WEBVTT 00:00:00.000 --> 00:00:01.973 align:middle line:90% [SQUEAKING] 00:00:01.973 --> 00:00:03.937 align:middle line:90% [RUSTLING] 00:00:03.937 --> 00:00:07.374 align:middle line:90% [CLICKING] 00:00:07.374 --> 00:00:15.945 align:middle line:90% 00:00:15.945 --> 00:00:17.320 align:middle line:84% JUEJUN HU: So in this lecture, we 00:00:17.320 --> 00:00:18.737 align:middle line:84% are going to actually turn it over 00:00:18.737 --> 00:00:22.960 align:middle line:84% to optical properties of amorphous materials. 00:00:22.960 --> 00:00:26.600 align:middle line:84% And in fact, optical properties is probably 00:00:26.600 --> 00:00:31.240 align:middle line:84% one of the most important reasons why people use glasses. 00:00:31.240 --> 00:00:35.340 align:middle line:84% So I'm actually posing this question here. 00:00:35.340 --> 00:00:38.120 align:middle line:84% What's so special about glass specifically in terms 00:00:38.120 --> 00:00:40.160 align:middle line:90% of their optical properties? 00:00:40.160 --> 00:00:41.820 align:middle line:90% You can think about it. 00:00:41.820 --> 00:00:43.720 align:middle line:90% You don't have to answer me. 00:00:43.720 --> 00:00:48.240 align:middle line:84% To me, there are three striking properties of glass materials 00:00:48.240 --> 00:00:50.880 align:middle line:84% that really make them so useful for all 00:00:50.880 --> 00:00:55.560 align:middle line:84% sorts of optical applications, the first one being refraction. 00:00:55.560 --> 00:00:59.730 align:middle line:84% You can pass light through a glass material 00:00:59.730 --> 00:01:01.690 align:middle line:84% because it has an index different from air 00:01:01.690 --> 00:01:02.970 align:middle line:90% and it's also transparent. 00:01:02.970 --> 00:01:04.690 align:middle line:84% It means that you can use it as a way 00:01:04.690 --> 00:01:07.230 align:middle line:84% to essentially change the light propagation direction, 00:01:07.230 --> 00:01:11.070 align:middle line:84% and therefore manipulate the light propagation behavior. 00:01:11.070 --> 00:01:12.850 align:middle line:84% This will be very, very important 00:01:12.850 --> 00:01:16.890 align:middle line:84% for essentially all types of optical devices. 00:01:16.890 --> 00:01:20.490 align:middle line:84% Just to give you an example, showing that we humans already 00:01:20.490 --> 00:01:22.970 align:middle line:84% have a very long history of using refraction 00:01:22.970 --> 00:01:27.230 align:middle line:84% for useful applications, in the image on the right-hand side, 00:01:27.230 --> 00:01:31.450 align:middle line:84% I'm showing you an optical device that uses refraction. 00:01:31.450 --> 00:01:33.910 align:middle line:90% Now, I want you to make a guess. 00:01:33.910 --> 00:01:37.570 align:middle line:90% What is that optical device for? 00:01:37.570 --> 00:01:39.190 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:01:39.190 --> 00:01:40.676 align:middle line:90% [LAUGHTER] 00:01:40.676 --> 00:01:42.230 align:middle line:90% JUEJUN HU: Where's the glass? 00:01:42.230 --> 00:01:45.050 align:middle line:90% 00:01:45.050 --> 00:01:46.270 align:middle line:90% Make a wild guess. 00:01:46.270 --> 00:01:49.370 align:middle line:84% AUDIENCE: Sailing device, so it hits the sunlight. 00:01:49.370 --> 00:01:51.555 align:middle line:84% AUDIENCE: I mean, I going to say sundial, but-- 00:01:51.555 --> 00:01:52.430 align:middle line:90% JUEJUN HU: OK, great. 00:01:52.430 --> 00:01:53.830 align:middle line:90% Well, we have some guesses here. 00:01:53.830 --> 00:01:57.820 align:middle line:90% It's a microscope. 00:01:57.820 --> 00:02:01.170 align:middle line:84% It's in fact one of the very first microscopes that 00:02:01.170 --> 00:02:04.530 align:middle line:84% was developed by the Dutch scientist Leeuwenhoek. 00:02:04.530 --> 00:02:08.729 align:middle line:84% So the way it works, if you look at it here, right at this point, 00:02:08.729 --> 00:02:11.810 align:middle line:84% there's actually a little glass sphere. 00:02:11.810 --> 00:02:15.250 align:middle line:84% So essentially they use a glass sphere as a ball lens 00:02:15.250 --> 00:02:18.203 align:middle line:90% to magnify objects. 00:02:18.203 --> 00:02:20.370 align:middle line:84% So when it's actually operating, what you have to do 00:02:20.370 --> 00:02:23.210 align:middle line:84% is put a sample on this little tip here. 00:02:23.210 --> 00:02:25.510 align:middle line:84% And you see these mechanical screws and things. 00:02:25.510 --> 00:02:27.610 align:middle line:84% This is used to adjust the position 00:02:27.610 --> 00:02:30.370 align:middle line:84% to adjust focus and adjust where you're looking at. 00:02:30.370 --> 00:02:34.330 align:middle line:84% And then you have to position it very closely to your eye 00:02:34.330 --> 00:02:37.690 align:middle line:84% and try to peek through a tiny little aperture behind the glass 00:02:37.690 --> 00:02:39.930 align:middle line:90% sphere. 00:02:39.930 --> 00:02:44.330 align:middle line:84% AUDIENCE: It's so much easier to be a scientist today. 00:02:44.330 --> 00:02:46.450 align:middle line:90% JUEJUN HU: Right. 00:02:46.450 --> 00:02:48.690 align:middle line:84% Well, first thing, this instrument 00:02:48.690 --> 00:02:50.330 align:middle line:90% is actually not easy to make. 00:02:50.330 --> 00:02:52.450 align:middle line:84% Back at the time, they didn't have the technique 00:02:52.450 --> 00:02:56.260 align:middle line:84% to very precisely polish glass to make high-quality lenses. 00:02:56.260 --> 00:02:58.440 align:middle line:84% So the way they actually make those little, 00:02:58.440 --> 00:03:00.940 align:middle line:84% tiny little spheres, is they have a molten glass. 00:03:00.940 --> 00:03:04.460 align:middle line:84% They just quickly pour it into sand or something, 00:03:04.460 --> 00:03:07.180 align:middle line:84% and then you essentially have little droplets jumping around. 00:03:07.180 --> 00:03:09.140 align:middle line:84% They then see through all those droplets 00:03:09.140 --> 00:03:13.260 align:middle line:84% and pick the ones that actually have a nice spherical shape. 00:03:13.260 --> 00:03:14.100 align:middle line:90% Put it there. 00:03:14.100 --> 00:03:16.760 align:middle line:84% And then using this, obviously you can imagine, 00:03:16.760 --> 00:03:18.840 align:middle line:84% this can be very, very difficult and challenging. 00:03:18.840 --> 00:03:23.140 align:middle line:90% But despite that, Leeuwenhoek. 00:03:23.140 --> 00:03:26.300 align:middle line:84% Published several big volumes of books 00:03:26.300 --> 00:03:28.620 align:middle line:84% just essentially documenting everything 00:03:28.620 --> 00:03:30.960 align:middle line:84% he has actually looked at under the microscope. 00:03:30.960 --> 00:03:32.180 align:middle line:90% This is actually one example. 00:03:32.180 --> 00:03:34.340 align:middle line:90% This is all hand-drawn. 00:03:34.340 --> 00:03:35.820 align:middle line:90% There's no Photoshop, obviously. 00:03:35.820 --> 00:03:37.760 align:middle line:90% There's no camera or whatever. 00:03:37.760 --> 00:03:41.540 align:middle line:84% So this is actually a flesh fiber, essentially 00:03:41.540 --> 00:03:43.580 align:middle line:90% fiber from meat. 00:03:43.580 --> 00:03:45.550 align:middle line:84% And you can look at all the details 00:03:45.550 --> 00:03:46.800 align:middle line:90% that's actually revealed here. 00:03:46.800 --> 00:03:48.092 align:middle line:90% This is all hand-drawn details. 00:03:48.092 --> 00:03:50.140 align:middle line:84% He was looking at it and then put it down 00:03:50.140 --> 00:03:52.700 align:middle line:84% on paper, which is quite remarkable. 00:03:52.700 --> 00:03:57.580 align:middle line:84% But anyway, now you see, this is essentially 00:03:57.580 --> 00:04:02.220 align:middle line:84% the ancestor for all the optical microscopes today. 00:04:02.220 --> 00:04:05.100 align:middle line:90% All right, so that's refraction. 00:04:05.100 --> 00:04:08.380 align:middle line:84% Now, the second very remarkable property of glass material I see 00:04:08.380 --> 00:04:10.860 align:middle line:90% is transparency. 00:04:10.860 --> 00:04:14.500 align:middle line:84% And in fact, glass materials are so 00:04:14.500 --> 00:04:16.579 align:middle line:84% transparent, they have such a low loss, 00:04:16.579 --> 00:04:23.260 align:middle line:84% that light can propagate within glass for hundreds of kilometers 00:04:23.260 --> 00:04:25.560 align:middle line:84% without having to essentially get re-amplified. 00:04:25.560 --> 00:04:27.700 align:middle line:84% And this very important property is 00:04:27.700 --> 00:04:30.240 align:middle line:84% what underlies today's internet of age. 00:04:30.240 --> 00:04:32.120 align:middle line:84% What I'm showing over here, this plot, 00:04:32.120 --> 00:04:36.820 align:middle line:84% this is essentially a map showing all the main undersea 00:04:36.820 --> 00:04:39.260 align:middle line:90% optical fiber networks. 00:04:39.260 --> 00:04:41.200 align:middle line:84% Without these optical fiber networks, 00:04:41.200 --> 00:04:43.100 align:middle line:84% you will not be able to quickly communicate 00:04:43.100 --> 00:04:44.520 align:middle line:90% with people around the globe. 00:04:44.520 --> 00:04:46.820 align:middle line:84% You will not be able to access essentially 00:04:46.820 --> 00:04:50.000 align:middle line:84% data from data centers in Europe, in UK, in China, 00:04:50.000 --> 00:04:50.800 align:middle line:90% everywhere. 00:04:50.800 --> 00:04:54.910 align:middle line:84% So this is really what enables the whole connected world 00:04:54.910 --> 00:04:55.610 align:middle line:90% nowadays. 00:04:55.610 --> 00:04:58.476 align:middle line:90% 00:04:58.476 --> 00:05:00.590 align:middle line:84% So we are going to discuss about mechanisms, 00:05:00.590 --> 00:05:02.990 align:middle line:84% why glass materials can be so transparent, what 00:05:02.990 --> 00:05:07.150 align:middle line:84% are the optical loss mechanisms, and how to actually engineer 00:05:07.150 --> 00:05:08.990 align:middle line:84% glass compositions so that you can achieve 00:05:08.990 --> 00:05:10.710 align:middle line:90% this remarkable transparency. 00:05:10.710 --> 00:05:15.110 align:middle line:84% Now, the last optical property we are going to discuss here 00:05:15.110 --> 00:05:18.030 align:middle line:90% is color. 00:05:18.030 --> 00:05:19.330 align:middle line:90% I'm showing you a photo here. 00:05:19.330 --> 00:05:22.470 align:middle line:84% This is actually from Barcelona in Spain. 00:05:22.470 --> 00:05:25.630 align:middle line:84% This is actually a dome window, a colored glass window for one 00:05:25.630 --> 00:05:28.030 align:middle line:90% of those buildings there. 00:05:28.030 --> 00:05:30.330 align:middle line:84% Again, even from ancient Roman times, 00:05:30.330 --> 00:05:32.230 align:middle line:84% people knew that actually by putting 00:05:32.230 --> 00:05:34.850 align:middle line:84% different kinds of elements, additives into glass materials, 00:05:34.850 --> 00:05:37.290 align:middle line:84% you can change the color of glasses. 00:05:37.290 --> 00:05:39.310 align:middle line:84% And this is a very useful characteristic 00:05:39.310 --> 00:05:41.150 align:middle line:84% to artists back in Medieval times 00:05:41.150 --> 00:05:43.390 align:middle line:84% when they tried to decorate the big cathedrals 00:05:43.390 --> 00:05:46.390 align:middle line:84% to modern artists, to all kinds of glassware, 00:05:46.390 --> 00:05:49.900 align:middle line:84% like what you see in an MIT glass lab. 00:05:49.900 --> 00:05:52.790 align:middle line:84% It's the same technique that people are still using today. 00:05:52.790 --> 00:05:56.350 align:middle line:84% So we'll be going over the chemistry and the physics of how 00:05:56.350 --> 00:06:00.710 align:middle line:84% to actually introduce color in glass materials. 00:06:00.710 --> 00:06:05.350 align:middle line:84% So now let's start taking a look at refraction. 00:06:05.350 --> 00:06:08.270 align:middle line:84% So speaking of optical properties 00:06:08.270 --> 00:06:11.950 align:middle line:84% we need to talk about Maxwell equations. 00:06:11.950 --> 00:06:14.950 align:middle line:84% There are four Maxwell equations. 00:06:14.950 --> 00:06:17.167 align:middle line:84% You don't have to memorize it, obviously. 00:06:17.167 --> 00:06:19.750 align:middle line:84% In fact, even though I've been working on optics and photonics 00:06:19.750 --> 00:06:23.930 align:middle line:84% for more than 20 years, every time I use Maxwell's equations, 00:06:23.930 --> 00:06:26.990 align:middle line:84% I just go to Wikipedia and look for it. 00:06:26.990 --> 00:06:30.490 align:middle line:84% Well, to be honest, I rarely use Maxwell's equations directly. 00:06:30.490 --> 00:06:33.410 align:middle line:84% Most of the time, we're using some kind of experiments. 00:06:33.410 --> 00:06:37.670 align:middle line:84% But if you look at these basic equations, the key takeaway 00:06:37.670 --> 00:06:39.850 align:middle line:84% message here, the way I'm quoting it, 00:06:39.850 --> 00:06:42.222 align:middle line:84% this is called a macroscopic differential form. 00:06:42.222 --> 00:06:44.430 align:middle line:84% You may have seen these spectral equations being cast 00:06:44.430 --> 00:06:46.590 align:middle line:90% in many different variants. 00:06:46.590 --> 00:06:49.960 align:middle line:84% For this particular macroscopic differential form, 00:06:49.960 --> 00:06:52.760 align:middle line:84% we are looking at the field itself-- 00:06:52.760 --> 00:06:56.680 align:middle line:84% for example, E electric field and B magnetic induction. 00:06:56.680 --> 00:06:58.840 align:middle line:84% These are the fields you will see in media and also 00:06:58.840 --> 00:07:00.960 align:middle line:90% in vacuums-- same. 00:07:00.960 --> 00:07:04.240 align:middle line:84% The material properties that we actually care about 00:07:04.240 --> 00:07:07.040 align:middle line:84% are hidden in these two variables here-- 00:07:07.040 --> 00:07:12.720 align:middle line:84% H and D. D is essentially dielectric displacement 00:07:12.720 --> 00:07:16.040 align:middle line:84% and H will be the magnetic field. 00:07:16.040 --> 00:07:21.120 align:middle line:84% They are linked to E and B through so-called constitutive 00:07:21.120 --> 00:07:22.520 align:middle line:90% relations. 00:07:22.520 --> 00:07:26.840 align:middle line:84% All the optical properties of materials basically 00:07:26.840 --> 00:07:36.280 align:middle line:84% are described in those constitutive relations 00:07:36.280 --> 00:07:38.360 align:middle line:84% Now, the other thing I also want to mention here 00:07:38.360 --> 00:07:41.027 align:middle line:84% is that when you are using this kind of macroscopic differential 00:07:41.027 --> 00:07:43.200 align:middle line:90% form. 00:07:43.200 --> 00:07:45.840 align:middle line:84% You have these terms here where I put a little subscript 00:07:45.840 --> 00:07:47.480 align:middle line:90% f for rho f and Jf. 00:07:47.480 --> 00:07:50.320 align:middle line:84% So rho is basically the charge density, 00:07:50.320 --> 00:07:52.200 align:middle line:90% J is the current density. 00:07:52.200 --> 00:07:54.960 align:middle line:84% With a subscript f, it means that when 00:07:54.960 --> 00:07:58.360 align:middle line:84% I'm writing Maxwell equations in this particular form, 00:07:58.360 --> 00:08:02.040 align:middle line:84% we should only consider the charge and current induced 00:08:02.040 --> 00:08:05.105 align:middle line:90% by the free charges. 00:08:05.105 --> 00:08:07.480 align:middle line:84% So free charges would be, for example, the free electrons 00:08:07.480 --> 00:08:10.640 align:middle line:84% in a metal wire that can easily move around 00:08:10.640 --> 00:08:12.260 align:middle line:84% across the entire conductive material. 00:08:12.260 --> 00:08:13.680 align:middle line:90% Those are the free charges. 00:08:13.680 --> 00:08:16.640 align:middle line:84% In dielectric material, what we have is basically 00:08:16.640 --> 00:08:18.520 align:middle line:90% the so-called bound charges. 00:08:18.520 --> 00:08:21.640 align:middle line:84% And as just a little quick review for general physics 00:08:21.640 --> 00:08:25.360 align:middle line:84% here, if you think about a piece of dielectric material 00:08:25.360 --> 00:08:29.080 align:middle line:84% that's electrically insulating, like glass, 00:08:29.080 --> 00:08:33.140 align:middle line:84% we have some polar molecules or chemical bonds. 00:08:33.140 --> 00:08:36.482 align:middle line:84% So when you actually apply electric field, 00:08:36.482 --> 00:08:37.440 align:middle line:90% what's going to happen? 00:08:37.440 --> 00:08:41.280 align:middle line:84% If you apply electric field in the material, say E, what's 00:08:41.280 --> 00:08:44.090 align:middle line:84% going to happen is that the source center 00:08:44.090 --> 00:08:47.410 align:middle line:84% of mass for the positive charge and negative charge 00:08:47.410 --> 00:08:49.230 align:middle line:84% is going to get spatially separated. 00:08:49.230 --> 00:08:52.730 align:middle line:90% So this is the positive charge. 00:08:52.730 --> 00:08:54.270 align:middle line:84% And then this is negative charge. 00:08:54.270 --> 00:08:57.050 align:middle line:84% When there is no electric field, then the center 00:08:57.050 --> 00:08:59.870 align:middle line:84% of mass for both charges will be completely aligned. 00:08:59.870 --> 00:09:01.410 align:middle line:90% So there is no net charge. 00:09:01.410 --> 00:09:03.370 align:middle line:84% But as soon as you apply electric fields, 00:09:03.370 --> 00:09:04.830 align:middle line:84% the positive charges move this way. 00:09:04.830 --> 00:09:06.830 align:middle line:84% Negative charges move in the opposite direction. 00:09:06.830 --> 00:09:12.710 align:middle line:84% So this then creates essentially little electric dipoles. 00:09:12.710 --> 00:09:23.010 align:middle line:90% 00:09:23.010 --> 00:09:25.650 align:middle line:84% So if you look at the net charge density, 00:09:25.650 --> 00:09:28.648 align:middle line:84% inside homogeneous material, you don't see any net charge 00:09:28.648 --> 00:09:30.690 align:middle line:84% density, because any positive charge on this side 00:09:30.690 --> 00:09:32.565 align:middle line:84% is essentially compensated by negative charge 00:09:32.565 --> 00:09:34.310 align:middle line:90% only on this right side. 00:09:34.310 --> 00:09:36.970 align:middle line:84% But on the surface, then you can actually 00:09:36.970 --> 00:09:38.930 align:middle line:84% get accumulation of these charges 00:09:38.930 --> 00:09:42.170 align:middle line:84% here because there is nothing to compensate against the surface 00:09:42.170 --> 00:09:44.090 align:middle line:90% charges. 00:09:44.090 --> 00:09:49.890 align:middle line:84% And then these surface charges should not 00:09:49.890 --> 00:09:52.770 align:middle line:84% be included in the Maxwell equation 00:09:52.770 --> 00:09:54.810 align:middle line:84% if you are writing it in this form here. 00:09:54.810 --> 00:09:58.090 align:middle line:84% Essentially, the surface charges are accounted for. 00:09:58.090 --> 00:10:01.690 align:middle line:84% When you are writing D here, the dielectric displacement, 00:10:01.690 --> 00:10:04.570 align:middle line:84% they are considered as part of the material response 00:10:04.570 --> 00:10:06.350 align:middle line:90% or the material polarization. 00:10:06.350 --> 00:10:07.970 align:middle line:84% So Rho f you should only consider 00:10:07.970 --> 00:10:12.730 align:middle line:84% charges coming from the free-roaming electrons. 00:10:12.730 --> 00:10:15.130 align:middle line:84% But more specifically, now if you 00:10:15.130 --> 00:10:16.750 align:middle line:84% look at the constitutive relations, 00:10:16.750 --> 00:10:18.810 align:middle line:84% which is what I mentioned, where all the material properties are 00:10:18.810 --> 00:10:20.450 align:middle line:90% essentially embedded in there. 00:10:20.450 --> 00:10:24.222 align:middle line:84% The general form for a general non-bianisotropic media-- 00:10:24.222 --> 00:10:25.930 align:middle line:84% again, we're not going to talk about what 00:10:25.930 --> 00:10:29.390 align:middle line:84% specifically the definition is for non-bianisotropic media. 00:10:29.390 --> 00:10:32.730 align:middle line:84% But for amorphous materials, they are typically anisotropic. 00:10:32.730 --> 00:10:35.370 align:middle line:84% So they satisfy this criteria here. 00:10:35.370 --> 00:10:37.130 align:middle line:84% And then you can essentially write D 00:10:37.130 --> 00:10:39.210 align:middle line:84% as epsilon E plus P. And same thing-- 00:10:39.210 --> 00:10:42.340 align:middle line:84% B you can relate it to a H and M. 00:10:42.340 --> 00:10:47.260 align:middle line:90% Now, P is the polarization. 00:10:47.260 --> 00:10:52.140 align:middle line:84% P is defined as the total dipole moment induced 00:10:52.140 --> 00:10:54.580 align:middle line:84% by external electric fields within a unit 00:10:54.580 --> 00:10:56.500 align:middle line:90% volume of the material. 00:10:56.500 --> 00:10:59.140 align:middle line:84% So basically, you add up all the dipole moments 00:10:59.140 --> 00:11:00.520 align:middle line:90% within a unit volume. 00:11:00.520 --> 00:11:04.780 align:middle line:84% That will give you actually the P. 00:11:04.780 --> 00:11:08.580 align:middle line:84% So what we are seeing here is if you have a material that's 00:11:08.580 --> 00:11:10.340 align:middle line:90% more polarizable. 00:11:10.340 --> 00:11:12.260 align:middle line:84% So typically if you have material 00:11:12.260 --> 00:11:15.620 align:middle line:84% consisting of heavier elements or consisting 00:11:15.620 --> 00:11:18.740 align:middle line:84% of essentially more polarizable chemical bonds, 00:11:18.740 --> 00:11:21.220 align:middle line:84% then you have a larger dipole moment 00:11:21.220 --> 00:11:23.272 align:middle line:84% that's induced by external electric fields. 00:11:23.272 --> 00:11:24.980 align:middle line:84% And you're going to get a larger P there. 00:11:24.980 --> 00:11:30.840 align:middle line:90% 00:11:30.840 --> 00:11:31.340 align:middle line:90% Yes, 00:11:31.340 --> 00:11:33.330 align:middle line:90% AUDIENCE: What is chi? 00:11:33.330 --> 00:11:35.460 align:middle line:84% JUEJUN HU: Chi is susceptibility. 00:11:35.460 --> 00:11:41.060 align:middle line:84% So basically, if the electric field is not 00:11:41.060 --> 00:11:44.100 align:middle line:84% too large, you can then basically 00:11:44.100 --> 00:11:48.740 align:middle line:84% do a Taylor expansion of P with respect to electric field E. 00:11:48.740 --> 00:11:50.200 align:middle line:84% As I said, if E is not too large, 00:11:50.200 --> 00:11:51.740 align:middle line:90% you only take the first order. 00:11:51.740 --> 00:11:53.900 align:middle line:84% Then you end up getting this equation here. 00:11:53.900 --> 00:11:56.620 align:middle line:84% And chi basically gives you essentially the 00:11:56.620 --> 00:11:58.040 align:middle line:90% proportionality constant. 00:11:58.040 --> 00:12:01.340 align:middle line:84% It's a material constant that allows you to characterize 00:12:01.340 --> 00:12:03.460 align:middle line:84% how polarizable the material is in response 00:12:03.460 --> 00:12:05.540 align:middle line:90% to external electric fields. 00:12:05.540 --> 00:12:07.660 align:middle line:84% The larger the susceptibility, the larger 00:12:07.660 --> 00:12:09.180 align:middle line:90% the induced dipole moment. 00:12:09.180 --> 00:12:11.500 align:middle line:84% And therefore, you have a more polarizable material. 00:12:11.500 --> 00:12:17.580 align:middle line:84% So materials consisting of heavy atoms tend to have a larger P. 00:12:17.580 --> 00:12:20.940 align:middle line:84% But mathematically, people typically don't use chi. 00:12:20.940 --> 00:12:23.300 align:middle line:84% What they will do is try to absorb chi 00:12:23.300 --> 00:12:26.340 align:middle line:84% into this relation between D and E here. 00:12:26.340 --> 00:12:29.240 align:middle line:84% And you end up having a very simple proportionality relation. 00:12:29.240 --> 00:12:31.820 align:middle line:84% So D becomes directly proportional 00:12:31.820 --> 00:12:33.540 align:middle line:90% to the applied electric field. 00:12:33.540 --> 00:12:35.940 align:middle line:84% The proportionality constant here, there 00:12:35.940 --> 00:12:37.510 align:middle line:90% are two ways of writing it. 00:12:37.510 --> 00:12:42.005 align:middle line:84% Sometimes people essentially put a epsilon null here. 00:12:42.005 --> 00:12:43.630 align:middle line:84% This is actually a vacuum permittivity. 00:12:43.630 --> 00:12:47.790 align:middle line:84% In this case, epsilon r becomes a number without unit. 00:12:47.790 --> 00:12:52.130 align:middle line:84% This is known as the dielectric constant or just permittivity, 00:12:52.130 --> 00:12:53.830 align:middle line:90% depending on who you ask. 00:12:53.830 --> 00:12:55.430 align:middle line:90% It's just a single number. 00:12:55.430 --> 00:12:57.190 align:middle line:84% Sometimes, some other people essentially 00:12:57.190 --> 00:12:58.930 align:middle line:84% combine epsilon 0 and epsilon r here. 00:12:58.930 --> 00:13:01.750 align:middle line:84% They also call it permittivity, which is confusing. 00:13:01.750 --> 00:13:03.698 align:middle line:84% But just keep in mind, permittivity sometimes 00:13:03.698 --> 00:13:05.490 align:middle line:84% actually has a unit or doesn't have a unit, 00:13:05.490 --> 00:13:07.157 align:middle line:84% depending on how you actually define it. 00:13:07.157 --> 00:13:11.590 align:middle line:84% But basically, this permittivity or dielectric constant 00:13:11.590 --> 00:13:14.590 align:middle line:84% is a measure of how polarizable material is when you 00:13:14.590 --> 00:13:17.790 align:middle line:90% apply external electric fields. 00:13:17.790 --> 00:13:19.910 align:middle line:84% What's relevant to optics is that you 00:13:19.910 --> 00:13:23.470 align:middle line:84% can derive from Maxwell equation this very simple relation there 00:13:23.470 --> 00:13:27.510 align:middle line:84% where refractive index directly scales with the square root 00:13:27.510 --> 00:13:31.590 align:middle line:90% of dielectric constant. 00:13:31.590 --> 00:13:34.750 align:middle line:84% This works in the case of non-magnetic media, which 00:13:34.750 --> 00:13:37.550 align:middle line:84% is usually the case for most of the material we're actually 00:13:37.550 --> 00:13:39.690 align:middle line:84% looking at here for most glass materials. 00:13:39.690 --> 00:13:44.110 align:middle line:84% So in this case, essentially, if you know the permittivity 00:13:44.110 --> 00:13:48.070 align:middle line:84% you can immediately derive the refractive index. 00:13:48.070 --> 00:13:50.910 align:middle line:84% So in essence, it says that refractive index is also 00:13:50.910 --> 00:13:54.270 align:middle line:84% a measure of the polarizability of the material. 00:13:54.270 --> 00:13:57.490 align:middle line:84% If the electric field can induce a larger dipole moment, 00:13:57.490 --> 00:14:00.210 align:middle line:84% the material also tends to have a higher refractive index. 00:14:00.210 --> 00:14:07.870 align:middle line:90% 00:14:07.870 --> 00:14:09.810 align:middle line:84% OK, one little caveat about this equation. 00:14:09.810 --> 00:14:12.310 align:middle line:84% Here, n equals to square root of epsilon r. 00:14:12.310 --> 00:14:15.670 align:middle line:84% So epsilon r and n, they are both frequency or 00:14:15.670 --> 00:14:19.390 align:middle line:90% wavelength-dependent. 00:14:19.390 --> 00:14:21.310 align:middle line:84% In order for this equation to be satisfied, 00:14:21.310 --> 00:14:23.790 align:middle line:84% you need to make sure you measure the n and the epsilon r 00:14:23.790 --> 00:14:27.863 align:middle line:84% at the same frequency or the same wavelength. 00:14:27.863 --> 00:14:30.030 align:middle line:84% This can sometimes be confusing, because when you're 00:14:30.030 --> 00:14:32.130 align:middle line:84% talking about dielectric constant permittivity, 00:14:32.130 --> 00:14:34.640 align:middle line:84% sometimes people assume that you are talking about either 00:14:34.640 --> 00:14:36.800 align:middle line:84% the DC value of the perpetuity, or you're 00:14:36.800 --> 00:14:39.880 align:middle line:84% talking about maybe in the I frequency domain, which 00:14:39.880 --> 00:14:42.720 align:middle line:84% is actually very different from the optical frequency 00:14:42.720 --> 00:14:46.720 align:middle line:84% permittivity [? there. ?] So that's why you just make sure 00:14:46.720 --> 00:14:50.040 align:middle line:84% when you're using that equation, you use it in the same frequency 00:14:50.040 --> 00:14:52.080 align:middle line:90% range. 00:14:52.080 --> 00:14:55.040 align:middle line:84% All right. so that's basically the very basics. 00:14:55.040 --> 00:14:57.880 align:middle line:84% Now let's take a look and come back to our actual amorphous 00:14:57.880 --> 00:14:59.200 align:middle line:90% materials. 00:14:59.200 --> 00:15:02.940 align:middle line:84% Let's consider the refractive index of glass materials. 00:15:02.940 --> 00:15:04.440 align:middle line:84% So we mentioned the refractive index 00:15:04.440 --> 00:15:06.800 align:middle line:84% is a measure of the dielectric polarizability 00:15:06.800 --> 00:15:07.960 align:middle line:90% inside the material. 00:15:07.960 --> 00:15:11.240 align:middle line:84% So we expect that something with a large electron 00:15:11.240 --> 00:15:14.240 align:middle line:84% density with a more polarizable electron cloud 00:15:14.240 --> 00:15:16.480 align:middle line:84% will tend to have a higher refractive index. 00:15:16.480 --> 00:15:18.440 align:middle line:84% So that's basically a trick people 00:15:18.440 --> 00:15:20.800 align:middle line:84% play in order to increase the refractive index of glass 00:15:20.800 --> 00:15:21.600 align:middle line:90% materials. 00:15:21.600 --> 00:15:24.560 align:middle line:84% What they do is they will try to add some kind of heavy elements 00:15:24.560 --> 00:15:27.440 align:middle line:84% into the glass matrix to boost the refractive index. 00:15:27.440 --> 00:15:30.280 align:middle line:84% One common example is to add lead. 00:15:30.280 --> 00:15:33.520 align:middle line:84% So that is basically the heaviest element 00:15:33.520 --> 00:15:37.640 align:middle line:84% or the element has the largest Z number that's still stable, 00:15:37.640 --> 00:15:41.960 align:middle line:84% meaning not radioactive Lead oxide also usually 00:15:41.960 --> 00:15:44.320 align:middle line:84% has very good solubility in many, many kinds 00:15:44.320 --> 00:15:45.480 align:middle line:90% of oxide glasses. 00:15:45.480 --> 00:15:47.280 align:middle line:84% So it's a very commonly used additive 00:15:47.280 --> 00:15:49.760 align:middle line:84% in order to create a higher refractive index glasses. 00:15:49.760 --> 00:15:53.520 align:middle line:90% 00:15:53.520 --> 00:15:55.320 align:middle line:84% If you don't want to use lead, especially 00:15:55.320 --> 00:15:57.680 align:middle line:84% because a lot of the essentially regular treatments 00:15:57.680 --> 00:16:00.480 align:middle line:84% now prohibit using of using of lead metal, 00:16:00.480 --> 00:16:04.340 align:middle line:84% you can use other kinds of heavy metals, heavy elements. 00:16:04.340 --> 00:16:07.960 align:middle line:84% In addition to composition, I want 00:16:07.960 --> 00:16:10.800 align:middle line:84% to mention that the structure itself of the glass 00:16:10.800 --> 00:16:14.808 align:middle line:84% also has an impact to the refractive index. 00:16:14.808 --> 00:16:17.100 align:middle line:84% You can think about the chemical bonding configuration. 00:16:17.100 --> 00:16:21.240 align:middle line:84% So for example, if you think about silica glass SiO2, 00:16:21.240 --> 00:16:24.520 align:middle line:84% because you have very strong chemical bonds, the electrons 00:16:24.520 --> 00:16:25.980 align:middle line:84% actually form the chemical bonds, 00:16:25.980 --> 00:16:28.340 align:middle line:84% gets very tightly localized into atoms. 00:16:28.340 --> 00:16:31.050 align:middle line:84% They actually form the chemical bond. 00:16:31.050 --> 00:16:34.970 align:middle line:84% So in this case, the polarizability is limited. 00:16:34.970 --> 00:16:37.450 align:middle line:84% You can therefore increase the polarizability 00:16:37.450 --> 00:16:41.090 align:middle line:84% by essentially introducing a non-bridging oxygen. If you put 00:16:41.090 --> 00:16:43.610 align:middle line:84% in some alkali-oxides into the glass matrix, for example, 00:16:43.610 --> 00:16:46.370 align:middle line:84% you can have non-bridging oxygen. 00:16:46.370 --> 00:16:48.850 align:middle line:84% And the electrons around this non-bridging oxygen 00:16:48.850 --> 00:16:53.450 align:middle line:84% are actually less localized and hence more polarizable 00:16:53.450 --> 00:16:57.050 align:middle line:84% compared to the case of SiO2 network. 00:16:57.050 --> 00:17:00.470 align:middle line:84% And that's why if you think about SiO2 glass, 00:17:00.470 --> 00:17:03.950 align:middle line:84% they typically has a refractive index of about 1.45, 00:17:03.950 --> 00:17:06.930 align:middle line:90% 1.46 in the wavelength range. 00:17:06.930 --> 00:17:09.290 align:middle line:84% If you go to a, say, soda-lime glass, 00:17:09.290 --> 00:17:13.130 align:middle line:84% it has an index of about 1.52, 1.53. 00:17:13.130 --> 00:17:15.730 align:middle line:84% So it's higher compared to just silica, 00:17:15.730 --> 00:17:18.210 align:middle line:84% basically because of the additional polarizability 00:17:18.210 --> 00:17:21.609 align:middle line:90% induced by these MBOs. 00:17:21.609 --> 00:17:25.050 align:middle line:84% I also want to mention that the refractive index also depends 00:17:25.050 --> 00:17:26.569 align:middle line:90% on the fictive temperature. 00:17:26.569 --> 00:17:31.050 align:middle line:84% So this is actually what I'm showing you in this plot here. 00:17:31.050 --> 00:17:32.630 align:middle line:84% If you look at the refractive index, 00:17:32.630 --> 00:17:36.010 align:middle line:84% it's a function of the cooling rate through which you actually 00:17:36.010 --> 00:17:37.690 align:middle line:90% make the glass. 00:17:37.690 --> 00:17:40.810 align:middle line:84% Typically, higher cooling rate leads to glass materials 00:17:40.810 --> 00:17:42.512 align:middle line:90% with lower refractive index. 00:17:42.512 --> 00:17:44.970 align:middle line:84% So in this case, the chemical composition of glass material 00:17:44.970 --> 00:17:45.970 align:middle line:90% is exactly the same. 00:17:45.970 --> 00:17:48.930 align:middle line:84% So the main factor that impacts the refractive index 00:17:48.930 --> 00:17:51.130 align:middle line:84% in this case is mostly just density. 00:17:51.130 --> 00:17:53.030 align:middle line:84% If you go to a faster cooling rate, 00:17:53.030 --> 00:17:55.610 align:middle line:84% then the materials tend to have a bit more free volume. 00:17:55.610 --> 00:17:58.410 align:middle line:84% As a result, per unit volume, the number 00:17:58.410 --> 00:18:00.970 align:middle line:84% of molecules in that same volume is actually less. 00:18:00.970 --> 00:18:03.250 align:middle line:84% And that's why you will have less p, less 00:18:03.250 --> 00:18:05.210 align:middle line:84% polarizability by definition, and therefore 00:18:05.210 --> 00:18:08.370 align:middle line:90% less smaller refractive index. 00:18:08.370 --> 00:18:11.970 align:middle line:84% So these are the basic ways how you can actually 00:18:11.970 --> 00:18:14.050 align:middle line:90% engineer the refractive index. 00:18:14.050 --> 00:18:15.730 align:middle line:84% The next topic I want to discuss here 00:18:15.730 --> 00:18:18.670 align:middle line:84% is actually the wavelength dependence of refractive index, 00:18:18.670 --> 00:18:20.490 align:middle line:90% which is the dispersion. 00:18:20.490 --> 00:18:22.050 align:middle line:84% Now, to understand dispersion, it's 00:18:22.050 --> 00:18:25.300 align:middle line:84% important to introduce this so-called Kramers-Kronig chronic 00:18:25.300 --> 00:18:28.900 align:middle line:90% relation here or K-K relation. 00:18:28.900 --> 00:18:32.340 align:middle line:84% Have you learned about K-K relation in any other classes? 00:18:32.340 --> 00:18:35.320 align:middle line:84% AUDIENCE: It's definitely come up. 00:18:35.320 --> 00:18:36.940 align:middle line:90% JUEJUN HU: Sounds familiar? 00:18:36.940 --> 00:18:43.820 align:middle line:84% Anyway, K-K relation basically says refractive index 00:18:43.820 --> 00:18:46.500 align:middle line:84% and optical absorption of a material, which 00:18:46.500 --> 00:18:48.420 align:middle line:84% seems like two separate quantities, 00:18:48.420 --> 00:18:51.420 align:middle line:84% they are actually interdependent. 00:18:51.420 --> 00:18:53.940 align:middle line:84% You cannot change the refractive index of material without 00:18:53.940 --> 00:18:56.500 align:middle line:84% modifying its optical absorption characteristics. 00:18:56.500 --> 00:18:57.940 align:middle line:90% That's what it says. 00:18:57.940 --> 00:19:00.860 align:middle line:90% You may wonder why. 00:19:00.860 --> 00:19:04.328 align:middle line:84% It actually has to do with causality. 00:19:04.328 --> 00:19:05.620 align:middle line:90% I'm not going to go through it. 00:19:05.620 --> 00:19:08.700 align:middle line:84% If you're really interested, I mean, in my other class 00:19:08.700 --> 00:19:10.360 align:middle line:84% where I talk about photonic materials, 00:19:10.360 --> 00:19:13.980 align:middle line:84% I actually give a discussion about why 00:19:13.980 --> 00:19:16.440 align:middle line:84% absorption and refractive index must be related. 00:19:16.440 --> 00:19:19.140 align:middle line:84% Otherwise, you're going to violate causality. 00:19:19.140 --> 00:19:21.260 align:middle line:84% Causality essentially means that the consequence 00:19:21.260 --> 00:19:25.410 align:middle line:84% or the results of something has to occur before that cause-- 00:19:25.410 --> 00:19:29.460 align:middle line:84% sorry, has to occur after the cause. 00:19:29.460 --> 00:19:31.700 align:middle line:84% But bottom line, what I will show you here 00:19:31.700 --> 00:19:34.523 align:middle line:84% is that this is a typical diagram that 00:19:34.523 --> 00:19:36.940 align:middle line:84% shows the relation between refractive index and absorption 00:19:36.940 --> 00:19:37.440 align:middle line:90% coefficient. 00:19:37.440 --> 00:19:39.220 align:middle line:84% In the refractive index, [INAUDIBLE] 00:19:39.220 --> 00:19:40.580 align:middle line:90% is the absorption coefficient. 00:19:40.580 --> 00:19:42.780 align:middle line:84% Now, definition of absorption coefficient-- just 00:19:42.780 --> 00:19:46.700 align:middle line:84% to remind you here, if you have a slab of material, 00:19:46.700 --> 00:19:50.260 align:middle line:90% let's say with thickness d. 00:19:50.260 --> 00:19:53.860 align:middle line:84% You have some light coming in initially 00:19:53.860 --> 00:19:56.620 align:middle line:90% with intensity-- let's say I0. 00:19:56.620 --> 00:19:59.820 align:middle line:84% And after passing through a material due to absorption 00:19:59.820 --> 00:20:03.180 align:middle line:84% its intensity must decrease to I. 00:20:03.180 --> 00:20:06.780 align:middle line:84% So I should be related to the incident intensity 00:20:06.780 --> 00:20:13.340 align:middle line:84% according to so-called Beer-Lambert law with e alpha d. 00:20:13.340 --> 00:20:17.180 align:middle line:84% Assuming you ignore any kind of surface reflection, 00:20:17.180 --> 00:20:19.220 align:middle line:84% then the light intensity inside the material 00:20:19.220 --> 00:20:22.910 align:middle line:84% basically would decay exponentially. 00:20:22.910 --> 00:20:25.870 align:middle line:84% And the so decay constant is given by alpha. 00:20:25.870 --> 00:20:27.830 align:middle line:84% This is the absorption coefficient. 00:20:27.830 --> 00:20:30.750 align:middle line:90% 00:20:30.750 --> 00:20:35.470 align:middle line:84% So the thickness has a unit of length, so centimeters 00:20:35.470 --> 00:20:36.210 align:middle line:90% basically. 00:20:36.210 --> 00:20:39.770 align:middle line:84% So then alpha is usually given in terms of inverse centimeter. 00:20:39.770 --> 00:20:44.150 align:middle line:90% 00:20:44.150 --> 00:20:46.270 align:middle line:84% All right, we're going to revisit the definition 00:20:46.270 --> 00:20:47.350 align:middle line:90% a bit later. 00:20:47.350 --> 00:20:50.550 align:middle line:84% But what I'm plotting here, alpha 00:20:50.550 --> 00:20:53.710 align:middle line:84% has the form of basically a peak at some particular center 00:20:53.710 --> 00:20:54.310 align:middle line:90% frequency. 00:20:54.310 --> 00:20:58.390 align:middle line:90% 00:20:58.390 --> 00:21:02.130 align:middle line:84% This is a pretty common form of optical absorption here. 00:21:02.130 --> 00:21:03.770 align:middle line:84% We essentially characterize this, 00:21:03.770 --> 00:21:05.750 align:middle line:84% there's some kind of a transition 00:21:05.750 --> 00:21:08.870 align:middle line:84% in the material with a transition energy centered 00:21:08.870 --> 00:21:11.110 align:middle line:90% at essentially h bar omega-- 00:21:11.110 --> 00:21:12.590 align:middle line:90% omega 0. 00:21:12.590 --> 00:21:15.470 align:middle line:84% So this could be, for example, you have an atomic level 00:21:15.470 --> 00:21:17.190 align:middle line:84% where the transition energy coincides 00:21:17.190 --> 00:21:18.990 align:middle line:90% with essentially M bar omega 0. 00:21:18.990 --> 00:21:21.788 align:middle line:84% It could be you have some kind of atomic vibration 00:21:21.788 --> 00:21:23.830 align:middle line:84% where the vibrational characteristic frequency is 00:21:23.830 --> 00:21:25.070 align:middle line:90% given by omega 0. 00:21:25.070 --> 00:21:27.830 align:middle line:84% In that case, if the incident photon 00:21:27.830 --> 00:21:31.470 align:middle line:84% has a frequency coinciding with the vibrational frequency, 00:21:31.470 --> 00:21:35.270 align:middle line:84% you are then going to excite that vibration, essentially 00:21:35.270 --> 00:21:38.950 align:middle line:84% converting a photon energy into vibrational energy, 00:21:38.950 --> 00:21:41.710 align:middle line:84% or essentially into a promoting electron from one energy level 00:21:41.710 --> 00:21:42.550 align:middle line:90% to another. 00:21:42.550 --> 00:21:46.230 align:middle line:84% It's essentially leading to absorption of photon. 00:21:46.230 --> 00:21:49.590 align:middle line:84% Now, the absorption show up essentially as a peak 00:21:49.590 --> 00:21:52.110 align:middle line:84% there with some essentially finite width. 00:21:52.110 --> 00:21:53.950 align:middle line:84% That's because this kind of transition 00:21:53.950 --> 00:21:56.970 align:middle line:84% usually has some kind of broadening mechanism, 00:21:56.970 --> 00:21:59.110 align:middle line:84% so that it doesn't occur strictly only 00:21:59.110 --> 00:22:00.425 align:middle line:90% at one particular energy. 00:22:00.425 --> 00:22:02.550 align:middle line:84% The broadening mechanism, there are many mechanisms 00:22:02.550 --> 00:22:03.970 align:middle line:84% that can do this kind of broadening there. 00:22:03.970 --> 00:22:05.345 align:middle line:84% We're not going to go through it. 00:22:05.345 --> 00:22:07.870 align:middle line:84% But phenomenologically, you can now 00:22:07.870 --> 00:22:09.510 align:middle line:84% capture the absorption coefficient 00:22:09.510 --> 00:22:12.230 align:middle line:84% of this kind of transition by essentially a function, 00:22:12.230 --> 00:22:14.310 align:middle line:84% like a peak function centers right 00:22:14.310 --> 00:22:16.690 align:middle line:90% at one particular frequency. 00:22:16.690 --> 00:22:20.680 align:middle line:84% With K-K relation, it specifies that if you 00:22:20.680 --> 00:22:23.640 align:middle line:84% have a absorption coefficient that peaks, 00:22:23.640 --> 00:22:28.360 align:middle line:84% the refractive index must show a dependence, like the blue curve 00:22:28.360 --> 00:22:30.600 align:middle line:90% on [INAUDIBLE]. 00:22:30.600 --> 00:22:32.880 align:middle line:84% A quick way to understand it mathematically 00:22:32.880 --> 00:22:35.080 align:middle line:84% is that you can see that this blue curve is almost 00:22:35.080 --> 00:22:38.457 align:middle line:84% like a derivative of the red curve. 00:22:38.457 --> 00:22:39.540 align:middle line:90% In fact, you can prove it. 00:22:39.540 --> 00:22:40.915 align:middle line:84% If you look at it mathematically, 00:22:40.915 --> 00:22:44.320 align:middle line:84% you look at the K-K relation, you 00:22:44.320 --> 00:22:47.880 align:middle line:84% can prove that it's like taking the derivative of the absorption 00:22:47.880 --> 00:22:48.500 align:middle line:90% coefficient. 00:22:48.500 --> 00:22:51.260 align:middle line:84% But if you look, what's the implication here. 00:22:51.260 --> 00:22:52.240 align:middle line:90% So a couple of things. 00:22:52.240 --> 00:22:55.320 align:middle line:84% One is that if you have absorption then 00:22:55.320 --> 00:22:58.605 align:middle line:84% the refractive index must be wavelength-dependent. 00:22:58.605 --> 00:23:00.480 align:middle line:84% If you have a wavelength-dependent refractive 00:23:00.480 --> 00:23:04.680 align:middle line:84% index, this is called dispersion. 00:23:04.680 --> 00:23:06.560 align:middle line:84% And if you look at how the refraction changes 00:23:06.560 --> 00:23:09.640 align:middle line:84% with wavelength, if you look at the regime that's 00:23:09.640 --> 00:23:13.560 align:middle line:84% far away from this absorption line, then the refractive index, 00:23:13.560 --> 00:23:15.760 align:middle line:84% whether it's on the left side or right side right, 00:23:15.760 --> 00:23:20.600 align:middle line:90% it will increase with frequency. 00:23:20.600 --> 00:23:22.400 align:middle line:84% Or in other words, the refractive index 00:23:22.400 --> 00:23:25.440 align:middle line:84% decreases as you go to longer wavelengths. 00:23:25.440 --> 00:23:30.135 align:middle line:84% This is called a normal dispersion. 00:23:30.135 --> 00:23:31.760 align:middle line:84% If you have normal dispersion, you also 00:23:31.760 --> 00:23:34.040 align:middle line:84% get anomalous dispersion, obviously. 00:23:34.040 --> 00:23:39.720 align:middle line:84% Anomalous dispersion happens around the resonance right here. 00:23:39.720 --> 00:23:42.640 align:middle line:84% Around the resonance, you get this line here 00:23:42.640 --> 00:23:44.960 align:middle line:84% where the refractive index actually 00:23:44.960 --> 00:23:47.400 align:middle line:84% decreases with increasing frequency, 00:23:47.400 --> 00:23:50.160 align:middle line:84% or it decreases as you go to shorter wavelength. 00:23:50.160 --> 00:23:51.880 align:middle line:84% That's called anomalous dispersion. 00:23:51.880 --> 00:23:54.680 align:middle line:90% 00:23:54.680 --> 00:23:56.920 align:middle line:84% The reason why it's called anomalous versus normal 00:23:56.920 --> 00:23:58.680 align:middle line:84% is because most of the time when people 00:23:58.680 --> 00:24:02.280 align:middle line:84% are using optical materials, they want to use it in a regime 00:24:02.280 --> 00:24:04.680 align:middle line:90% where it's transparent. 00:24:04.680 --> 00:24:07.680 align:middle line:84% If it's transparent, you must be far away from this absorption 00:24:07.680 --> 00:24:08.420 align:middle line:90% line layer. 00:24:08.420 --> 00:24:11.560 align:middle line:84% And therefore, you usually see this refractive index 00:24:11.560 --> 00:24:14.100 align:middle line:84% will actually decrease as you go to longer wavelengths. 00:24:14.100 --> 00:24:17.210 align:middle line:84% That's why people call it normal dispersion. 00:24:17.210 --> 00:24:18.810 align:middle line:84% And anomalous dispersion essentially 00:24:18.810 --> 00:24:21.230 align:middle line:84% only takes place where you have a strong absorption. 00:24:21.230 --> 00:24:24.770 align:middle line:90% 00:24:24.770 --> 00:24:26.070 align:middle line:90% So that's the first thing here. 00:24:26.070 --> 00:24:29.130 align:middle line:84% We are going to go back and take a look at that in real materials 00:24:29.130 --> 00:24:30.890 align:middle line:90% later. 00:24:30.890 --> 00:24:34.410 align:middle line:84% The second thing is if you look at the refractive index, 00:24:34.410 --> 00:24:37.910 align:middle line:84% the limiting values at the high frequency and low frequency, 00:24:37.910 --> 00:24:39.210 align:middle line:90% they are not the same. 00:24:39.210 --> 00:24:42.150 align:middle line:84% What I'm plotting here is refractive index minus 1. 00:24:42.150 --> 00:24:45.570 align:middle line:84% So you see that for this side, as you go to the lower 00:24:45.570 --> 00:24:48.010 align:middle line:84% frequency, the refractive index is actually 00:24:48.010 --> 00:24:51.130 align:middle line:84% higher than on the higher frequency end. 00:24:51.130 --> 00:24:54.170 align:middle line:84% There's a little step as you cross this [? resonant ?] 00:24:54.170 --> 00:24:56.250 align:middle line:90% line here. 00:24:56.250 --> 00:25:00.130 align:middle line:84% This essentially corresponds to the polarizability contribution 00:25:00.130 --> 00:25:01.430 align:middle line:90% coming from the resonance. 00:25:01.430 --> 00:25:04.770 align:middle line:90% 00:25:04.770 --> 00:25:09.170 align:middle line:84% So for example, suppose this resonance is caused by vibration 00:25:09.170 --> 00:25:10.770 align:middle line:90% of, say, some kind of atoms. 00:25:10.770 --> 00:25:14.610 align:middle line:90% 00:25:14.610 --> 00:25:17.170 align:middle line:84% Now, you can imagine that this atom, essentially 00:25:17.170 --> 00:25:19.530 align:middle line:84% this vibration, will get to the maximum amplitude 00:25:19.530 --> 00:25:24.210 align:middle line:84% when you coincide with this resonant frequency. 00:25:24.210 --> 00:25:28.410 align:middle line:84% If you go to an extremely high frequency, much higher 00:25:28.410 --> 00:25:30.970 align:middle line:84% than the characteristic vibrational frequency, then 00:25:30.970 --> 00:25:34.050 align:middle line:84% this fast oscillating electric field, 00:25:34.050 --> 00:25:36.610 align:middle line:84% the atom itself will not be able to keep up 00:25:36.610 --> 00:25:40.010 align:middle line:84% with this rapid oscillation of the electric field. 00:25:40.010 --> 00:25:42.450 align:middle line:84% So then essentially, it will stop vibrating 00:25:42.450 --> 00:25:46.610 align:middle line:84% and therefore, it will stop contributing to polarization. 00:25:46.610 --> 00:25:50.850 align:middle line:84% So it means that at the high-frequency end, 00:25:50.850 --> 00:25:54.170 align:middle line:84% this atomic vibration will no longer contribute 00:25:54.170 --> 00:25:56.570 align:middle line:84% to polarizability, and therefore no longer 00:25:56.570 --> 00:25:59.930 align:middle line:90% contribute to refractive index. 00:25:59.930 --> 00:26:04.250 align:middle line:84% So essentially, this index step you are seeing here 00:26:04.250 --> 00:26:06.730 align:middle line:84% is, as I said, is the polarizability contribution 00:26:06.730 --> 00:26:08.810 align:middle line:84% coming from this particular resonance 00:26:08.810 --> 00:26:10.270 align:middle line:90% or this particular vibration. 00:26:10.270 --> 00:26:16.340 align:middle line:90% 00:26:16.340 --> 00:26:19.060 align:middle line:90% Does that make sense? 00:26:19.060 --> 00:26:21.080 align:middle line:84% We can take a look at one real example here, 00:26:21.080 --> 00:26:23.620 align:middle line:84% or more specific example here, about why this is actually 00:26:23.620 --> 00:26:24.660 align:middle line:90% relevant. 00:26:24.660 --> 00:26:28.237 align:middle line:84% So now what I'm showing you here-- well, 00:26:28.237 --> 00:26:29.820 align:middle line:84% let's take a look at actual refractive 00:26:29.820 --> 00:26:31.520 align:middle line:90% index of glass materials. 00:26:31.520 --> 00:26:34.020 align:middle line:84% In glass materials, let's start by looking at the absorption 00:26:34.020 --> 00:26:35.940 align:middle line:90% coefficient. 00:26:35.940 --> 00:26:38.860 align:middle line:84% There are typically two classes of absorption mechanism 00:26:38.860 --> 00:26:40.780 align:middle line:90% there coming from vibrations. 00:26:40.780 --> 00:26:42.780 align:middle line:90% One is electronic absorption. 00:26:42.780 --> 00:26:44.940 align:middle line:84% This can come from, again, discrete energy levels 00:26:44.940 --> 00:26:47.240 align:middle line:84% or electron levels, like you have dopants in glass materials. 00:26:47.240 --> 00:26:49.032 align:middle line:84% Or you can have essentially conduction band 00:26:49.032 --> 00:26:49.820 align:middle line:90% and valence band. 00:26:49.820 --> 00:26:52.288 align:middle line:84% If your photon energy is larger than the bandgap, 00:26:52.288 --> 00:26:54.580 align:middle line:84% you can essentially promote electrons from valence band 00:26:54.580 --> 00:26:55.980 align:middle line:90% to conduction band. 00:26:55.980 --> 00:26:58.260 align:middle line:84% So that's essentially electron absorption. 00:26:58.260 --> 00:27:02.220 align:middle line:84% You can think of it as essentially photons inducing 00:27:02.220 --> 00:27:07.140 align:middle line:84% electron resonance or electron vibration if you want. 00:27:07.140 --> 00:27:11.220 align:middle line:84% You can also have atomic absorption or ionic absorption. 00:27:11.220 --> 00:27:14.160 align:middle line:84% This has to do with the atomic vibration I was talking about. 00:27:14.160 --> 00:27:17.660 align:middle line:90% 00:27:17.660 --> 00:27:19.380 align:middle line:84% The light can essentially also drive 00:27:19.380 --> 00:27:22.500 align:middle line:90% the oscillation of electrons-- 00:27:22.500 --> 00:27:24.820 align:middle line:90% sorry, of atoms. 00:27:24.820 --> 00:27:31.380 align:middle line:84% And then if the light frequency coincides 00:27:31.380 --> 00:27:34.420 align:middle line:84% with the characteristic resonant frequency of the atoms, 00:27:34.420 --> 00:27:36.420 align:middle line:84% then you are essentially converting the energy 00:27:36.420 --> 00:27:40.480 align:middle line:84% from the optical domain into essentially atomic vibration, 00:27:40.480 --> 00:27:43.060 align:middle line:90% which is heat. 00:27:43.060 --> 00:27:46.340 align:middle line:84% So that's why this kind of atomic absorption 00:27:46.340 --> 00:27:49.340 align:middle line:84% is usually also called a phonon absorption, 00:27:49.340 --> 00:27:51.660 align:middle line:84% because essentially atomic vibration is basically 00:27:51.660 --> 00:27:53.080 align:middle line:90% phonon OK. 00:27:53.080 --> 00:27:56.860 align:middle line:90% 00:27:56.860 --> 00:27:59.740 align:middle line:84% Now, as you can imagine, because atoms are a lot heavier compared 00:27:59.740 --> 00:28:03.420 align:middle line:84% to electrons, the characteristic vibrational frequency for atoms 00:28:03.420 --> 00:28:06.160 align:middle line:84% will be a lot lower compared to that of electrons. 00:28:06.160 --> 00:28:08.990 align:middle line:84% So typically, this kind of atomic absorption 00:28:08.990 --> 00:28:12.230 align:middle line:84% that will take place at much longer wavelength. 00:28:12.230 --> 00:28:14.510 align:middle line:84% So for glass materials, that's transparent 00:28:14.510 --> 00:28:16.550 align:middle line:90% in the visible regime. 00:28:16.550 --> 00:28:18.430 align:middle line:84% The electronic absorption would typically 00:28:18.430 --> 00:28:19.890 align:middle line:90% happen in the UV range. 00:28:19.890 --> 00:28:22.950 align:middle line:90% 00:28:22.950 --> 00:28:25.310 align:middle line:84% The atomic absorption on the other hand, this 00:28:25.310 --> 00:28:28.173 align:middle line:90% is usually in the mid-infrared. 00:28:28.173 --> 00:28:29.590 align:middle line:84% So we're talking about wavelengths 00:28:29.590 --> 00:28:33.710 align:middle line:84% from a few microns-- say 5 microns all the way up to 20, 00:28:33.710 --> 00:28:38.550 align:middle line:90% 30 microns 00:28:38.550 --> 00:28:40.650 align:middle line:84% All right, so that's the absorption coefficient. 00:28:40.650 --> 00:28:43.030 align:middle line:84% Now what about the corresponding refractive index? 00:28:43.030 --> 00:28:45.270 align:middle line:84% We can apply our calculation here. 00:28:45.270 --> 00:28:47.830 align:middle line:84% And along every absorption peak, you 00:28:47.830 --> 00:28:51.430 align:middle line:84% see a little function, like this zigzag function, 00:28:51.430 --> 00:28:54.990 align:middle line:84% So this is what a typical refractive index 00:28:54.990 --> 00:28:59.990 align:middle line:84% is going to look like, starting from this low frequency, 00:28:59.990 --> 00:29:01.270 align:middle line:90% so long wavelengths. 00:29:01.270 --> 00:29:03.910 align:middle line:84% At very long wavelengths, the oscillation 00:29:03.910 --> 00:29:06.550 align:middle line:84% of the electric field is actually slow. 00:29:06.550 --> 00:29:11.430 align:middle line:84% So both atoms and electrons can keep up. 00:29:11.430 --> 00:29:14.550 align:middle line:84% And therefore, both atomic polarization 00:29:14.550 --> 00:29:16.590 align:middle line:84% and electronic polarization will be 00:29:16.590 --> 00:29:20.430 align:middle line:84% able to contribute to refractive index at low frequencies. 00:29:20.430 --> 00:29:22.990 align:middle line:84% So for low frequencies, we are talking about essentially 00:29:22.990 --> 00:29:25.990 align:middle line:84% from 0 frequency to microwave all 00:29:25.990 --> 00:29:30.230 align:middle line:84% the way to [INAUDIBLE] infrared, so tens of microns, 00:29:30.230 --> 00:29:31.810 align:middle line:90% hundreds of microns, terahertz. 00:29:31.810 --> 00:29:34.310 align:middle line:84% That's the range where both atoms and electrons contribute 00:29:34.310 --> 00:29:36.150 align:middle line:90% to refractive index. 00:29:36.150 --> 00:29:39.910 align:middle line:84% Now, if you goes to the more visible or near infrared 00:29:39.910 --> 00:29:44.110 align:middle line:84% wavelength range, you move past the vibrational frequency 00:29:44.110 --> 00:29:46.190 align:middle line:90% of atoms. 00:29:46.190 --> 00:29:49.150 align:middle line:84% Then in this case, you only get electrons 00:29:49.150 --> 00:29:51.230 align:middle line:84% contributing to polarization because atoms 00:29:51.230 --> 00:29:52.450 align:middle line:90% can no longer keep up. 00:29:52.450 --> 00:29:55.510 align:middle line:90% 00:29:55.510 --> 00:29:58.070 align:middle line:84% So for typical materials, when you 00:29:58.070 --> 00:30:01.330 align:middle line:84% are talking about optical frequency regime polarizability, 00:30:01.330 --> 00:30:03.880 align:middle line:84% which is usually visible on near-infrared. 00:30:03.880 --> 00:30:06.880 align:middle line:84% The refractive index pretty much solely 00:30:06.880 --> 00:30:09.600 align:middle line:84% comes from only electronic contributions. 00:30:09.600 --> 00:30:12.840 align:middle line:90% 00:30:12.840 --> 00:30:16.760 align:middle line:84% OK, so that's the refractive index in the most common sense. 00:30:16.760 --> 00:30:23.600 align:middle line:84% Now finally, if you move past UV you go to the X-ray or gamma ray 00:30:23.600 --> 00:30:28.320 align:middle line:84% regime, then even electrons cannot follow the oscillation 00:30:28.320 --> 00:30:29.380 align:middle line:90% of the electric field. 00:30:29.380 --> 00:30:32.000 align:middle line:90% 00:30:32.000 --> 00:30:36.400 align:middle line:84% And the refractive index now will be close to unity 00:30:36.400 --> 00:30:37.820 align:middle line:84% because there is no polarization. 00:30:37.820 --> 00:30:39.600 align:middle line:84% Now, if you look closely into this curve 00:30:39.600 --> 00:30:42.360 align:middle line:84% here, at the high-frequency end, the curve actually 00:30:42.360 --> 00:30:44.240 align:middle line:90% approaches unity from below. 00:30:44.240 --> 00:30:48.497 align:middle line:84% So it means that refractive index is actually less than 1. 00:30:48.497 --> 00:30:50.080 align:middle line:84% That's actually the typically the case 00:30:50.080 --> 00:30:51.740 align:middle line:90% for X-rays or gamma rays. 00:30:51.740 --> 00:30:55.340 align:middle line:84% If you look for the different refractive materials X-ray, 00:30:55.340 --> 00:31:00.320 align:middle line:84% they are all 0.99 something They are slightly below 1. 00:31:00.320 --> 00:31:02.560 align:middle line:84% It's exactly because of the K-K relation and the fact 00:31:02.560 --> 00:31:06.800 align:middle line:84% that no electrons can respond to X-ray frequency oscillation. 00:31:06.800 --> 00:31:11.000 align:middle line:84% And that's also exactly why X-ray optics is so difficult 00:31:11.000 --> 00:31:14.320 align:middle line:84% because people always want X-ray optics to essentially manipulate 00:31:14.320 --> 00:31:17.460 align:middle line:84% x-rays for X-ray imaging or those type of applications. 00:31:17.460 --> 00:31:19.480 align:middle line:84% Invisible frequency range, you can easily 00:31:19.480 --> 00:31:21.960 align:middle line:84% make lenses because you have materials with large index 00:31:21.960 --> 00:31:23.780 align:middle line:90% differences like glass and air. 00:31:23.780 --> 00:31:26.320 align:middle line:84% You can efficiently use refraction 00:31:26.320 --> 00:31:28.200 align:middle line:84% to control light propagation direction. 00:31:28.200 --> 00:31:30.480 align:middle line:84% The problem with X-rays is that all the materials 00:31:30.480 --> 00:31:34.040 align:middle line:90% have indexes very close to 1. 00:31:34.040 --> 00:31:36.040 align:middle line:84% And that's why it's become very, very difficult 00:31:36.040 --> 00:31:40.380 align:middle line:84% to actually create refractive optics in the X-ray range. 00:31:40.380 --> 00:31:43.120 align:middle line:84% In fact, people usually use diffractive elements 00:31:43.120 --> 00:31:46.680 align:middle line:84% to change the light propagation direction, X-ray frequencies, 00:31:46.680 --> 00:31:49.420 align:middle line:84% which brings a whole lot of complications there. 00:31:49.420 --> 00:31:53.160 align:middle line:90% 00:31:53.160 --> 00:31:56.720 align:middle line:84% All right, so let's see what the spectrum looks like. 00:31:56.720 --> 00:32:02.470 align:middle line:84% Now, in terms of dispersion, you again have normal dispersion. 00:32:02.470 --> 00:32:04.530 align:middle line:90% You have anomalous dispersion. 00:32:04.530 --> 00:32:07.270 align:middle line:84% Now, for most transparent glasses, 00:32:07.270 --> 00:32:08.950 align:middle line:84% if you want it to be transparent, 00:32:08.950 --> 00:32:12.090 align:middle line:84% you want the electron absorption to locate in UV. 00:32:12.090 --> 00:32:14.530 align:middle line:84% You want the phonon absorption to locate in IR. 00:32:14.530 --> 00:32:16.410 align:middle line:84% So in between, in the visible regime, 00:32:16.410 --> 00:32:18.350 align:middle line:84% you have no absorption mechanism there. 00:32:18.350 --> 00:32:20.730 align:middle line:84% And that's why it becomes transparent. 00:32:20.730 --> 00:32:22.850 align:middle line:84% What that also means is that you must 00:32:22.850 --> 00:32:24.930 align:middle line:84% be looking at the normal dispersion regime 00:32:24.930 --> 00:32:27.290 align:middle line:84% when you're looking at the transparency range. 00:32:27.290 --> 00:32:30.450 align:middle line:84% So refractive index tends to monotonically decrease 00:32:30.450 --> 00:32:34.090 align:middle line:90% as you go to longer wavelengths. 00:32:34.090 --> 00:32:37.490 align:middle line:84% So to quantitatively characterize 00:32:37.490 --> 00:32:42.007 align:middle line:84% this dispersion behavior-- this is called chromatic dispersion, 00:32:42.007 --> 00:32:43.590 align:middle line:84% people typically use this number here. 00:32:43.590 --> 00:32:46.650 align:middle line:84% This is called Abbe number or V number. 00:32:46.650 --> 00:32:52.210 align:middle line:84% It's defined-- you can look at the equation here, nD, nF, nC. 00:32:52.210 --> 00:32:54.210 align:middle line:84% These are the refractive indices of the material 00:32:54.210 --> 00:32:58.610 align:middle line:90% at three specific wavelengths. 00:32:58.610 --> 00:33:01.610 align:middle line:84% They are chosen because these are specific absorption 00:33:01.610 --> 00:33:03.130 align:middle line:90% lines in the solar spectrum. 00:33:03.130 --> 00:33:06.050 align:middle line:84% That's why people choose those numbers. 00:33:06.050 --> 00:33:09.550 align:middle line:84% Now, if you look at this V number here, 00:33:09.550 --> 00:33:12.190 align:middle line:84% the numerator is basically refractive index, 00:33:12.190 --> 00:33:13.770 align:middle line:90% referring to the minus 1. 00:33:13.770 --> 00:33:18.030 align:middle line:84% Denominator nF is at a shorter wavelength, 00:33:18.030 --> 00:33:19.690 align:middle line:84% so it's a higher refractive index. 00:33:19.690 --> 00:33:22.330 align:middle line:84% So you have a normal dispersion media. nF 00:33:22.330 --> 00:33:25.570 align:middle line:90% f should be greater than nC. 00:33:25.570 --> 00:33:28.890 align:middle line:84% So V number will be a positive number. 00:33:28.890 --> 00:33:31.890 align:middle line:84% And also, if the material is more dispersive, 00:33:31.890 --> 00:33:34.330 align:middle line:84% you have a more drastic dependence of refractive index 00:33:34.330 --> 00:33:35.590 align:middle line:90% as a function of wavelength. 00:33:35.590 --> 00:33:39.610 align:middle line:84% Then the difference between nF and nC will be larger. 00:33:39.610 --> 00:33:45.090 align:middle line:84% And therefore you should have a smaller V number. 00:33:45.090 --> 00:33:47.930 align:middle line:84% So smaller V number essentially corresponds to material 00:33:47.930 --> 00:33:49.810 align:middle line:90% that's more dispersive. 00:33:49.810 --> 00:33:52.290 align:middle line:84% Its wavelength more strongly depends-- sorry, 00:33:52.290 --> 00:33:55.470 align:middle line:84% its refractive index more strongly depends on wavelength. 00:33:55.470 --> 00:34:03.100 align:middle line:90% 00:34:03.100 --> 00:34:06.660 align:middle line:84% All right, now let's take a look at glass materials. 00:34:06.660 --> 00:34:08.880 align:middle line:84% If you go to a glass vendor website, 00:34:08.880 --> 00:34:10.980 align:middle line:84% the most famous one in particular for this plot 00:34:10.980 --> 00:34:13.900 align:middle line:90% is actually from Schott glasses. 00:34:13.900 --> 00:34:16.139 align:middle line:84% On this plot, horizontal axis would 00:34:16.139 --> 00:34:18.100 align:middle line:90% be the Abbe number, V number. 00:34:18.100 --> 00:34:20.699 align:middle line:84% Vertical axis would be the refractive index 00:34:20.699 --> 00:34:22.580 align:middle line:90% at one particular wavelength. 00:34:22.580 --> 00:34:23.400 align:middle line:90% This is nd. 00:34:23.400 --> 00:34:25.000 align:middle line:90% Now notice here little caveat. 00:34:25.000 --> 00:34:29.060 align:middle line:84% This nd is lowercase D. This is different from this uppercase D 00:34:29.060 --> 00:34:30.100 align:middle line:90% here. 00:34:30.100 --> 00:34:33.300 align:middle line:84% So the wavelength point is actually slightly different. 00:34:33.300 --> 00:34:36.139 align:middle line:90% It doesn't really matter. 00:34:36.139 --> 00:34:39.199 align:middle line:84% Bottom line-- if you look at this plot here, 00:34:39.199 --> 00:34:43.139 align:middle line:84% this red point corresponds to one particular combination 00:34:43.139 --> 00:34:46.340 align:middle line:84% that you can find in the product catalog from Schott. 00:34:46.340 --> 00:34:48.980 align:middle line:84% You can directly order it off the shelf, basically. 00:34:48.980 --> 00:34:52.139 align:middle line:84% If you look at this plot here, most of the data points 00:34:52.139 --> 00:34:55.830 align:middle line:84% go along this diagonal direction. 00:34:55.830 --> 00:34:59.950 align:middle line:84% So what it means is that a glass material with high refractive 00:34:59.950 --> 00:35:03.170 align:middle line:84% index also tends to have a small V number, 00:35:03.170 --> 00:35:07.350 align:middle line:84% and therefore tends to have higher dispersion. 00:35:07.350 --> 00:35:08.770 align:middle line:90% This is a general rule of thumb. 00:35:08.770 --> 00:35:11.470 align:middle line:84% High-index materials tend to have a higher 00:35:11.470 --> 00:35:12.810 align:middle line:90% dispersion in this case. 00:35:12.810 --> 00:35:15.990 align:middle line:84% Now, intuitively, you can also understand 00:35:15.990 --> 00:35:17.310 align:middle line:90% what's actually going on here. 00:35:17.310 --> 00:35:18.727 align:middle line:84% If you want to get high refractive 00:35:18.727 --> 00:35:23.190 align:middle line:84% index, what you need to do, you need to add heavy elements. 00:35:23.190 --> 00:35:25.990 align:middle line:84% Heavy elements tend to reduce the bandgap. 00:35:25.990 --> 00:35:30.455 align:middle line:90% 00:35:30.455 --> 00:35:32.350 align:middle line:84% So when you reduce the bandgap, it 00:35:32.350 --> 00:35:34.710 align:middle line:84% means that you are essentially shifting this absorption 00:35:34.710 --> 00:35:37.290 align:middle line:84% line towards the longer wavelength end. 00:35:37.290 --> 00:35:40.310 align:middle line:90% 00:35:40.310 --> 00:35:43.430 align:middle line:84% And if you push this feature towards the longer wavelength 00:35:43.430 --> 00:35:46.310 align:middle line:84% end, you can see the slope actually increases here. 00:35:46.310 --> 00:35:48.670 align:middle line:84% And that's why the material becomes more dispersive. 00:35:48.670 --> 00:35:51.128 align:middle line:84% You are pushing this feature essentially to the right side. 00:35:51.128 --> 00:35:53.890 align:middle line:84% So if you push it to the right side for the visible range, 00:35:53.890 --> 00:35:55.812 align:middle line:84% you're sampling this part of the curve, 00:35:55.812 --> 00:35:57.270 align:middle line:84% rather than this part of the curve. 00:35:57.270 --> 00:35:58.450 align:middle line:90% So then it has a higher slope. 00:35:58.450 --> 00:36:00.033 align:middle line:84% That's why it becomes more dispersive. 00:36:00.033 --> 00:36:02.470 align:middle line:84% So general rule of thumb, high index, usually the material 00:36:02.470 --> 00:36:04.230 align:middle line:90% also is more dispersive. 00:36:04.230 --> 00:36:06.550 align:middle line:84% So now if you look at the material 00:36:06.550 --> 00:36:08.010 align:middle line:90% it actually has a high index. 00:36:08.010 --> 00:36:11.550 align:middle line:84% These glasses are typically labeled with the last letter F. 00:36:11.550 --> 00:36:13.997 align:middle line:90% These are called flint glasses. 00:36:13.997 --> 00:36:15.830 align:middle line:84% They are the glass materials typically doped 00:36:15.830 --> 00:36:18.470 align:middle line:84% with heavy elements like lead And they 00:36:18.470 --> 00:36:20.990 align:middle line:84% are characterized high index and also high dispersion. 00:36:20.990 --> 00:36:24.910 align:middle line:84% On the other end these are the glasses ending with the letter 00:36:24.910 --> 00:36:29.990 align:middle line:84% K. These are usually called a crown glass So soda-lime glass 00:36:29.990 --> 00:36:34.670 align:middle line:84% that we use every day is a kind of crown glass 00:36:34.670 --> 00:36:39.150 align:middle line:84% So crown glasses tend to have a low index and low dispersion. 00:36:39.150 --> 00:36:43.510 align:middle line:84% The extreme here is if you go to this one, FK. 00:36:43.510 --> 00:36:47.510 align:middle line:84% FK are actually crown glasses doped with fluorine, 00:36:47.510 --> 00:36:52.640 align:middle line:84% F. So fluorine is a very, very small atom. 00:36:52.640 --> 00:36:54.340 align:middle line:84% It has very few outer shell electrons. 00:36:54.340 --> 00:36:56.305 align:middle line:84% It also has a very small atomic radius. 00:36:56.305 --> 00:36:57.680 align:middle line:84% So essentially, all the electrons 00:36:57.680 --> 00:37:00.560 align:middle line:84% are tightly bound to the atomic nucleus. 00:37:00.560 --> 00:37:03.840 align:middle line:84% And what that means is that the polarizability of fluorine atoms 00:37:03.840 --> 00:37:04.880 align:middle line:90% is very low. 00:37:04.880 --> 00:37:06.720 align:middle line:84% The electrons just don't want to move around 00:37:06.720 --> 00:37:10.598 align:middle line:84% too much So any kind of fluorine-doped glasses 00:37:10.598 --> 00:37:12.640 align:middle line:84% tend to have much lower refractive index compared 00:37:12.640 --> 00:37:15.080 align:middle line:84% to other kinds of glass materials 00:37:15.080 --> 00:37:18.080 align:middle line:84% The extreme is if you go to a fluorite. 00:37:18.080 --> 00:37:21.000 align:middle line:84% A fluorite is basically like calcium fluoride-- 00:37:21.000 --> 00:37:22.300 align:middle line:90% for example, CaF2. 00:37:22.300 --> 00:37:26.280 align:middle line:84% So CaF2, its index is actually 1.4, 00:37:26.280 --> 00:37:28.700 align:middle line:84% and it has a V Number of about 95. 00:37:28.700 --> 00:37:32.200 align:middle line:84% So it's actually somewhere here out of the chart. 00:37:32.200 --> 00:37:34.680 align:middle line:84% So by essentially tuning the chemical composition, 00:37:34.680 --> 00:37:37.263 align:middle line:84% you can essentially change the dispersion and refractive index 00:37:37.263 --> 00:37:39.260 align:middle line:90% over a pretty wide range 00:37:39.260 --> 00:37:41.760 align:middle line:84% Now you may wonder why people care about that. 00:37:41.760 --> 00:37:43.560 align:middle line:84% In fact, before I go to that, I mentioned 00:37:43.560 --> 00:37:46.600 align:middle line:84% that in addition to glasses, another commonly used amorphous 00:37:46.600 --> 00:37:48.960 align:middle line:84% material for optics is optical polymers. 00:37:48.960 --> 00:37:53.520 align:middle line:84% And optical polymers tend to more populate this corner here, 00:37:53.520 --> 00:37:56.287 align:middle line:84% which means that for the same refractive index, 00:37:56.287 --> 00:37:58.120 align:middle line:84% they tend to have higher dispersion compared 00:37:58.120 --> 00:38:00.520 align:middle line:84% to the inorganic glass counterpart 00:38:00.520 --> 00:38:03.000 align:middle line:84% And this capability is actually useful 00:38:03.000 --> 00:38:04.920 align:middle line:84% because people can actually use this kind 00:38:04.920 --> 00:38:07.760 align:middle line:84% of a chromatic dispersion of materials 00:38:07.760 --> 00:38:10.440 align:middle line:84% to engineer the wavelength-dependent response 00:38:10.440 --> 00:38:12.080 align:middle line:90% of optical devices. 00:38:12.080 --> 00:38:17.300 align:middle line:84% So what I'm showing you here on the photo, 00:38:17.300 --> 00:38:19.880 align:middle line:84% this top left corner here, this is basically 00:38:19.880 --> 00:38:23.100 align:middle line:84% a dispersion spectrometer-- prism dispersive spectrometer. 00:38:23.100 --> 00:38:26.700 align:middle line:84% Its mechanism of operation is fairly straightforward. 00:38:26.700 --> 00:38:28.960 align:middle line:84% This is the same as what Sir Isaac Newton used, 00:38:28.960 --> 00:38:31.020 align:middle line:90% his prism to separate sunlight. 00:38:31.020 --> 00:38:33.160 align:middle line:84% You can essentially split a polychromatic light 00:38:33.160 --> 00:38:34.982 align:middle line:84% into its individual wavelength components, 00:38:34.982 --> 00:38:36.440 align:middle line:84% and therefore measure the intensity 00:38:36.440 --> 00:38:38.940 align:middle line:84% as a function of wavelength to give you actually a spectrum. 00:38:38.940 --> 00:38:41.360 align:middle line:84% So in this case, having a material 00:38:41.360 --> 00:38:45.280 align:middle line:84% that's heavily dispersive is actually advantageous. 00:38:45.280 --> 00:38:50.010 align:middle line:84% Now, the flip case is when you are trying to essentially make 00:38:50.010 --> 00:38:52.350 align:middle line:84% some kind of imaging instruments-- for example, 00:38:52.350 --> 00:38:53.353 align:middle line:90% a lens. 00:38:53.353 --> 00:38:55.770 align:middle line:84% In a lens, we know that the light at different wavelengths 00:38:55.770 --> 00:38:57.770 align:middle line:84% essentially has different refractive indices. 00:38:57.770 --> 00:38:59.890 align:middle line:84% The light at shorter wavelengths, 00:38:59.890 --> 00:39:02.610 align:middle line:84% like blue light, blue color light. if it's normal dispersive 00:39:02.610 --> 00:39:04.850 align:middle line:84% material, they should have high refractive index. 00:39:04.850 --> 00:39:08.490 align:middle line:84% So it means that if you try to focus light onto one point here, 00:39:08.490 --> 00:39:10.610 align:middle line:84% the focal length for the blue light 00:39:10.610 --> 00:39:12.810 align:middle line:84% is going to be shorter compared to the focal length 00:39:12.810 --> 00:39:14.170 align:middle line:90% of the red light. 00:39:14.170 --> 00:39:17.110 align:middle line:84% So now if you have a fixed image plane-- 00:39:17.110 --> 00:39:19.995 align:middle line:84% this is, for example, your photographic film or your CMOS 00:39:19.995 --> 00:39:21.870 align:middle line:84% image sensor [? it's ?] actually lying there. 00:39:21.870 --> 00:39:26.090 align:middle line:84% Then instead of having a single very sharp image, what 00:39:26.090 --> 00:39:29.250 align:middle line:84% you get is a blurred image, because essentially, 00:39:29.250 --> 00:39:30.850 align:middle line:84% the different parts of the spectrum 00:39:30.850 --> 00:39:33.330 align:middle line:84% get focused at different vertical depths there. 00:39:33.330 --> 00:39:37.050 align:middle line:84% So this is known as chromatic aberration. 00:39:37.050 --> 00:39:38.968 align:middle line:84% And you can look at this photo here. 00:39:38.968 --> 00:39:40.510 align:middle line:84% This is actually a photo of the moon. 00:39:40.510 --> 00:39:43.090 align:middle line:84% You can clearly see that if you zoom in, 00:39:43.090 --> 00:39:46.370 align:middle line:84% essentially all these images here, they are not sharp. 00:39:46.370 --> 00:39:48.050 align:middle line:84% You see this kind of color fringes 00:39:48.050 --> 00:39:50.890 align:middle line:84% essentially due to this kind of color aberration. 00:39:50.890 --> 00:39:56.090 align:middle line:84% So how do you correct for this kind of chromatic dispersion? 00:39:56.090 --> 00:40:00.210 align:middle line:84% The answer is that you go to not just a single lens. 00:40:00.210 --> 00:40:03.830 align:middle line:84% You try to make a lens out of multiple materials. 00:40:03.830 --> 00:40:06.210 align:middle line:84% You can, for example, make a doublet. 00:40:06.210 --> 00:40:08.350 align:middle line:84% You have essentially one piece of lens here. 00:40:08.350 --> 00:40:09.870 align:middle line:90% You might offer one material. 00:40:09.870 --> 00:40:11.730 align:middle line:84% You put another piece of lens made out 00:40:11.730 --> 00:40:13.690 align:middle line:90% of a different kind of material. 00:40:13.690 --> 00:40:15.130 align:middle line:84% I'm not very good at drawing this. 00:40:15.130 --> 00:40:18.570 align:middle line:84% And by using two materials with different dispersion 00:40:18.570 --> 00:40:20.210 align:middle line:84% characteristics, you will then be 00:40:20.210 --> 00:40:23.510 align:middle line:84% able to compensate for this kind of chromatic aberration. 00:40:23.510 --> 00:40:26.530 align:middle line:90% 00:40:26.530 --> 00:40:30.450 align:middle line:84% I want to show you this little plot here. 00:40:30.450 --> 00:40:34.090 align:middle line:84% So if you look at the simple length consisting 00:40:34.090 --> 00:40:36.370 align:middle line:84% of only one single material, then this 00:40:36.370 --> 00:40:37.890 align:middle line:84% is typically what the focal length 00:40:37.890 --> 00:40:40.050 align:middle line:84% is going to look like as a function of wavelength. 00:40:40.050 --> 00:40:42.740 align:middle line:90% 00:40:42.740 --> 00:40:45.300 align:middle line:84% This black line essentially indicates the wavelength 00:40:45.300 --> 00:40:48.020 align:middle line:84% you actually design the lens to actually operate at. 00:40:48.020 --> 00:40:49.860 align:middle line:84% If it's only one single material, 00:40:49.860 --> 00:40:52.478 align:middle line:84% its wavelength is going to monotonically increase as you 00:40:52.478 --> 00:40:53.520 align:middle line:90% go to longer wavelengths. 00:40:53.520 --> 00:40:55.645 align:middle line:84% And therefore, you only hit this desired wavelength 00:40:55.645 --> 00:40:57.700 align:middle line:90% at one single point. 00:40:57.700 --> 00:41:01.420 align:middle line:84% If you use two materials to make a doublet, 00:41:01.420 --> 00:41:04.580 align:middle line:84% then you can create a so-called an achromat. 00:41:04.580 --> 00:41:08.900 align:middle line:84% That essentially gives rise to, at two different wavelength 00:41:08.900 --> 00:41:11.460 align:middle line:84% points. you can satisfy your design specification 00:41:11.460 --> 00:41:13.700 align:middle line:90% in terms of focal length. 00:41:13.700 --> 00:41:15.340 align:middle line:84% If you introduce more materials you 00:41:15.340 --> 00:41:17.180 align:middle line:84% can get apochromat, meaning that you 00:41:17.180 --> 00:41:19.600 align:middle line:84% have three points that actually hit the same wavelength. 00:41:19.600 --> 00:41:22.180 align:middle line:84% You can also get super achromat, which essentially 00:41:22.180 --> 00:41:23.840 align:middle line:90% have four different points. 00:41:23.840 --> 00:41:26.540 align:middle line:84% They all align with the design-specified focal length. 00:41:26.540 --> 00:41:29.900 align:middle line:84% OK, now I'm going to show you one design 00:41:29.900 --> 00:41:32.580 align:middle line:90% of this kind of super achromat. 00:41:32.580 --> 00:41:34.700 align:middle line:84% Let's look at the next slide here. 00:41:34.700 --> 00:41:39.265 align:middle line:84% It's of course pretty complicated. 00:41:39.265 --> 00:41:41.140 align:middle line:84% This is actually one of the classical designs 00:41:41.140 --> 00:41:42.400 align:middle line:90% that was actually done. 00:41:42.400 --> 00:41:45.800 align:middle line:84% This one was done quite a while ago. 00:41:45.800 --> 00:41:51.700 align:middle line:84% OK you have a total of six pieces of lenses 00:41:51.700 --> 00:41:54.940 align:middle line:84% In order to achieve this kind of super achromat behavior. 00:41:54.940 --> 00:41:56.380 align:middle line:84% Now, what's even more important is 00:41:56.380 --> 00:41:59.340 align:middle line:84% that if you look at this length L2 piece, 00:41:59.340 --> 00:42:01.880 align:middle line:84% this piece is made of a fluorite. 00:42:01.880 --> 00:42:04.560 align:middle line:84% In this case, it's calcium fluoride. 00:42:04.560 --> 00:42:07.080 align:middle line:84% Now, calcium fluoride is actually not a glass. 00:42:07.080 --> 00:42:08.820 align:middle line:90% It's a crystalline material. 00:42:08.820 --> 00:42:10.920 align:middle line:84% It's actually not easy to process. 00:42:10.920 --> 00:42:12.960 align:middle line:90% It's actually single crystal 00:42:12.960 --> 00:42:15.020 align:middle line:84% You have to do essentially grinding and polishing 00:42:15.020 --> 00:42:16.120 align:middle line:90% to actually get it. 00:42:16.120 --> 00:42:20.582 align:middle line:84% And also it's actually a somewhat hygroscopic. 00:42:20.582 --> 00:42:22.540 align:middle line:84% If you're leaving air for a long period of time 00:42:22.540 --> 00:42:24.860 align:middle line:84% in an environment with high moisture, 00:42:24.860 --> 00:42:27.700 align:middle line:84% you are going to cause fogging of the lens. 00:42:27.700 --> 00:42:32.840 align:middle line:84% So this kind of super-accurate math can be very expensive. 00:42:32.840 --> 00:42:34.940 align:middle line:84% And that's why if you look at high-end cameras, 00:42:34.940 --> 00:42:38.313 align:middle line:84% essentially the lens heads, they cost quite a fortune. 00:42:38.313 --> 00:42:40.230 align:middle line:84% It's actually because of this kind of behavior 00:42:40.230 --> 00:42:41.790 align:middle line:84% that people are trying to compensate 00:42:41.790 --> 00:42:46.290 align:middle line:84% for the chromatic aberration of lenses. 00:42:46.290 --> 00:42:48.230 align:middle line:84% So this is one example where people 00:42:48.230 --> 00:42:51.808 align:middle line:84% are trying to suppress chromatic aberration. 00:42:51.808 --> 00:42:53.350 align:middle line:84% What I'm going to give you here. this 00:42:53.350 --> 00:42:54.808 align:middle line:84% is actually an example where people 00:42:54.808 --> 00:42:57.190 align:middle line:84% are in this case trying to use chromatic aberration 00:42:57.190 --> 00:42:58.990 align:middle line:84% as a feature rather than as a bug. 00:42:58.990 --> 00:43:03.150 align:middle line:84% So the context here is that people want to essentially split 00:43:03.150 --> 00:43:06.150 align:middle line:84% sunlight into different spectral components for more efficient 00:43:06.150 --> 00:43:07.590 align:middle line:90% solar energy collection. 00:43:07.590 --> 00:43:11.030 align:middle line:84% So in the last lecture, we actually 00:43:11.030 --> 00:43:12.970 align:middle line:84% talked about this concept of tandem cells. 00:43:12.970 --> 00:43:15.870 align:middle line:84% A tandem cell, essentially you have this kind 00:43:15.870 --> 00:43:19.070 align:middle line:84% of vertical stack of solar cells, the top one having 00:43:19.070 --> 00:43:20.050 align:middle line:90% the largest bandgap. 00:43:20.050 --> 00:43:23.070 align:middle line:84% And you decrease bandgap as you move down the stack. 00:43:23.070 --> 00:43:26.030 align:middle line:84% The whole idea is that you want to have each solar cell 00:43:26.030 --> 00:43:30.030 align:middle line:84% to absorb the sunlight only near its bandgap. 00:43:30.030 --> 00:43:34.430 align:middle line:84% So if you have-- for example, this is say the bandgap. 00:43:34.430 --> 00:43:37.110 align:middle line:84% Suppose you have a photon with energy that's 00:43:37.110 --> 00:43:38.530 align:middle line:90% much larger than the bandgap. 00:43:38.530 --> 00:43:40.390 align:middle line:84% Then what's going to happen is that it's 00:43:40.390 --> 00:43:42.750 align:middle line:84% going to promote, for example, this electron 00:43:42.750 --> 00:43:47.190 align:middle line:84% to an energy level that's way above the conduction band edge. 00:43:47.190 --> 00:43:49.170 align:middle line:84% Then what happens is that afterwards, 00:43:49.170 --> 00:43:52.990 align:middle line:84% this electron is then going to relax towards the conduction 00:43:52.990 --> 00:43:56.430 align:middle line:84% band edge due to a process called thermalization. 00:43:56.430 --> 00:43:58.990 align:middle line:84% Then all the energy, this energy difference 00:43:58.990 --> 00:44:01.150 align:middle line:84% between this level and the conduction band edge, 00:44:01.150 --> 00:44:04.470 align:middle line:84% is essentially wasted in the form of heat. 00:44:04.470 --> 00:44:05.770 align:middle line:90% So that's undesirable. 00:44:05.770 --> 00:44:08.190 align:middle line:84% That's why it's best the solar cell becomes 00:44:08.190 --> 00:44:11.590 align:middle line:84% most efficient if you try to use it to only absorb 00:44:11.590 --> 00:44:16.710 align:middle line:84% light that has energy slightly above the bandgap. 00:44:16.710 --> 00:44:19.430 align:middle line:84% So that's why people use these kinds of tandem cells, where 00:44:19.430 --> 00:44:22.670 align:middle line:84% each cell essentially only absorbs sunlight above bandgap. 00:44:22.670 --> 00:44:24.550 align:middle line:84% And then you stack them together. 00:44:24.550 --> 00:44:26.547 align:middle line:84% But the problem with the tandem cell 00:44:26.547 --> 00:44:28.130 align:middle line:84% is that, as I mentioned in last class, 00:44:28.130 --> 00:44:32.090 align:middle line:84% these cells essentially are in series connections, 00:44:32.090 --> 00:44:33.950 align:middle line:84% So the current has to pass through all 00:44:33.950 --> 00:44:37.440 align:middle line:90% the cells in a common path. 00:44:37.440 --> 00:44:40.240 align:middle line:84% It means that the photocurrent for all the cells 00:44:40.240 --> 00:44:42.680 align:middle line:84% must be exactly equal to each other. 00:44:42.680 --> 00:44:44.920 align:middle line:84% Otherwise, the overall current input 00:44:44.920 --> 00:44:49.600 align:middle line:84% becomes limited by the cell that has the lowest photocurrent. 00:44:49.600 --> 00:44:52.840 align:middle line:84% OK, so this is usually done by very carefully designing 00:44:52.840 --> 00:44:55.560 align:middle line:84% the thickness and the absorption of each cell. 00:44:55.560 --> 00:44:58.440 align:middle line:84% So split the solar spectrum into different segments, 00:44:58.440 --> 00:45:02.120 align:middle line:84% such that each segment produces the same amount of photocurrent. 00:45:02.120 --> 00:45:05.800 align:middle line:84% That's theoretically possible, but in practice, 00:45:05.800 --> 00:45:07.920 align:middle line:84% in actual operation conditions, the problem 00:45:07.920 --> 00:45:10.640 align:middle line:84% is that you get clouds, for example. 00:45:10.640 --> 00:45:13.000 align:middle line:84% You can get dust accumulating on your panels. 00:45:13.000 --> 00:45:16.280 align:middle line:84% You may get a bird flying by, some shadowing effect. 00:45:16.280 --> 00:45:18.760 align:middle line:84% All of those can actually change the spectrum. 00:45:18.760 --> 00:45:21.320 align:middle line:84% And therefore, it means that most of the time, this tandem 00:45:21.320 --> 00:45:23.720 align:middle line:84% cell will not be able to operate at its designed optimal 00:45:23.720 --> 00:45:26.160 align:middle line:90% condition. 00:45:26.160 --> 00:45:28.080 align:middle line:84% So that's why tandem cells actually are mostly 00:45:28.080 --> 00:45:29.903 align:middle line:90% used for space applications. 00:45:29.903 --> 00:45:30.820 align:middle line:90% There's no atmosphere. 00:45:30.820 --> 00:45:32.680 align:middle line:90% There's no dusk. 00:45:32.680 --> 00:45:34.380 align:middle line:84% So you always are pointing at the sun, 00:45:34.380 --> 00:45:36.767 align:middle line:90% get the right condition. 00:45:36.767 --> 00:45:38.600 align:middle line:84% But people still want high-efficiency cells. 00:45:38.600 --> 00:45:40.480 align:middle line:84% So one proposal, is instead of trying 00:45:40.480 --> 00:45:42.320 align:middle line:84% to stack solar cells vertically, you 00:45:42.320 --> 00:45:44.960 align:middle line:84% try to put them in a lateral array. 00:45:44.960 --> 00:45:47.800 align:middle line:84% You have strips of solar cells And you 00:45:47.800 --> 00:45:50.640 align:middle line:84% try to split sunlight laterally so that each cell essentially 00:45:50.640 --> 00:45:53.800 align:middle line:84% only collects a specific spectral component. 00:45:53.800 --> 00:45:55.620 align:middle line:84% Now it comes back to the problem. 00:45:55.620 --> 00:45:58.200 align:middle line:84% How do you efficiently split different wavelength components 00:45:58.200 --> 00:45:59.040 align:middle line:90% of sunlight. 00:45:59.040 --> 00:46:03.120 align:middle line:84% So one way of doing it is try to do exactly the opposite of what 00:46:03.120 --> 00:46:05.720 align:middle line:90% you do in a achromatic lens. 00:46:05.720 --> 00:46:07.260 align:middle line:84% You just try to mitigate dispersion. 00:46:07.260 --> 00:46:10.680 align:middle line:90% You try to maximize dispersion. 00:46:10.680 --> 00:46:14.840 align:middle line:84% You can design this kind of double prism structures. 00:46:14.840 --> 00:46:18.480 align:middle line:84% These two prisms have essentially a similar refractive 00:46:18.480 --> 00:46:20.840 align:middle line:84% index at one particular wavelength point. 00:46:20.840 --> 00:46:24.320 align:middle line:84% But they have opposite dispersion characteristics. 00:46:24.320 --> 00:46:27.305 align:middle line:84% So when the light passes through the interface between these two 00:46:27.305 --> 00:46:29.680 align:middle line:84% prisms here, because they have basically the same refract 00:46:29.680 --> 00:46:32.055 align:middle line:84% index, there's basically no reflection, very little loss. 00:46:32.055 --> 00:46:34.610 align:middle line:84% But as I pass through, due to the different dispersion 00:46:34.610 --> 00:46:36.210 align:middle line:84% behavior, they are going to split 00:46:36.210 --> 00:46:37.650 align:middle line:84% the different spectral components 00:46:37.650 --> 00:46:40.730 align:middle line:84% and let them go in two different directions. 00:46:40.730 --> 00:46:42.490 align:middle line:84% It's basically the exact opposite 00:46:42.490 --> 00:46:44.850 align:middle line:84% of why you're trying to design an achromatic doublet. 00:46:44.850 --> 00:46:48.490 align:middle line:84% You try to increase the separation 00:46:48.490 --> 00:46:50.730 align:middle line:84% of the different spectral components. 00:46:50.730 --> 00:46:53.810 align:middle line:84% So yeah, this is actually one example 00:46:53.810 --> 00:46:56.470 align:middle line:84% of this kind of a solar spectrum splitter here. 00:46:56.470 --> 00:46:58.790 align:middle line:84% You can clearly see that you see the color fringes. 00:46:58.790 --> 00:46:59.810 align:middle line:84% It's actually coming from the fact 00:46:59.810 --> 00:47:01.270 align:middle line:90% that you're splitting sunlight. 00:47:01.270 --> 00:47:03.270 align:middle line:84% You can then combine it with essentially a lens. 00:47:03.270 --> 00:47:04.645 align:middle line:84% You can put it in the essentially 00:47:04.645 --> 00:47:06.250 align:middle line:84% in the same optical design with two 00:47:06.250 --> 00:47:08.243 align:middle line:84% kind of glass materials' optical dispersion. 00:47:08.243 --> 00:47:10.410 align:middle line:84% And then you will be able to actually split sunlight 00:47:10.410 --> 00:47:13.330 align:middle line:90% into different components. 00:47:13.330 --> 00:47:14.610 align:middle line:90% All right. 00:47:14.610 --> 00:47:19.062 align:middle line:84% so this is basically about optical refraction. 00:47:19.062 --> 00:47:20.770 align:middle line:84% Any questions about refraction before you 00:47:20.770 --> 00:47:25.050 align:middle line:90% go to a transparency or loss? 00:47:25.050 --> 00:47:27.290 align:middle line:90% OK. 00:47:27.290 --> 00:47:29.570 align:middle line:84% So now coming to the second characteristic 00:47:29.570 --> 00:47:32.230 align:middle line:84% of a glass [INAUDIBLE] about essentially transparency. 00:47:32.230 --> 00:47:34.950 align:middle line:84% So what I'm plotting on this plot here, 00:47:34.950 --> 00:47:37.730 align:middle line:84% this is the optical loss spectrum in silica glass 00:47:37.730 --> 00:47:41.122 align:middle line:90% materials-- silica glass fiber. 00:47:41.122 --> 00:47:43.190 align:middle line:84% The horizontal axis is wavelength. 00:47:43.190 --> 00:47:46.810 align:middle line:90% Vertical axis is a loss. 00:47:46.810 --> 00:47:51.850 align:middle line:84% But this loss is measured in dB per kilometer 00:47:51.850 --> 00:47:56.810 align:middle line:84% So the definition of dB this is basically 00:47:56.810 --> 00:47:59.270 align:middle line:84% intensity in a logarithmic scale right. 00:47:59.270 --> 00:48:06.530 align:middle line:84% So dB is basically given as 10 times logarithm 10 00:48:06.530 --> 00:48:11.315 align:middle line:84% of the starting intensity over the intensity 00:48:11.315 --> 00:48:12.690 align:middle line:84% after you pass through a material 00:48:12.690 --> 00:48:24.810 align:middle line:84% there So in fact, what you can do, 00:48:24.810 --> 00:48:28.700 align:middle line:84% because we know we have a number [INAUDIBLE], you can directly 00:48:28.700 --> 00:48:31.620 align:middle line:84% plug [INAUDIBLE] into this equation. 00:48:31.620 --> 00:48:32.560 align:middle line:90% Let's see what we get. 00:48:32.560 --> 00:48:34.620 align:middle line:90% It becomes 10. 00:48:34.620 --> 00:48:39.680 align:middle line:84% I know divided by I is e alpha d. 00:48:39.680 --> 00:48:45.100 align:middle line:84% So it becomes logarithm 10e alpha D. 00:48:45.100 --> 00:48:59.160 align:middle line:84% And this essentially gives us 10 alpha d logarithm 10e. 00:48:59.160 --> 00:49:08.100 align:middle line:90% 00:49:08.100 --> 00:49:14.520 align:middle line:84% If you move d to the other side, d is basically length right. 00:49:14.520 --> 00:49:18.760 align:middle line:84% So then what you get will be dB per length, dB per centimeter, 00:49:18.760 --> 00:49:20.900 align:middle line:90% dB per kilometer. 00:49:20.900 --> 00:49:22.580 align:middle line:84% So now what you see here is that there 00:49:22.580 --> 00:49:25.260 align:middle line:84% is a very simple quantitative relation between these two unit 00:49:25.260 --> 00:49:26.380 align:middle line:90% systems here. 00:49:26.380 --> 00:49:28.880 align:middle line:84% Alpha can be the unit of centimeter inverse. 00:49:28.880 --> 00:49:31.660 align:middle line:84% It can also be the unit of dB per centimeter or dB 00:49:31.660 --> 00:49:32.940 align:middle line:90% per kilometer. 00:49:32.940 --> 00:49:36.280 align:middle line:84% And these two are trivially connected by this equation 00:49:36.280 --> 00:49:43.460 align:middle line:84% here-- dB per length is just 10 times alpha logarithm 10e, 00:49:43.460 --> 00:49:45.200 align:middle line:90% which equals to. 00:49:45.200 --> 00:49:48.180 align:middle line:90% 00:49:48.180 --> 00:49:50.800 align:middle line:90% 0.23. 00:49:50.800 --> 00:49:59.340 align:middle line:84% So 10 times logarithm 10e is just 0.23. 00:49:59.340 --> 00:50:02.300 align:middle line:84% That's why I'm including it on my slide this last equation 00:50:02.300 --> 00:50:02.980 align:middle line:90% here. 00:50:02.980 --> 00:50:05.460 align:middle line:84% dB per centimeter can be trivially connected 00:50:05.460 --> 00:50:07.520 align:middle line:84% to inverse centimeter with that relation. 00:50:07.520 --> 00:50:09.120 align:middle line:84% There it's wavelength independent. 00:50:09.120 --> 00:50:13.660 align:middle line:84% In this derivation, there is no wavelength whatsoever 00:50:13.660 --> 00:50:17.960 align:middle line:84% So it's a universal relation for all wavelengths. 00:50:17.960 --> 00:50:22.380 align:middle line:90% 00:50:22.380 --> 00:50:25.750 align:middle line:84% Now, another some useful relation to also remember here 00:50:25.750 --> 00:50:29.230 align:middle line:84% is that because dB is in a 10 base logarithm. 00:50:29.230 --> 00:50:31.730 align:middle line:84% So if the light intensity decreases to 10%, 00:50:31.730 --> 00:50:32.970 align:middle line:90% you have 10 dB. 00:50:32.970 --> 00:50:36.010 align:middle line:90% It decreases 1% you have 20 dB. 00:50:36.010 --> 00:50:40.910 align:middle line:84% It decreases to 50%, 10 logarithm 10 of 0.5 00:50:40.910 --> 00:50:44.710 align:middle line:90% is very close to 3. 00:50:44.710 --> 00:50:46.910 align:middle line:84% That's why in optics, and in electronics 00:50:46.910 --> 00:50:49.770 align:middle line:84% as well, when people are talking about 3 dB, 00:50:49.770 --> 00:50:52.590 align:middle line:90% it essentially means half. 00:50:52.590 --> 00:50:54.528 align:middle line:84% If you talk about three dB splitter, 00:50:54.528 --> 00:50:57.070 align:middle line:84% it means that essentially you have a splitter, a split light, 00:50:57.070 --> 00:51:01.590 align:middle line:84% to 50% 3 dB attenuator means that essentially cuts off 00:51:01.590 --> 00:51:02.570 align:middle line:90% half of the light. 00:51:02.570 --> 00:51:05.830 align:middle line:90% So 3 dB basically means half. 00:51:05.830 --> 00:51:08.070 align:middle line:84% I will leave it to you as a little homework exercise 00:51:08.070 --> 00:51:11.830 align:middle line:90% to figure out the 6 DB p size. 00:51:11.830 --> 00:51:14.630 align:middle line:90% What's the 6 dB p size? 00:51:14.630 --> 00:51:16.190 align:middle line:90% It's a quarter pizza. 00:51:16.190 --> 00:51:20.070 align:middle line:90% 00:51:20.070 --> 00:51:21.190 align:middle line:90% It's in logarithmic scale. 00:51:21.190 --> 00:51:24.750 align:middle line:84% 6 dB decibels is 2 3 decibels, so it's a square of 1/2, 00:51:24.750 --> 00:51:27.430 align:middle line:90% so it's a quarter pizza. 00:51:27.430 --> 00:51:30.510 align:middle line:84% And then 9 dB is one [INAUDIBLE] pizza. 00:51:30.510 --> 00:51:32.910 align:middle line:90% Now, [INAUDIBLE]. 00:51:32.910 --> 00:51:38.250 align:middle line:84% OK, anyway, what's remarkable about glass materials, 00:51:38.250 --> 00:51:40.250 align:middle line:84% if you look at this particular wavelength here, 00:51:40.250 --> 00:51:43.790 align:middle line:84% 1,550 nanometers, or 1.55 microns, 00:51:43.790 --> 00:51:47.160 align:middle line:84% its loss is actually as low as 0.2db/km. 00:51:47.160 --> 00:51:50.910 align:middle line:84% 0.2 dB is about 4% So it means you can send light 00:51:50.910 --> 00:51:52.990 align:middle line:84% through this silica glass material, propagates 00:51:52.990 --> 00:51:54.450 align:middle line:90% for 1 kilometer. 00:51:54.450 --> 00:51:58.710 align:middle line:90% You lose only 4% of the light. 00:51:58.710 --> 00:52:00.177 align:middle line:90% This is really quite remarkable. 00:52:00.177 --> 00:52:02.010 align:middle line:84% I mean, you talk about transparent material, 00:52:02.010 --> 00:52:04.370 align:middle line:84% like, window pane glasses, it may appear transparent. 00:52:04.370 --> 00:52:06.287 align:middle line:84% But if you look from the side, you immediately 00:52:06.287 --> 00:52:08.520 align:middle line:84% see this kind of green tint, indicating 00:52:08.520 --> 00:52:10.270 align:middle line:84% that some of the light is actually getting 00:52:10.270 --> 00:52:13.010 align:middle line:90% absorbed because of impurities. 00:52:13.010 --> 00:52:17.630 align:middle line:84% But in a high purity silica, you can propagate for kilometers 00:52:17.630 --> 00:52:20.160 align:middle line:90% with minimal attenuation. 00:52:20.160 --> 00:52:23.440 align:middle line:84% So this is really what enables the whole, essentially, 00:52:23.440 --> 00:52:25.700 align:middle line:84% fiber optic network and fiber optic communications. 00:52:25.700 --> 00:52:27.420 align:middle line:90% That's the backbone of internet. 00:52:27.420 --> 00:52:30.280 align:middle line:84% And that's why the inventor of this low-loss glass 00:52:30.280 --> 00:52:33.640 align:middle line:84% fiber, Charles Kao, was awarded the Nobel Prize of physics 00:52:33.640 --> 00:52:37.640 align:middle line:84% in 2009 for his groundbreaking contributions 00:52:37.640 --> 00:52:41.320 align:middle line:84% to enable low loss light transmission fibers. 00:52:41.320 --> 00:52:44.920 align:middle line:84% Now, the reason he can win this Nobel Prize there 00:52:44.920 --> 00:52:47.840 align:middle line:84% is because this is really essentially a triumph 00:52:47.840 --> 00:52:49.560 align:middle line:90% of the materials science. 00:52:49.560 --> 00:52:52.980 align:middle line:84% He looked a lot into how to actually purify glass materials, 00:52:52.980 --> 00:52:55.042 align:middle line:84% how to understand the different loss mechanisms. 00:52:55.042 --> 00:52:57.000 align:middle line:84% Therefore, you can achieve essentially low-loss 00:52:57.000 --> 00:52:57.820 align:middle line:90% light propagation. 00:52:57.820 --> 00:53:01.120 align:middle line:84% So in the next slide here, I'm just 00:53:01.120 --> 00:53:04.440 align:middle line:84% going to summarize what are the loss mechanisms in glass 00:53:04.440 --> 00:53:08.017 align:middle line:84% materials or more generally in any kind of materials. 00:53:08.017 --> 00:53:09.600 align:middle line:84% All right, starting from the first one 00:53:09.600 --> 00:53:11.475 align:middle line:84% this is actually straightforward-- electronic 00:53:11.475 --> 00:53:12.240 align:middle line:90% absorption. 00:53:12.240 --> 00:53:14.040 align:middle line:84% This is the main absorption mechanism 00:53:14.040 --> 00:53:16.200 align:middle line:84% in any kind of semiconductor optoelectronic device. 00:53:16.200 --> 00:53:18.880 align:middle line:90% 00:53:18.880 --> 00:53:21.740 align:middle line:84% If you have a photon energy greater than the bandgap, 00:53:21.740 --> 00:53:25.920 align:middle line:84% you promote electron from valence band to conduction band, 00:53:25.920 --> 00:53:28.680 align:middle line:84% And you convert essentially electron energy 00:53:28.680 --> 00:53:31.420 align:middle line:84% to photon energy into the electronic domain. 00:53:31.420 --> 00:53:33.480 align:middle line:90% So that's electronic absorption. 00:53:33.480 --> 00:53:35.020 align:middle line:84% It can also come from-- for example, 00:53:35.020 --> 00:53:38.360 align:middle line:84% you have some dopant atoms where the energy level separation 00:53:38.360 --> 00:53:40.240 align:middle line:84% between two discrete energy levels 00:53:40.240 --> 00:53:42.500 align:middle line:84% happens to align with some optical frequency. 00:53:42.500 --> 00:53:45.040 align:middle line:84% Then you can promote essentially or excite the atoms 00:53:45.040 --> 00:53:46.920 align:middle line:84% from the ground state to excited state. 00:53:46.920 --> 00:53:47.760 align:middle line:90% Same thing. 00:53:47.760 --> 00:53:49.960 align:middle line:84% Like hydrogen atoms, you see absorption lines 00:53:49.960 --> 00:53:51.380 align:middle line:90% also due to electron absorption. 00:53:51.380 --> 00:53:52.560 align:middle line:90% Straightforward 00:53:52.560 --> 00:53:54.340 align:middle line:84% Now, next one-- phonon absorption. 00:53:54.340 --> 00:53:56.280 align:middle line:84% I've also already mentioned about it. 00:53:56.280 --> 00:53:58.960 align:middle line:84% Phonon absorption has to do with essentially the vibration 00:53:58.960 --> 00:54:01.960 align:middle line:84% of the atoms or the chemical bonds, basically. 00:54:01.960 --> 00:54:04.720 align:middle line:84% You can picture these chemical bonds 00:54:04.720 --> 00:54:06.800 align:middle line:84% as you have masses or atoms attached 00:54:06.800 --> 00:54:08.360 align:middle line:90% to the end of the spring. 00:54:08.360 --> 00:54:10.800 align:middle line:84% And so if the vibrational frequency of the chemical bonds 00:54:10.800 --> 00:54:13.480 align:middle line:84% coincides with the oscillation frequency 00:54:13.480 --> 00:54:15.360 align:middle line:84% of electromagnetic field, then you 00:54:15.360 --> 00:54:17.250 align:middle line:84% can convert photon energy into essentially 00:54:17.250 --> 00:54:20.290 align:middle line:90% phonon or vibrational energy. 00:54:20.290 --> 00:54:23.970 align:middle line:84% So just to show you one example of phonon absorption, 00:54:23.970 --> 00:54:25.730 align:middle line:84% I'm showing you this picture here. 00:54:25.730 --> 00:54:29.810 align:middle line:84% You want to guess who that guy is? 00:54:29.810 --> 00:54:31.870 align:middle line:90% AUDIENCE: Is it [INAUDIBLE]? 00:54:31.870 --> 00:54:32.950 align:middle line:90% JUEJUN HU: Very good. 00:54:32.950 --> 00:54:35.170 align:middle line:90% [CHUCKLES] 00:54:35.170 --> 00:54:37.670 align:middle line:84% I think last time, last year when I was teaching this class, 00:54:37.670 --> 00:54:38.962 align:middle line:90% I was asking the same question. 00:54:38.962 --> 00:54:43.118 align:middle line:84% And they would be like, this is Morpheus from the movie Matrix. 00:54:43.118 --> 00:54:44.410 align:middle line:90% No, I don't look like Morpheus. 00:54:44.410 --> 00:54:45.370 align:middle line:90% Not at all. 00:54:45.370 --> 00:54:46.890 align:middle line:84% My main point for showing that is 00:54:46.890 --> 00:54:50.210 align:middle line:84% that-- look at my glasses, which is metal oxide glasses. 00:54:50.210 --> 00:54:51.190 align:middle line:90% It's completely opaque. 00:54:51.190 --> 00:54:52.670 align:middle line:84% You don't see my eyes through it. 00:54:52.670 --> 00:54:55.510 align:middle line:84% So the glasses is transparent in the visible regime. 00:54:55.510 --> 00:54:57.650 align:middle line:84% But if you go to infrared, this is actually 00:54:57.650 --> 00:54:58.790 align:middle line:90% thermal infrared image. 00:54:58.790 --> 00:55:00.505 align:middle line:84% Because the wavelength is longer, 00:55:00.505 --> 00:55:03.130 align:middle line:84% vibrational frequency lower, the vibrational frequency actually 00:55:03.130 --> 00:55:06.610 align:middle line:84% coincides with the, essentially, oscillation of silicon oxygen 00:55:06.610 --> 00:55:08.230 align:middle line:90% bond in oxide glasses. 00:55:08.230 --> 00:55:11.290 align:middle line:84% And that's why they absorb very heavily as you 00:55:11.290 --> 00:55:12.350 align:middle line:90% go to longer wavelengths. 00:55:12.350 --> 00:55:15.210 align:middle line:90% That's why it's opaque. 00:55:15.210 --> 00:55:18.190 align:middle line:84% All right, next one, direct scattering. 00:55:18.190 --> 00:55:19.610 align:middle line:90% What's this picture? 00:55:19.610 --> 00:55:22.370 align:middle line:84% AUDIENCE: [INAUDIBLE] Jurassic Park. 00:55:22.370 --> 00:55:24.490 align:middle line:84% JUEJUN HU: Jurassic World to be exact. 00:55:24.490 --> 00:55:27.090 align:middle line:90% And what's that thing? 00:55:27.090 --> 00:55:28.433 align:middle line:90% AUDIENCE: It's like the-- 00:55:28.433 --> 00:55:29.350 align:middle line:90% JUEJUN HU: Gyrosphere. 00:55:29.350 --> 00:55:30.810 align:middle line:90% It's OK. 00:55:30.810 --> 00:55:32.270 align:middle line:84% When you actually watch the movie-- 00:55:32.270 --> 00:55:32.770 align:middle line:90% OK. 00:55:32.770 --> 00:55:34.710 align:middle line:90% When you watch the movie-- 00:55:34.710 --> 00:55:36.290 align:middle line:90% I know it's an airplane movie. 00:55:36.290 --> 00:55:39.610 align:middle line:84% But when you are on an airplane watching that movie, 00:55:39.610 --> 00:55:42.490 align:middle line:84% did you recall what material they used 00:55:42.490 --> 00:55:44.370 align:middle line:90% to make the gyrosphere out of? 00:55:44.370 --> 00:55:47.630 align:middle line:90% AUDIENCE: Transparent ceramic? 00:55:47.630 --> 00:55:48.670 align:middle line:90% JUEJUN HU: Yeah, I know. 00:55:48.670 --> 00:55:50.110 align:middle line:90% I saw the revealed answer there. 00:55:50.110 --> 00:55:51.510 align:middle line:84% Give me the chemical composition. 00:55:51.510 --> 00:55:52.330 align:middle line:90% AUDIENCE: Oh. 00:55:52.330 --> 00:55:53.230 align:middle line:84% JUEJUN HU: It's material science. 00:55:53.230 --> 00:55:54.350 align:middle line:90% You should be proficient. 00:55:54.350 --> 00:55:58.367 align:middle line:84% OK, there are many, many, many, many scientific flaws 00:55:58.367 --> 00:55:58.950 align:middle line:90% in that movie. 00:55:58.950 --> 00:56:01.930 align:middle line:84% But there's one thing they got right. 00:56:01.930 --> 00:56:05.610 align:middle line:84% They said that the gyrosphere is made of a transparent aluminum 00:56:05.610 --> 00:56:09.790 align:middle line:84% oxynitride, which is indeed a transparent ceramic. 00:56:09.790 --> 00:56:11.610 align:middle line:84% And it's actually a transparent ceramic 00:56:11.610 --> 00:56:13.300 align:middle line:84% known for very high mechanical strength. 00:56:13.300 --> 00:56:14.092 align:middle line:90% You can understand. 00:56:14.092 --> 00:56:16.200 align:middle line:84% Its aluminum, oxygen, and nitrogen, small atoms, 00:56:16.200 --> 00:56:17.400 align:middle line:90% very strong chemical bonds. 00:56:17.400 --> 00:56:19.140 align:middle line:90% It's basically sapphire. 00:56:19.140 --> 00:56:19.780 align:middle line:90% So that's why. 00:56:19.780 --> 00:56:20.405 align:middle line:90% It makes sense. 00:56:20.405 --> 00:56:21.780 align:middle line:84% AUDIENCE: [INAUDIBLE] if you were 00:56:21.780 --> 00:56:23.340 align:middle line:84% to make that [INAUDIBLE] would use 00:56:23.340 --> 00:56:23.860 align:middle line:90% JUEJUN HU: Sorry? 00:56:23.860 --> 00:56:25.220 align:middle line:84% AUDIENCE: That if you were to make that, that would 00:56:25.220 --> 00:56:26.560 align:middle line:90% be the material you would use. 00:56:26.560 --> 00:56:29.380 align:middle line:84% JUEJUN HU: I'm not going to write that thing 00:56:29.380 --> 00:56:30.920 align:middle line:90% to see dinosaurs. 00:56:30.920 --> 00:56:32.520 align:middle line:84% I don't think it's safe, basically. 00:56:32.520 --> 00:56:36.392 align:middle line:84% But yeah, as I'm saying, it's a less transparent. 00:56:36.392 --> 00:56:37.600 align:middle line:90% I'm not talking about safety. 00:56:37.600 --> 00:56:39.225 align:middle line:84% I'm talking about it being transparent. 00:56:39.225 --> 00:56:43.140 align:middle line:84% Now, why are most ceramics opaque. 00:56:43.140 --> 00:56:44.860 align:middle line:84% If you look at normal materials, ceramics 00:56:44.860 --> 00:56:47.603 align:middle line:84% are opaque, because ceramics are a polycrystalline material. 00:56:47.603 --> 00:56:50.020 align:middle line:84% In a polycarbonate material, you all the different grains. 00:56:50.020 --> 00:56:51.652 align:middle line:84% If it's an anisotropic material, it 00:56:51.652 --> 00:56:53.860 align:middle line:84% means that different grains at different orientations 00:56:53.860 --> 00:56:55.303 align:middle line:84% have different refractive indexes. 00:56:55.303 --> 00:56:56.720 align:middle line:84% So as light propagates through it, 00:56:56.720 --> 00:56:58.762 align:middle line:84% you actually get lots of scattering, essentially, 00:56:58.762 --> 00:57:00.720 align:middle line:84% from that refractive index homogeneity. 00:57:00.720 --> 00:57:03.380 align:middle line:84% In addition to that, you also get essentially grain 00:57:03.380 --> 00:57:05.820 align:middle line:90% boundaries, integranular phase. 00:57:05.820 --> 00:57:08.980 align:middle line:84% Those intergranular phase also has different refractive index 00:57:08.980 --> 00:57:11.180 align:middle line:84% compared to the grain matrix itself. 00:57:11.180 --> 00:57:13.303 align:middle line:84% So all of this reflecting the fluctuation 00:57:13.303 --> 00:57:14.720 align:middle line:84% is what leads to light scattering. 00:57:14.720 --> 00:57:18.500 align:middle line:84% And that's why normal ceramics tend to be opaque. 00:57:18.500 --> 00:57:21.700 align:middle line:84% So the trick to make transparent ceramics like aluminum 00:57:21.700 --> 00:57:23.860 align:middle line:84% oxynitride, usually what people do 00:57:23.860 --> 00:57:27.060 align:middle line:84% is to find a material system that's isotropic, 00:57:27.060 --> 00:57:29.020 align:middle line:90% like cubic crystal systems. 00:57:29.020 --> 00:57:30.940 align:middle line:84% So a cubic crystal system, they are isotropic, 00:57:30.940 --> 00:57:32.980 align:middle line:84% so that regardless of orientation of the grain. 00:57:32.980 --> 00:57:35.660 align:middle line:84% You always have the same refractive index-- first step. 00:57:35.660 --> 00:57:37.980 align:middle line:84% Second step is that you have to optimize your process 00:57:37.980 --> 00:57:40.540 align:middle line:84% to essentially eliminate the formation of any kind 00:57:40.540 --> 00:57:43.500 align:middle line:90% of intergranular phase. 00:57:43.500 --> 00:57:45.620 align:middle line:84% So the light will just zip through essentially 00:57:45.620 --> 00:57:46.920 align:middle line:90% a uniform media. 00:57:46.920 --> 00:57:48.080 align:middle line:90% It's easier said than done. 00:57:48.080 --> 00:57:49.940 align:middle line:84% People spent a long time just to develop 00:57:49.940 --> 00:57:52.940 align:middle line:84% those transparency materials, but that's the key. 00:57:52.940 --> 00:57:54.860 align:middle line:84% Bottom line is that if you have any kind 00:57:54.860 --> 00:57:57.460 align:middle line:84% of a structural inhomogeneity, whether it's 00:57:57.460 --> 00:58:01.160 align:middle line:84% due to crystalline grain, grain boundaries or maybe micro-voids, 00:58:01.160 --> 00:58:03.100 align:middle line:84% microcracks all of those are going 00:58:03.100 --> 00:58:05.260 align:middle line:84% to lead to essentially scattering of light. 00:58:05.260 --> 00:58:08.180 align:middle line:84% Now, the scattering is a bit different 00:58:08.180 --> 00:58:09.470 align:middle line:90% from actual absorption. 00:58:09.470 --> 00:58:11.822 align:middle line:84% For these two mechanisms here, this absorption, 00:58:11.822 --> 00:58:14.030 align:middle line:84% you're converting photon energy into something else-- 00:58:14.030 --> 00:58:15.350 align:middle line:90% into heat, basically. 00:58:15.350 --> 00:58:17.810 align:middle line:84% But for scattering, you're not really absorbing the light. 00:58:17.810 --> 00:58:20.270 align:middle line:84% You're just diverting the propagation direction of light. 00:58:20.270 --> 00:58:25.570 align:middle line:84% But effectively, this is also light wasted. 00:58:25.570 --> 00:58:29.630 align:middle line:90% Now, last one this is for glass. 00:58:29.630 --> 00:58:33.610 align:middle line:84% So for defects, this only exists in crappy glass materials. 00:58:33.610 --> 00:58:36.830 align:middle line:84% In glass with micro-voids like air bubbles or glasses 00:58:36.830 --> 00:58:39.990 align:middle line:84% with microcracks, that's when the defects comes in. 00:58:39.990 --> 00:58:42.190 align:middle line:84% But for the last one, Rayleigh scattering, 00:58:42.190 --> 00:58:46.310 align:middle line:84% this is universal to all amorphous materials. 00:58:46.310 --> 00:58:48.470 align:middle line:84% The reason we have Rayleigh scattering 00:58:48.470 --> 00:58:51.510 align:middle line:84% is because, if you think about amorphous networks, 00:58:51.510 --> 00:58:54.270 align:middle line:84% if you zoom in to look at atomic scale, 00:58:54.270 --> 00:58:56.390 align:middle line:84% every location of the network is going 00:58:56.390 --> 00:58:59.910 align:middle line:84% to be slightly different because of the [? incoherence ?] 00:58:59.910 --> 00:59:02.230 align:middle line:84% of the physical nature of glass structure. 00:59:02.230 --> 00:59:06.710 align:middle line:84% So what that also means is that the local polarizability 00:59:06.710 --> 00:59:11.110 align:middle line:84% or the local refractive index is different for all 00:59:11.110 --> 00:59:13.190 align:middle line:90% the different locations. 00:59:13.190 --> 00:59:15.150 align:middle line:84% So now when the light propagates through, 00:59:15.150 --> 00:59:17.470 align:middle line:84% it effectively sees this kind of fluctuation 00:59:17.470 --> 00:59:20.310 align:middle line:84% of refractive indices, which then leads to scattering. 00:59:20.310 --> 00:59:23.950 align:middle line:84% That's called Rayleigh scattering. 00:59:23.950 --> 00:59:26.190 align:middle line:84% Rayleigh scattering is actually universal to any kind 00:59:26.190 --> 00:59:30.810 align:middle line:84% of a non-uniform materials or known non-crystalline material-- 00:59:30.810 --> 00:59:34.070 align:middle line:84% any kind non-crystalline material, even like air. 00:59:34.070 --> 00:59:35.890 align:middle line:84% Air molecules are running around randomly. 00:59:35.890 --> 00:59:37.470 align:middle line:84% So there's also really scattering 00:59:37.470 --> 00:59:40.350 align:middle line:84% because of air molecules, the random motion of air molecules. 00:59:40.350 --> 00:59:44.010 align:middle line:84% And that's actually why the sky is blue. 00:59:44.010 --> 00:59:46.710 align:middle line:84% It is because this Rayleigh scattering scatters 00:59:46.710 --> 00:59:49.710 align:middle line:84% more strongly the blue light than other shorter, longer 00:59:49.710 --> 00:59:53.430 align:middle line:90% wavelengths of the spectrum. 00:59:53.430 --> 00:59:55.750 align:middle line:84% But Rayleigh scattering is a lot weaker 00:59:55.750 --> 00:59:57.847 align:middle line:84% compared to defect scattering, basically 00:59:57.847 --> 00:59:59.930 align:middle line:84% because of length scale we are talking about here. 00:59:59.930 --> 01:00:03.470 align:middle line:84% The microscopic defects, we are talking about hundreds 01:00:03.470 --> 01:00:05.940 align:middle line:84% of nanometer microns, so comparable to light wavelengths. 01:00:05.940 --> 01:00:07.620 align:middle line:84% So light gets very strongly scattered. 01:00:07.620 --> 01:00:10.480 align:middle line:84% But for Rayleigh scattering this atomic inhomogeneity 01:00:10.480 --> 01:00:13.840 align:middle line:84% takes place at atomic scale, much smaller than wavelengths. 01:00:13.840 --> 01:00:17.480 align:middle line:84% For Rayleigh scattering, the scattered light intensity 01:00:17.480 --> 01:00:22.060 align:middle line:84% scales with wavelength to the negative fourth power. 01:00:22.060 --> 01:00:23.680 align:middle line:90% This is for Rayleigh scattering. 01:00:23.680 --> 01:00:26.140 align:middle line:84% So if you go to longer wavelength-- 01:00:26.140 --> 01:00:28.960 align:middle line:84% or I should say lambda divided by a, 01:00:28.960 --> 01:00:33.720 align:middle line:84% where a is a characteristic length scale 01:00:33.720 --> 01:00:35.840 align:middle line:90% of the inhomogeneity. 01:00:35.840 --> 01:00:39.480 align:middle line:84% So if your nonuniformity becomes a lot smaller compared 01:00:39.480 --> 01:00:42.400 align:middle line:84% to wavelength, then this Rayleigh scattering 01:00:42.400 --> 01:00:43.960 align:middle line:84% becomes a lot more insignificant. 01:00:43.960 --> 01:00:48.480 align:middle line:84% And that's why glass materials can be very, very transparent 01:00:48.480 --> 01:00:50.460 align:middle line:84% despite the presence of Rayleigh scattering. 01:00:50.460 --> 01:00:54.540 align:middle line:90% 01:00:54.540 --> 01:01:02.240 align:middle line:84% So if you now look at this plot here, at the short wavelength n, 01:01:02.240 --> 01:01:06.600 align:middle line:84% this is bound by essentially Rayleigh scattering there. 01:01:06.600 --> 01:01:09.200 align:middle line:84% Long wavelengths n, this is actually due to a chemical bond 01:01:09.200 --> 01:01:10.280 align:middle line:90% vibration. 01:01:10.280 --> 01:01:12.420 align:middle line:84% In the middle, you have the lowest loss window, 01:01:12.420 --> 01:01:15.880 align:middle line:84% which gives rise to this remarkable 0.2 dB per kilometer. 01:01:15.880 --> 01:01:18.720 align:middle line:84% This is usually between-- you are 01:01:18.720 --> 01:01:21.720 align:middle line:84% seeking a trade-off between Rayleigh scattering 01:01:21.720 --> 01:01:26.280 align:middle line:84% and the phonon absorption in glass that's free of defects. 01:01:26.280 --> 01:01:29.520 align:middle line:84% So I will go into more details about these different kinds 01:01:29.520 --> 01:01:32.460 align:middle line:84% of loss mechanisms in glass materials in the next lecture. 01:01:32.460 --> 01:01:36.840 align:middle line:84% For the remaining 10, 15 minutes, what I will do, 01:01:36.840 --> 01:01:39.800 align:middle line:84% I will actually show you a little demo 01:01:39.800 --> 01:01:43.440 align:middle line:84% that shows that indeed, you can get a glass material that's 01:01:43.440 --> 01:01:45.600 align:middle line:84% transparent at different wavelength regimes. 01:01:45.600 --> 01:01:49.080 align:middle line:84% So what I have here, I have actually 01:01:49.080 --> 01:01:52.020 align:middle line:84% brought along with me a little infrared camera, 01:01:52.020 --> 01:01:52.900 align:middle line:90% a thermal camera. 01:01:52.900 --> 01:01:56.120 align:middle line:90% 01:01:56.120 --> 01:02:01.970 align:middle line:84% What I will do, let me try to project it to a screen here. 01:02:01.970 --> 01:02:05.410 align:middle line:90% Let me go to Zoom. 01:02:05.410 --> 01:02:12.010 align:middle line:84% And let me try to join Zoom from here, so I can share screen. 01:02:12.010 --> 01:02:13.950 align:middle line:90% So now let me start the app. 01:02:13.950 --> 01:02:16.570 align:middle line:84% I have brought along with me a little-- 01:02:16.570 --> 01:02:18.430 align:middle line:84% this is actually a little infrared camera. 01:02:18.430 --> 01:02:22.330 align:middle line:90% 01:02:22.330 --> 01:02:25.570 align:middle line:84% So this is actually what the camera looks like. 01:02:25.570 --> 01:02:28.330 align:middle line:84% Right here, this is actually camera lens. 01:02:28.330 --> 01:02:30.218 align:middle line:84% It's a lens made of chalcogenide glass. 01:02:30.218 --> 01:02:32.010 align:middle line:84% We have mentioned that chalcogenide glasses 01:02:32.010 --> 01:02:34.177 align:middle line:84% tend to be transparent at infrared wavelength range. 01:02:34.177 --> 01:02:35.930 align:middle line:90% So that's actually what happens. 01:02:35.930 --> 01:02:38.190 align:middle line:90% And let me plug it in. 01:02:38.190 --> 01:02:42.888 align:middle line:90% 01:02:42.888 --> 01:02:44.930 align:middle line:84% If you want, you can come around and take a look. 01:02:44.930 --> 01:02:46.730 align:middle line:90% It may be a bit easier. 01:02:46.730 --> 01:02:50.150 align:middle line:84% But I will also try to project it to the screen as well. 01:02:50.150 --> 01:02:55.970 align:middle line:90% 01:02:55.970 --> 01:03:00.050 align:middle line:90% OK camera. 01:03:00.050 --> 01:03:02.030 align:middle line:90% And study the app. 01:03:02.030 --> 01:03:10.250 align:middle line:90% 01:03:10.250 --> 01:03:12.310 align:middle line:84% OK, now I want to share my screen. 01:03:12.310 --> 01:03:25.650 align:middle line:90% 01:03:25.650 --> 01:03:28.300 align:middle line:84% OK, now you see the screen share. 01:03:28.300 --> 01:03:29.550 align:middle line:90% Now let me turn on the camera. 01:03:29.550 --> 01:03:31.570 align:middle line:90% Actually, let me see. 01:03:31.570 --> 01:03:33.430 align:middle line:90% Let me [INAUDIBLE] this way. 01:03:33.430 --> 01:03:39.090 align:middle line:90% 01:03:39.090 --> 01:03:40.030 align:middle line:90% Then let's see. 01:03:40.030 --> 01:03:41.890 align:middle line:90% Let me turn on the camera. 01:03:41.890 --> 01:03:45.978 align:middle line:90% All right, already working. 01:03:45.978 --> 01:03:47.225 align:middle line:90% AUDIENCE: Am I hot? 01:03:47.225 --> 01:03:47.850 align:middle line:90% AUDIENCE: Yeah. 01:03:47.850 --> 01:03:49.283 align:middle line:90% JUEJUN HU: You are, yes. 01:03:49.283 --> 01:03:50.950 align:middle line:84% It's actually measuring the temperature. 01:03:50.950 --> 01:03:53.047 align:middle line:90% It's actually [INAUDIBLE] 01:03:53.047 --> 01:03:53.922 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:03:53.922 --> 01:03:56.650 align:middle line:84% JUEJUN HU: I think it's better to look at glasses. 01:03:56.650 --> 01:03:58.660 align:middle line:90% [LAUGHTER] 01:03:58.660 --> 01:04:01.380 align:middle line:84% OK, now what do I want to do, we can actually change the color 01:04:01.380 --> 01:04:02.140 align:middle line:90% scales if we want. 01:04:02.140 --> 01:04:04.220 align:middle line:84% [INAUDIBLE] need to make better apps. 01:04:04.220 --> 01:04:09.100 align:middle line:84% I bring along with me glasses-- two kinds of glasses. 01:04:09.100 --> 01:04:12.660 align:middle line:84% So this is just a regular soda-lime glass light. 01:04:12.660 --> 01:04:14.823 align:middle line:90% Now try to hold it like this. 01:04:14.823 --> 01:04:16.240 align:middle line:84% You can put your finger behind it. 01:04:16.240 --> 01:04:17.740 align:middle line:84% You can first look at the finger, 01:04:17.740 --> 01:04:19.320 align:middle line:90% and then you could cover it up. 01:04:19.320 --> 01:04:22.583 align:middle line:84% So the two of you, however you want to do it. 01:04:22.583 --> 01:04:24.500 align:middle line:84% Let me first try to get it to work [INAUDIBLE] 01:04:24.500 --> 01:04:26.780 align:middle line:90% if you're looking at finger. 01:04:26.780 --> 01:04:28.980 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:04:28.980 --> 01:04:31.250 align:middle line:90% 01:04:31.250 --> 01:04:32.000 align:middle line:90% AUDIENCE: Oh yeah. 01:04:32.000 --> 01:04:32.520 align:middle line:90% That's true. 01:04:32.520 --> 01:04:33.300 align:middle line:90% JUEJUN HU: All right. 01:04:33.300 --> 01:04:34.008 align:middle line:90% Now I can see it. 01:04:34.008 --> 01:04:35.420 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:04:35.420 --> 01:04:37.200 align:middle line:84% JUEJUN HU: So where's the finger? 01:04:37.200 --> 01:04:39.180 align:middle line:90% Let me see. 01:04:39.180 --> 01:04:42.940 align:middle line:90% Maybe try to put [INAUDIBLE]. 01:04:42.940 --> 01:04:44.480 align:middle line:90% It's actually here. 01:04:44.480 --> 01:04:45.232 align:middle line:90% AUDIENCE: Oh. 01:04:45.232 --> 01:04:45.940 align:middle line:90% JUEJUN HU: I see. 01:04:45.940 --> 01:04:47.300 align:middle line:90% OK, all right, good. 01:04:47.300 --> 01:04:52.420 align:middle line:84% All right, now try to put the glass in front of the finger. 01:04:52.420 --> 01:04:53.920 align:middle line:90% I have to try to [INAUDIBLE]. 01:04:53.920 --> 01:04:56.380 align:middle line:90% OK, now block it. 01:04:56.380 --> 01:04:58.040 align:middle line:90% What do you see? 01:04:58.040 --> 01:04:59.540 align:middle line:84% AUDIENCE: My fingers [INAUDIBLE]. 01:04:59.540 --> 01:05:02.200 align:middle line:84% JUEJUN HU: The glass [INAUDIBLE]. 01:05:02.200 --> 01:05:02.700 align:middle line:90% See? 01:05:02.700 --> 01:05:04.120 align:middle line:84% You can no longer see your finger. 01:05:04.120 --> 01:05:07.780 align:middle line:84% So this shows that for thermal infrared, 01:05:07.780 --> 01:05:10.740 align:middle line:84% we are talking about wavelengths of the order of, like, 8 01:05:10.740 --> 01:05:12.792 align:middle line:90% to 10, 8 to 12 microns. 01:05:12.792 --> 01:05:14.500 align:middle line:84% This normal transparent glass is actually 01:05:14.500 --> 01:05:17.700 align:middle line:84% completely opaque at that wavelength. 01:05:17.700 --> 01:05:21.860 align:middle line:84% [INAUDIBLE] myself moving or you are moving? 01:05:21.860 --> 01:05:24.380 align:middle line:90% Now let's try this one. 01:05:24.380 --> 01:05:26.140 align:middle line:84% This is the chalcogenide glass plate 01:05:26.140 --> 01:05:29.900 align:middle line:84% that I have distributed around in the first lecture, which 01:05:29.900 --> 01:05:31.720 align:middle line:84% is completely opaque in the visible. 01:05:31.720 --> 01:05:36.420 align:middle line:90% So this, you see nothing. 01:05:36.420 --> 01:05:39.140 align:middle line:84% All right, now your finger again. 01:05:39.140 --> 01:05:41.980 align:middle line:90% Try to find your finger. 01:05:41.980 --> 01:05:43.320 align:middle line:90% Make sure to get a bit closer. 01:05:43.320 --> 01:05:44.060 align:middle line:90% AUDIENCE: OK. 01:05:44.060 --> 01:05:44.935 align:middle line:90% JUEJUN HU: All right. 01:05:44.935 --> 01:05:47.704 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:05:47.704 --> 01:05:49.460 align:middle line:90% JUEJUN HU: Do you see? 01:05:49.460 --> 01:05:52.180 align:middle line:84% Maybe [INAUDIBLE] clean background. 01:05:52.180 --> 01:05:53.750 align:middle line:90% Yeah, OK, good. 01:05:53.750 --> 01:05:55.210 align:middle line:90% That's a bit easier. 01:05:55.210 --> 01:05:55.710 align:middle line:90% See? 01:05:55.710 --> 01:05:57.910 align:middle line:90% You still see your finger. 01:05:57.910 --> 01:05:59.630 align:middle line:90% Move around. 01:05:59.630 --> 01:06:00.590 align:middle line:90% Yup. 01:06:00.590 --> 01:06:01.370 align:middle line:90% See, it's moving. 01:06:01.370 --> 01:06:03.010 align:middle line:84% AUDIENCE: Yeah, it's still there. 01:06:03.010 --> 01:06:05.890 align:middle line:84% JUEJUN HU: Yup, so this piece is actually completely transparent. 01:06:05.890 --> 01:06:10.430 align:middle line:84% I mean, I can [? probably ?] also put my finger. 01:06:10.430 --> 01:06:14.050 align:middle line:84% You can clearly see my finger behind the piece of glass. 01:06:14.050 --> 01:06:21.070 align:middle line:90% 01:06:21.070 --> 01:06:24.390 align:middle line:84% Well, we are going to explain why this transparent layer, why 01:06:24.390 --> 01:06:26.270 align:middle line:84% this piece of material is transparent 01:06:26.270 --> 01:06:27.733 align:middle line:90% versus the oxide glass. 01:06:27.733 --> 01:06:29.150 align:middle line:84% But the whole idea is that you can 01:06:29.150 --> 01:06:31.390 align:middle line:84% tailor essentially the atomic composition, 01:06:31.390 --> 01:06:33.670 align:middle line:84% and therefore change the vibrational frequency 01:06:33.670 --> 01:06:36.710 align:middle line:84% of the atoms to push the phonon absorption 01:06:36.710 --> 01:06:39.290 align:middle line:84% edge to much longer wavelengths to make it transparent. 01:06:39.290 --> 01:06:42.275 align:middle line:90% 01:06:42.275 --> 01:06:43.270 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:06:43.270 --> 01:06:45.020 align:middle line:84% JUEJUN HU: Taking a picture of the camera. 01:06:45.020 --> 01:06:47.926 align:middle line:90% [CHUCKLES] 01:06:47.926 --> 01:06:50.310 align:middle line:90% 01:06:50.310 --> 01:06:54.775 align:middle line:84% OK, I think we are actually going to stop here. 01:06:54.775 --> 01:06:56.150 align:middle line:84% If you want to take a selfie, you 01:06:56.150 --> 01:06:57.910 align:middle line:90% can use this [INAUDIBLE] selfie. 01:06:57.910 --> 01:07:01.540 align:middle line:84% I have all kinds of color schemes. 01:07:01.540 --> 01:07:51.000 align:middle line:90%