and say
that the light uniformly illuminates

29
00:01:20,532 --> 00:01:23,760
the metal surface and just say how much
light gets to the other side?

30
00:01:23,760 --> 00:01:26,000
Simple question, right?
So a simple question

31
00:01:26,000 --> 00:01:27,850
of course is going to have a simple
answer, right?

32
00:01:27,850 --> 00:01:31,880
The total area of the metal sheet,
including the holes Will be that.

33
00:01:31,880 --> 00:01:34,730
And the total area covered by just the
holes is that.

34
00:01:34,730 --> 00:01:36,840
It's the number of holes times pi R
squared.

35
00:01:36,840 --> 00:01:37,310
Right?

36
00:01:37,310 --> 00:01:42,160
And that ratio of the area covered by the
holes divided by the total area,

37
00:01:42,160 --> 00:01:43,910
which is obviously a ratio that is less

38
00:01:43,910 --> 00:01:46,920
than one would be the fraction
transmitted, right?

39
00:01:46,920 --> 00:01:49,130
The light that falls on a hole is going to
go through.

40
00:01:49,130 --> 00:01:51,020
The light that misses a hole and falls on
a metal is

41
00:01:51,020 --> 00:01:53,570
not going to go through.
That's the simple way to think about it.

42
00:01:53,570 --> 00:01:55,460
It would be very strange if we ever saw

43
00:01:55,460 --> 00:01:58,410
a fraction transmitted that was greater
than that ratio.

44
00:01:58,410 --> 00:01:59,430
That would be a strange result.

45
00:02:00,600 --> 00:02:03,940
So now let's see what happens when we make
the hole smaller, right?

46
00:02:03,940 --> 00:02:05,950
We're going to start with big holes and
we'll start making them

47
00:02:05,950 --> 00:02:08,560
smaller and smaller and smaller until we
get into the nano range.

48
00:02:08,560 --> 00:02:13,630
Well, before we get there obviously since
this ratio is

49
00:02:13,630 --> 00:02:16,300
proportional to the square of the radius
we can imagine

50
00:02:16,300 --> 00:02:18,390
that the fraction transmitted is also
going to decrease

51
00:02:18,390 --> 00:02:19,680
in proportion to the square of the radius.

52
00:02:19,680 --> 00:02:20,920
In other words, we're making the area of

53
00:02:20,920 --> 00:02:23,090
the hole smaller so less light will get
through.

54
00:02:23,090 --> 00:02:24,790
No surprise there, right?

55
00:02:24,790 --> 00:02:27,050
So what's the interesting thing that
happens?

56
00:02:27,050 --> 00:02:29,600
Well, there are really two interesting
things that happen.

57
00:02:29,600 --> 00:02:32,930
Number one is what happens when you
decrease the size of the holes to

58
00:02:32,930 --> 00:02:36,600
the point where you reach a size equal to
the wavelength of the light.

59
00:02:36,600 --> 00:02:38,350
Well at that point, the amount of

60
00:02:38,350 --> 00:02:41,480
light transmitted continues to decrease,
but even faster,

61
00:02:41,480 --> 00:02:42,080
okay?

62
00:02:42,080 --> 00:02:44,390
And this is an effect that's been
understood for decades.

63
00:02:44,390 --> 00:02:45,450
For quite some time.

64
00:02:45,450 --> 00:02:46,550
And it has to do with the fact that

65
00:02:46,550 --> 00:02:49,260
light has a characteristic length scale,
which is its wavelength.

66
00:02:49,260 --> 00:02:50,880
And if you try to shove light of a

67
00:02:50,880 --> 00:02:53,200
given wavelength through a hole that's
smaller than that.

68
00:02:53,200 --> 00:02:54,840
It gets harder and harder to do.

69
00:02:54,840 --> 00:02:57,600
Light does not like to propagate through
sub wavelength holes.

70
00:02:57,600 --> 00:03:00,610
And so, the fraction transmitted starts to
drop much

71
00:03:00,610 --> 00:03:04,110
more rapidly as you get down below the
wavelength.

72
00:03:04,110 --> 00:03:08,050
That's maybe a little surprising, but not
shocking.

73
00:03:08,050 --> 00:03:10,490
The shocking thing is number two here.

74
00:03:10,490 --> 00:03:13,170
So under certain special circumstances,
what we can see.

75
00:03:13,170 --> 00:03:15,430
Is that the light transmitted through the
holes actually

76
00:03:15,430 --> 00:03:20,170
skyrockets and becomes enormous, okay, so
that's really surprising.

77
00:03:20,170 --> 00:03:22,400
So here's an example, this has been done a
number of times.

78
00:03:22,400 --> 00:03:24,510
This is one example that I'm illustrating
here, and

79
00:03:24,510 --> 00:03:28,230
this shows you that the holes cover about
you

80
00:03:28,230 --> 00:03:29,850
know, a certain percentage of the area of
the

81
00:03:29,850 --> 00:03:33,270
film, shown here, but at a, at a certain
wavelength,

82
00:03:33,270 --> 00:03:36,540
the transmitted light is actually way up
here in percentage.

83
00:03:36,540 --> 00:03:38,370
And that's kind of very surprising.

84
00:03:38,370 --> 00:03:41,920
It's sort of as surprising as if you saw
this happen, right?

85
00:03:41,920 --> 00:03:44,950
Something big being shoved into a really
little hole.

86
00:03:44,950 --> 00:03:46,880
Doesn't seem like it ought to be possible.

87
00:03:46,880 --> 00:03:49,490
And yet, here it is, there's experimental
data.

88
00:03:49,490 --> 00:03:50,650
So, how can we understand this?

89
00:03:50,650 --> 00:03:52,660
This is, I mean this is really worth

90
00:03:52,660 --> 00:03:54,820
stopping and scratching your head and
saying what?

91
00:03:54,820 --> 00:03:55,940
What did you just say?

92
00:03:55,940 --> 00:03:58,730
In that previous example the holes covered
only

93
00:03:58,730 --> 00:04:01,340
about 28% of the area, but 78% of the
incident

94
00:04:01,340 --> 00:04:04,290
light reaches the other side of the, of
the metal screen.

95
00:04:04,290 --> 00:04:05,270
How is that possible?

96
00:04:05,270 --> 00:04:07,380
In other words, the amount of, the
fraction transmitted is

97
00:04:07,380 --> 00:04:10,420
greater than that area ratio that we
started this discussion with.

98
00:04:10,420 --> 00:04:12,510
In fact it's about 2.8 times.

99
00:04:12,510 --> 00:04:13,880
So, it gets even stranger.

100
00:04:13,880 --> 00:04:16,240
Here's another example of an experiment
that has been

101
00:04:16,240 --> 00:04:18,680
done recently, and if you do things just
right.

102
00:04:18,680 --> 00:04:21,990
You can actually see that the transmitted
fraction can actually approach 100%.

103
00:04:21,990 --> 00:04:23,900
So, in this example here,

104
00:04:23,900 --> 00:04:26,845
the holes cover about 30% of the area, but

105
00:04:26,845 --> 00:04:29,390
100% of the light gets through at a
certain frequency.

106
00:04:29,390 --> 00:04:32,130
Notice that this is strongly
frequency-dependent, right?

107
00:04:32,130 --> 00:04:35,460
At one particular frequency, you see 100%
of the light getting through.

108
00:04:36,470 --> 00:04:38,990
So, clearly something very interesting is
going on here.

109
00:04:40,790 --> 00:04:43,090
So, the key to it all is plasmons, and so

110
00:04:43,090 --> 00:04:45,570
what's going on is, let's imagine an
incoming light wave.

111
00:04:45,570 --> 00:04:47,860
This is a sort of a cartoon explanation.

112
00:04:47,860 --> 00:04:49,110
incident on our piece of metal,

113
00:04:49,110 --> 00:04:51,010
which is shown here.
With a bunch of holes in it.

114
00:04:51,010 --> 00:04:52,780
Well, some of the light is going to hit a
hole, right?

115
00:04:52,780 --> 00:04:54,100
And that light'll go straight through.

116
00:04:54,100 --> 00:04:56,060
But some of the light is going to hit the
metal surface.

117
00:04:56,060 --> 00:04:58,600
And what can happen is, a fraction of the
energy of that light wave

118
00:04:58,600 --> 00:05:01,120
can convert into plasmons, which are
surface

119
00:05:01,120 --> 00:05:03,240
waves that propagate along the metal
surface.

120
00:05:03,240 --> 00:05:06,560
And when those plasmons reach the holes,
they can funnel through the holes, and

121
00:05:06,560 --> 00:05:10,470
so you can get light propagating through
the holes that didn't actually hit a hole.

122
00:05:10,470 --> 00:05:14,140
So you can get transmission that is
greater than that area ratio.

123
00:05:14,140 --> 00:05:18,490
Those surface waves are known as surface
plasmons, and they are

124
00:05:18,490 --> 00:05:20,760
the key to understanding this phenomena

125
00:05:20,760 --> 00:05:22,710
of extraordinary transmission through
small holes.

126
00:05:24,780 --> 00:05:26,870
So, the reason we know this is happening.

127
00:05:26,870 --> 00:05:29,300
Well, there's a bunch of experiments and
theories and things, but

128
00:05:29,300 --> 00:05:32,040
this is an experiment which nicely
illustrates how we know this.

129
00:05:32,040 --> 00:05:34,870
This is an experiment which shows only a
single hole, not a bunch of holes.

130
00:05:34,870 --> 00:05:39,550
So, it's just one hole and that hole is
surrounded by a groove.

131
00:05:39,550 --> 00:05:40,500
That's what this circle is.

132
00:05:40,500 --> 00:05:42,860
This is a groove in the metal that doesn't
go all the way through.

133
00:05:42,860 --> 00:05:44,070
It's just a, a groove.

134
00:05:44,070 --> 00:05:46,680
So, here's a cross section which shows the
groove.

135
00:05:46,680 --> 00:05:50,060
And what we see is, that there's two
transmissions

136
00:05:50,060 --> 00:05:52,250
of light as a function of time.

137
00:05:52,250 --> 00:05:54,920
First what you see is the light that gets
directly transmitted through.

138
00:05:54,920 --> 00:05:56,390
That's that big red pulse.

139
00:05:56,390 --> 00:05:58,140
And then at a delayed time, you see the

140
00:05:58,140 --> 00:06:01,390
light that was transmitted through by
plasma unassisted transmission.

141
00:06:01,390 --> 00:06:03,640
In other words, the light that hits the
groove,

142
00:06:03,640 --> 00:06:06,490
excited a plasmon which then propogates
into the center.

143
00:06:06,490 --> 00:06:07,590
And then follows through.

144
00:06:07,590 --> 00:06:08,880
And it comes out later in time because

145
00:06:08,880 --> 00:06:11,310
it's gotta do that extra stuff, which
takes time.

146
00:06:11,310 --> 00:06:15,410
So we can, if we can resolve things in the
time domain we can really see these two

147
00:06:15,410 --> 00:06:18,770
separate transmission phenomena and that's
a really nice illustration of

148
00:06:18,770 --> 00:06:20,790
how we know why this is working the way
it's working.

149
00:06:22,150 --> 00:06:24,490
So I want to make a little bit of an aside
and point out that in that

150
00:06:24,490 --> 00:06:26,900
previous example I just showed you, the
hole

151
00:06:26,900 --> 00:06:28,980
was almost a half a millimeter in
diameter.

152
00:06:28,980 --> 00:06:32,410
So, is this really nano-optics?
Well, I think it is.

153
00:06:32,410 --> 00:06:34,360
sometimes I refer to it as kilo
nano-optics,

154
00:06:34,360 --> 00:06:36,220
which is a little bit of a joke.

155
00:06:36,220 --> 00:06:38,950
but the point is a serious point.

156
00:06:38,950 --> 00:06:41,210
And that is that in plasmonics,

157
00:06:41,210 --> 00:06:46,500
the study of plasmons, often, the size of
the hole is not the important number.

158
00:06:46,500 --> 00:06:48,030
What's the important number is the size of
the

159
00:06:48,030 --> 00:06:50,620
hole in ratio to the wavelength of the
light.

160
00:06:50,620 --> 00:06:52,960
So this ratio is the number that matters.

161
00:06:52,960 --> 00:06:55,550
And so for nano-optics you might say the
wavelength is 500

162
00:06:55,550 --> 00:06:59,490
nanometers and we're talking about 115
nanometer hole or something like that.

163
00:06:59,490 --> 00:07:01,550
In the previous example, the size of the
hole was

164
00:07:01,550 --> 00:07:04,480
half a millimeter but the wavelength was
three millimeters, right?

165
00:07:04,480 --> 00:07:06,280
So that ratio is the same And so

166
00:07:06,280 --> 00:07:10,090
in many cases, the physics is the,
depending only on that ratio.

167
00:07:10,090 --> 00:07:13,620
So you can scale up the size of your
holes, or your

168
00:07:13,620 --> 00:07:17,290
plasmonic structures, and also scale the
wavelength, and get the same physics.

169
00:07:17,290 --> 00:07:20,210
And in many cases, that's an easier way to
do the experiment.

170
00:07:20,210 --> 00:07:22,310
So it's an easier platform with which we

171
00:07:22,310 --> 00:07:25,510
can use to study the physics of plasmonic
phenomena.

172
00:07:25,510 --> 00:07:28,640
And so, this idea of scaling is really
important in electromagnetics.

173
00:07:28,640 --> 00:07:31,470
So, now, let's get back to a more rigorous
definition of what's

174
00:07:31,470 --> 00:07:32,240
a plasmon?

175
00:07:32,240 --> 00:07:36,050
A plasmon is an oscillation of all the
electrons in a metal.

176
00:07:36,050 --> 00:07:38,570
Or a large number of electrons in the
metal.

177
00:07:38,570 --> 00:07:43,070
Earlier in week two, we talked about how
current is the flow

178
00:07:43,070 --> 00:07:46,100
of electrons and we made an analogy to
water in a pipe.

179
00:07:46,100 --> 00:07:48,760
Well, that analogy sort of works here too,
because

180
00:07:48,760 --> 00:07:51,620
all of the electrons sort of behave like a
fluid.

181
00:07:51,620 --> 00:07:53,360
And they are an incompressible fluid and
they will

182
00:07:53,360 --> 00:07:56,580
move collectively, just like waves on the
surface of water.

183
00:07:56,580 --> 00:07:59,860
So a plasmon is, is a wave in the, in the
electron density.

184
00:07:59,860 --> 00:08:02,740
You get a bunch of electrons, then not so
many, then a bunch, then not so many.

185
00:08:02,740 --> 00:08:05,850
And that will move, right.
And so that's what a plasmon is.

186
00:08:05,850 --> 00:08:08,720
So a way to picture this is imagine you
have thin metal film.

187
00:08:08,720 --> 00:08:10,350
Imagine you take all the electrons in that

188
00:08:10,350 --> 00:08:12,750
film and displace them up by a small
amount.

189
00:08:12,750 --> 00:08:15,150
Now you have a little bit of a negative
charge on top and a

190
00:08:15,150 --> 00:08:16,960
little bit of residual positive charge on

191
00:08:16,960 --> 00:08:18,950
the bottom where the electrons have been
removed.

192
00:08:18,950 --> 00:08:22,280
And those will attract each other and so
that whole block of fluid will slosh.

193
00:08:22,280 --> 00:08:26,200
And oscillate back and forth.
So, that's a plasmon in this metal film.

194
00:08:26,200 --> 00:08:29,990
Now, the, what a plasmon looks like will
depend on the geometry of the metal.

195
00:08:29,990 --> 00:08:33,040
So, for example, if you have a, a metal
surface, you

196
00:08:33,040 --> 00:08:36,270
can have a plasmon wave that will
propagate along that metal surface.

197
00:08:36,270 --> 00:08:37,920
And this is an illustration of what that
looks like.

198
00:08:37,920 --> 00:08:40,500
The red arrows show the electric field,
which

199
00:08:40,500 --> 00:08:43,450
is the electromagnetic field which is
propagating along.

200
00:08:44,550 --> 00:08:47,323
And associated with that is an increase in
electron density, and then

201
00:08:47,323 --> 00:08:50,020
a decrease, and then an increase, and then
a decrease.

202
00:08:50,020 --> 00:08:52,470
So, you have an electron density wave and
an

203
00:08:52,470 --> 00:08:56,580
electromagnetic wave propagating together
across the surface of the metal.

204
00:08:56,580 --> 00:08:58,700
And that's really a plasmon on the
surface.

205
00:08:58,700 --> 00:09:00,520
What are some special things about
plasmons?

206
00:09:00,520 --> 00:09:03,260
Well, first of all, they are a coupled
excitation, as I've said.

207
00:09:03,260 --> 00:09:07,500
You have to have the electrons oscillating
as a, a collective group.

208
00:09:07,500 --> 00:09:11,400
And you also have an electromagnetic wave
oscillating back and forth.

209
00:09:11,400 --> 00:09:12,670
at the same frequency.

210
00:09:12,670 --> 00:09:15,410
So, in phase with it, right?
So, those two things are grouped.

211
00:09:15,410 --> 00:09:19,090
You can't have one or, and not the other.
You have to have both.

212
00:09:19,090 --> 00:09:21,760
The second thing about plasmons is, unlike
light

213
00:09:21,760 --> 00:09:24,660
waves in empty space, they're not limited
by diffraction.

214
00:09:24,660 --> 00:09:27,620
So, if you take a plasmonic structure and
taper it down.

215
00:09:27,620 --> 00:09:31,020
And then have a plasmon propagating along,
it may taper, too,

216
00:09:31,020 --> 00:09:34,070
and become much, much smaller than the
wavelength of the light.

217
00:09:34,070 --> 00:09:34,545
So,

218
00:09:34,545 --> 00:09:34,960
[INAUDIBLE]

219
00:09:34,960 --> 00:09:37,490
can be used to beat the diffraction limit
in some sense.

220
00:09:37,490 --> 00:09:39,870
You can make electromagnetic energy
localized

221
00:09:39,870 --> 00:09:43,090
in a sub-wavelength volume using plasmonic
structures.

222
00:09:43,090 --> 00:09:46,150
And the third thing is that plasmons live
very close to metal surfaces.

223
00:09:46,150 --> 00:09:47,520
Which has two important consequences.

224
00:09:47,520 --> 00:09:51,790
Number one is that the electromagnetic
field near the surface can be really big.

225
00:09:51,790 --> 00:09:54,210
Much bigger than the electromagnetic field
intensity

226
00:09:54,210 --> 00:09:55,890
that you used to excite the thing.

227
00:09:55,890 --> 00:09:58,030
And number two, they're very sensitive to

228
00:09:58,030 --> 00:10:00,040
what's happening near the surface, which
enables

229
00:10:00,040 --> 00:10:02,090
some really sensitive sensing
applications, that

230
00:10:02,090 --> 00:10:04,140
we will discuss in a subsequent lecture.

231
00:10:04,140 --> 00:10:07,300
So the ideas here, are that plasmons

232
00:10:07,300 --> 00:10:10,740
are an oscillation of the electron fluid,
right?

233
00:10:10,740 --> 00:10:13,890
And coupled to that is an oscillation of
the electromagnetic wave.

234
00:10:13,890 --> 00:10:15,870
So they're a coupled oscillation.

235
00:10:15,870 --> 00:10:17,890
They can be localized on a nano-structure.

236
00:10:17,890 --> 00:10:21,540
Or they can propagate across a surface for
long distances.

237
00:10:21,540 --> 00:10:25,170
and one surprising consequence of
plasmons, that we discussed here, is this

238
00:10:25,170 --> 00:10:27,710
efficient funneling of light through
nano-holes, which

239
00:10:27,710 --> 00:10:30,960
leads to this phenomena of extraordinary
optical transmission.

240
00:10:30,960 --> 00:10:35,100
Which I think is a really in, great
illustration of how plasmons can lead

241
00:10:35,100 --> 00:10:37,800
to counter intuitive behavior of the way

242
00:10:37,800 --> 00:10:41,190
light waves interact with metal nano
structures.

243
00:10:41,190 --> 00:10:41,770
Thanks for listening.