WEBVTT 00:00:00.000 --> 00:00:01.976 align:middle line:90% [SQUEAKING] 00:00:01.976 --> 00:00:03.206 align:middle line:90% [RUSTLING] 00:00:03.206 --> 00:00:04.928 align:middle line:90% [CLICKING] 00:00:04.928 --> 00:00:16.803 align:middle line:90% 00:00:16.803 --> 00:00:18.220 align:middle line:84% JUEJUN HU: So in the last lecture, 00:00:18.220 --> 00:00:22.745 align:middle line:84% we already discussed about these four different loss mechanisms. 00:00:22.745 --> 00:00:24.120 align:middle line:84% One thing to again emphasize here 00:00:24.120 --> 00:00:29.000 align:middle line:84% is the language we use to describe these loss mechanisms. 00:00:29.000 --> 00:00:32.320 align:middle line:84% So we say loss and attenuation, which encompasses 00:00:32.320 --> 00:00:35.000 align:middle line:90% both absorption and scattering. 00:00:35.000 --> 00:00:37.980 align:middle line:84% We want to make a distinction between the two, 00:00:37.980 --> 00:00:39.380 align:middle line:84% because the first two mechanisms, 00:00:39.380 --> 00:00:40.630 align:middle line:90% these are actually absorption. 00:00:40.630 --> 00:00:42.600 align:middle line:84% It means that you actually convert photons 00:00:42.600 --> 00:00:44.780 align:middle line:90% into, eventually, heat. 00:00:44.780 --> 00:00:48.170 align:middle line:84% But for the last two mechanisms, these are actually scattering. 00:00:48.170 --> 00:00:49.920 align:middle line:84% It means that the photons are still there. 00:00:49.920 --> 00:00:53.560 align:middle line:84% Their propagating direction is just diverted, 00:00:53.560 --> 00:00:55.160 align:middle line:90% which constitutes loss. 00:00:55.160 --> 00:00:58.780 align:middle line:90% But this is not absorption. 00:00:58.780 --> 00:00:59.330 align:middle line:90% Yes? 00:00:59.330 --> 00:01:02.890 align:middle line:84% AUDIENCE: Wait, so loss and attenuation both mean? 00:01:02.890 --> 00:01:05.890 align:middle line:84% JUEJUN HU: Loss and attenuation both cover absorption 00:01:05.890 --> 00:01:06.550 align:middle line:90% and scattering. 00:01:06.550 --> 00:01:06.970 align:middle line:90% AUDIENCE: OK. 00:01:06.970 --> 00:01:08.210 align:middle line:84% JUEJUN HU: But if you talk about absorption, 00:01:08.210 --> 00:01:10.390 align:middle line:84% it's only essentially energy conversion involved. 00:01:10.390 --> 00:01:14.830 align:middle line:84% So that's the one thing I just want to highlight here. 00:01:14.830 --> 00:01:19.330 align:middle line:84% So we have already mentioned that in amorphous materials, 00:01:19.330 --> 00:01:20.930 align:middle line:84% well-prepared amorphous materials, 00:01:20.930 --> 00:01:24.010 align:middle line:84% you should have electronic absorption, phonon absorption, 00:01:24.010 --> 00:01:25.950 align:middle line:84% and also Rayleigh scattering present. 00:01:25.950 --> 00:01:29.610 align:middle line:84% Defect scattering, this is non-existent 00:01:29.610 --> 00:01:31.930 align:middle line:84% if you have a defect-free material. 00:01:31.930 --> 00:01:34.690 align:middle line:84% So now what I'm doing in this slide here 00:01:34.690 --> 00:01:37.410 align:middle line:84% is that I'm essentially listing all 00:01:37.410 --> 00:01:42.530 align:middle line:84% the possible contributing mechanisms in glass materials. 00:01:42.530 --> 00:01:45.610 align:middle line:84% I have categorized it into two categories, so extrinsic 00:01:45.610 --> 00:01:48.410 align:middle line:90% versus intrinsic attenuation. 00:01:48.410 --> 00:01:50.650 align:middle line:84% For extrinsic, I mean that this is 00:01:50.650 --> 00:01:55.070 align:middle line:84% something not relevant to the pure glass materials. 00:01:55.070 --> 00:01:56.890 align:middle line:84% It's due to some kind of impurities 00:01:56.890 --> 00:01:59.710 align:middle line:84% or due to some dopant you add into the glass. 00:01:59.710 --> 00:02:02.990 align:middle line:84% Whereas intrinsic attenuation is something directly associated 00:02:02.990 --> 00:02:06.410 align:middle line:90% with the glass network itself. 00:02:06.410 --> 00:02:09.710 align:middle line:84% So for extrinsic absorption, as I said, 00:02:09.710 --> 00:02:12.310 align:middle line:84% this is due to impurities or dopants. 00:02:12.310 --> 00:02:16.330 align:middle line:84% This is usually caused by some impurities, 00:02:16.330 --> 00:02:20.670 align:middle line:84% for example, like transition metal or rare earth ions. 00:02:20.670 --> 00:02:25.350 align:middle line:84% And transition metals has unfilled 3D electron shells. 00:02:25.350 --> 00:02:28.590 align:middle line:84% Rare earth ions has unfilled 4f electron shells. 00:02:28.590 --> 00:02:30.790 align:middle line:84% We'll see a bit more details in the next few slides. 00:02:30.790 --> 00:02:34.830 align:middle line:84% But basically, these empty orbitals essentially 00:02:34.830 --> 00:02:36.830 align:middle line:84% means that there's a lot of possible transitions 00:02:36.830 --> 00:02:39.790 align:middle line:84% that can take place between the different electron energy 00:02:39.790 --> 00:02:40.830 align:middle line:90% levels. 00:02:40.830 --> 00:02:43.350 align:middle line:84% And when the incident photon has energy 00:02:43.350 --> 00:02:46.218 align:middle line:84% that coincides with one of these transition energies, 00:02:46.218 --> 00:02:48.510 align:middle line:84% then you can actually promote electron to excited state 00:02:48.510 --> 00:02:52.230 align:middle line:84% and therefore essentially lead to a loss of photon. 00:02:52.230 --> 00:02:54.130 align:middle line:84% So that's basically electronic in nature. 00:02:54.130 --> 00:02:55.773 align:middle line:84% If you look at my color code here, 00:02:55.773 --> 00:02:56.940 align:middle line:90% I have my color coding here. 00:02:56.940 --> 00:02:58.315 align:middle line:84% I use three different colors that 00:02:58.315 --> 00:03:00.780 align:middle line:84% represent different kind of absorption mechanisms. 00:03:00.780 --> 00:03:04.000 align:middle line:84% You can also have extrinsic absorption 00:03:04.000 --> 00:03:08.800 align:middle line:84% coming from vibrational or chemical bond phonon absorption. 00:03:08.800 --> 00:03:12.040 align:middle line:84% So one example for that would be oxygen impurities 00:03:12.040 --> 00:03:13.600 align:middle line:90% in chalcogenide glass. 00:03:13.600 --> 00:03:16.158 align:middle line:84% We mentioned that chalcogenide glasses, 00:03:16.158 --> 00:03:18.200 align:middle line:84% people like to use them for infrared transmission 00:03:18.200 --> 00:03:18.768 align:middle line:90% applications. 00:03:18.768 --> 00:03:21.060 align:middle line:84% This is what we showed in the demo in the last lecture. 00:03:21.060 --> 00:03:24.640 align:middle line:84% So the reason they can actually transmit this infrared radiation 00:03:24.640 --> 00:03:28.120 align:middle line:84% is because they consist of heavy atoms, which give you 00:03:28.120 --> 00:03:30.400 align:middle line:84% weaker chemical bonds, lower phonon vibrational 00:03:30.400 --> 00:03:33.360 align:middle line:84% frequency, and therefore it pushes the transmission window 00:03:33.360 --> 00:03:35.160 align:middle line:90% to a much longer wavelength. 00:03:35.160 --> 00:03:37.440 align:middle line:84% However, if you get oxygen impurity 00:03:37.440 --> 00:03:39.728 align:middle line:84% getting into chalcogenides, they are much lighter. 00:03:39.728 --> 00:03:41.520 align:middle line:84% They also form much stronger chemical bonds 00:03:41.520 --> 00:03:43.000 align:middle line:90% compared to chalcogens. 00:03:43.000 --> 00:03:45.240 align:middle line:84% So then that's going to essentially lead 00:03:45.240 --> 00:03:48.160 align:middle line:84% to impurity absorption bands due to this phonon 00:03:48.160 --> 00:03:52.440 align:middle line:84% vibration associated with oxide chemical bonds. 00:03:52.440 --> 00:03:55.690 align:middle line:84% So that's why for those manufacturers of infrared optics 00:03:55.690 --> 00:03:58.330 align:middle line:84% based on chalcogenide glasses, it is really important 00:03:58.330 --> 00:04:01.770 align:middle line:84% that every step of that process has to be done in a low oxygen 00:04:01.770 --> 00:04:02.510 align:middle line:90% environment. 00:04:02.510 --> 00:04:04.310 align:middle line:84% They actually process them, all the glass materials, 00:04:04.310 --> 00:04:06.018 align:middle line:84% if you look at it, how they do it, always 00:04:06.018 --> 00:04:08.430 align:middle line:84% in glove boxes, nothing in the atmosphere. 00:04:08.430 --> 00:04:11.690 align:middle line:84% So that's quite different from oxides. 00:04:11.690 --> 00:04:14.355 align:middle line:84% Now for intrinsic attenuation, we 00:04:14.355 --> 00:04:16.730 align:middle line:84% are going to essentially go over the different electronic 00:04:16.730 --> 00:04:19.610 align:middle line:84% absorption mechanisms in the next few slides, phonon 00:04:19.610 --> 00:04:21.950 align:middle line:84% as well as also Rayleigh scattering. 00:04:21.950 --> 00:04:25.150 align:middle line:84% So we'll go through them basically one by one. 00:04:25.150 --> 00:04:30.490 align:middle line:84% So now let's start by taking a look at electronic absorption. 00:04:30.490 --> 00:04:33.370 align:middle line:90% 00:04:33.370 --> 00:04:35.850 align:middle line:84% So on this slide here, again I'm showing 00:04:35.850 --> 00:04:38.250 align:middle line:84% you the density of states plot that I quoted 00:04:38.250 --> 00:04:39.970 align:middle line:90% from the previous lectures. 00:04:39.970 --> 00:04:43.300 align:middle line:84% The key features for the electronic band absorption 00:04:43.300 --> 00:04:45.050 align:middle line:84% in an amorphous material is that you don't 00:04:45.050 --> 00:04:46.650 align:middle line:90% have a well-defined bandgap. 00:04:46.650 --> 00:04:49.050 align:middle line:84% The density of states never really goes to 0. 00:04:49.050 --> 00:04:54.070 align:middle line:84% And you can have those localized states either located 00:04:54.070 --> 00:04:57.310 align:middle line:84% at Urbach bandtail, which is resulting from disorder 00:04:57.310 --> 00:05:00.150 align:middle line:84% of the entire lattice, or you can also 00:05:00.150 --> 00:05:03.150 align:middle line:84% have those localized states that's confined 00:05:03.150 --> 00:05:04.470 align:middle line:90% near the middle of bandgap. 00:05:04.470 --> 00:05:06.270 align:middle line:84% And these are the tightly bound states 00:05:06.270 --> 00:05:09.190 align:middle line:84% that usually are associated with single atoms or single chemical 00:05:09.190 --> 00:05:11.230 align:middle line:90% bonds, like dangling bonds. 00:05:11.230 --> 00:05:14.430 align:middle line:84% So because of the presence of all these states, 00:05:14.430 --> 00:05:15.963 align:middle line:84% unlike crystalline materials, where 00:05:15.963 --> 00:05:18.630 align:middle line:84% essentially if you have energy, if it's defect free, if you have 00:05:18.630 --> 00:05:20.963 align:middle line:84% a photon energy below the bandgap, then you will not get 00:05:20.963 --> 00:05:21.570 align:middle line:90% absorbed. 00:05:21.570 --> 00:05:22.445 align:middle line:90% You just zip through. 00:05:22.445 --> 00:05:23.630 align:middle line:90% It's perfectly transparent. 00:05:23.630 --> 00:05:27.352 align:middle line:84% But for amorphous materials, you always get non-zero absorption 00:05:27.352 --> 00:05:29.310 align:middle line:84% regardless of photon energy, because you always 00:05:29.310 --> 00:05:31.830 align:middle line:84% have this continuous distribution 00:05:31.830 --> 00:05:33.150 align:middle line:90% of density of states. 00:05:33.150 --> 00:05:40.270 align:middle line:84% So we'll be looking at a few mechanisms here. 00:05:40.270 --> 00:05:42.930 align:middle line:84% If your photon energy is sufficiently large, 00:05:42.930 --> 00:05:45.550 align:middle line:84% so that you can essentially promote 00:05:45.550 --> 00:05:49.592 align:middle line:84% one electron from the extended states in the valence band 00:05:49.592 --> 00:05:51.300 align:middle line:84% to the extended state in conduction band, 00:05:51.300 --> 00:05:53.050 align:middle line:84% and you still get band-to-band transition, 00:05:53.050 --> 00:05:57.320 align:middle line:84% you can also have a transition between the extended states 00:05:57.320 --> 00:05:58.660 align:middle line:90% to the localized states. 00:05:58.660 --> 00:06:01.260 align:middle line:84% These are what's responsible for so-called Urbach 00:06:01.260 --> 00:06:02.140 align:middle line:90% bandtail absorption. 00:06:02.140 --> 00:06:05.360 align:middle line:90% 00:06:05.360 --> 00:06:08.240 align:middle line:84% You also have absorption related to essentially 00:06:08.240 --> 00:06:10.700 align:middle line:90% those mid-gap states. 00:06:10.700 --> 00:06:13.080 align:middle line:84% These are basically a defect state absorption there. 00:06:13.080 --> 00:06:18.600 align:middle line:84% And finally, if you have free electrons or free carriers 00:06:18.600 --> 00:06:24.560 align:middle line:84% in the conduction of the valence band, those can also move. 00:06:24.560 --> 00:06:27.160 align:middle line:84% And they can be driven to oscillate 00:06:27.160 --> 00:06:29.600 align:middle line:84% under the external electric field. 00:06:29.600 --> 00:06:32.580 align:middle line:84% And that can actually contribute to additional absorption there. 00:06:32.580 --> 00:06:35.960 align:middle line:84% That's called a free carrier absorption, FCA. 00:06:35.960 --> 00:06:38.160 align:middle line:84% So these are the four mechanisms that's 00:06:38.160 --> 00:06:40.423 align:middle line:90% present in amorphous materials. 00:06:40.423 --> 00:06:41.840 align:middle line:84% In crystalline materials, you also 00:06:41.840 --> 00:06:44.520 align:middle line:84% get 1 and 4 and maybe defect state absorption, 00:06:44.520 --> 00:06:48.160 align:middle line:84% if it's a defective semiconductor, but much 00:06:48.160 --> 00:06:52.850 align:middle line:84% less contribution coming from the localized states. 00:06:52.850 --> 00:06:56.250 align:middle line:84% So for the band-to-band transition, 00:06:56.250 --> 00:06:58.130 align:middle line:84% in the previous lecture, I have already 00:06:58.130 --> 00:07:00.590 align:middle line:84% mentioned about this quantity called Tauc gap. 00:07:00.590 --> 00:07:04.230 align:middle line:84% I mentioned that Tauc gap is really just a fitting parameter. 00:07:04.230 --> 00:07:06.630 align:middle line:84% It doesn't have a very concrete physical significance. 00:07:06.630 --> 00:07:09.730 align:middle line:84% It just roughly tells you where the density of states 00:07:09.730 --> 00:07:11.770 align:middle line:90% becomes small. 00:07:11.770 --> 00:07:16.610 align:middle line:84% And this is the fitting formula for the Tauc gap. 00:07:16.610 --> 00:07:19.370 align:middle line:84% So what you will do, like in this plot here, 00:07:19.370 --> 00:07:22.250 align:middle line:84% is you are plotting essentially alpha h-bar omega square root, 00:07:22.250 --> 00:07:24.250 align:middle line:84% where alpha is the absorption coefficient, 00:07:24.250 --> 00:07:26.890 align:middle line:84% h-bar omega will basically be the photon energy. 00:07:26.890 --> 00:07:29.570 align:middle line:84% And you plot it against the photon energy. 00:07:29.570 --> 00:07:31.710 align:middle line:84% And what you will see on this kind of plot, 00:07:31.710 --> 00:07:33.290 align:middle line:84% like the example I'm showing here, 00:07:33.290 --> 00:07:35.850 align:middle line:84% is typically you will get a linear regime that 00:07:35.850 --> 00:07:39.310 align:middle line:84% allows you to fit the intercept with horizontal axis. 00:07:39.310 --> 00:07:42.590 align:middle line:90% That gives you the Tauc gap. 00:07:42.590 --> 00:07:46.790 align:middle line:84% If it is an indirect bandgap semi-crystalline semiconductor, 00:07:46.790 --> 00:07:48.870 align:middle line:84% then the absorption will be pretty well described 00:07:48.870 --> 00:07:50.630 align:middle line:90% by just a simple straight line. 00:07:50.630 --> 00:07:53.350 align:middle line:84% But for amorphous materials, you also 00:07:53.350 --> 00:07:56.350 align:middle line:84% notice that the absorption doesn't go to 0, even if you 00:07:56.350 --> 00:07:58.230 align:middle line:90% go below this energy there. 00:07:58.230 --> 00:08:00.390 align:middle line:84% So this little tail here, this is 00:08:00.390 --> 00:08:03.330 align:middle line:90% the Urbach bandtail absorption. 00:08:03.330 --> 00:08:06.070 align:middle line:90% 00:08:06.070 --> 00:08:08.350 align:middle line:84% I'm listing here the equation that people typically 00:08:08.350 --> 00:08:10.270 align:middle line:84% use to characterize the Urbach bandtail. 00:08:10.270 --> 00:08:14.030 align:middle line:84% You notice this exponential dependence, only photon energy 00:08:14.030 --> 00:08:14.823 align:middle line:90% here. 00:08:14.823 --> 00:08:16.990 align:middle line:84% That's because the density of states for Urbach tail 00:08:16.990 --> 00:08:20.670 align:middle line:84% tend to decay exponentially as you move into the bandgap. 00:08:20.670 --> 00:08:25.010 align:middle line:84% So to fit this kind of Urbach bandtail absorption, 00:08:25.010 --> 00:08:27.630 align:middle line:84% people actually use a different kind of plot here. 00:08:27.630 --> 00:08:33.909 align:middle line:84% What you do is you basically plot alpha in logarithmic scale. 00:08:33.909 --> 00:08:40.909 align:middle line:84% So if you put a logarithm alpha, then what do you get? 00:08:40.909 --> 00:08:45.270 align:middle line:84% You essentially have a logarithm alpha u, 00:08:45.270 --> 00:08:48.820 align:middle line:84% and then the exponential just comes out. 00:08:48.820 --> 00:08:59.500 align:middle line:84% It becomes also plus h-bar omega minus E. I use Eg there, 00:08:59.500 --> 00:09:01.660 align:middle line:84% but you can use Tauc gap, ET, either way. 00:09:01.660 --> 00:09:06.440 align:middle line:84% So either Tauc gap or bandgap, either way, divided by Eu. 00:09:06.440 --> 00:09:16.020 align:middle line:90% 00:09:16.020 --> 00:09:18.340 align:middle line:84% So therefore, once you do this kind of plot, 00:09:18.340 --> 00:09:20.520 align:middle line:84% as I'm showing you on the slide here, 00:09:20.520 --> 00:09:23.160 align:middle line:84% you will also get a linear regime here. 00:09:23.160 --> 00:09:25.830 align:middle line:84% So region A, this is basically band-to-band absorption, 00:09:25.830 --> 00:09:28.080 align:middle line:84% characterized by a very strong absorption coefficient. 00:09:28.080 --> 00:09:30.080 align:middle line:84% Now here, this linear regime gives you 00:09:30.080 --> 00:09:31.302 align:middle line:90% essentially Urbach bandtail. 00:09:31.302 --> 00:09:32.760 align:middle line:84% According to the equation there, it 00:09:32.760 --> 00:09:34.340 align:middle line:84% should show up as a linear dependence 00:09:34.340 --> 00:09:37.280 align:middle line:84% if you plot the logarithm alpha as a function of h-bar omega. 00:09:37.280 --> 00:09:39.920 align:middle line:90% 00:09:39.920 --> 00:09:42.280 align:middle line:84% And then from this slope of this line 00:09:42.280 --> 00:09:49.130 align:middle line:84% here, you can also essentially extrapolate Eu, or basically 00:09:49.130 --> 00:09:49.950 align:middle line:90% 1 over Eu. 00:09:49.950 --> 00:09:51.583 align:middle line:90% That gives you the slope. 00:09:51.583 --> 00:09:53.250 align:middle line:84% And then for the intercept, you can then 00:09:53.250 --> 00:09:54.710 align:middle line:90% determine what alpha u is. 00:09:54.710 --> 00:09:57.450 align:middle line:84% So that's how you actually fit this equation 00:09:57.450 --> 00:09:59.130 align:middle line:90% from experimental data here. 00:09:59.130 --> 00:10:00.675 align:middle line:84% AUDIENCE: And Eu and alpha u are? 00:10:00.675 --> 00:10:02.050 align:middle line:84% JUEJUN HU: Essentially, these are 00:10:02.050 --> 00:10:04.810 align:middle line:84% parameters used to characterize the Urbach bandtail. 00:10:04.810 --> 00:10:08.090 align:middle line:84% Eu gives you how fast the density of states 00:10:08.090 --> 00:10:09.310 align:middle line:90% decays into bandgap. 00:10:09.310 --> 00:10:12.630 align:middle line:84% The larger the Eu is, the faster it will decay. 00:10:12.630 --> 00:10:15.750 align:middle line:84% Essentially, you have a narrow Urbach bandtail, practically. 00:10:15.750 --> 00:10:19.110 align:middle line:84% And alpha u is just essentially a pre-exponential constant. 00:10:19.110 --> 00:10:21.623 align:middle line:84% The higher alpha u, the more states you get. 00:10:21.623 --> 00:10:23.290 align:middle line:84% AUDIENCE: They're just state parameters. 00:10:23.290 --> 00:10:25.290 align:middle line:84% JUEJUN HU: Yeah, these are basically parameters. 00:10:25.290 --> 00:10:27.130 align:middle line:84% But they do relate to structure disorder. 00:10:27.130 --> 00:10:28.730 align:middle line:84% So the larger the structure disorder, 00:10:28.730 --> 00:10:30.410 align:middle line:84% you expect that you actually have a larger alpha u, 00:10:30.410 --> 00:10:31.030 align:middle line:90% for example. 00:10:31.030 --> 00:10:31.572 align:middle line:90% AUDIENCE: OK. 00:10:31.572 --> 00:10:33.698 align:middle line:84% JUEJUN HU: Because you essentially get more states, 00:10:33.698 --> 00:10:34.990 align:middle line:90% more of those localized states. 00:10:34.990 --> 00:10:36.650 align:middle line:90% That's basically the idea. 00:10:36.650 --> 00:10:39.170 align:middle line:90% Yeah. 00:10:39.170 --> 00:10:41.350 align:middle line:84% Also, if you look at the plot here, 00:10:41.350 --> 00:10:43.910 align:middle line:84% we divide up the absorption into three regimes. 00:10:43.910 --> 00:10:46.510 align:middle line:84% We say that A is band to band, B is Urbach tail. 00:10:46.510 --> 00:10:48.030 align:middle line:84% You notice here that there's also 00:10:48.030 --> 00:10:52.030 align:middle line:84% this C here that does not conform to the Urbach bandtail 00:10:52.030 --> 00:10:52.530 align:middle line:90% model. 00:10:52.530 --> 00:10:54.350 align:middle line:84% Essentially, you get additional excess absorption 00:10:54.350 --> 00:10:56.770 align:middle line:84% as you go deep into the bandgap for those small energy regimes. 00:10:56.770 --> 00:10:58.990 align:middle line:84% Those are typically associated with defect states 00:10:58.990 --> 00:10:59.990 align:middle line:90% like dangling bonds. 00:10:59.990 --> 00:11:03.630 align:middle line:90% 00:11:03.630 --> 00:11:05.750 align:middle line:84% And the strength of this kind of absorption 00:11:05.750 --> 00:11:10.290 align:middle line:84% will closely depend on how defective your material is. 00:11:10.290 --> 00:11:14.810 align:middle line:84% We mentioned that this part of absorption, for example, 00:11:14.810 --> 00:11:17.150 align:middle line:84% if you think about amorphous silicon, 00:11:17.150 --> 00:11:19.830 align:middle line:84% you're going to get a lot of this kind of mid-gap state 00:11:19.830 --> 00:11:22.570 align:middle line:84% absorption if you deposit amorphous silicon by, 00:11:22.570 --> 00:11:25.630 align:middle line:84% say electron evaporation where there's no hydrogen. 00:11:25.630 --> 00:11:27.830 align:middle line:84% Whereas if you do PECVD, you expect 00:11:27.830 --> 00:11:29.635 align:middle line:84% this kind of tail absorption will decrease 00:11:29.635 --> 00:11:31.510 align:middle line:84% pretty drastically because most of the states 00:11:31.510 --> 00:11:32.810 align:middle line:90% are going to get passivated. 00:11:32.810 --> 00:11:35.150 align:middle line:84% So this is a very strong function 00:11:35.150 --> 00:11:37.190 align:middle line:84% of the processing condition and microstructure 00:11:37.190 --> 00:11:38.490 align:middle line:90% of the amorphous materials. 00:11:38.490 --> 00:11:42.400 align:middle line:90% 00:11:42.400 --> 00:11:44.360 align:middle line:84% The other thing I also want to mention here 00:11:44.360 --> 00:11:48.160 align:middle line:84% is that the relative magnitude of this kind of absorption here. 00:11:48.160 --> 00:11:50.760 align:middle line:84% So for band-to-band absorption, because we 00:11:50.760 --> 00:11:54.720 align:middle line:84% are talking about essentially a large number of extended states, 00:11:54.720 --> 00:11:58.400 align:middle line:84% the absorption coefficients tend to be very high. 00:11:58.400 --> 00:12:02.680 align:middle line:84% They are typically above at least 1,000 inverse centimeters 00:12:02.680 --> 00:12:06.440 align:middle line:90% for band-to-band absorption. 00:12:06.440 --> 00:12:08.160 align:middle line:84% Similar to crystalline materials, 00:12:08.160 --> 00:12:09.920 align:middle line:90% very strong absorption. 00:12:09.920 --> 00:12:13.470 align:middle line:84% Now for the Urbach bandtail, as you can see from this plot here, 00:12:13.470 --> 00:12:15.720 align:middle line:84% the typical absorption coefficient for Urbach bandtail 00:12:15.720 --> 00:12:18.160 align:middle line:84% is of the order of 10 to the maybe to the 1 or 10 00:12:18.160 --> 00:12:20.040 align:middle line:90% to the 2 inverse centimeters. 00:12:20.040 --> 00:12:22.600 align:middle line:84% Whereas for the mid-gap state absorption, 00:12:22.600 --> 00:12:24.060 align:middle line:90% they really get pretty weak. 00:12:24.060 --> 00:12:26.580 align:middle line:84% It's of the order 1 inverse centimeter. 00:12:26.580 --> 00:12:29.320 align:middle line:84% So it's 3 to 4 orders of magnitude 00:12:29.320 --> 00:12:31.800 align:middle line:84% lower compared to band-to-band transmission. 00:12:31.800 --> 00:12:36.440 align:middle line:90% 00:12:36.440 --> 00:12:39.730 align:middle line:84% And that's why despite the fact that you 00:12:39.730 --> 00:12:42.170 align:middle line:84% may get this kind of a defect state absorption 00:12:42.170 --> 00:12:44.470 align:middle line:84% here, because the absorption can be sufficiently weak, 00:12:44.470 --> 00:12:46.690 align:middle line:84% people can still make functional, transparent 00:12:46.690 --> 00:12:48.532 align:middle line:84% optical devices out of amorphous materials, 00:12:48.532 --> 00:12:49.990 align:middle line:84% even like amorphous semiconductors, 00:12:49.990 --> 00:12:53.250 align:middle line:84% like amorphous silicon, in this kind of a low absorption 00:12:53.250 --> 00:12:56.093 align:middle line:84% regime here, despite the presence of those defect states. 00:12:56.093 --> 00:12:57.510 align:middle line:84% People actually make, for example, 00:12:57.510 --> 00:13:00.370 align:middle line:84% amorphous silicon waveguides with decent losses, provided 00:13:00.370 --> 00:13:02.610 align:middle line:84% that they can passivate these kind of defect states 00:13:02.610 --> 00:13:04.290 align:middle line:90% to a sufficiently low level. 00:13:04.290 --> 00:13:05.350 align:middle line:90% So it's still acceptable. 00:13:05.350 --> 00:13:07.267 align:middle line:84% It can still be used as a transparent material 00:13:07.267 --> 00:13:09.510 align:middle line:84% even in the presence of these defect states. 00:13:09.510 --> 00:13:14.050 align:middle line:90% 00:13:14.050 --> 00:13:18.210 align:middle line:84% Now, last mechanism here, free carrier absorption. 00:13:18.210 --> 00:13:20.210 align:middle line:84% So the way to understand free carrier absorption 00:13:20.210 --> 00:13:22.730 align:middle line:84% is that anything that's electrically conductive 00:13:22.730 --> 00:13:26.610 align:middle line:90% is also optically absorptive. 00:13:26.610 --> 00:13:29.132 align:middle line:84% The reason something conducts electricity, most of the time, 00:13:29.132 --> 00:13:30.590 align:middle line:84% it's basically electronic carriers, 00:13:30.590 --> 00:13:33.250 align:middle line:84% you have electrons and holes that can freely move around. 00:13:33.250 --> 00:13:35.870 align:middle line:84% But when electrons and holes are moving around, 00:13:35.870 --> 00:13:39.630 align:middle line:84% you inevitably get some kind of dissipation mechanisms. 00:13:39.630 --> 00:13:42.870 align:middle line:84% The electrons can essentially get scattered by the lattice. 00:13:42.870 --> 00:13:45.790 align:middle line:84% In the process, they essentially exchange energy with lattice, 00:13:45.790 --> 00:13:48.310 align:middle line:84% leading to energy dissipation from essentially 00:13:48.310 --> 00:13:51.230 align:middle line:84% the electronic domain into the basic heat. 00:13:51.230 --> 00:13:53.630 align:middle line:84% So you are basically heating up the material 00:13:53.630 --> 00:13:57.430 align:middle line:84% in that process due to this dissipation mechanism. 00:13:57.430 --> 00:14:00.870 align:middle line:84% And this can be characterized by the Drude model, which 00:14:00.870 --> 00:14:04.470 align:middle line:84% I suppose you have learned to model in 3033? 00:14:04.470 --> 00:14:05.250 align:middle line:90% OK, yeah. 00:14:05.250 --> 00:14:06.750 align:middle line:84% So basically in Drude model, there's 00:14:06.750 --> 00:14:09.430 align:middle line:84% essentially this kind of damping term that characterizes 00:14:09.430 --> 00:14:12.110 align:middle line:84% any kind of friction, the effectivity the electron 00:14:12.110 --> 00:14:14.530 align:middle line:84% experiences as they move around in the lattice there. 00:14:14.530 --> 00:14:17.070 align:middle line:84% So the damping term is what accounts for the energy 00:14:17.070 --> 00:14:20.070 align:middle line:84% loss going from optical domain into basically 00:14:20.070 --> 00:14:21.390 align:middle line:90% phonons or thermal domain. 00:14:21.390 --> 00:14:23.630 align:middle line:84% So what I'm showing you here, this 00:14:23.630 --> 00:14:29.030 align:middle line:84% is basically the change of refractive index and absorption 00:14:29.030 --> 00:14:29.850 align:middle line:90% coefficient. 00:14:29.850 --> 00:14:32.170 align:middle line:84% So this is real and imaginary power refractive index-- 00:14:32.170 --> 00:14:34.480 align:middle line:84% real power is n, imaginary power is k. 00:14:34.480 --> 00:14:37.600 align:middle line:84% The expression is coming from the classical Drude model. 00:14:37.600 --> 00:14:41.225 align:middle line:84% Now, what we see here is that Drude model not only predicts 00:14:41.225 --> 00:14:43.600 align:middle line:84% an absorption increase-- that's what we call free carrier 00:14:43.600 --> 00:14:46.560 align:middle line:84% absorption-- it also says that the refractive index 00:14:46.560 --> 00:14:51.040 align:middle line:84% of the material also changes if you have free carriers. 00:14:51.040 --> 00:14:54.660 align:middle line:84% That's called a free-carrier plasma dispersion. 00:14:54.660 --> 00:15:00.800 align:middle line:90% 00:15:00.800 --> 00:15:04.380 align:middle line:84% You can understand it also from a KK relation perspective, 00:15:04.380 --> 00:15:06.560 align:middle line:90% Kramers-Kronig relation. 00:15:06.560 --> 00:15:08.685 align:middle line:84% When you change the absorption, inevitably you also 00:15:08.685 --> 00:15:10.852 align:middle line:84% change the refractive index because they're actually 00:15:10.852 --> 00:15:11.880 align:middle line:90% tied up together. 00:15:11.880 --> 00:15:16.900 align:middle line:84% So this is actually a way to modulate the refractive index 00:15:16.900 --> 00:15:18.400 align:middle line:84% of materials by essentially changing 00:15:18.400 --> 00:15:19.960 align:middle line:90% the free-carrier concentration. 00:15:19.960 --> 00:15:21.520 align:middle line:84% This is actually something useful, 00:15:21.520 --> 00:15:24.938 align:middle line:84% like people in state-of-the-art optical communications, 00:15:24.938 --> 00:15:27.480 align:middle line:84% they can actually make optical switches out of this mechanism 00:15:27.480 --> 00:15:29.730 align:middle line:84% by essentially injecting carriers into semiconductors, 00:15:29.730 --> 00:15:32.557 align:middle line:84% change the refractive index, and therefore change the phase 00:15:32.557 --> 00:15:34.890 align:middle line:84% of the light propagating through them to create all kind 00:15:34.890 --> 00:15:35.830 align:middle line:90% of optical switches. 00:15:35.830 --> 00:15:39.770 align:middle line:90% 00:15:39.770 --> 00:15:41.650 align:middle line:84% With the caveat that any index change 00:15:41.650 --> 00:15:44.250 align:middle line:84% is accompanied with absorption change in this particular case 00:15:44.250 --> 00:15:44.750 align:middle line:90% here. 00:15:44.750 --> 00:15:49.052 align:middle line:90% 00:15:49.052 --> 00:15:50.927 align:middle line:84% So since you already learned the Drude model, 00:15:50.927 --> 00:15:52.469 align:middle line:84% I'm not going to go into much details 00:15:52.469 --> 00:15:53.990 align:middle line:84% about this particular equation here. 00:15:53.990 --> 00:15:56.130 align:middle line:84% But one thing I do want to highlight 00:15:56.130 --> 00:15:59.847 align:middle line:84% is that if you go to some textbook, semiconductor physics 00:15:59.847 --> 00:16:01.930 align:middle line:84% textbook, they usually give you an expression that 00:16:01.930 --> 00:16:06.250 align:middle line:84% looks slightly different from what I'm showing here. 00:16:06.250 --> 00:16:10.570 align:middle line:84% I want to mention that those equations most often do not 00:16:10.570 --> 00:16:15.110 align:middle line:90% apply to amorphous materials. 00:16:15.110 --> 00:16:17.970 align:middle line:84% The reason I'm saying that is because for most semiconductor 00:16:17.970 --> 00:16:20.690 align:middle line:84% physics textbooks, they are dealing with free electrons 00:16:20.690 --> 00:16:22.250 align:middle line:90% with very high mobility. 00:16:22.250 --> 00:16:24.730 align:middle line:84% We mentioned that the mobility typically is 1,000 or even 00:16:24.730 --> 00:16:28.570 align:middle line:84% higher volt-centimeters squared, whatever. 00:16:28.570 --> 00:16:33.990 align:middle line:84% So for those electrons with very high mobility, 00:16:33.990 --> 00:16:40.190 align:middle line:84% the larger the mobility, the smaller the damping term is 00:16:40.190 --> 00:16:42.772 align:middle line:84% and the less free-carrier absorption, which makes sense. 00:16:42.772 --> 00:16:44.230 align:middle line:84% If you have high mobility, it means 00:16:44.230 --> 00:16:47.030 align:middle line:84% that there's essentially less friction, less dissipation, 00:16:47.030 --> 00:16:51.830 align:middle line:84% so therefore there's less energy converted to heat. 00:16:51.830 --> 00:16:55.350 align:middle line:84% However, that approximation actually 00:16:55.350 --> 00:16:57.670 align:middle line:84% fails when you go to amorphous materials 00:16:57.670 --> 00:16:59.870 align:middle line:84% because you get lots of lattice disorder. 00:16:59.870 --> 00:17:02.390 align:middle line:84% And as a result, you get very strong phonon scattering, very 00:17:02.390 --> 00:17:04.910 align:middle line:84% strong scattering of the electrons. 00:17:04.910 --> 00:17:06.829 align:middle line:84% And the mobility in amorphous materials 00:17:06.829 --> 00:17:09.030 align:middle line:84% tends to be much lower, as we have seen. 00:17:09.030 --> 00:17:12.130 align:middle line:84% And because of that, if you are plotting, for example, 00:17:12.130 --> 00:17:13.630 align:middle line:84% in this case, what I'm plotting here 00:17:13.630 --> 00:17:15.880 align:middle line:84% is actually imaginary part of the dielectric constant, 00:17:15.880 --> 00:17:18.369 align:middle line:84% which is related to absorption, as a function of mobility. 00:17:18.369 --> 00:17:22.230 align:middle line:84% You see that the imaginary part actually peaks at some mobility 00:17:22.230 --> 00:17:24.530 align:middle line:84% here, which is about 100 centimeters squared 00:17:24.530 --> 00:17:26.150 align:middle line:90% per volt per second. 00:17:26.150 --> 00:17:28.109 align:middle line:84% Below that, for amorphous materials, 00:17:28.109 --> 00:17:31.600 align:middle line:84% we are typically talking about mobility in this region here. 00:17:31.600 --> 00:17:35.440 align:middle line:84% Within this side, the lower the mobility, 00:17:35.440 --> 00:17:37.180 align:middle line:84% the lower the free-carrier absorption, 00:17:37.180 --> 00:17:39.520 align:middle line:84% which is completely opposite from what you would predict 00:17:39.520 --> 00:17:41.520 align:middle line:84% based on those approximation equations 00:17:41.520 --> 00:17:44.160 align:middle line:84% in what you see in semiconductor physics textbook. 00:17:44.160 --> 00:17:45.600 align:middle line:84% One way to intuitively understand 00:17:45.600 --> 00:17:47.760 align:middle line:84% it is think of the limiting case. 00:17:47.760 --> 00:17:49.980 align:middle line:84% If mobility is 0, you basically get insulator. 00:17:49.980 --> 00:17:55.080 align:middle line:84% If it's an insulator, obviously you get no free carrier loss. 00:17:55.080 --> 00:17:58.575 align:middle line:84% What happens here is as the mobility gets very low, 00:17:58.575 --> 00:18:00.200 align:middle line:84% these electrons are actually undergoing 00:18:00.200 --> 00:18:02.760 align:middle line:84% this oscillatory motion, the distance they move 00:18:02.760 --> 00:18:05.640 align:middle line:84% essentially becomes very, very small. 00:18:05.640 --> 00:18:08.240 align:middle line:84% Well, that's the result. The dissipation effect essentially 00:18:08.240 --> 00:18:10.760 align:middle line:84% becomes less significant because of the very small distance 00:18:10.760 --> 00:18:11.860 align:middle line:90% they move. 00:18:11.860 --> 00:18:14.000 align:middle line:90% So that's the physics behind it. 00:18:14.000 --> 00:18:16.440 align:middle line:84% But the reason I want to highlight it is I 00:18:16.440 --> 00:18:19.600 align:middle line:84% want to mention that free-carrier absorption, number 00:18:19.600 --> 00:18:21.560 align:middle line:84% one, they tend to be insignificant 00:18:21.560 --> 00:18:26.320 align:middle line:84% in amorphous materials because of the very small mobility here. 00:18:26.320 --> 00:18:29.050 align:middle line:84% OK, number two is that when you actually 00:18:29.050 --> 00:18:33.250 align:middle line:84% need to carry a free-carrier absorption amorphous materials, 00:18:33.250 --> 00:18:36.570 align:middle line:84% make sure to use the original formulation here 00:18:36.570 --> 00:18:38.170 align:middle line:90% without approximation. 00:18:38.170 --> 00:18:41.370 align:middle line:84% Don't quote the equations from typical semiconductor physics 00:18:41.370 --> 00:18:42.290 align:middle line:90% textbook. 00:18:42.290 --> 00:18:44.290 align:middle line:84% Most of the time, there's an implicit assumption 00:18:44.290 --> 00:18:46.787 align:middle line:84% that mobility is high when they give you those equations. 00:18:46.787 --> 00:18:48.870 align:middle line:84% So you have to use the original formulas in there. 00:18:48.870 --> 00:18:52.730 align:middle line:90% 00:18:52.730 --> 00:18:54.430 align:middle line:90% Is there a question? 00:18:54.430 --> 00:18:54.930 align:middle line:90% OK. 00:18:54.930 --> 00:18:58.985 align:middle line:90% 00:18:58.985 --> 00:19:00.610 align:middle line:84% So just to summarize, this is something 00:19:00.610 --> 00:19:01.652 align:middle line:90% I have already mentioned. 00:19:01.652 --> 00:19:03.485 align:middle line:84% When you're looking at electronic absorption 00:19:03.485 --> 00:19:05.090 align:middle line:84% in amorphous materials, band-to-band, 00:19:05.090 --> 00:19:07.410 align:middle line:84% they tend to be very high, similar to in crystalline 00:19:07.410 --> 00:19:10.090 align:middle line:84% solids, above 1,000 inverse centimeter. 00:19:10.090 --> 00:19:13.490 align:middle line:84% Bandtail is typically like a few 100 inverse centimeters. 00:19:13.490 --> 00:19:15.250 align:middle line:84% Free-carrier absorption, they tend 00:19:15.250 --> 00:19:18.410 align:middle line:84% to be pretty low, generally negligible 00:19:18.410 --> 00:19:21.330 align:middle line:84% except in some exceptional cases in amorphous materials. 00:19:21.330 --> 00:19:26.050 align:middle line:90% 00:19:26.050 --> 00:19:27.450 align:middle line:90% So that's electronic absorption. 00:19:27.450 --> 00:19:29.450 align:middle line:84% Now next we are going to look at here, 00:19:29.450 --> 00:19:31.430 align:middle line:84% this is essentially phonon absorption 00:19:31.430 --> 00:19:33.830 align:middle line:90% coming from lattice vibrations. 00:19:33.830 --> 00:19:35.570 align:middle line:84% As I mentioned in previous lectures, 00:19:35.570 --> 00:19:37.670 align:middle line:84% the way to model this kind of absorption 00:19:37.670 --> 00:19:40.590 align:middle line:84% is to think of chemical bonds, essentially 00:19:40.590 --> 00:19:43.030 align:middle line:84% approximating them as a masses attached 00:19:43.030 --> 00:19:44.430 align:middle line:90% to the end of the spring. 00:19:44.430 --> 00:19:47.670 align:middle line:84% And then you can now characterize 00:19:47.670 --> 00:19:50.550 align:middle line:84% the characteristic resonant frequency 00:19:50.550 --> 00:19:53.790 align:middle line:84% of this kind of a simple harmonic oscillator 00:19:53.790 --> 00:19:56.220 align:middle line:84% with this equation here, where k in this case 00:19:56.220 --> 00:20:02.030 align:middle line:84% is the spring constant and m is the reduced mass of the spring. 00:20:02.030 --> 00:20:05.998 align:middle line:84% Sorry, I'm using a k in the previous slide. 00:20:05.998 --> 00:20:07.790 align:middle line:84% There k is emerging power refractive index. 00:20:07.790 --> 00:20:08.927 align:middle line:90% Here k is spring constant. 00:20:08.927 --> 00:20:10.010 align:middle line:90% It's a bit confusing here. 00:20:10.010 --> 00:20:11.290 align:middle line:90% I should really correct it. 00:20:11.290 --> 00:20:14.750 align:middle line:90% 00:20:14.750 --> 00:20:19.990 align:middle line:84% Now, if you look at the table on the right-hand side 00:20:19.990 --> 00:20:23.015 align:middle line:84% here, what I'm listing, these are the typical sort 00:20:23.015 --> 00:20:26.600 align:middle line:84% of chemical bonds that's present in amorphous materials. 00:20:26.600 --> 00:20:30.960 align:middle line:84% And this is essentially the absorption band in microns, 00:20:30.960 --> 00:20:32.100 align:middle line:90% in terms of wavelength. 00:20:32.100 --> 00:20:34.040 align:middle line:84% Now, one thing we immediately notice here 00:20:34.040 --> 00:20:35.540 align:middle line:84% is that if you look at, for example, 00:20:35.540 --> 00:20:40.400 align:middle line:84% oxygen, O-H, versus S-H, this is basically 00:20:40.400 --> 00:20:43.060 align:middle line:84% isoelectronic substitution, oxygen and sulfur. 00:20:43.060 --> 00:20:44.860 align:middle line:84% They are basically isoelectronic. 00:20:44.860 --> 00:20:48.480 align:middle line:84% You'll notice that as you increase the mass of the atoms, 00:20:48.480 --> 00:20:52.160 align:middle line:84% the absorption bands tend to red shift, go to longer wavelengths. 00:20:52.160 --> 00:20:54.720 align:middle line:84% Same thing applies if you look at, say silicon-oxygen, 00:20:54.720 --> 00:20:57.062 align:middle line:84% germanium-oxygen, again isoelectronic substitution, 00:20:57.062 --> 00:20:58.520 align:middle line:84% you see absorption band essentially 00:20:58.520 --> 00:20:59.720 align:middle line:90% pushes the long wavelength. 00:20:59.720 --> 00:21:03.060 align:middle line:84% So let's go back to what we have talked about. 00:21:03.060 --> 00:21:07.040 align:middle line:84% As you increase the atomic radius, you tend to have, 00:21:07.040 --> 00:21:09.720 align:middle line:84% of course, larger atomic mass, right? 00:21:09.720 --> 00:21:12.080 align:middle line:84% And larger atomic radius also means 00:21:12.080 --> 00:21:14.280 align:middle line:84% that the interaction between the atomic nuclei 00:21:14.280 --> 00:21:16.920 align:middle line:84% and the outer shell electrons also gets weaker. 00:21:16.920 --> 00:21:19.520 align:middle line:84% So you also have weaker chemical bonds, and therefore 00:21:19.520 --> 00:21:22.370 align:middle line:90% a reduced spring constant. 00:21:22.370 --> 00:21:28.970 align:middle line:84% Both vectors will point to a lower phonon vibrational energy. 00:21:28.970 --> 00:21:32.170 align:middle line:84% So the phonon absorption band would then 00:21:32.170 --> 00:21:34.030 align:middle line:90% be pushed to longer wavelength. 00:21:34.030 --> 00:21:44.130 align:middle line:90% 00:21:44.130 --> 00:21:47.870 align:middle line:84% If you go back to the absorption curve, for example, 00:21:47.870 --> 00:21:51.430 align:middle line:84% we are showing here, let's say, for silica glass, 00:21:51.430 --> 00:21:55.530 align:middle line:84% we mentioned that at the longer wavelength end, 00:21:55.530 --> 00:21:59.170 align:middle line:84% the absorption is basically dominated by phonon absorption. 00:21:59.170 --> 00:22:02.510 align:middle line:84% Now if you look at the table I show you in the next few slides, 00:22:02.510 --> 00:22:05.690 align:middle line:84% for Si-O, the phonon absorption actually 00:22:05.690 --> 00:22:07.350 align:middle line:90% centers at about 9 microns. 00:22:07.350 --> 00:22:09.010 align:middle line:84% That's the vibrational frequency. 00:22:09.010 --> 00:22:12.650 align:middle line:84% We are talking about 1-point-something microns here. 00:22:12.650 --> 00:22:15.475 align:middle line:84% So we are looking at essentially a very long tail coming 00:22:15.475 --> 00:22:16.850 align:middle line:84% from the primary absorption band. 00:22:16.850 --> 00:22:18.390 align:middle line:90% It's exponentially the case. 00:22:18.390 --> 00:22:22.190 align:middle line:84% We are looking at a very small tail tale here. 00:22:22.190 --> 00:22:27.830 align:middle line:84% But if you want to extend this transparency window of glasses 00:22:27.830 --> 00:22:30.830 align:middle line:84% into longer wavelengths, what you will have to do 00:22:30.830 --> 00:22:34.390 align:middle line:84% is to essentially substitute oxygen or silicon with something 00:22:34.390 --> 00:22:37.030 align:middle line:84% that's heavier so that this curve can then 00:22:37.030 --> 00:22:38.007 align:middle line:90% move in this direction. 00:22:38.007 --> 00:22:40.590 align:middle line:84% And therefore you can actually extend this transparency window 00:22:40.590 --> 00:22:42.070 align:middle line:90% into longer wavelength range. 00:22:42.070 --> 00:22:46.664 align:middle line:90% 00:22:46.664 --> 00:22:48.410 align:middle line:84% So that's actually what people do. 00:22:48.410 --> 00:22:51.270 align:middle line:84% For example, that's why chalcogenide glasses 00:22:51.270 --> 00:22:52.230 align:middle line:90% come into play. 00:22:52.230 --> 00:22:54.950 align:middle line:84% So what I'm showing you on this figure on the left-hand side 00:22:54.950 --> 00:22:58.750 align:middle line:84% here, basically this is the wavelength. 00:22:58.750 --> 00:23:01.550 align:middle line:84% And each of these colored bars essentially 00:23:01.550 --> 00:23:03.870 align:middle line:84% represent the optical transparency window 00:23:03.870 --> 00:23:05.830 align:middle line:84% for the different materials here. 00:23:05.830 --> 00:23:08.670 align:middle line:84% So you see clearly that silicon, they are transparent 00:23:08.670 --> 00:23:10.790 align:middle line:90% up to about 7 microns-ish. 00:23:10.790 --> 00:23:12.808 align:middle line:84% Germanium, because it's actually heavier, 00:23:12.808 --> 00:23:14.350 align:middle line:84% it's actually transparent pretty much 00:23:14.350 --> 00:23:17.790 align:middle line:84% across the entire mid-infrared wavelength regime where people 00:23:17.790 --> 00:23:19.400 align:middle line:90% care about for thermal imaging. 00:23:19.400 --> 00:23:21.060 align:middle line:84% That's a demo I did in the last lecture 00:23:21.060 --> 00:23:23.880 align:middle line:84% for essentially thermal imaging or night vision. 00:23:23.880 --> 00:23:26.420 align:middle line:84% They are transparent up to about 16 microns, 00:23:26.420 --> 00:23:30.840 align:middle line:84% which is well adequate for most of thermal imaging applications. 00:23:30.840 --> 00:23:33.320 align:middle line:84% Typical blackbody radiation wavelengths for human body 00:23:33.320 --> 00:23:35.920 align:middle line:84% is like 8 to 12 microns, like 10 microns-ish. 00:23:35.920 --> 00:23:38.100 align:middle line:84% As you go to higher and higher temperature, 00:23:38.100 --> 00:23:41.420 align:middle line:84% that emission band shifts to a shorter wavelength. 00:23:41.420 --> 00:23:44.200 align:middle line:84% So that's why the typical wavelength regime of interest 00:23:44.200 --> 00:23:47.066 align:middle line:84% for thermal imaging is somewhere between 3 to 12 microns 00:23:47.066 --> 00:23:49.560 align:middle line:90% is the typical band. 00:23:49.560 --> 00:23:52.238 align:middle line:84% So that's why for a long time, when 00:23:52.238 --> 00:23:54.280 align:middle line:84% people are trying to make those infrared cameras, 00:23:54.280 --> 00:23:56.200 align:middle line:84% they like to use a single crystal 00:23:56.200 --> 00:23:58.560 align:middle line:90% germanium to make it less. 00:23:58.560 --> 00:24:02.060 align:middle line:84% The problem with single crystal germanium, a few issues here. 00:24:02.060 --> 00:24:03.800 align:middle line:84% One is that they're a single crystal. 00:24:03.800 --> 00:24:05.400 align:middle line:84% So in order to make lenses, you have 00:24:05.400 --> 00:24:07.240 align:middle line:84% to do a very careful grinding and polishing 00:24:07.240 --> 00:24:08.760 align:middle line:90% that gets quite expensive. 00:24:08.760 --> 00:24:11.880 align:middle line:84% Also, germanium is known to have a very high 00:24:11.880 --> 00:24:13.420 align:middle line:90% thermo-optic coefficient. 00:24:13.420 --> 00:24:16.210 align:middle line:84% As you raise in temperature, you generate lots of free carriers 00:24:16.210 --> 00:24:18.070 align:middle line:84% because germanium has a very small bandgap. 00:24:18.070 --> 00:24:19.945 align:middle line:84% This not only causes free-carrier absorption, 00:24:19.945 --> 00:24:22.530 align:middle line:84% it also causes a refractive index change due to KK relation. 00:24:22.530 --> 00:24:24.910 align:middle line:84% So as a result, it means that your lens, the focal length 00:24:24.910 --> 00:24:26.490 align:middle line:84% actually changes with temperature. 00:24:26.490 --> 00:24:28.230 align:middle line:90% This leads to a big issue there. 00:24:28.230 --> 00:24:31.850 align:middle line:84% And finally, there's also supply chain issue recently 00:24:31.850 --> 00:24:33.690 align:middle line:84% because China turns out to be the largest 00:24:33.690 --> 00:24:34.670 align:middle line:90% supplier of germanium. 00:24:34.670 --> 00:24:37.810 align:middle line:90% So I'm going to stop there. 00:24:37.810 --> 00:24:40.052 align:middle line:84% So that's why for quite some time, 00:24:40.052 --> 00:24:42.010 align:middle line:84% people have been trying to look for essentially 00:24:42.010 --> 00:24:43.970 align:middle line:84% alternative materials to germanium lenses. 00:24:43.970 --> 00:24:46.262 align:middle line:84% And one of the candidates they came up with, obviously, 00:24:46.262 --> 00:24:47.930 align:middle line:90% are these chalcogenide glasses. 00:24:47.930 --> 00:24:51.250 align:middle line:84% This is actually one example here. 00:24:51.250 --> 00:24:54.090 align:middle line:84% This one still contains germanium, not 100%, 00:24:54.090 --> 00:24:55.350 align:middle line:90% but still contains germanium. 00:24:55.350 --> 00:24:56.933 align:middle line:84% But there are alternative compositions 00:24:56.933 --> 00:25:00.550 align:middle line:84% where there is no germanium, if you want it. 00:25:00.550 --> 00:25:03.850 align:middle line:84% This is a very common formalism called BlackDiamond 00:25:03.850 --> 00:25:05.570 align:middle line:84% that people use for infrared optics. 00:25:05.570 --> 00:25:07.930 align:middle line:84% Again, I don't know why they call it BlackDiamond. 00:25:07.930 --> 00:25:12.050 align:middle line:84% From every aspect, it's property seems to be opposite to diamond. 00:25:12.050 --> 00:25:14.345 align:middle line:84% Diamond is meant to be expensive. 00:25:14.345 --> 00:25:16.470 align:middle line:84% These glasses are essentially low-cost alternatives 00:25:16.470 --> 00:25:18.390 align:middle line:90% to germanium lenses. 00:25:18.390 --> 00:25:20.730 align:middle line:84% Diamond is known for very good mechanical properties, 00:25:20.730 --> 00:25:22.110 align:middle line:90% very hard material. 00:25:22.110 --> 00:25:25.010 align:middle line:84% These glasses, if you ever do use the infrared optics, 00:25:25.010 --> 00:25:27.830 align:middle line:84% I would recommend that you be very, very careful. 00:25:27.830 --> 00:25:29.470 align:middle line:84% Because of the heavy atoms, they tend 00:25:29.470 --> 00:25:31.110 align:middle line:84% to have weaker chemical bonds, so they 00:25:31.110 --> 00:25:33.152 align:middle line:84% have a much poorer mechanical properties compared 00:25:33.152 --> 00:25:34.310 align:middle line:90% to the rest of glasses. 00:25:34.310 --> 00:25:36.050 align:middle line:84% You can very easily scratch them. 00:25:36.050 --> 00:25:38.115 align:middle line:84% So be very careful with those kind of materials. 00:25:38.115 --> 00:25:40.490 align:middle line:84% So anyway, I don't know why they got called BlackDiamond, 00:25:40.490 --> 00:25:42.390 align:middle line:90% but it is what it is. 00:25:42.390 --> 00:25:44.690 align:middle line:84% The advantage of these materials is that, of course, 00:25:44.690 --> 00:25:47.190 align:middle line:84% you can see from this plot here, a lot of these chalcogenide 00:25:47.190 --> 00:25:51.550 align:middle line:84% glasses, they exhibit very wide transparency window 00:25:51.550 --> 00:25:52.710 align:middle line:90% in the infrared. 00:25:52.710 --> 00:25:55.550 align:middle line:84% And because they're amorphous, it's also very easy 00:25:55.550 --> 00:25:59.070 align:middle line:84% to actually process them into lens geometries 00:25:59.070 --> 00:26:02.070 align:middle line:84% by just simple compression molding techniques. 00:26:02.070 --> 00:26:04.990 align:middle line:84% So that's why they are really drawing a lot of interest 00:26:04.990 --> 00:26:06.598 align:middle line:90% in infrared optics there. 00:26:06.598 --> 00:26:08.890 align:middle line:84% The camera I showed you in the last lecture, as I said, 00:26:08.890 --> 00:26:11.690 align:middle line:84% the lens is actually made of one of those chalcogenide glasses. 00:26:11.690 --> 00:26:17.680 align:middle line:90% 00:26:17.680 --> 00:26:19.920 align:middle line:84% All right, next mechanism, we are talking 00:26:19.920 --> 00:26:21.400 align:middle line:90% about Rayleigh scattering. 00:26:21.400 --> 00:26:23.733 align:middle line:84% We have already mentioned that Rayleigh scattering comes 00:26:23.733 --> 00:26:27.140 align:middle line:84% from atomic scale inhomogeneity intrinsic to amorphous network. 00:26:27.140 --> 00:26:29.420 align:middle line:84% If you think about amorphous glass materials, 00:26:29.420 --> 00:26:32.320 align:middle line:84% you zoom in to look at every local geometries 00:26:32.320 --> 00:26:36.440 align:middle line:84% there, due to the statistical nature of amorphous structure, 00:26:36.440 --> 00:26:39.880 align:middle line:84% you are definitely going to get slight fluctuations 00:26:39.880 --> 00:26:42.520 align:middle line:84% of the atomic density at different locations. 00:26:42.520 --> 00:26:44.760 align:middle line:84% As a result, different atomic density 00:26:44.760 --> 00:26:49.800 align:middle line:84% essentially also means that you get different polarizability. 00:26:49.800 --> 00:26:51.520 align:middle line:84% So different polarizability gives you 00:26:51.520 --> 00:26:52.760 align:middle line:90% different refractive index. 00:26:52.760 --> 00:26:55.100 align:middle line:84% So as light propagates through this amorphous material, 00:26:55.100 --> 00:26:58.000 align:middle line:84% you see this slight refractive index fluctuation that 00:26:58.000 --> 00:26:59.240 align:middle line:90% then leads to a scattering. 00:26:59.240 --> 00:27:02.708 align:middle line:84% This is what's called Rayleigh scattering. 00:27:02.708 --> 00:27:05.000 align:middle line:84% I also want to mention again that this kind of Rayleigh 00:27:05.000 --> 00:27:08.520 align:middle line:84% scattering applies not only to amorphous glasses. 00:27:08.520 --> 00:27:12.170 align:middle line:84% Any kind of a structurally disordered material 00:27:12.170 --> 00:27:14.890 align:middle line:90% also has a Rayleigh scattering. 00:27:14.890 --> 00:27:16.810 align:middle line:84% The good example here would be air. 00:27:16.810 --> 00:27:18.130 align:middle line:90% Think of ideal gas. 00:27:18.130 --> 00:27:20.010 align:middle line:84% In ideal gas, all the molecules are not 00:27:20.010 --> 00:27:22.090 align:middle line:84% interacting with each other, and therefore 00:27:22.090 --> 00:27:23.850 align:middle line:84% the coordinate of the atoms are basically 00:27:23.850 --> 00:27:26.290 align:middle line:84% independent of each other, of all the molecules. 00:27:26.290 --> 00:27:28.370 align:middle line:84% So what that also means is that there's always 00:27:28.370 --> 00:27:30.910 align:middle line:84% statistical fluctuations of density in air, 00:27:30.910 --> 00:27:34.890 align:middle line:84% just due to the random motion of air molecules. 00:27:34.890 --> 00:27:38.330 align:middle line:84% Now this is also going to lead to Rayleigh scattering. 00:27:38.330 --> 00:27:41.530 align:middle line:84% And that's why basically the sky is blue. 00:27:41.530 --> 00:27:44.010 align:middle line:84% Because if you look at the Rayleigh scattering formula 00:27:44.010 --> 00:27:47.710 align:middle line:84% here, the loss in this case-- this is not absorption, 00:27:47.710 --> 00:27:49.910 align:middle line:84% this is a loss coefficient, in this case-- 00:27:49.910 --> 00:27:53.850 align:middle line:84% it scales with wavelength to the negative 4th power. 00:27:53.850 --> 00:27:57.210 align:middle line:84% So blue and purple light get scattered a lot stronger 00:27:57.210 --> 00:28:00.090 align:middle line:84% compared to red or orange part of the spectrum. 00:28:00.090 --> 00:28:02.343 align:middle line:84% And that's why the sky appears blue. 00:28:02.343 --> 00:28:04.010 align:middle line:84% It's not purple because human eye is not 00:28:04.010 --> 00:28:05.302 align:middle line:90% very sensitive to purple light. 00:28:05.302 --> 00:28:06.630 align:middle line:90% So that's why it's blue. 00:28:06.630 --> 00:28:10.710 align:middle line:90% 00:28:10.710 --> 00:28:12.550 align:middle line:84% Now, one key thing to emphasize here 00:28:12.550 --> 00:28:17.590 align:middle line:84% is that Rayleigh scattering is only present 00:28:17.590 --> 00:28:20.710 align:middle line:90% if a material is inhomogeneous. 00:28:20.710 --> 00:28:23.910 align:middle line:84% If it's homogeneous, then there is no Rayleigh scattering. 00:28:23.910 --> 00:28:26.150 align:middle line:84% If it's a perfect, single crystalline material, 00:28:26.150 --> 00:28:28.450 align:middle line:84% no defects, then there's no Rayleigh scattering. 00:28:28.450 --> 00:28:30.950 align:middle line:84% It really only comes from this atomic-scale fluctuation 00:28:30.950 --> 00:28:31.590 align:middle line:90% of density. 00:28:31.590 --> 00:28:39.830 align:middle line:90% 00:28:39.830 --> 00:28:42.590 align:middle line:84% For glass materials, more specifically, I'm 00:28:42.590 --> 00:28:45.070 align:middle line:84% showing you here, this is actually a quantitative model 00:28:45.070 --> 00:28:46.630 align:middle line:84% people have developed to characterize 00:28:46.630 --> 00:28:47.870 align:middle line:90% Rayleigh scattering. 00:28:47.870 --> 00:28:51.665 align:middle line:84% And the coefficient here, A1, it gets pretty complicated. 00:28:51.665 --> 00:28:53.290 align:middle line:84% You see lots of different numbers here. 00:28:53.290 --> 00:28:55.470 align:middle line:84% Again, you don't need to memorize it, obviously. 00:28:55.470 --> 00:28:57.390 align:middle line:84% But I just want to highlight a few terms here. 00:28:57.390 --> 00:28:59.590 align:middle line:84% One is that it scales with refractive index 00:28:59.590 --> 00:29:01.750 align:middle line:90% to the eighth power. 00:29:01.750 --> 00:29:04.630 align:middle line:84% So the higher the refractive index, the stronger 00:29:04.630 --> 00:29:06.810 align:middle line:84% the Rayleigh scattering gets, which makes sense. 00:29:06.810 --> 00:29:08.280 align:middle line:84% If you have high refractive index, 00:29:08.280 --> 00:29:11.360 align:middle line:84% it essentially means that the polarizability fluctuation is 00:29:11.360 --> 00:29:13.120 align:middle line:90% also going to be a lot larger. 00:29:13.120 --> 00:29:15.820 align:middle line:84% So therefore light is going to see a lot larger inhomogeneity. 00:29:15.820 --> 00:29:17.945 align:middle line:84% And therefore you have a lot more scattering there. 00:29:17.945 --> 00:29:20.280 align:middle line:84% Second thing is that you notice that you 00:29:20.280 --> 00:29:25.200 align:middle line:84% have a Tf coming in, also kB as well coming into the equation. 00:29:25.200 --> 00:29:27.080 align:middle line:90% Tf is fictive temperature. 00:29:27.080 --> 00:29:29.240 align:middle line:84% It's basically roughly the temperature where 00:29:29.240 --> 00:29:32.440 align:middle line:90% glass transition takes place. 00:29:32.440 --> 00:29:34.440 align:middle line:90% So why does Tf come into play? 00:29:34.440 --> 00:29:36.892 align:middle line:84% The way these density fluctuations are introduced, 00:29:36.892 --> 00:29:38.600 align:middle line:84% if you think about glass-forming process, 00:29:38.600 --> 00:29:40.040 align:middle line:90% you start from the melt. 00:29:40.040 --> 00:29:42.023 align:middle line:90% In the melt, it's ergodic. 00:29:42.023 --> 00:29:43.440 align:middle line:84% You can essentially have all kinds 00:29:43.440 --> 00:29:44.880 align:middle line:90% of structural fluctuations. 00:29:44.880 --> 00:29:47.360 align:middle line:84% As you start to cool down through the glass transition 00:29:47.360 --> 00:29:51.280 align:middle line:84% regime, the glass structure essentially becomes non-ergodic. 00:29:51.280 --> 00:29:53.240 align:middle line:84% So at some point, you are going to freeze 00:29:53.240 --> 00:29:55.960 align:middle line:84% into one specific configuration, geometrical configuration. 00:29:55.960 --> 00:30:00.960 align:middle line:84% The density fluctuation associated 00:30:00.960 --> 00:30:03.360 align:middle line:84% with that particular structural configuration 00:30:03.360 --> 00:30:07.490 align:middle line:84% is actually dictated by the thermal fluctuation. 00:30:07.490 --> 00:30:09.210 align:middle line:84% Any structural fluctuation relates 00:30:09.210 --> 00:30:11.090 align:middle line:90% to essentially thermal energy. 00:30:11.090 --> 00:30:13.610 align:middle line:90% That's why kB come into play. 00:30:13.610 --> 00:30:15.810 align:middle line:84% Now, more specifically, when you are 00:30:15.810 --> 00:30:18.030 align:middle line:84% gauging this kind of structural fluctuation there, 00:30:18.030 --> 00:30:21.210 align:middle line:84% you should be looking at the glass-forming temperature. 00:30:21.210 --> 00:30:24.130 align:middle line:84% Because that's when the structure is actually getting 00:30:24.130 --> 00:30:26.010 align:middle line:90% frozen there. 00:30:26.010 --> 00:30:27.570 align:middle line:84% So that's why when you are looking 00:30:27.570 --> 00:30:32.530 align:middle line:84% at the structural fluctuation, it scales with the kB Tf. 00:30:32.530 --> 00:30:35.770 align:middle line:84% This is the thermal energy before the structure essentially 00:30:35.770 --> 00:30:37.650 align:middle line:90% becomes frozen. 00:30:37.650 --> 00:30:40.950 align:middle line:84% So the larger the Tf there, the more thermal energy you get, 00:30:40.950 --> 00:30:42.430 align:middle line:84% the higher the density fluctuation. 00:30:42.430 --> 00:30:44.170 align:middle line:90% That's why you have Tf here. 00:30:44.170 --> 00:30:46.330 align:middle line:90% It's related to glass forming. 00:30:46.330 --> 00:30:51.090 align:middle line:84% Last part, beta, this is the isothermal compressibility. 00:30:51.090 --> 00:30:52.890 align:middle line:84% Isothermal compressibility is essentially 00:30:52.890 --> 00:30:55.050 align:middle line:84% defined as how much volume change 00:30:55.050 --> 00:30:58.090 align:middle line:84% you can introduce per unit pressure 00:30:58.090 --> 00:31:00.290 align:middle line:90% you apply on the material 00:31:00.290 --> 00:31:03.130 align:middle line:84% So a material with higher isothermal compressibility 00:31:03.130 --> 00:31:05.790 align:middle line:84% means that essentially it more easily deforms 00:31:05.790 --> 00:31:07.870 align:middle line:84% with the same amount of a given pressure. 00:31:07.870 --> 00:31:11.430 align:middle line:84% So of course, if a material can deform more easily 00:31:11.430 --> 00:31:13.870 align:middle line:84% with larger beta, you get more density fluctuation, 00:31:13.870 --> 00:31:16.850 align:middle line:84% and therefore you should have a higher Rayleigh scattering. 00:31:16.850 --> 00:31:18.710 align:middle line:84% So that's why some of these terms, they 00:31:18.710 --> 00:31:21.597 align:middle line:84% actually come into play in this equation there. 00:31:21.597 --> 00:31:23.430 align:middle line:84% And photoelastic constant, this is basically 00:31:23.430 --> 00:31:27.608 align:middle line:84% just how much refractive index change you get per unit strain. 00:31:27.608 --> 00:31:29.150 align:middle line:84% So obviously again, higher refractive 00:31:29.150 --> 00:31:31.370 align:middle line:84% index difference, higher the scattering. 00:31:31.370 --> 00:31:34.690 align:middle line:90% 00:31:34.690 --> 00:31:38.190 align:middle line:84% So this kind of local density fluctuation already scattering 00:31:38.190 --> 00:31:41.050 align:middle line:84% is universal to all amorphous materials. 00:31:41.050 --> 00:31:42.230 align:middle line:90% They are always present. 00:31:42.230 --> 00:31:46.220 align:middle line:84% They can be quite small because unlike defect scattering, 00:31:46.220 --> 00:31:47.970 align:middle line:84% the length scale we're talking about here, 00:31:47.970 --> 00:31:50.750 align:middle line:90% this is really atomic scale. 00:31:50.750 --> 00:31:53.830 align:middle line:84% Because Rayleigh scattering also decreases to the essentially 00:31:53.830 --> 00:31:57.350 align:middle line:84% to the negative 4th power with respect to a characteristic 00:31:57.350 --> 00:31:59.430 align:middle line:90% length scale of the scatterers. 00:31:59.430 --> 00:32:03.800 align:middle line:84% So for small-scale fluctuations, the corresponding loss 00:32:03.800 --> 00:32:05.480 align:middle line:90% is a lot weaker. 00:32:05.480 --> 00:32:08.563 align:middle line:84% And that's why glass materials can still 00:32:08.563 --> 00:32:10.480 align:middle line:84% be extremely transparent, despite the presence 00:32:10.480 --> 00:32:12.120 align:middle line:84% of this kind of Rayleigh scattering. 00:32:12.120 --> 00:32:14.910 align:middle line:84% Unlike polystyrene ceramics, which have much larger grains, 00:32:14.910 --> 00:32:16.660 align:middle line:84% therefore induce much stronger scattering. 00:32:16.660 --> 00:32:19.840 align:middle line:84% That's why they tend to be opaque. 00:32:19.840 --> 00:32:23.640 align:middle line:84% The second source that relates to Rayleigh scattering here 00:32:23.640 --> 00:32:26.920 align:middle line:84% is what's called concentration scattering. 00:32:26.920 --> 00:32:30.480 align:middle line:84% Concentration scattering has to do with multi-component glass 00:32:30.480 --> 00:32:31.400 align:middle line:90% materials. 00:32:31.400 --> 00:32:32.900 align:middle line:84% Let's just take a random example. 00:32:32.900 --> 00:32:35.720 align:middle line:84% Let's say you have instead of SiO2, 00:32:35.720 --> 00:32:38.600 align:middle line:84% let's say you put some germanium in there. 00:32:38.600 --> 00:32:43.200 align:middle line:84% So this will be Si, this is a 1 minus x. 00:32:43.200 --> 00:32:46.480 align:middle line:90% This is x. 00:32:46.480 --> 00:32:48.600 align:middle line:84% So if you throw in some germanium dopants 00:32:48.600 --> 00:32:51.720 align:middle line:84% into a SiO2 glass, then germanium 00:32:51.720 --> 00:32:54.980 align:middle line:84% can also occupy the site where silicon normally sits. 00:32:54.980 --> 00:32:58.360 align:middle line:84% They're still 4-4 coordinated, same as silicon. 00:32:58.360 --> 00:33:00.850 align:middle line:84% But what you imagine is that now if you only 00:33:00.850 --> 00:33:04.490 align:middle line:84% look at the sites that's supposedly occupied by silicon, 00:33:04.490 --> 00:33:05.930 align:middle line:84% you now have a random distribution 00:33:05.930 --> 00:33:07.390 align:middle line:90% of germanium and silicon. 00:33:07.390 --> 00:33:10.610 align:middle line:90% 00:33:10.610 --> 00:33:13.890 align:middle line:84% And germanium has a higher polarizability 00:33:13.890 --> 00:33:16.110 align:middle line:84% compared to silicon because it's a heavy atom. 00:33:16.110 --> 00:33:20.010 align:middle line:90% 00:33:20.010 --> 00:33:23.490 align:middle line:84% So it means that this random distribution of these two 00:33:23.490 --> 00:33:27.250 align:middle line:84% kinds of atoms also leads to additional fluctuation 00:33:27.250 --> 00:33:30.770 align:middle line:84% of polarizability and hence refractive index. 00:33:30.770 --> 00:33:33.950 align:middle line:84% So this is going to lead to additional scattering loss here. 00:33:33.950 --> 00:33:37.170 align:middle line:84% This is what's called a concentration scattering. 00:33:37.170 --> 00:33:40.550 align:middle line:84% It really only applies to this kind of multi-component glass. 00:33:40.550 --> 00:33:43.523 align:middle line:84% If it's SiO2, concentrated scattering is basically 0. 00:33:43.523 --> 00:33:45.690 align:middle line:84% But as soon as you start to add some kind of dopant, 00:33:45.690 --> 00:33:48.410 align:middle line:84% chemical modifiers, as long as you 00:33:48.410 --> 00:33:51.730 align:middle line:84% have random population of lattice sites due to two 00:33:51.730 --> 00:33:53.130 align:middle line:84% different kind of atoms, then you 00:33:53.130 --> 00:33:55.210 align:middle line:84% start to get concentration scattering. 00:33:55.210 --> 00:34:07.390 align:middle line:90% 00:34:07.390 --> 00:34:08.409 align:middle line:90% Yes? 00:34:08.409 --> 00:34:10.870 align:middle line:84% AUDIENCE: So the concentration scattering, 00:34:10.870 --> 00:34:15.909 align:middle line:84% is that only for substitutional or would 00:34:15.909 --> 00:34:22.989 align:middle line:84% like an alkali glass that has also some other elements 00:34:22.989 --> 00:34:23.710 align:middle line:90% but not-- 00:34:23.710 --> 00:34:25.710 align:middle line:84% JUEJUN HU: Well, in fact, if you think about it, 00:34:25.710 --> 00:34:28.531 align:middle line:84% like for example, it applies even for interstitial as well. 00:34:28.531 --> 00:34:29.989 align:middle line:84% Even in crystalline material, think 00:34:29.989 --> 00:34:31.989 align:middle line:84% about crystalline material, you put in some kind 00:34:31.989 --> 00:34:34.190 align:middle line:90% of interstitial dopants. 00:34:34.190 --> 00:34:36.590 align:middle line:84% The distribution of dopants in the interstitial site 00:34:36.590 --> 00:34:38.270 align:middle line:84% is also random, statistically random. 00:34:38.270 --> 00:34:39.989 align:middle line:84% So it means that there are also little fluctuations 00:34:39.989 --> 00:34:42.310 align:middle line:84% of local polarizability and therefore also scattering. 00:34:42.310 --> 00:34:43.867 align:middle line:84% It usually tends to be pretty weak. 00:34:43.867 --> 00:34:45.909 align:middle line:84% That's why people don't care about it, especially 00:34:45.909 --> 00:34:46.889 align:middle line:90% in crystalline materials. 00:34:46.889 --> 00:34:48.347 align:middle line:84% In crystalline materials, you don't 00:34:48.347 --> 00:34:51.949 align:middle line:84% have a media like fiber, which is kilometers long, that require 00:34:51.949 --> 00:34:53.042 align:middle line:90% that level of low loss. 00:34:53.042 --> 00:34:54.750 align:middle line:84% So that's why people typically don't even 00:34:54.750 --> 00:34:55.889 align:middle line:90% care about that kind of loss. 00:34:55.889 --> 00:34:56.650 align:middle line:90% But it is present. 00:34:56.650 --> 00:34:57.480 align:middle line:90% It's is definitely not 0. 00:34:57.480 --> 00:34:57.760 align:middle line:90% AUDIENCE: OK. 00:34:57.760 --> 00:35:00.385 align:middle line:84% JUEJUN HU: Yeah, as long as you get random spatial distribution 00:35:00.385 --> 00:35:02.360 align:middle line:84% of something, some kind of scatterers, 00:35:02.360 --> 00:35:04.340 align:middle line:90% you get scattering loss. 00:35:04.340 --> 00:35:04.840 align:middle line:90% Yeah. 00:35:04.840 --> 00:35:07.520 align:middle line:90% 00:35:07.520 --> 00:35:09.680 align:middle line:84% All right, so we have gone through essentially all 00:35:09.680 --> 00:35:11.138 align:middle line:84% these different kinds of mechanisms 00:35:11.138 --> 00:35:14.440 align:middle line:84% about losses in glass materials. if you put all of them together, 00:35:14.440 --> 00:35:16.440 align:middle line:84% you will get a plot like what I'm showing here. 00:35:16.440 --> 00:35:19.920 align:middle line:84% Now notice here, the vertical scale, horizontal scale, 00:35:19.920 --> 00:35:21.420 align:middle line:84% these are both in logarithmic scale. 00:35:21.420 --> 00:35:23.640 align:middle line:84% So this logarithmic absorption coefficient or logarithmic loss 00:35:23.640 --> 00:35:25.000 align:middle line:90% coefficient, I should say. 00:35:25.000 --> 00:35:27.620 align:middle line:84% And then the horizontal axis is logarithmic wavelength. 00:35:27.620 --> 00:35:30.300 align:middle line:90% So look at the terms here. 00:35:30.300 --> 00:35:34.320 align:middle line:84% The first one, A1 and A2 over lambda to negative 4th power, 00:35:34.320 --> 00:35:37.240 align:middle line:90% this is Rayleigh scattering. 00:35:37.240 --> 00:35:41.160 align:middle line:84% A1 corresponds to Rayleigh scattering universal 00:35:41.160 --> 00:35:43.000 align:middle line:90% to amorphous materials. 00:35:43.000 --> 00:35:45.880 align:middle line:84% A2 is an additional coefficient we introduce here 00:35:45.880 --> 00:35:47.660 align:middle line:84% to account for concentration scattering. 00:35:47.660 --> 00:35:51.906 align:middle line:90% 00:35:51.906 --> 00:35:56.330 align:middle line:84% Second one, B, this term, this is coming 00:35:56.330 --> 00:35:58.970 align:middle line:90% from electronic absorption. 00:35:58.970 --> 00:36:00.510 align:middle line:84% If you look at the expression here, 00:36:00.510 --> 00:36:03.450 align:middle line:84% basically it says that absorption decays exponentially 00:36:03.450 --> 00:36:05.330 align:middle line:90% as you increase wavelength. 00:36:05.330 --> 00:36:07.450 align:middle line:84% This is really coming from those defect states. 00:36:07.450 --> 00:36:12.170 align:middle line:90% 00:36:12.170 --> 00:36:14.290 align:middle line:84% And finally, last term here, this 00:36:14.290 --> 00:36:16.410 align:middle line:84% is coming from phonon absorption. 00:36:16.410 --> 00:36:18.550 align:middle line:84% Again, similar to electronic absorption, 00:36:18.550 --> 00:36:21.610 align:middle line:84% for phonon absorption, you basically 00:36:21.610 --> 00:36:23.810 align:middle line:84% have absorption peak that corresponds 00:36:23.810 --> 00:36:27.330 align:middle line:84% to the vibrational frequency of the lattice. 00:36:27.330 --> 00:36:30.210 align:middle line:84% But as you move away from that vibrational peak, 00:36:30.210 --> 00:36:32.270 align:middle line:84% the absorption decays exponentially. 00:36:32.270 --> 00:36:37.850 align:middle line:90% 00:36:37.850 --> 00:36:39.910 align:middle line:84% Now if you put it on this plot here, 00:36:39.910 --> 00:36:42.210 align:middle line:84% you can see three different regimes here. 00:36:42.210 --> 00:36:44.450 align:middle line:84% At the very short wavelength, this 00:36:44.450 --> 00:36:50.350 align:middle line:84% is typically where you have high energy photons. 00:36:50.350 --> 00:36:53.430 align:middle line:84% You can excite these electronic transitions. 00:36:53.430 --> 00:36:56.710 align:middle line:84% Then you get electronic absorption here. 00:36:56.710 --> 00:36:58.998 align:middle line:84% This usually depends on the glass material. 00:36:58.998 --> 00:37:00.790 align:middle line:84% You can actually look at the glass material 00:37:00.790 --> 00:37:02.873 align:middle line:84% and tell where the electronic absorption comes in. 00:37:02.873 --> 00:37:04.970 align:middle line:84% Essentially, if it's like silica, 00:37:04.970 --> 00:37:06.430 align:middle line:90% it's perfectly transparent. 00:37:06.430 --> 00:37:08.563 align:middle line:84% So you only get electronic absorption really 00:37:08.563 --> 00:37:09.670 align:middle line:90% in the UV range. 00:37:09.670 --> 00:37:12.150 align:middle line:84% If it's like chalcogenide, they're opaque in visible, 00:37:12.150 --> 00:37:14.390 align:middle line:84% so then you can actually absorb photons with energy 00:37:14.390 --> 00:37:17.090 align:middle line:90% like a couple of EVs. 00:37:17.090 --> 00:37:22.230 align:middle line:84% If you get to a longer wavelength here, lower energy, 00:37:22.230 --> 00:37:24.910 align:middle line:84% you get this linear regime here in the double logarithm 00:37:24.910 --> 00:37:26.670 align:middle line:84% plot with a slope that corresponds 00:37:26.670 --> 00:37:28.470 align:middle line:90% to basically 1 over 4. 00:37:28.470 --> 00:37:30.270 align:middle line:90% This is Rayleigh scattering. 00:37:30.270 --> 00:37:33.750 align:middle line:84% So Rayleigh scattering tend to take over 00:37:33.750 --> 00:37:38.390 align:middle line:84% in the transparency regime of glass materials. 00:37:38.390 --> 00:37:40.230 align:middle line:84% And then the long wavelength absorption 00:37:40.230 --> 00:37:42.710 align:middle line:84% is really bound by phonon absorption. 00:37:42.710 --> 00:37:45.750 align:middle line:84% So in between Rayleigh scattering and phonon 00:37:45.750 --> 00:37:49.550 align:middle line:84% absorption, you can define the minimum loss window 00:37:49.550 --> 00:37:51.920 align:middle line:90% for glass materials. 00:37:51.920 --> 00:37:54.938 align:middle line:84% This is where the glass material gets most transparent, 00:37:54.938 --> 00:37:55.980 align:middle line:90% right in the middle here. 00:37:55.980 --> 00:38:08.120 align:middle line:90% 00:38:08.120 --> 00:38:11.240 align:middle line:84% So now once you put it down, let's 00:38:11.240 --> 00:38:13.500 align:middle line:84% take a look at some actual real examples here. 00:38:13.500 --> 00:38:16.192 align:middle line:90% 00:38:16.192 --> 00:38:18.760 align:middle line:84% On the left-hand side, this is the absorption coefficient 00:38:18.760 --> 00:38:20.280 align:middle line:84% of silica glass, which I basically 00:38:20.280 --> 00:38:21.540 align:middle line:90% have shown in previous slides. 00:38:21.540 --> 00:38:24.640 align:middle line:84% There are a few different curves here. 00:38:24.640 --> 00:38:27.080 align:middle line:84% The thicker lines, these actually 00:38:27.080 --> 00:38:30.800 align:middle line:84% correspond to glasses with impurities. 00:38:30.800 --> 00:38:33.520 align:middle line:84% In silica glass, the most common impurity 00:38:33.520 --> 00:38:35.688 align:middle line:84% is basically hydrogen coming from water. 00:38:35.688 --> 00:38:37.980 align:middle line:84% If there's a water, they get incorporated into lattice, 00:38:37.980 --> 00:38:39.000 align:middle line:90% basically hydrogen. 00:38:39.000 --> 00:38:47.460 align:middle line:84% O-H has a high-order absorption at about 1.4 microns. 00:38:47.460 --> 00:38:48.500 align:middle line:90% Let me see. 00:38:48.500 --> 00:38:51.200 align:middle line:84% If you come over here, the O-H functional group, 00:38:51.200 --> 00:38:54.620 align:middle line:84% the primary absorption band is about 2.9 microns. 00:38:54.620 --> 00:38:56.483 align:middle line:84% But you also get high-order harmonics. 00:38:56.483 --> 00:38:58.400 align:middle line:84% Essentially, if you look at phonon absorption, 00:38:58.400 --> 00:39:01.860 align:middle line:84% you can excite one phonon, which gives you h-bar omega. 00:39:01.860 --> 00:39:06.700 align:middle line:84% You can also excite two phonons, then you get 2 h-bar omega. 00:39:06.700 --> 00:39:09.340 align:middle line:84% So it means that in addition to this primary absorption 00:39:09.340 --> 00:39:11.180 align:middle line:84% band, which has a high strength, you also 00:39:11.180 --> 00:39:15.580 align:middle line:84% get higher order, what they call overtones. 00:39:15.580 --> 00:39:19.740 align:middle line:90% Higher-order overtones. 00:39:19.740 --> 00:39:24.420 align:middle line:84% So these overtones are roughly integer multiples, 00:39:24.420 --> 00:39:28.640 align:middle line:84% in terms of the frequency, for the primary absorption band. 00:39:28.640 --> 00:39:31.300 align:middle line:84% So in wavelength, this then corresponds to about 1.4, 00:39:31.300 --> 00:39:32.560 align:middle line:90% 1.5 microns. 00:39:32.560 --> 00:39:36.180 align:middle line:84% So that's why the high-order overtone is what's 00:39:36.180 --> 00:39:38.140 align:middle line:90% causing this little peak there. 00:39:38.140 --> 00:39:40.980 align:middle line:84% And that's why if you look back into Charles Kao, when he first 00:39:40.980 --> 00:39:43.260 align:middle line:84% developed these fibers, he has to spend lots of time 00:39:43.260 --> 00:39:45.677 align:middle line:84% looking into how to actually purify these glasses in order 00:39:45.677 --> 00:39:47.260 align:middle line:84% to get rid of all these impurities. 00:39:47.260 --> 00:39:49.482 align:middle line:84% Now, in the bottom here, this gray line, 00:39:49.482 --> 00:39:51.190 align:middle line:84% this gives you the absorption coefficient 00:39:51.190 --> 00:39:53.310 align:middle line:90% of a high-purity silica glass. 00:39:53.310 --> 00:39:55.950 align:middle line:84% You see that, again, this end, short wavelength end, this 00:39:55.950 --> 00:39:57.470 align:middle line:84% is basically Rayleigh scattering. 00:39:57.470 --> 00:39:59.150 align:middle line:84% Long wavelength end, this is really 00:39:59.150 --> 00:40:02.390 align:middle line:84% phonon absorption coming from Si-O bond by vibration, out here 00:40:02.390 --> 00:40:04.670 align:middle line:90% at 9 microns, this is very tail. 00:40:04.670 --> 00:40:09.350 align:middle line:84% This defines the lowest loss window for silica glass at 1.55 00:40:09.350 --> 00:40:12.270 align:middle line:90% microns, or 1,550 nanometers. 00:40:12.270 --> 00:40:14.850 align:middle line:84% This is a very important wavelength. 00:40:14.850 --> 00:40:18.790 align:middle line:90% 00:40:18.790 --> 00:40:22.350 align:middle line:84% All the internet data in long-haul communications, 00:40:22.350 --> 00:40:24.990 align:middle line:84% that takes place all around this wavelength. 00:40:24.990 --> 00:40:27.670 align:middle line:84% They all take place right around this wavelength here 00:40:27.670 --> 00:40:30.050 align:middle line:84% because of the low-loss characteristics. 00:40:30.050 --> 00:40:37.052 align:middle line:90% 00:40:37.052 --> 00:40:38.510 align:middle line:84% If you have fiber to the home, this 00:40:38.510 --> 00:40:39.930 align:middle line:90% is how they actually send data. 00:40:39.930 --> 00:40:41.550 align:middle line:84% This is the wavelength they use to actually send data 00:40:41.550 --> 00:40:43.990 align:middle line:84% to your home or send the data across the Atlantic. 00:40:43.990 --> 00:40:46.913 align:middle line:90% This is what they use. 00:40:46.913 --> 00:40:49.120 align:middle line:84% Now, this is already pretty impressive 00:40:49.120 --> 00:40:52.180 align:middle line:84% because as we mentioned, you can get to 0.2 db per kilometer, 00:40:52.180 --> 00:40:53.520 align:middle line:90% which is really good. 00:40:53.520 --> 00:40:55.140 align:middle line:84% But there has been lots of efforts, 00:40:55.140 --> 00:40:58.300 align:middle line:84% people are trying to push for even lower loss glass materials. 00:40:58.300 --> 00:41:00.375 align:middle line:84% So that you can have, for example, 00:41:00.375 --> 00:41:02.000 align:middle line:84% essentially fiber communication systems 00:41:02.000 --> 00:41:04.040 align:middle line:84% without having to amplify or regenerate 00:41:04.040 --> 00:41:07.080 align:middle line:84% the signal over longer distances. 00:41:07.080 --> 00:41:10.880 align:middle line:84% So that's why especially like in the early 2000s during 00:41:10.880 --> 00:41:13.440 align:middle line:84% the telecom bubble time, there has been lots of interest 00:41:13.440 --> 00:41:16.160 align:middle line:84% looking into alternative glass materials outside silica 00:41:16.160 --> 00:41:18.120 align:middle line:90% to achieve even lower loss. 00:41:18.120 --> 00:41:21.880 align:middle line:84% The general strategy there is to look into material systems 00:41:21.880 --> 00:41:24.272 align:middle line:90% with lower phonon energy. 00:41:24.272 --> 00:41:26.480 align:middle line:84% Because what happens with low phonon energy materials 00:41:26.480 --> 00:41:28.313 align:middle line:84% is that it means that this photon absorption 00:41:28.313 --> 00:41:31.620 align:middle line:84% peak, this side, is going to get pushed to longer wavelengths. 00:41:31.620 --> 00:41:34.200 align:middle line:84% There's not much you can do about Rayleigh scattering. 00:41:34.200 --> 00:41:37.640 align:middle line:84% But if you push the phonon absorption peak into the longer 00:41:37.640 --> 00:41:40.662 align:middle line:84% wavelength, you can extend this transmission window 00:41:40.662 --> 00:41:43.120 align:middle line:84% down to a much longer wavelength here, which also gives you 00:41:43.120 --> 00:41:45.500 align:middle line:90% a lower loss. 00:41:45.500 --> 00:41:47.920 align:middle line:84% So that's why I'm quoting you this paper here. 00:41:47.920 --> 00:41:50.148 align:middle line:90% This is actually from 1980s. 00:41:50.148 --> 00:41:51.440 align:middle line:90% This is theoretical prediction. 00:41:51.440 --> 00:41:52.690 align:middle line:90% This is not experimental data. 00:41:52.690 --> 00:41:56.100 align:middle line:84% They predicted that for some of these fluoride glasses, also 00:41:56.100 --> 00:41:58.100 align:middle line:84% some chalcogenide glasses, you see 00:41:58.100 --> 00:42:00.060 align:middle line:84% that the transparency window is pushed 00:42:00.060 --> 00:42:01.740 align:middle line:90% to much longer wavelengths. 00:42:01.740 --> 00:42:05.020 align:middle line:84% You can get a much lower absorption in these glass 00:42:05.020 --> 00:42:08.148 align:middle line:90% materials compared to silica. 00:42:08.148 --> 00:42:09.940 align:middle line:84% Now obviously we know that nobody is really 00:42:09.940 --> 00:42:12.020 align:middle line:84% trying to make or replace silica glass fiber 00:42:12.020 --> 00:42:14.150 align:middle line:84% network using those kind of exotic glass materials. 00:42:14.150 --> 00:42:15.400 align:middle line:90% There are a few reasons there. 00:42:15.400 --> 00:42:17.020 align:middle line:84% For practical reasons, these materials 00:42:17.020 --> 00:42:18.520 align:middle line:84% are a lot more difficult to process. 00:42:18.520 --> 00:42:19.960 align:middle line:90% They are not nearly as robust. 00:42:19.960 --> 00:42:24.060 align:middle line:84% They tend to be a lot more fragile both mechanically 00:42:24.060 --> 00:42:27.020 align:middle line:84% and also from the liquid fragility point. 00:42:27.020 --> 00:42:28.600 align:middle line:84% They tend to be a lot more fragile. 00:42:28.600 --> 00:42:30.380 align:middle line:84% It means that they are a lot more sensitive to temperature 00:42:30.380 --> 00:42:32.500 align:middle line:84% variations, if you think about it and draw a plot, 00:42:32.500 --> 00:42:33.780 align:middle line:84% any temperature fluctuation is going 00:42:33.780 --> 00:42:35.760 align:middle line:84% to lead to a very large change of viscosity, 00:42:35.760 --> 00:42:37.880 align:middle line:84% so they're a lot more difficult to process. 00:42:37.880 --> 00:42:39.380 align:middle line:90% That's one reason. 00:42:39.380 --> 00:42:41.760 align:middle line:84% Second reason, if you look at this plot here, 00:42:41.760 --> 00:42:43.990 align:middle line:84% turns out that these loss numbers are actually 00:42:43.990 --> 00:42:46.890 align:middle line:84% unrealistic, even from a theoretical perspective, 00:42:46.890 --> 00:42:49.470 align:middle line:84% because in these early calculations, 00:42:49.470 --> 00:42:53.910 align:middle line:84% they completely forgot about concentration scattering. 00:42:53.910 --> 00:42:56.050 align:middle line:84% If you have these kind of multi-component glasses, 00:42:56.050 --> 00:42:58.690 align:middle line:84% obviously, you imagine that these different metal ions, 00:42:58.690 --> 00:43:00.648 align:middle line:84% they can occupy different lattice sites leading 00:43:00.648 --> 00:43:03.630 align:middle line:84% to rhythm fluctuation, it's going to completely overshadow 00:43:03.630 --> 00:43:05.990 align:middle line:90% these low-loss benefits. 00:43:05.990 --> 00:43:08.590 align:middle line:84% Now you may argue germanium sulfide, 00:43:08.590 --> 00:43:11.210 align:middle line:84% it looks like a single-component glass. 00:43:11.210 --> 00:43:14.310 align:middle line:84% Maybe it can be a low-loss candidate. 00:43:14.310 --> 00:43:16.910 align:middle line:84% Turns out no, because chalcogenides 00:43:16.910 --> 00:43:19.550 align:middle line:84% is somewhat annoying in this regard, 00:43:19.550 --> 00:43:22.550 align:middle line:84% that they have different microstructure units. 00:43:22.550 --> 00:43:23.790 align:middle line:90% Take a very simple example. 00:43:23.790 --> 00:43:27.270 align:middle line:84% If you think about As2S3, this is archetypal, most commonly 00:43:27.270 --> 00:43:28.550 align:middle line:90% used chalcogenide glass. 00:43:28.550 --> 00:43:33.790 align:middle line:84% There are actually two kinds of structural units in As2S3 glass. 00:43:33.790 --> 00:43:38.510 align:middle line:84% One is the regular As2S3, and then the other 00:43:38.510 --> 00:43:45.840 align:middle line:84% is As4S4 plus S. Because arsenic trisulfide actually 00:43:45.840 --> 00:43:49.480 align:middle line:84% has two polymorphs, if you look at the crystalline structures. 00:43:49.480 --> 00:43:53.080 align:middle line:84% And as a result, there are two corresponding structural units 00:43:53.080 --> 00:43:55.600 align:middle line:84% that are present in amorphous network. 00:43:55.600 --> 00:43:58.080 align:middle line:90% This is basically a orpiment. 00:43:58.080 --> 00:43:59.440 align:middle line:90% This is another one, realgar. 00:43:59.440 --> 00:44:02.755 align:middle line:84% And As4S4, they also, because they are excess sulfur, 00:44:02.755 --> 00:44:04.880 align:middle line:84% this sulfur actually forms in chains, linear chains 00:44:04.880 --> 00:44:06.860 align:middle line:90% or in rings around the lattice. 00:44:06.860 --> 00:44:09.540 align:middle line:84% So even if it looks like a single component glass, 00:44:09.540 --> 00:44:15.040 align:middle line:84% if you cannot eliminate these two kind of local structure 00:44:15.040 --> 00:44:17.753 align:middle line:84% moieties, if you cannot eliminate this kind of structure 00:44:17.753 --> 00:44:20.420 align:middle line:84% inhomogeneity, you're also going to get lots of scattering loss, 00:44:20.420 --> 00:44:22.640 align:middle line:84% similar to concentration scattering. 00:44:22.640 --> 00:44:28.320 align:middle line:84% So that's why SiO2 still is the dominant glass 00:44:28.320 --> 00:44:29.680 align:middle line:90% material people use. 00:44:29.680 --> 00:44:32.440 align:middle line:84% Now, in the homework assignment, in the P-set, 00:44:32.440 --> 00:44:34.333 align:middle line:84% I do give you a question asking you, 00:44:34.333 --> 00:44:38.520 align:middle line:84% can you still predict a glass or at least postulate 00:44:38.520 --> 00:44:41.180 align:middle line:84% a glass composition that will give you even lower loss 00:44:41.180 --> 00:44:42.740 align:middle line:90% compared to silica. 00:44:42.740 --> 00:44:44.280 align:middle line:90% OK, I'll let you think about it. 00:44:44.280 --> 00:44:47.060 align:middle line:84% I have already had all of those mechanisms here. 00:44:47.060 --> 00:44:49.900 align:middle line:84% Try to come up with one with reasonable assumptions there, 00:44:49.900 --> 00:44:51.540 align:middle line:84% accounting for all the loss mechanisms. 00:44:51.540 --> 00:44:54.180 align:middle line:90% 00:44:54.180 --> 00:44:56.300 align:middle line:84% Any more questions about loss before we move on 00:44:56.300 --> 00:44:58.960 align:middle line:90% to coloring in glasses? 00:44:58.960 --> 00:45:04.260 align:middle line:90% 00:45:04.260 --> 00:45:05.220 align:middle line:90% All good? 00:45:05.220 --> 00:45:07.060 align:middle line:90% Crystal clear? 00:45:07.060 --> 00:45:07.960 align:middle line:90% No scattering. 00:45:07.960 --> 00:45:11.360 align:middle line:90% 00:45:11.360 --> 00:45:13.280 align:middle line:84% So now let's switch gears a little bit, 00:45:13.280 --> 00:45:16.040 align:middle line:84% talk about coloring of glass materials. 00:45:16.040 --> 00:45:17.540 align:middle line:84% This is actually a photo I took when 00:45:17.540 --> 00:45:19.640 align:middle line:90% I visited Rutgers University. 00:45:19.640 --> 00:45:22.580 align:middle line:84% They have a pretty comprehensive glass lab sponsored by Corning. 00:45:22.580 --> 00:45:25.820 align:middle line:84% And this is one of the displays they have. 00:45:25.820 --> 00:45:27.760 align:middle line:84% It shows different colored glasses 00:45:27.760 --> 00:45:29.920 align:middle line:84% and what's the chemistry actually behind them. 00:45:29.920 --> 00:45:32.700 align:middle line:84% So that's what we're going to talk about in the next section 00:45:32.700 --> 00:45:34.380 align:middle line:90% here. 00:45:34.380 --> 00:45:37.310 align:middle line:90% So how do you generate color. 00:45:37.310 --> 00:45:41.050 align:middle line:84% Simply put, color, in order to get color, 00:45:41.050 --> 00:45:44.300 align:middle line:84% you need to introduce a wavelength-dependent loss. 00:45:44.300 --> 00:45:46.050 align:middle line:84% It can be wavelength-dependent absorption. 00:45:46.050 --> 00:45:47.650 align:middle line:84% It can be wavelength-dependent scattering. 00:45:47.650 --> 00:45:49.775 align:middle line:84% But you need some kind of wavelength-dependent loss 00:45:49.775 --> 00:45:51.030 align:middle line:90% mechanisms to get color. 00:45:51.030 --> 00:45:54.150 align:middle line:84% So you can do that either by absorption 00:45:54.150 --> 00:45:55.170 align:middle line:90% or do it by scattering. 00:45:55.170 --> 00:45:56.870 align:middle line:90% We're going to look at both. 00:45:56.870 --> 00:45:59.950 align:middle line:84% Starting from absorption, the easiest way 00:45:59.950 --> 00:46:02.070 align:middle line:84% to generate wavelength-dependent absorption 00:46:02.070 --> 00:46:04.050 align:middle line:84% is to put in some kind of dopant ions, 00:46:04.050 --> 00:46:07.310 align:middle line:84% typically transition metal or rare earth metal. 00:46:07.310 --> 00:46:09.510 align:middle line:84% As I mentioned in the beginning of class, 00:46:09.510 --> 00:46:14.510 align:middle line:84% those ions have unfilled, either 3D or 4f shells. 00:46:14.510 --> 00:46:18.670 align:middle line:84% So this gives rise to a large number of possible electron 00:46:18.670 --> 00:46:19.410 align:middle line:90% transitions. 00:46:19.410 --> 00:46:20.910 align:middle line:84% And then these electron transitions, 00:46:20.910 --> 00:46:22.950 align:middle line:84% they lead to wavelength-selective absorption, 00:46:22.950 --> 00:46:25.470 align:middle line:84% essentially absorption peaks centering around the transition 00:46:25.470 --> 00:46:27.310 align:middle line:84% energy, which you can use to generate 00:46:27.310 --> 00:46:30.950 align:middle line:90% all different kinds of colors. 00:46:30.950 --> 00:46:33.630 align:middle line:84% So one example here, this one, this 00:46:33.630 --> 00:46:37.880 align:middle line:84% is erbium, which is a rare earth ion. 00:46:37.880 --> 00:46:43.080 align:middle line:84% This is the energy level diagram I've quoted from this book here. 00:46:43.080 --> 00:46:46.880 align:middle line:84% There are a total of 41 energy levels in erbium 3-plus ion due 00:46:46.880 --> 00:46:49.140 align:middle line:90% to spin orbit split. 00:46:49.140 --> 00:46:50.398 align:middle line:90% So it's quite complex. 00:46:50.398 --> 00:46:52.940 align:middle line:84% Now, fortunately, you don't have to worry about most of them. 00:46:52.940 --> 00:46:54.773 align:middle line:84% Most of them are technologically irrelevant. 00:46:54.773 --> 00:46:56.018 align:middle line:90% People don't care about it. 00:46:56.018 --> 00:46:57.560 align:middle line:84% The reason I want to cite erbium here 00:46:57.560 --> 00:47:00.120 align:middle line:84% is because it has one transition that 00:47:00.120 --> 00:47:06.600 align:middle line:84% corresponds to photon energy of 1.54 microns. 00:47:06.600 --> 00:47:07.900 align:middle line:90% Does that number ring a bell? 00:47:07.900 --> 00:47:10.880 align:middle line:90% 00:47:10.880 --> 00:47:13.640 align:middle line:84% It's very closely aligned with the low loss 00:47:13.640 --> 00:47:18.620 align:middle line:90% window of silica fibers. 00:47:18.620 --> 00:47:21.440 align:middle line:84% This is a very fortunate coincidence. 00:47:21.440 --> 00:47:24.000 align:middle line:84% That's why erbium actually becomes technologically very 00:47:24.000 --> 00:47:26.960 align:middle line:84% important for optical communications, because 00:47:26.960 --> 00:47:29.440 align:middle line:90% of that 1.54 transition there. 00:47:29.440 --> 00:47:32.340 align:middle line:84% What I'm showing you here, you can see that it's 1.54. 00:47:32.340 --> 00:47:34.260 align:middle line:84% It centers at 1.54, but there's always 00:47:34.260 --> 00:47:35.955 align:middle line:84% some kind of broadening mechanism 00:47:35.955 --> 00:47:37.580 align:middle line:84% so that the transition actually covers, 00:47:37.580 --> 00:47:42.580 align:middle line:84% that's 1.54, but essentially covers a reasonable bandwidth. 00:47:42.580 --> 00:47:45.020 align:middle line:84% This covers essentially all the wavelengths 00:47:45.020 --> 00:47:48.380 align:middle line:84% that's needed for optical communication. 00:47:48.380 --> 00:47:50.120 align:middle line:84% So that's why what people can do, 00:47:50.120 --> 00:47:56.260 align:middle line:84% they can make amplifiers out of this kind of erbium glass. 00:47:56.260 --> 00:47:59.220 align:middle line:84% So the type of amplifier people use 00:47:59.220 --> 00:48:04.300 align:middle line:84% is called erbium-doped fiber amplifier, or EDFA. 00:48:04.300 --> 00:48:06.540 align:middle line:84% But basically what they have here is 00:48:06.540 --> 00:48:09.600 align:middle line:84% you can simplify the energy band diagram into erbium, 00:48:09.600 --> 00:48:11.860 align:middle line:84% into a simple three-level system. 00:48:11.860 --> 00:48:14.900 align:middle line:84% Essentially, you have a ground state. 00:48:14.900 --> 00:48:18.347 align:middle line:84% There are actually two relevant energy levels, really. 00:48:18.347 --> 00:48:19.680 align:middle line:90% Again, there are many variables. 00:48:19.680 --> 00:48:21.260 align:middle line:90% We'll only look at two of them. 00:48:21.260 --> 00:48:23.540 align:middle line:84% The transition energy for this one, this 00:48:23.540 --> 00:48:27.140 align:middle line:84% corresponds to wavelength of about 980 nanometers. 00:48:27.140 --> 00:48:32.950 align:middle line:84% This is our 1,540 nanometer transition. 00:48:32.950 --> 00:48:36.070 align:middle line:84% Now, when you try to use this erbium ion as an amplifier 00:48:36.070 --> 00:48:39.030 align:middle line:84% media, what you will do is you start by essentially pumping, 00:48:39.030 --> 00:48:40.970 align:middle line:90% optically pump the system. 00:48:40.970 --> 00:48:44.270 align:middle line:84% You essentially promote lots of the electrons from ground state 00:48:44.270 --> 00:48:48.150 align:middle line:84% into this upper state right here. 00:48:48.150 --> 00:48:50.862 align:middle line:84% Now this upper state, turns out it's not very stable. 00:48:50.862 --> 00:48:51.570 align:middle line:90% It's short lived. 00:48:51.570 --> 00:48:52.690 align:middle line:90% It has a short lifetime. 00:48:52.690 --> 00:48:57.250 align:middle line:84% So a lot of these electrons then relax into this state. 00:48:57.250 --> 00:49:03.582 align:middle line:90% 00:49:03.582 --> 00:49:06.830 align:middle line:84% So if you pump hard enough, then that 00:49:06.830 --> 00:49:11.190 align:middle line:84% means you can actually generate lots of carriers at this excited 00:49:11.190 --> 00:49:13.150 align:middle line:84% state here such that you actually 00:49:13.150 --> 00:49:17.990 align:middle line:90% get a population inversion. 00:49:17.990 --> 00:49:19.690 align:middle line:84% Once you have population inversion, 00:49:19.690 --> 00:49:22.590 align:middle line:84% if you send a photon with an energy that 00:49:22.590 --> 00:49:25.230 align:middle line:84% aligns with this wavelength here, 00:49:25.230 --> 00:49:28.110 align:middle line:84% then it's going to trigger essentially excitation 00:49:28.110 --> 00:49:31.240 align:middle line:84% or deexcitation of this energy level here. 00:49:31.240 --> 00:49:32.960 align:middle line:84% And this, in the process, you essentially 00:49:32.960 --> 00:49:38.440 align:middle line:84% duplicate the photons, which then give you an amplification. 00:49:38.440 --> 00:49:40.900 align:middle line:84% So that's actually what people do in erbium-doped fiber 00:49:40.900 --> 00:49:41.400 align:middle line:90% amplifier. 00:49:41.400 --> 00:49:44.320 align:middle line:84% It's basically a section of fiber with high erbium doping 00:49:44.320 --> 00:49:45.920 align:middle line:90% concentration. 00:49:45.920 --> 00:49:47.457 align:middle line:84% And you can do that with changing 00:49:47.457 --> 00:49:50.040 align:middle line:84% the glass formula, for example, using phosphate glasses, which 00:49:50.040 --> 00:49:53.960 align:middle line:90% is what sometimes people use. 00:49:53.960 --> 00:49:55.340 align:middle line:90% You put lots of erbium there. 00:49:55.340 --> 00:49:57.540 align:middle line:84% You then use a laser diode to essentially pump 00:49:57.540 --> 00:50:01.200 align:middle line:84% in this kind of for, example, 980 nanometer light. 00:50:01.200 --> 00:50:04.360 align:middle line:84% Then this 980 nanometer is going to lead to population inversion 00:50:04.360 --> 00:50:05.665 align:middle line:90% in that section of fiber. 00:50:05.665 --> 00:50:07.040 align:middle line:84% So then when your signal actually 00:50:07.040 --> 00:50:08.940 align:middle line:84% comes in to the same section of fiber, 00:50:08.940 --> 00:50:11.080 align:middle line:84% it's then going to get amplified. 00:50:11.080 --> 00:50:14.640 align:middle line:84% So that's how to actually transmit 00:50:14.640 --> 00:50:17.960 align:middle line:84% signal across very, very long distances. 00:50:17.960 --> 00:50:20.320 align:middle line:84% You need to essentially do this reamplification once 00:50:20.320 --> 00:50:23.080 align:middle line:84% in a while to boost the signal levels 00:50:23.080 --> 00:50:24.880 align:middle line:90% for optical communications. 00:50:24.880 --> 00:50:32.310 align:middle line:90% 00:50:32.310 --> 00:50:34.060 align:middle line:84% Basically, this is one example to show you 00:50:34.060 --> 00:50:38.420 align:middle line:84% that you can introduce essentially 00:50:38.420 --> 00:50:40.300 align:middle line:84% light emission and similarly also absorption, 00:50:40.300 --> 00:50:42.180 align:middle line:90% because this is all reciprocal. 00:50:42.180 --> 00:50:44.620 align:middle line:84% So if you have photons with 1,540 nanometer comes 00:50:44.620 --> 00:50:46.140 align:middle line:84% in, if it's not population inverted, 00:50:46.140 --> 00:50:48.780 align:middle line:84% it's going to cause wavelength selective absorption. 00:50:48.780 --> 00:50:50.540 align:middle line:84% So what I'm showing you on this plot here, 00:50:50.540 --> 00:50:54.740 align:middle line:84% this is the absorption cross-section 00:50:54.740 --> 00:50:56.453 align:middle line:90% of erbium in these glasses. 00:50:56.453 --> 00:50:58.620 align:middle line:84% So it means that you can see that this absorption is 00:50:58.620 --> 00:50:59.745 align:middle line:90% quite wavelength selective. 00:50:59.745 --> 00:51:02.140 align:middle line:84% It peaks right at this 1,514 nanometers. 00:51:02.140 --> 00:51:05.018 align:middle line:84% Now this is technologically important for communications. 00:51:05.018 --> 00:51:07.060 align:middle line:84% It does nothing to coloring because it's actually 00:51:07.060 --> 00:51:08.160 align:middle line:90% infrared wavelengths. 00:51:08.160 --> 00:51:09.003 align:middle line:90% You cannot see it. 00:51:09.003 --> 00:51:11.420 align:middle line:84% But the same mechanism, if you shift the absorption energy 00:51:11.420 --> 00:51:13.660 align:middle line:84% levels to the visible window, then you 00:51:13.660 --> 00:51:16.300 align:middle line:84% can actually get essentially the selective colors. 00:51:16.300 --> 00:51:18.680 align:middle line:84% So in the table on the left-hand side here, 00:51:18.680 --> 00:51:21.180 align:middle line:84% I'm showing you the different kind of ions 00:51:21.180 --> 00:51:22.440 align:middle line:90% and their transition levels. 00:51:22.440 --> 00:51:25.260 align:middle line:84% Essentially, they give rise to different colors. 00:51:25.260 --> 00:51:29.070 align:middle line:84% For rare earth, most of the time the transition 00:51:29.070 --> 00:51:30.750 align:middle line:84% tends to be at longer wavelength, 00:51:30.750 --> 00:51:32.750 align:middle line:84% so there is only a handful of them that actually 00:51:32.750 --> 00:51:34.530 align:middle line:90% generate some colors there. 00:51:34.530 --> 00:51:36.030 align:middle line:84% Most of the time, if you want to get 00:51:36.030 --> 00:51:38.590 align:middle line:84% more saturated, stronger color, people tend 00:51:38.590 --> 00:51:41.270 align:middle line:90% to use transition metal ions. 00:51:41.270 --> 00:51:44.042 align:middle line:84% Their transition energy usually lies in the visible region. 00:51:44.042 --> 00:51:45.750 align:middle line:84% You can see there are very diverse colors 00:51:45.750 --> 00:51:48.590 align:middle line:84% you can generate with these transition metal ions. 00:51:48.590 --> 00:51:51.005 align:middle line:90% 00:51:51.005 --> 00:51:53.630 align:middle line:84% One good example of transition metal ion that actually give you 00:51:53.630 --> 00:52:00.422 align:middle line:84% this color is just a iron, iron 2-plus. 00:52:00.422 --> 00:52:02.630 align:middle line:84% Most of the windowpane glasses, they look transparent 00:52:02.630 --> 00:52:05.172 align:middle line:84% from surface normal direction, but if you look from the side, 00:52:05.172 --> 00:52:06.790 align:middle line:90% you see this green tint there. 00:52:06.790 --> 00:52:08.790 align:middle line:84% And that's because you always have 00:52:08.790 --> 00:52:10.270 align:middle line:90% a little bit of iron impurity. 00:52:10.270 --> 00:52:15.150 align:middle line:90% 00:52:15.150 --> 00:52:18.550 align:middle line:84% So if you're looking for colorless 00:52:18.550 --> 00:52:21.810 align:middle line:84% glasses without this green tint, two ways of doing it. 00:52:21.810 --> 00:52:25.920 align:middle line:84% If it's more high-end optical elements, 00:52:25.920 --> 00:52:29.060 align:middle line:84% in that case, essentially, you purify the glass, 00:52:29.060 --> 00:52:31.600 align:middle line:84% get rid of any of the iron impurities. 00:52:31.600 --> 00:52:34.320 align:middle line:84% For other applications where you don't really care that much 00:52:34.320 --> 00:52:37.080 align:middle line:84% about this kind of absorption layer, what you could do, 00:52:37.080 --> 00:52:41.040 align:middle line:84% an easier way, is to leverage the fact that iron has two 00:52:41.040 --> 00:52:42.855 align:middle line:84% valence states, 2-plus and 3-plus. 00:52:42.855 --> 00:52:44.480 align:middle line:84% And they exhibit different colors here. 00:52:44.480 --> 00:52:47.440 align:middle line:84% 2-plus is green, 3-plus is yellow. 00:52:47.440 --> 00:52:49.440 align:middle line:84% And green and yellow, it turns out 00:52:49.440 --> 00:52:52.160 align:middle line:90% they are complementary colors. 00:52:52.160 --> 00:52:54.560 align:middle line:84% So what you can do is that you can actually 00:52:54.560 --> 00:52:59.720 align:middle line:84% oxidize, subject glass materials into oxidizing environment, 00:52:59.720 --> 00:53:03.000 align:middle line:84% and transform some of the Fe2-plus ions 00:53:03.000 --> 00:53:04.920 align:middle line:90% into Fe3-plus ions. 00:53:04.920 --> 00:53:07.720 align:middle line:84% If you get the ratio correctly, then you 00:53:07.720 --> 00:53:11.877 align:middle line:84% can actually get seemingly colorless glass materials 00:53:11.877 --> 00:53:13.960 align:middle line:84% by essentially balancing the absorption at the two 00:53:13.960 --> 00:53:16.120 align:middle line:90% different wavelengths. 00:53:16.120 --> 00:53:17.560 align:middle line:84% Again, it doesn't work if you have 00:53:17.560 --> 00:53:19.100 align:middle line:90% high-end optical instruments. 00:53:19.100 --> 00:53:20.320 align:middle line:84% Because when you're doing that, you're actually 00:53:20.320 --> 00:53:21.840 align:middle line:90% introducing S-S absorption. 00:53:21.840 --> 00:53:23.720 align:middle line:84% You're not getting rid of absorption, 00:53:23.720 --> 00:53:26.940 align:middle line:84% but it works quite well if it's just for aesthetics, just 00:53:26.940 --> 00:53:28.840 align:middle line:90% to get it perfectly colorless. 00:53:28.840 --> 00:53:31.980 align:middle line:90% That's what you would do. 00:53:31.980 --> 00:53:34.340 align:middle line:84% This is one case you may not want the color. 00:53:34.340 --> 00:53:35.880 align:middle line:84% When you actually want the color, 00:53:35.880 --> 00:53:37.740 align:middle line:84% these are some examples where you can get 00:53:37.740 --> 00:53:39.300 align:middle line:90% all kinds of colorings there. 00:53:39.300 --> 00:53:43.580 align:middle line:84% Cobalt blue, this is a very well-known glass formulation 00:53:43.580 --> 00:53:45.020 align:middle line:90% to get blue colors. 00:53:45.020 --> 00:53:48.540 align:middle line:84% Chromium, again gives you this very highly saturated 00:53:48.540 --> 00:53:49.540 align:middle line:90% green color. 00:53:49.540 --> 00:53:53.420 align:middle line:84% Manganese, it's called amethyst, manganese amethyst, basically 00:53:53.420 --> 00:53:54.460 align:middle line:90% a purple color. 00:53:54.460 --> 00:53:58.020 align:middle line:84% Now this last example here, uranium. 00:53:58.020 --> 00:54:03.140 align:middle line:84% Uranium doping gives you this kind of a light yellowish color 00:54:03.140 --> 00:54:04.900 align:middle line:90% that looks similar to Vaseline. 00:54:04.900 --> 00:54:07.060 align:middle line:84% That's why they also call it Vaseline glass. 00:54:07.060 --> 00:54:09.518 align:middle line:84% They are also unique in that if you expose them 00:54:09.518 --> 00:54:12.060 align:middle line:84% to sunlight for some time and then you move them and actually 00:54:12.060 --> 00:54:16.800 align:middle line:84% illuminate them with UV, you just directly 00:54:16.800 --> 00:54:20.400 align:middle line:84% illuminate with UV, in a dark room, they're going to glow. 00:54:20.400 --> 00:54:23.530 align:middle line:84% You get this very nice green fluorescence. 00:54:23.530 --> 00:54:26.800 align:middle line:90% 00:54:26.800 --> 00:54:30.110 align:middle line:84% Now, these uranium glasses, they're actually pretty popular 00:54:30.110 --> 00:54:32.330 align:middle line:84% starting from 19th century for quite a while, 00:54:32.330 --> 00:54:33.590 align:middle line:90% for several decades. 00:54:33.590 --> 00:54:38.190 align:middle line:84% And then starting in late 1930s, they basically disappeared from 00:54:38.190 --> 00:54:39.710 align:middle line:90% commercial markets. 00:54:39.710 --> 00:54:40.817 align:middle line:90% You want to guess why? 00:54:40.817 --> 00:54:41.650 align:middle line:90% AUDIENCE: Radiation. 00:54:41.650 --> 00:54:43.590 align:middle line:84% AUDIENCE: Because they're made of uranium. 00:54:43.590 --> 00:54:47.167 align:middle line:90% 00:54:47.167 --> 00:54:48.750 align:middle line:84% JUEJUN HU: Sorry, what was that again? 00:54:48.750 --> 00:54:49.583 align:middle line:90% AUDIENCE: Radiation. 00:54:49.583 --> 00:54:51.403 align:middle line:90% JUEJUN HU: Radiation, OK. 00:54:51.403 --> 00:54:52.910 align:middle line:90% Sort of. 00:54:52.910 --> 00:54:55.570 align:middle line:84% Turns out the uranium contained in these glasses is pretty low. 00:54:55.570 --> 00:54:57.630 align:middle line:90% It's at most, a couple percent. 00:54:57.630 --> 00:55:00.508 align:middle line:84% So it's not really that much of a health hazard. 00:55:00.508 --> 00:55:02.050 align:middle line:84% The radiation is actually pretty low. 00:55:02.050 --> 00:55:03.270 align:middle line:84% You can detect the radiation if you 00:55:03.270 --> 00:55:04.950 align:middle line:84% have a high-sensitivity Geiger counter, 00:55:04.950 --> 00:55:06.830 align:middle line:84% but it doesn't really cause a lot of harm 00:55:06.830 --> 00:55:09.750 align:middle line:84% unless you sleep with it and stay with it all the time. 00:55:09.750 --> 00:55:14.096 align:middle line:84% So they are, in general, considered safe. 00:55:14.096 --> 00:55:16.310 align:middle line:84% The reason they disappear from commercial market is 00:55:16.310 --> 00:55:19.420 align:middle line:84% because towards the end of 1930s, you have what? 00:55:19.420 --> 00:55:21.320 align:middle line:90% Manhattan Project. 00:55:21.320 --> 00:55:23.220 align:middle line:84% So the government essentially confiscated. 00:55:23.220 --> 00:55:26.000 align:middle line:84% They essentially have a monopoly on all uranium supplies 00:55:26.000 --> 00:55:29.740 align:middle line:84% because they want to make atomic bombs. 00:55:29.740 --> 00:55:30.820 align:middle line:90% So in fact, that's why. 00:55:30.820 --> 00:55:32.920 align:middle line:90% AUDIENCE: For the bombs! 00:55:32.920 --> 00:55:36.520 align:middle line:84% JUEJUN HU: We want these glasses, not bombs. 00:55:36.520 --> 00:55:39.832 align:middle line:84% In the 1950s after the Second World War, 00:55:39.832 --> 00:55:42.040 align:middle line:84% there was actually a short period where they actually 00:55:42.040 --> 00:55:44.118 align:middle line:84% restored the supply of uranium glasses. 00:55:44.118 --> 00:55:46.660 align:middle line:84% But it quickly, again disappears because the Cold War begins. 00:55:46.660 --> 00:55:50.280 align:middle line:84% And then again, they want to make more bombs. 00:55:50.280 --> 00:55:52.320 align:middle line:84% So if you ever get a chance to get 00:55:52.320 --> 00:55:55.960 align:middle line:84% your hands on one of these Vaseline glass, keep it. 00:55:55.960 --> 00:55:57.840 align:middle line:84% They tend to be quite pricey because there 00:55:57.840 --> 00:55:59.500 align:middle line:90% is no stable supply nowadays. 00:55:59.500 --> 00:56:02.560 align:middle line:90% 00:56:02.560 --> 00:56:06.460 align:middle line:84% AUDIENCE: What if we contact course 22? 00:56:06.460 --> 00:56:09.360 align:middle line:90% 00:56:09.360 --> 00:56:11.200 align:middle line:90% JUEJUN HU: Ask them for uranium? 00:56:11.200 --> 00:56:14.480 align:middle line:90% Good idea. 00:56:14.480 --> 00:56:20.980 align:middle line:84% AUDIENCE: Course 22 in glass lab to make and sell. 00:56:20.980 --> 00:56:23.100 align:middle line:84% JUEJUN HU: You need to convince MIT EHS 00:56:23.100 --> 00:56:26.080 align:middle line:84% that you are playing around with the uranium in the glass lab. 00:56:26.080 --> 00:56:28.580 align:middle line:84% You're not doing something that's more dangerous than that. 00:56:28.580 --> 00:56:31.520 align:middle line:84% AUDIENCE: So once the uranium's in the glass, 00:56:31.520 --> 00:56:33.460 align:middle line:90% it's stable in there? 00:56:33.460 --> 00:56:34.820 align:middle line:90% JUEJUN HU: 23, obviously. 00:56:34.820 --> 00:56:36.760 align:middle line:90% This is going to be like, yeah. 00:56:36.760 --> 00:56:44.740 align:middle line:84% It contains a little isotope of 354, obviously. 00:56:44.740 --> 00:56:46.160 align:middle line:90% You don't need a lot of uranium. 00:56:46.160 --> 00:56:47.760 align:middle line:84% Just a little bit uranium, like 1%, 00:56:47.760 --> 00:56:50.487 align:middle line:84% a couple percent will bring you this very nice. 00:56:50.487 --> 00:56:51.320 align:middle line:90% That's all you need. 00:56:51.320 --> 00:56:51.920 align:middle line:90% That's all you need. 00:56:51.920 --> 00:56:52.600 align:middle line:90% Not a lot. 00:56:52.600 --> 00:56:55.550 align:middle line:90% You don't want a lot anyway. 00:56:55.550 --> 00:56:56.590 align:middle line:90% AUDIENCE: The cup. 00:56:56.590 --> 00:56:57.840 align:middle line:90% JUEJUN HU: Oh, right, the cup. 00:56:57.840 --> 00:56:58.860 align:middle line:90% You've seen that before. 00:56:58.860 --> 00:56:59.600 align:middle line:90% Well, scattering. 00:56:59.600 --> 00:57:01.600 align:middle line:84% This is the second mechanism to introduce color. 00:57:01.600 --> 00:57:03.183 align:middle line:84% There, we are looking into essentially 00:57:03.183 --> 00:57:06.912 align:middle line:90% wavelength-dependent scattering. 00:57:06.912 --> 00:57:09.070 align:middle line:84% There are two kinds of scattering mechanisms. 00:57:09.070 --> 00:57:10.820 align:middle line:84% You can just introduce a scattering simply 00:57:10.820 --> 00:57:13.318 align:middle line:90% by putting in some nanocrystals. 00:57:13.318 --> 00:57:14.860 align:middle line:84% And that kind of scattering basically 00:57:14.860 --> 00:57:16.030 align:middle line:90% is Rayleigh scattering. 00:57:16.030 --> 00:57:18.310 align:middle line:84% Rayleigh scattering tends to be pretty featureless. 00:57:18.310 --> 00:57:22.510 align:middle line:84% We said that scattering intensity scales with wavelength 00:57:22.510 --> 00:57:24.150 align:middle line:90% to the negative 4th power. 00:57:24.150 --> 00:57:27.990 align:middle line:84% So it monotonically decreases as you go to longer wavelength. 00:57:27.990 --> 00:57:31.870 align:middle line:84% So for those glass materials that 00:57:31.870 --> 00:57:34.910 align:middle line:84% contains just a simple dielectric scattering centers 00:57:34.910 --> 00:57:40.190 align:middle line:84% like nanocrystals, they tend to be so-called opalescent. 00:57:40.190 --> 00:57:43.090 align:middle line:84% An opalescent glass has this kind of unique behavior here. 00:57:43.090 --> 00:57:45.010 align:middle line:90% This is what's shown here. 00:57:45.010 --> 00:57:46.670 align:middle line:84% Basically, what it's doing here, you 00:57:46.670 --> 00:57:48.330 align:middle line:84% have a piece of opalescent glass. 00:57:48.330 --> 00:57:51.430 align:middle line:84% You put it on the edge of this white paper. 00:57:51.430 --> 00:57:53.670 align:middle line:84% You notice the different colors on two sides. 00:57:53.670 --> 00:57:55.505 align:middle line:84% On this side where there's essentially 00:57:55.505 --> 00:57:57.630 align:middle line:84% nothing at the bottom, it's just a dark background, 00:57:57.630 --> 00:58:00.875 align:middle line:84% the color you're seeing here kind of scatters light. 00:58:00.875 --> 00:58:02.750 align:middle line:84% Those are the essentially backscattered light 00:58:02.750 --> 00:58:04.230 align:middle line:90% due to the nanocrystals. 00:58:04.230 --> 00:58:05.890 align:middle line:84% And for those backscattered light, 00:58:05.890 --> 00:58:08.330 align:middle line:84% you get more stronger scattering at shorter wavelength. 00:58:08.330 --> 00:58:09.890 align:middle line:90% And that's why it appears blue. 00:58:09.890 --> 00:58:13.550 align:middle line:84% Same mechanism as why the sky is blue. 00:58:13.550 --> 00:58:17.240 align:middle line:84% On the other hand, if you look at the transmitted color, 00:58:17.240 --> 00:58:19.220 align:middle line:84% you can see the transmitted light spot here. 00:58:19.220 --> 00:58:21.960 align:middle line:90% It has this very intense amber. 00:58:21.960 --> 00:58:24.760 align:middle line:84% It has this amber color because all 00:58:24.760 --> 00:58:28.340 align:middle line:84% the short wavelength component preferentially gets scattered. 00:58:28.340 --> 00:58:31.017 align:middle line:84% So what's left behind is this long wavelength component. 00:58:31.017 --> 00:58:32.600 align:middle line:84% That's why it appears orange or amber. 00:58:32.600 --> 00:58:35.760 align:middle line:90% 00:58:35.760 --> 00:58:38.560 align:middle line:84% Now if you look at it against the background here, 00:58:38.560 --> 00:58:44.440 align:middle line:84% it looks yellowish because this white background reflects 00:58:44.440 --> 00:58:47.220 align:middle line:84% most of the transmitted orange light. 00:58:47.220 --> 00:58:50.400 align:middle line:84% There's also a little bit of a blue scatter 00:58:50.400 --> 00:58:52.615 align:middle line:84% light, but not completely because the blue scatter 00:58:52.615 --> 00:58:54.740 align:middle line:84% light essentially gets scattered in all directions. 00:58:54.740 --> 00:58:56.920 align:middle line:84% So only some of that essentially comes back. 00:58:56.920 --> 00:58:59.560 align:middle line:84% So you get a much stronger component of amber 00:58:59.560 --> 00:59:02.000 align:middle line:84% with a minor component of blue, which is 00:59:02.000 --> 00:59:04.440 align:middle line:90% what gives you a yellow here. 00:59:04.440 --> 00:59:07.280 align:middle line:84% So this is also quite a common characteristic 00:59:07.280 --> 00:59:09.020 align:middle line:84% for color formation through scattering. 00:59:09.020 --> 00:59:11.395 align:middle line:84% If you look at it through different kinds of illumination 00:59:11.395 --> 00:59:13.180 align:middle line:84% modes at different angles, you tend 00:59:13.180 --> 00:59:15.120 align:middle line:84% to get different color, basically, 00:59:15.120 --> 00:59:18.380 align:middle line:84% because of this kind of a unique attribute of scattering there. 00:59:18.380 --> 00:59:21.900 align:middle line:84% Now, that's for opalescent glass. 00:59:21.900 --> 00:59:26.120 align:middle line:84% Downside about opalescent glass is that because again, 00:59:26.120 --> 00:59:28.620 align:middle line:84% Rayleigh scattering is just depend on lambda to negative 4th 00:59:28.620 --> 00:59:28.880 align:middle line:90% power. 00:59:28.880 --> 00:59:30.422 align:middle line:84% There's not much you can do about it. 00:59:30.422 --> 00:59:33.500 align:middle line:84% So you really cannot very actively try to change it 00:59:33.500 --> 00:59:35.032 align:middle line:90% to generate different colors. 00:59:35.032 --> 00:59:36.740 align:middle line:84% If you want to generate different colors, 00:59:36.740 --> 00:59:38.760 align:middle line:84% you want to introduce scattering mechanisms, 00:59:38.760 --> 00:59:41.180 align:middle line:84% they are a lot more sensitive to wavelength. 00:59:41.180 --> 00:59:45.300 align:middle line:84% So that's why people are using metal nanoparticles, 00:59:45.300 --> 00:59:48.240 align:middle line:84% because they support so-called a plasmon resonance. 00:59:48.240 --> 00:59:50.560 align:middle line:84% I assume you have learned a little bit of that in 3033. 00:59:50.560 --> 00:59:51.820 align:middle line:84% You probably did the experiment trying 00:59:51.820 --> 00:59:53.560 align:middle line:84% to measure metal nanoparticle solutions. 00:59:53.560 --> 00:59:56.060 align:middle line:84% Is that the experiment still there? 00:59:56.060 --> 00:59:57.560 align:middle line:90% No? 00:59:57.560 --> 00:59:58.727 align:middle line:90% It used to be there. 00:59:58.727 --> 01:00:01.060 align:middle line:84% You have to measure essentially like colloidal solutions 01:00:01.060 --> 01:00:02.640 align:middle line:90% of metallic nanoparticles. 01:00:02.640 --> 01:00:04.520 align:middle line:84% They do have this kind of very intense color. 01:00:04.520 --> 01:00:05.020 align:middle line:90% Yes? 01:00:05.020 --> 01:00:06.770 align:middle line:84% AUDIENCE: Maybe, but it hasn't been since. 01:00:06.770 --> 01:00:07.603 align:middle line:90% JUEJUN HU: Whatever. 01:00:07.603 --> 01:00:09.060 align:middle line:90% AUDIENCE: We talked about it. 01:00:09.060 --> 01:00:10.518 align:middle line:84% JUEJUN HU: Bottom line, if you have 01:00:10.518 --> 01:00:14.070 align:middle line:84% little metallic nanoparticles, you have lots of free electrons, 01:00:14.070 --> 01:00:16.040 align:middle line:84% radiation comes in, electromagnetic field 01:00:16.040 --> 01:00:17.790 align:middle line:84% is going to drive the electron oscillation 01:00:17.790 --> 01:00:19.590 align:middle line:90% in the metallic nanoparticles. 01:00:19.590 --> 01:00:24.830 align:middle line:84% So as a result, you separate the center 01:00:24.830 --> 01:00:27.602 align:middle line:84% of mass between the positive and negative charges. 01:00:27.602 --> 01:00:29.310 align:middle line:84% And this kind of oscillation can actually 01:00:29.310 --> 01:00:34.470 align:middle line:84% be amplified if the size of the nanoparticle and the wavelength 01:00:34.470 --> 01:00:38.030 align:middle line:84% of the incident radiation has some specific values. 01:00:38.030 --> 01:00:43.620 align:middle line:84% That's called a local surface plasmonic resonance, LSPR. 01:00:43.620 --> 01:00:46.310 align:middle line:90% LSPR. 01:00:46.310 --> 01:00:51.190 align:middle line:84% Bottom line, because it's a resonance, 01:00:51.190 --> 01:00:54.590 align:middle line:84% it means that this kind of scattering 01:00:54.590 --> 01:00:59.650 align:middle line:84% is enhanced at one particular wavelength. 01:00:59.650 --> 01:01:02.150 align:middle line:84% And you can tune that resonance wavelength 01:01:02.150 --> 01:01:04.650 align:middle line:84% by changing the composition of metal nanoparticle, 01:01:04.650 --> 01:01:06.470 align:middle line:84% change the size, change the shape. 01:01:06.470 --> 01:01:07.910 align:middle line:84% So there are lots of knobs you can 01:01:07.910 --> 01:01:11.320 align:middle line:84% use to essentially tune the wavelength-dependent scattering 01:01:11.320 --> 01:01:13.000 align:middle line:90% behavior. 01:01:13.000 --> 01:01:16.220 align:middle line:84% And this is a lot more useful for coloring of glass materials, 01:01:16.220 --> 01:01:19.160 align:middle line:84% because now, as I said, you have many, many additional knobs 01:01:19.160 --> 01:01:21.895 align:middle line:84% that you can use to engineer color. 01:01:21.895 --> 01:01:23.520 align:middle line:84% This is also something that people have 01:01:23.520 --> 01:01:26.865 align:middle line:90% known for thousands of years. 01:01:26.865 --> 01:01:28.240 align:middle line:84% As I said, you probably have seen 01:01:28.240 --> 01:01:29.740 align:middle line:90% this picture many, many times. 01:01:29.740 --> 01:01:33.040 align:middle line:84% This is one example, people like to cite 01:01:33.040 --> 01:01:35.540 align:middle line:84% to prove that people are already using nanotechnology, 01:01:35.540 --> 01:01:38.200 align:middle line:84% despite that they have no idea what nanotechnology is. 01:01:38.200 --> 01:01:41.200 align:middle line:84% This is from ancient Roman times, Lycurgus cup. 01:01:41.200 --> 01:01:43.200 align:middle line:84% They have this kind of unique color because 01:01:43.200 --> 01:01:44.740 align:middle line:90% of metallic nanoparticles. 01:01:44.740 --> 01:01:46.680 align:middle line:84% And you also see that the color actually 01:01:46.680 --> 01:01:48.080 align:middle line:90% depends on illumination. 01:01:48.080 --> 01:01:49.800 align:middle line:84% So if you look at it from the outside, 01:01:49.800 --> 01:01:51.717 align:middle line:84% you're looking at essentially scattered light. 01:01:51.717 --> 01:01:53.085 align:middle line:90% That's why it appears green. 01:01:53.085 --> 01:01:55.460 align:middle line:84% But if you have essentially a light source put it inside, 01:01:55.460 --> 01:01:59.880 align:middle line:84% you look at the transmitted color, it becomes pink and red. 01:01:59.880 --> 01:02:01.900 align:middle line:84% Because again you see the complementary color. 01:02:01.900 --> 01:02:03.608 align:middle line:84% The scattered color mostly gets diverted. 01:02:03.608 --> 01:02:06.140 align:middle line:84% You're looking at only the light that's less scattered. 01:02:06.140 --> 01:02:09.400 align:middle line:84% That's why you have different colors there. 01:02:09.400 --> 01:02:15.180 align:middle line:84% But even until today, addition of metallic nanoparticles 01:02:15.180 --> 01:02:18.380 align:middle line:84% is still a very prevalent technique for people 01:02:18.380 --> 01:02:20.340 align:middle line:84% to generate color in glass materials. 01:02:20.340 --> 01:02:24.180 align:middle line:84% In fact, the process they tend to use 01:02:24.180 --> 01:02:27.300 align:middle line:84% is called the striking color or color striking. 01:02:27.300 --> 01:02:29.820 align:middle line:84% It's just a terminology that you use 01:02:29.820 --> 01:02:32.530 align:middle line:84% to describe a group of glasses where 01:02:32.530 --> 01:02:34.780 align:middle line:84% you have to heat them up, go through some kind of heat 01:02:34.780 --> 01:02:37.720 align:middle line:84% treatment to generate, to reveal the real color. 01:02:37.720 --> 01:02:43.920 align:middle line:90% 01:02:43.920 --> 01:02:46.580 align:middle line:84% So the specific chemistry and the recipe 01:02:46.580 --> 01:02:51.100 align:middle line:84% that people use for color striking usually is proprietary. 01:02:51.100 --> 01:02:53.500 align:middle line:84% You can buy different kind of striking colors 01:02:53.500 --> 01:02:55.840 align:middle line:84% from online catalogs like glass vendors, 01:02:55.840 --> 01:02:58.203 align:middle line:84% but they will not tell you how they actually make it. 01:02:58.203 --> 01:02:59.620 align:middle line:84% And of course, you don't know what 01:02:59.620 --> 01:03:02.118 align:middle line:90% the underlying mechanism is. 01:03:02.118 --> 01:03:04.660 align:middle line:84% A few ones that people know very well, for example, this one, 01:03:04.660 --> 01:03:06.053 align:middle line:90% gold-ruby striking. 01:03:06.053 --> 01:03:07.470 align:middle line:84% This is a standard one that people 01:03:07.470 --> 01:03:08.710 align:middle line:84% want to use to essentially generate 01:03:08.710 --> 01:03:11.130 align:middle line:84% this kind of very intense, highly saturated red color. 01:03:11.130 --> 01:03:15.950 align:middle line:84% The mechanism behind it is in the untreated glass. 01:03:15.950 --> 01:03:20.590 align:middle line:84% So in unannealed glass, gold exists in the form of ion. 01:03:20.590 --> 01:03:22.310 align:middle line:84% If it exists in the form of gold ion, 01:03:22.310 --> 01:03:24.710 align:middle line:84% then it's perfectly transparent, so it's colorless. 01:03:24.710 --> 01:03:28.110 align:middle line:84% But if you heat it up, you anneal it, 01:03:28.110 --> 01:03:30.590 align:middle line:84% then you actually reduce this gold ion 01:03:30.590 --> 01:03:32.450 align:middle line:90% into gold nanoparticles. 01:03:32.450 --> 01:03:34.270 align:middle line:84% They start to essentially precipitate out 01:03:34.270 --> 01:03:36.528 align:middle line:90% from the glass matrix. 01:03:36.528 --> 01:03:38.070 align:middle line:84% And then it goes through this process 01:03:38.070 --> 01:03:40.110 align:middle line:90% of nucleation and growth. 01:03:40.110 --> 01:03:42.730 align:middle line:84% So by controlling the annealing temperature and duration, 01:03:42.730 --> 01:03:44.390 align:middle line:84% you can basically control the size 01:03:44.390 --> 01:03:46.070 align:middle line:90% of these metallic nanoparticles. 01:03:46.070 --> 01:03:48.830 align:middle line:84% It's classical kinetics, nucleation growth, 01:03:48.830 --> 01:03:50.090 align:middle line:90% Ostwald ripening. 01:03:50.090 --> 01:03:53.710 align:middle line:84% That's what all takes place during this firing process. 01:03:53.710 --> 01:03:56.550 align:middle line:84% But then gold nanoparticles, they 01:03:56.550 --> 01:04:00.950 align:middle line:84% can generate this kind of very intense red color after firing. 01:04:00.950 --> 01:04:05.380 align:middle line:84% So that's how you actually get a striking color in this case. 01:04:05.380 --> 01:04:10.168 align:middle line:90% 01:04:10.168 --> 01:04:11.960 align:middle line:84% Again, as I said, there are many other kind 01:04:11.960 --> 01:04:13.180 align:middle line:90% of striking color examples. 01:04:13.180 --> 01:04:15.520 align:middle line:84% You can actually buy them from online catalog. 01:04:15.520 --> 01:04:18.040 align:middle line:84% If you burn it with a butane torch, which 01:04:18.040 --> 01:04:19.760 align:middle line:84% I have done at home, you can actually 01:04:19.760 --> 01:04:21.880 align:middle line:84% generate different kinds of colors. 01:04:21.880 --> 01:04:22.980 align:middle line:90% Interesting exercise. 01:04:22.980 --> 01:04:25.920 align:middle line:90% 01:04:25.920 --> 01:04:29.412 align:middle line:84% So up to this point, we have been talking about static color. 01:04:29.412 --> 01:04:31.120 align:middle line:84% If you generate one color, it's basically 01:04:31.120 --> 01:04:34.080 align:middle line:84% fixed for the lifetime of the glass material. 01:04:34.080 --> 01:04:36.320 align:middle line:84% You can also control dynamic color generation 01:04:36.320 --> 01:04:39.160 align:middle line:84% through so-called photochromic or electrochromic glasses. 01:04:39.160 --> 01:04:41.415 align:middle line:84% So essentially, photochromic, it means 01:04:41.415 --> 01:04:44.040 align:middle line:84% that if you illuminate the glass material with light, typically 01:04:44.040 --> 01:04:45.900 align:middle line:84% UV, they can actually change the color. 01:04:45.900 --> 01:04:47.400 align:middle line:84% Same thing, electrochromic, it means 01:04:47.400 --> 01:04:49.067 align:middle line:84% that you actually apply electric voltage 01:04:49.067 --> 01:04:50.220 align:middle line:90% across the glass material. 01:04:50.220 --> 01:04:54.200 align:middle line:84% You can actually change the color appearance. 01:04:54.200 --> 01:04:59.400 align:middle line:84% For photochromic, the chemistry can be pretty simple. 01:04:59.400 --> 01:05:02.740 align:middle line:84% Usually, most commonly, what people 01:05:02.740 --> 01:05:06.460 align:middle line:84% do is they add a silver chloride into glass materials 01:05:06.460 --> 01:05:08.020 align:middle line:90% during the batching process. 01:05:08.020 --> 01:05:13.000 align:middle line:84% Now, silver chloride, normally is basically silver ion. 01:05:13.000 --> 01:05:15.700 align:middle line:90% 01:05:15.700 --> 01:05:22.700 align:middle line:84% But under UV illumination, they can 01:05:22.700 --> 01:05:28.100 align:middle line:84% transform into silver nanoparticles, 01:05:28.100 --> 01:05:30.900 align:middle line:90% which then generates color. 01:05:30.900 --> 01:05:34.100 align:middle line:84% There are commercial products you can buy, 01:05:34.100 --> 01:05:37.313 align:middle line:84% those kind of sunglasses, they're sensitive to sunlight. 01:05:37.313 --> 01:05:39.480 align:middle line:84% Essentially, when you generate silver nanoparticles, 01:05:39.480 --> 01:05:43.180 align:middle line:84% they start to absorb sunlight and reduce the transparency 01:05:43.180 --> 01:05:44.120 align:middle line:90% of the material. 01:05:44.120 --> 01:05:46.900 align:middle line:90% So that's one way of doing it. 01:05:46.900 --> 01:05:48.620 align:middle line:84% If you are not using it in organic glass 01:05:48.620 --> 01:05:52.280 align:middle line:84% as a matrix, a lot of those kind of color-changing sunglasses, 01:05:52.280 --> 01:05:53.800 align:middle line:84% they are now made of polycarbonate, 01:05:53.800 --> 01:05:55.020 align:middle line:90% which is basically a polymer. 01:05:55.020 --> 01:05:58.620 align:middle line:84% In that case, they use actually photosensitive organic molecule 01:05:58.620 --> 01:06:00.170 align:middle line:84% to introduce similar transitions. 01:06:00.170 --> 01:06:03.310 align:middle line:84% So it's not silver anymore, but mechanism is similar. 01:06:03.310 --> 01:06:05.630 align:middle line:84% So both are still being used depending 01:06:05.630 --> 01:06:07.710 align:middle line:90% on which vendor you go to. 01:06:07.710 --> 01:06:11.350 align:middle line:84% But that's a photochromic color generation mechanism. 01:06:11.350 --> 01:06:16.230 align:middle line:84% For electrochromic, you probably have seen those kind of windows 01:06:16.230 --> 01:06:20.070 align:middle line:84% if you sit in a Boeing 787 Dreamliner, 01:06:20.070 --> 01:06:21.650 align:middle line:84% instead of having the window shades, 01:06:21.650 --> 01:06:23.483 align:middle line:84% you have a little button underneath it where 01:06:23.483 --> 01:06:25.510 align:middle line:84% you can press and change the transparency. 01:06:25.510 --> 01:06:27.550 align:middle line:84% That's basically electrochromic glasses. 01:06:27.550 --> 01:06:29.910 align:middle line:84% Again, there are multiple mechanisms 01:06:29.910 --> 01:06:32.350 align:middle line:90% of electrochromic glasses. 01:06:32.350 --> 01:06:35.990 align:middle line:84% What they are using specifically for the Dreamliner, 01:06:35.990 --> 01:06:38.890 align:middle line:84% they actually use an organic molecule. 01:06:38.890 --> 01:06:43.190 align:middle line:84% By essentially oxidizing it and reducing it, essentially 01:06:43.190 --> 01:06:45.470 align:middle line:84% pumping ions into it, you can actually 01:06:45.470 --> 01:06:47.110 align:middle line:84% change the transparency of the material 01:06:47.110 --> 01:06:50.210 align:middle line:84% and therefore change the color basically. 01:06:50.210 --> 01:06:53.375 align:middle line:90% 01:06:53.375 --> 01:06:55.190 align:middle line:84% So that's one example how you can actually 01:06:55.190 --> 01:06:58.720 align:middle line:84% introduce color change in glass materials. 01:06:58.720 --> 01:07:00.300 align:middle line:84% I will show you another example here. 01:07:00.300 --> 01:07:05.480 align:middle line:84% For this example, it's entirely inorganic components. 01:07:05.480 --> 01:07:08.348 align:middle line:84% And what they have demonstrated in this study 01:07:08.348 --> 01:07:10.640 align:middle line:84% is that they were able to generate not just two states, 01:07:10.640 --> 01:07:12.182 align:middle line:84% like opaque transmissive states, they 01:07:12.182 --> 01:07:14.760 align:middle line:84% were able to actually generate three different states 01:07:14.760 --> 01:07:16.460 align:middle line:90% to give more functionalities. 01:07:16.460 --> 01:07:20.560 align:middle line:84% So in the component, the glass consists 01:07:20.560 --> 01:07:23.560 align:middle line:84% of basically two transparent electrodes, sandwiched 01:07:23.560 --> 01:07:26.480 align:middle line:84% in between them, there's electrolytes 01:07:26.480 --> 01:07:29.640 align:middle line:84% with an ion reservoir that contains a lot of lithium ion. 01:07:29.640 --> 01:07:33.320 align:middle line:84% And the glass also contains niobium oxide 01:07:33.320 --> 01:07:35.880 align:middle line:90% as one of the matrix materials. 01:07:35.880 --> 01:07:38.440 align:middle line:84% So when you start to apply a bias across these two 01:07:38.440 --> 01:07:46.180 align:middle line:84% electrolytes, initially, you generate lots of free electrons. 01:07:46.180 --> 01:07:50.640 align:middle line:84% You inject lots of free electrons into the nanocrystals. 01:07:50.640 --> 01:07:53.600 align:middle line:84% So once you put a lot of free electrons into the crystals, 01:07:53.600 --> 01:07:57.540 align:middle line:84% you then start introducing free carrier absorption. 01:07:57.540 --> 01:08:01.140 align:middle line:84% And for free carrier absorption, its absorption coefficient 01:08:01.140 --> 01:08:04.020 align:middle line:84% increases as you go to a longer wavelength. 01:08:04.020 --> 01:08:06.518 align:middle line:84% So it means that in this particular state, initially, 01:08:06.518 --> 01:08:09.060 align:middle line:84% when there is no voltage, it's basically a transparent glass. 01:08:09.060 --> 01:08:11.340 align:middle line:84% It allows all the radiation to get through. 01:08:11.340 --> 01:08:14.660 align:middle line:84% But then when you go to this electron-injected state, 01:08:14.660 --> 01:08:17.180 align:middle line:84% because of the presence of free carrier absorption, 01:08:17.180 --> 01:08:21.300 align:middle line:84% the longer wavelength components get preferentially absorbed. 01:08:21.300 --> 01:08:23.540 align:middle line:84% So it means that the infrared radiation 01:08:23.540 --> 01:08:28.260 align:middle line:84% tends to get absorbed versus the visible part of the spectrum. 01:08:28.260 --> 01:08:31.040 align:middle line:84% So in this mode here, this is what they call cool mode. 01:08:31.040 --> 01:08:33.859 align:middle line:84% This is what you may want to use, for example, during daytime 01:08:33.859 --> 01:08:34.899 align:middle line:90% in the summer day. 01:08:34.899 --> 01:08:37.779 align:middle line:84% You still want the visible light to transmit through 01:08:37.779 --> 01:08:39.122 align:middle line:90% for illumination. 01:08:39.122 --> 01:08:40.580 align:middle line:84% But for the infrared radiation, you 01:08:40.580 --> 01:08:43.180 align:middle line:84% want to reject it to keep the room cool. 01:08:43.180 --> 01:08:44.720 align:middle line:90% So this is what you use here. 01:08:44.720 --> 01:08:46.675 align:middle line:84% This is still a visibly transparent state, 01:08:46.675 --> 01:08:48.300 align:middle line:84% but free carrier absorption selectively 01:08:48.300 --> 01:08:50.460 align:middle line:90% absorb infrared radiation. 01:08:50.460 --> 01:08:53.939 align:middle line:84% Finally, if you continue to increase the voltage, 01:08:53.939 --> 01:08:56.870 align:middle line:84% then you lead to the motion of the lithium ions here. 01:08:56.870 --> 01:09:00.189 align:middle line:84% And then this actually changes the structure 01:09:00.189 --> 01:09:01.370 align:middle line:90% of the glass network. 01:09:01.370 --> 01:09:04.710 align:middle line:84% So through this kind of redox reaction, 01:09:04.710 --> 01:09:08.490 align:middle line:84% you form this kind of lithium niobium oxide crystals, 01:09:08.490 --> 01:09:10.777 align:middle line:90% which has a brown-gray color. 01:09:10.777 --> 01:09:13.069 align:middle line:84% So this then turns the color into essentially something 01:09:13.069 --> 01:09:13.950 align:middle line:90% opaque. 01:09:13.950 --> 01:09:15.950 align:middle line:84% So then this will allow you to block 01:09:15.950 --> 01:09:18.810 align:middle line:84% both infrared radiation and also the invisible radiation. 01:09:18.810 --> 01:09:20.750 align:middle line:84% So this is what they call the dark mode here. 01:09:20.750 --> 01:09:24.630 align:middle line:90% 01:09:24.630 --> 01:09:27.929 align:middle line:84% So this slide, this is actually a little photo showing 01:09:27.929 --> 01:09:30.310 align:middle line:90% the actual operation of glass. 01:09:30.310 --> 01:09:32.330 align:middle line:84% You can see that right-hand side here, 01:09:32.330 --> 01:09:34.687 align:middle line:84% this is actually where it's perfectly transparent. 01:09:34.687 --> 01:09:36.229 align:middle line:84% In the middle here, this is where you 01:09:36.229 --> 01:09:37.890 align:middle line:90% have this kind of a cool mode. 01:09:37.890 --> 01:09:39.930 align:middle line:84% You see a little bit of tint but not too much. 01:09:39.930 --> 01:09:41.450 align:middle line:84% Most of the visible light still gets through. 01:09:41.450 --> 01:09:44.075 align:middle line:84% And then right here, this is the cool mode where essentially it 01:09:44.075 --> 01:09:45.350 align:middle line:90% becomes a lot darker. 01:09:45.350 --> 01:09:47.774 align:middle line:84% So there are lots of interesting things you can do. 01:09:47.774 --> 01:09:49.149 align:middle line:84% This has been an area of research 01:09:49.149 --> 01:09:51.170 align:middle line:84% that people have been doing for a few decades, 01:09:51.170 --> 01:09:53.545 align:middle line:84% essentially looking at all kinds of different chemistries 01:09:53.545 --> 01:09:55.680 align:middle line:84% where you can modulate the optical properties 01:09:55.680 --> 01:09:56.900 align:middle line:90% of these glass materials. 01:09:56.900 --> 01:10:00.640 align:middle line:84% So I'm looking forward to hearing more from your course 01:10:00.640 --> 01:10:01.900 align:middle line:90% project about that. 01:10:01.900 --> 01:10:04.600 align:middle line:90% 01:10:04.600 --> 01:10:06.160 align:middle line:84% So now just to summarize what we've 01:10:06.160 --> 01:10:08.320 align:middle line:84% talked about here, bottom line, there 01:10:08.320 --> 01:10:10.040 align:middle line:84% are three important optical attributes 01:10:10.040 --> 01:10:13.600 align:middle line:84% we have discussed about-- refraction, loss or attenuation, 01:10:13.600 --> 01:10:14.840 align:middle line:90% and coloring. 01:10:14.840 --> 01:10:17.720 align:middle line:84% For refraction, you need to know what's 01:10:17.720 --> 01:10:21.920 align:middle line:84% the microscopic mechanism, electronic 01:10:21.920 --> 01:10:23.260 align:middle line:90% and atomic polarization. 01:10:23.260 --> 01:10:26.400 align:middle line:84% You need to understand the wavelength dependence 01:10:26.400 --> 01:10:30.120 align:middle line:84% of the refractive index due to the KK relation. 01:10:30.120 --> 01:10:33.640 align:middle line:84% And then for loss, we talk about four different loss mechanisms. 01:10:33.640 --> 01:10:37.600 align:middle line:84% And coloring essentially is just how you actually engineer 01:10:37.600 --> 01:10:40.520 align:middle line:84% the wavelength dependence of optical loss in glass materials 01:10:40.520 --> 01:10:43.040 align:middle line:84% in order to generate different colors. 01:10:43.040 --> 01:10:43.840 align:middle line:90% All right? 01:10:43.840 --> 01:10:46.680 align:middle line:84% Any more questions about this before we 01:10:46.680 --> 01:10:48.280 align:middle line:90% conclude this lecture here? 01:10:48.280 --> 01:10:50.900 align:middle line:84% In the next lecture, we're going to talk about the application 01:10:50.900 --> 01:10:51.360 align:middle line:90% side. 01:10:51.360 --> 01:10:52.735 align:middle line:84% We are going to discuss about how 01:10:52.735 --> 01:10:55.600 align:middle line:84% you can use glass materials as the optical fibers 01:10:55.600 --> 01:10:59.580 align:middle line:84% and waveguides to transmit light. 01:10:59.580 --> 01:11:00.240 align:middle line:90% All right. 01:11:00.240 --> 01:11:02.010 align:middle line:90% Thank you. 01:11:02.010 --> 01:11:50.000 align:middle line:90%