WEBVTT 00:00:00.090 --> 00:00:02.490 The following content is provided under a Creative 00:00:02.490 --> 00:00:04.030 Commons license. 00:00:04.030 --> 00:00:06.330 Your support will help MIT OpenCourseWare 00:00:06.330 --> 00:00:10.690 continue to offer high quality educational resources for free. 00:00:10.690 --> 00:00:13.320 To make a donation or view additional materials 00:00:13.320 --> 00:00:17.260 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.260 --> 00:00:18.450 at ocw.mit.edu. 00:00:21.120 --> 00:00:23.220 SHAOUL EZEKIEL: This next demonstration 00:00:23.220 --> 00:00:27.420 is about the laser line width or the spectral width of the laser 00:00:27.420 --> 00:00:29.110 radiation. 00:00:29.110 --> 00:00:33.720 Now theory predicts that the line width of a laser 00:00:33.720 --> 00:00:38.460 should be very, very narrow, much narrower then 00:00:38.460 --> 00:00:41.910 a fraction of a Hertz, in fact, of the order of 10 00:00:41.910 --> 00:00:46.440 to the minus 3, 10 to the minus 4 Hertz or even smaller. 00:00:46.440 --> 00:00:48.690 In practice, we don't see that. 00:00:48.690 --> 00:00:51.830 In practice, if you measure the laser line width, 00:00:51.830 --> 00:00:56.850 you find sometimes it's hundreds of kilohertz, megahertz, 00:00:56.850 --> 00:01:00.680 and even tens or hundreds of megahertz. 00:01:00.680 --> 00:01:03.030 So what is really going on here, then? 00:01:03.030 --> 00:01:08.000 What's the discrepancy between theory and practice? 00:01:08.000 --> 00:01:09.710 In order to explain what's going on, 00:01:09.710 --> 00:01:13.340 I'm going to review some fundamentals about lasers. 00:01:13.340 --> 00:01:18.170 Here is a laser, simple laser. 00:01:18.170 --> 00:01:21.860 It's made up of a helium neon discharge tube. 00:01:21.860 --> 00:01:25.310 And the discharge tube is terminated by two mirrors. 00:01:25.310 --> 00:01:28.220 And there's nothing else inside the cavity 00:01:28.220 --> 00:01:34.250 besides the discharge tube and the two mirrors. 00:01:34.250 --> 00:01:38.900 Now the cavity resonance associated with this length 00:01:38.900 --> 00:01:41.240 cavity, then, is certainly determined 00:01:41.240 --> 00:01:46.490 by the length of the cavity and the refractive index 00:01:46.490 --> 00:01:52.010 of the medium between the two mirrors 00:01:52.010 --> 00:01:54.770 so that if we have a cavity resonance 00:01:54.770 --> 00:02:01.430 within the bandwidth of the helium neon amplifier, then-- 00:02:01.430 --> 00:02:03.740 and then we have, of course, gain 00:02:03.740 --> 00:02:06.650 that's bigger than the losses in the cavity-- 00:02:06.650 --> 00:02:10.100 then we'll have oscillation at the cavity resonance. 00:02:10.100 --> 00:02:12.020 So then the frequency of the laser 00:02:12.020 --> 00:02:14.660 is determined by the cavity resonance 00:02:14.660 --> 00:02:19.680 that is within the bandwidth of the amplifier. 00:02:19.680 --> 00:02:23.720 So the frequency, then, will fluctuate 00:02:23.720 --> 00:02:31.160 if the optical length of the cavity will fluctuate due to, 00:02:31.160 --> 00:02:35.620 let's say, due to temperature, vibrations, 00:02:35.620 --> 00:02:38.200 fluctuations in the power supply, 00:02:38.200 --> 00:02:41.510 that changes the refractive index and so on. 00:02:41.510 --> 00:02:44.500 So in practice, then, the laser frequency 00:02:44.500 --> 00:02:46.120 will just move all over the place 00:02:46.120 --> 00:02:51.460 depending on the mechanical design of the laser. 00:02:54.310 --> 00:02:57.870 So that if you want to measure this line 00:02:57.870 --> 00:03:00.847 width, this practical line width of a laser, 00:03:00.847 --> 00:03:02.430 then you would take-- one way of doing 00:03:02.430 --> 00:03:05.880 it is to take two such lasers oscillating 00:03:05.880 --> 00:03:09.150 at a single frequency in each one of them. 00:03:09.150 --> 00:03:10.770 And then you beat them. 00:03:10.770 --> 00:03:15.030 And you look at the beat on an electronic spectrum analyzer. 00:03:15.030 --> 00:03:18.160 And you'll find that that beat is, 00:03:18.160 --> 00:03:20.670 as I mentioned before, can vary anywhere from hundreds 00:03:20.670 --> 00:03:24.930 of megahertz down to a few kilohertz depending, 00:03:24.930 --> 00:03:28.680 again, on the design of the laser. 00:03:28.680 --> 00:03:34.200 In order to measure or observe the intrinsic line width-- 00:03:34.200 --> 00:03:36.780 this is the line width that's predicted 00:03:36.780 --> 00:03:40.020 by Shallon Town many, many years ago, 00:03:40.020 --> 00:03:43.890 this line width is of the order of, as I said before, 00:03:43.890 --> 00:03:46.690 10 to the minus 3, 10 the minus 4 Hertz 00:03:46.690 --> 00:03:48.750 for a 1 milliwatt laser. 00:03:51.290 --> 00:03:54.800 This width is due to fundamental noise sources 00:03:54.800 --> 00:03:56.900 such as spontaneous emission. 00:03:56.900 --> 00:04:01.808 And it doesn't depend on any length of the cavity 00:04:01.808 --> 00:04:03.350 and the optical length of the cavity. 00:04:03.350 --> 00:04:06.070 Here, we assume that everything else is fixed. 00:04:06.070 --> 00:04:08.750 But only the spontaneous emission 00:04:08.750 --> 00:04:12.320 is giving us the residual line width. 00:04:12.320 --> 00:04:17.070 In order to measure this fundamental line width, 00:04:17.070 --> 00:04:23.000 it's very difficult to do it by using two lasers. 00:04:23.000 --> 00:04:26.630 Because it's very difficult to stabilize the length 00:04:26.630 --> 00:04:30.460 of the cavities in each laser. 00:04:30.460 --> 00:04:35.570 There are techniques using wide band feedback stabilization 00:04:35.570 --> 00:04:40.940 loops to reduce the vibrations and the drift of a laser 00:04:40.940 --> 00:04:41.720 cavity. 00:04:41.720 --> 00:04:44.900 But still, it still would be difficult to reach 00:04:44.900 --> 00:04:47.300 the fundamental line width. 00:04:47.300 --> 00:04:48.960 So in this demonstration, we're going 00:04:48.960 --> 00:04:53.660 to give you a feel for how small the laser line width can 00:04:53.660 --> 00:04:56.900 be using some simple concepts. 00:04:56.900 --> 00:05:00.050 Before I go on to describe what we're going to do, 00:05:00.050 --> 00:05:04.130 I'm going to show you what an ideal way of measuring 00:05:04.130 --> 00:05:07.280 or observing the laser line width is. 00:05:07.280 --> 00:05:16.097 Here is a ring cavity made up of three mirrors. 00:05:16.097 --> 00:05:18.180 Here's one mirror, another mirror, another mirror. 00:05:18.180 --> 00:05:20.520 It's a triangular cavity. 00:05:20.520 --> 00:05:21.780 Here's the cathode. 00:05:21.780 --> 00:05:26.290 And there are two anodes, one over here and one over here. 00:05:26.290 --> 00:05:29.010 So we have, say, helium neon discharged 00:05:29.010 --> 00:05:32.130 within the resonator. 00:05:32.130 --> 00:05:36.390 Because it's a ring, we're going to get two laser oscillations, 00:05:36.390 --> 00:05:40.290 one in the clockwise direction and the other one 00:05:40.290 --> 00:05:43.270 in the counterclockwise direction. 00:05:43.270 --> 00:05:47.720 If we take the two outputs and we beat them, 00:05:47.720 --> 00:05:54.800 then the beat frequency will give us essentially the sum 00:05:54.800 --> 00:06:00.740 of the two individual spectral widths of the two laser 00:06:00.740 --> 00:06:01.640 frequencies. 00:06:01.640 --> 00:06:04.830 Now, because the cavity is common to both 00:06:04.830 --> 00:06:07.130 and the refractive index variations 00:06:07.130 --> 00:06:09.500 are common to both frequencies, then 00:06:09.500 --> 00:06:12.320 this would give you probably about the best measurement 00:06:12.320 --> 00:06:15.950 of the true line width or the intrinsic line 00:06:15.950 --> 00:06:18.530 width of the laser. 00:06:18.530 --> 00:06:22.700 But that's not what we're going to demonstrate here. 00:06:22.700 --> 00:06:24.200 What we're going to use, we're going 00:06:24.200 --> 00:06:28.340 to use our simple laser here. 00:06:28.340 --> 00:06:33.620 And because of the length of this cavity, 00:06:33.620 --> 00:06:36.680 we get two modes, two cavity modes 00:06:36.680 --> 00:06:41.750 that are within the bandwidth of the helium neon amplifier. 00:06:41.750 --> 00:06:47.230 And since the cavity is common to both modes, 00:06:47.230 --> 00:06:51.680 except for the fact that they are separated by c over 2L 00:06:51.680 --> 00:06:54.920 where c is the velocity of light and an L is 00:06:54.920 --> 00:06:57.110 the optical length of the cavity, 00:06:57.110 --> 00:06:59.540 other than that, the fluctuations 00:06:59.540 --> 00:07:03.170 and the drift of the cavity should be common to both. 00:07:03.170 --> 00:07:07.520 So by then beating the two outputs associated 00:07:07.520 --> 00:07:13.640 with these two modes in this laser on an electronic spectrum 00:07:13.640 --> 00:07:17.195 analyzer, then the line width that we'll 00:07:17.195 --> 00:07:19.070 measure with the electronic spectrum analyzer 00:07:19.070 --> 00:07:25.160 will give us a measure of how narrow the spectral width 00:07:25.160 --> 00:07:28.060 of the individual laser is. 00:07:28.060 --> 00:07:31.230 The set up we're going to use is over here. 00:07:31.230 --> 00:07:36.200 Now, in this box I have a laser just like this. 00:07:36.200 --> 00:07:38.000 The reason why we use this box is 00:07:38.000 --> 00:07:42.732 to keep the environment at a constant temperature, 00:07:42.732 --> 00:07:44.690 or as close to constant temperature as possible 00:07:44.690 --> 00:07:49.730 and also to isolate against vibrations so that the laser 00:07:49.730 --> 00:07:52.250 cavity is not shaking too much. 00:07:52.250 --> 00:07:56.980 The output from the laser goes through a polarizer. 00:07:56.980 --> 00:08:05.140 Now, since this cavity is made up of internal mirrors-- 00:08:05.140 --> 00:08:07.290 there's nothing else between the two mirrors 00:08:07.290 --> 00:08:09.390 except for the discharge tube-- 00:08:09.390 --> 00:08:11.860 the two modes that will oscillate 00:08:11.860 --> 00:08:15.750 will have orthogonal polarization. 00:08:15.750 --> 00:08:18.900 So that by using a polarizer like this, 00:08:18.900 --> 00:08:23.640 I can select either frequency. 00:08:23.640 --> 00:08:26.730 Or, if I put it 45 degrees, I can 00:08:26.730 --> 00:08:31.560 select both laser frequencies. 00:08:31.560 --> 00:08:33.450 So after the polarizer, then, I reflect 00:08:33.450 --> 00:08:37.090 the light by this mirror, and then this mirror, 00:08:37.090 --> 00:08:41.162 onto an optical spectrum analyzer, 00:08:41.162 --> 00:08:43.120 which is a scanning Fabry-Perot interferometer. 00:08:43.120 --> 00:08:48.690 Now the length of this scanning Fabry-Perot is about 10 00:08:48.690 --> 00:08:53.160 centimeters, which means that the free spectral range is 00:08:53.160 --> 00:08:56.680 about 1 1/2 gigahertz. 00:08:56.680 --> 00:09:01.110 So now we are ready to look at the output of this spectrum 00:09:01.110 --> 00:09:05.010 analyzer on an oscilloscope over here. 00:09:05.010 --> 00:09:09.690 We see the output when we have the polarizer adjusted 00:09:09.690 --> 00:09:12.900 so that only one laser frequency is 00:09:12.900 --> 00:09:15.840 allowed to be observed by the scanning Fabry-Perot 00:09:15.840 --> 00:09:16.770 interferometer. 00:09:16.770 --> 00:09:20.100 What we're seeing is the free spectral range of the scanning 00:09:20.100 --> 00:09:23.550 Fabry-Perot, which is 1 1/2 gigahertz. 00:09:23.550 --> 00:09:29.250 So, as you can see, eight big boxes and corresponds to 1 1/2 00:09:29.250 --> 00:09:30.150 gigahertz. 00:09:30.150 --> 00:09:34.020 And the laser is oscillating at a single frequency. 00:09:34.020 --> 00:09:39.980 Now let me adjust the polarizer so that I bring up 00:09:39.980 --> 00:09:46.020 the other mode, as observed by the scanning Fabry-Perot. 00:09:46.020 --> 00:09:50.070 Now you can see that the other laser frequency is about three 00:09:50.070 --> 00:09:53.350 big boxes away from here, from this mode, 00:09:53.350 --> 00:09:57.150 which means that the separation if you do your arithmetic, 00:09:57.150 --> 00:10:00.170 since eight boxes corresponds to 1 1/2 gigahertz, 00:10:00.170 --> 00:10:05.660 then three will correspond to about 550 megahertz. 00:10:05.660 --> 00:10:09.040 Now, if I rotate the polarizer even more 00:10:09.040 --> 00:10:13.730 to block out the first laser frequency 00:10:13.730 --> 00:10:21.040 I showed you before, I up with only this frequency 00:10:21.040 --> 00:10:23.540 of the laser over here. 00:10:23.540 --> 00:10:25.833 There we are. 00:10:25.833 --> 00:10:27.250 So then, again, just it's a matter 00:10:27.250 --> 00:10:31.330 of adjusting then the polarizer to have either one frequency go 00:10:31.330 --> 00:10:37.240 to the Fabry-Perot or the two frequencies simultaneously. 00:10:37.240 --> 00:10:40.060 Right now we have both of them simultaneously 00:10:40.060 --> 00:10:42.380 incident on the Fabry-Perot interferometer. 00:10:42.380 --> 00:10:46.150 Again, as you can see, the separation is 550 megahertz. 00:10:46.150 --> 00:10:47.980 Now, the width that you see here, 00:10:47.980 --> 00:10:50.110 it has nothing to do with the laser line width. 00:10:50.110 --> 00:10:53.740 It is determined by the width of the scanning Fabry-Perot 00:10:53.740 --> 00:10:55.366 interferometer. 00:10:55.366 --> 00:10:58.690 Of course, if the laser jitters a lot, 00:10:58.690 --> 00:11:01.840 then you would see the width of the laser here. 00:11:01.840 --> 00:11:04.660 But right now, the width of the scanning Fabry-Perot 00:11:04.660 --> 00:11:09.610 is much bigger than the width of the individual laser 00:11:09.610 --> 00:11:10.811 oscillations. 00:11:13.970 --> 00:11:17.150 Now we're ready to look at the beat frequency 00:11:17.150 --> 00:11:20.900 between these two modes. 00:11:20.900 --> 00:11:24.530 So we need-- for this, we need a wide band detector that 00:11:24.530 --> 00:11:30.920 can measure a beat note much bigger than, or at least as big 00:11:30.920 --> 00:11:33.560 as 550 megahertz. 00:11:33.560 --> 00:11:36.890 The setup is over here. 00:11:36.890 --> 00:11:39.710 Here is the laser again. 00:11:39.710 --> 00:11:41.990 And the output of the laser, again 00:11:41.990 --> 00:11:44.510 passes through the polarizer. 00:11:44.510 --> 00:11:47.420 And then we take a little bit of the light through this beam 00:11:47.420 --> 00:11:52.730 splitter here and reflect it by this mirror and onto this lens. 00:11:52.730 --> 00:11:54.830 And this lens here will focus the light 00:11:54.830 --> 00:11:58.390 onto this fast detector. 00:11:58.390 --> 00:12:01.290 And that's how we're going to measure the beat frequency 00:12:01.290 --> 00:12:03.810 between the two lasers. 00:12:03.810 --> 00:12:08.850 So now, let's look at the output of the electronic spectrum 00:12:08.850 --> 00:12:12.630 analyzer here on the scope. 00:12:12.630 --> 00:12:15.360 Now, on your screen you see-- 00:12:15.360 --> 00:12:16.860 in the lower part of the screen, you 00:12:16.860 --> 00:12:20.050 see the output of the scanning Fabry-Perot interferometer 00:12:20.050 --> 00:12:23.280 where we show you the two frequencies of the laser 00:12:23.280 --> 00:12:26.220 separated by 550 megahertz. 00:12:26.220 --> 00:12:28.950 And in the upper part is the output 00:12:28.950 --> 00:12:31.680 of the electronic spectrum analyzer 00:12:31.680 --> 00:12:37.770 where the scale is 20 kilohertz per box. 00:12:37.770 --> 00:12:43.440 And the center frequency over here is 557 megahertz, 00:12:43.440 --> 00:12:45.540 which is close to what we estimated 00:12:45.540 --> 00:12:47.430 from the scanning Fabry-Perot. 00:12:47.430 --> 00:12:52.830 The resolution here is three kilohertz. 00:12:52.830 --> 00:12:54.855 All right, so now what I'm going to do, just 00:12:54.855 --> 00:12:58.200 to make sure that, indeed, this beat output is coming 00:12:58.200 --> 00:13:00.000 from the laser, what I'm going to do now 00:13:00.000 --> 00:13:04.320 is rotate the polarizer to get only one frequency 00:13:04.320 --> 00:13:08.640 and see if we can extinguish the beat. 00:13:08.640 --> 00:13:12.800 So, as you see on this screen here, 00:13:12.800 --> 00:13:20.360 I'm going to be then extinguishing 00:13:20.360 --> 00:13:24.260 one of the modes that enters the fast detector and also 00:13:24.260 --> 00:13:25.820 the scanning Fabry-Perot. 00:13:25.820 --> 00:13:27.920 And as we watch over here the output 00:13:27.920 --> 00:13:31.850 of the electronic spectrum analyzer and see 00:13:31.850 --> 00:13:37.995 it gets smaller and smaller until we have nothing at all. 00:13:37.995 --> 00:13:38.620 So here we are. 00:13:38.620 --> 00:13:41.020 There's only one frequency oscillating in the laser. 00:13:41.020 --> 00:13:43.030 And there is no beat. 00:13:43.030 --> 00:13:49.090 All right, so now let me bring up the other frequency. 00:13:49.090 --> 00:13:52.510 Now we have two of them, then, going into the detector 00:13:52.510 --> 00:13:56.590 and into the scanning Fabry-Perot. 00:13:56.590 --> 00:14:00.790 And we get back our beat frequency 00:14:00.790 --> 00:14:06.810 centered on 557 megahertz. 00:14:06.810 --> 00:14:10.590 All right, now this resolution is not so wonderful. 00:14:10.590 --> 00:14:13.920 And it's limited by the setting that I 00:14:13.920 --> 00:14:17.800 have used on the electronic spectrum analyzer. 00:14:17.800 --> 00:14:19.800 What I'm going to do now is I'm going 00:14:19.800 --> 00:14:26.190 to change to our highest resolution of 200 Hertz per box 00:14:26.190 --> 00:14:29.055 with a resolution limit of 30 Hertz. 00:14:36.710 --> 00:14:37.760 Here we are. 00:14:37.760 --> 00:14:41.900 Now we have 200 Hertz per box and a resolution of 30 Hertz, 00:14:41.900 --> 00:14:43.520 which I hope you can see. 00:14:43.520 --> 00:14:45.920 Now I'm going to have single sweep 00:14:45.920 --> 00:14:51.650 scans to look at the spectral width of the two lasers. 00:14:51.650 --> 00:14:52.370 So here we go. 00:15:02.120 --> 00:15:04.870 So here we are. 00:15:04.870 --> 00:15:09.810 We can see that, again with a scale of 200 Hertz per box, 00:15:09.810 --> 00:15:13.770 and the resolution is 30 Hertz, we 00:15:13.770 --> 00:15:18.090 see that the spectrum that we can observe 00:15:18.090 --> 00:15:22.170 is indeed very close to the instrumental line 00:15:22.170 --> 00:15:25.200 width of 30 Hertz. 00:15:25.200 --> 00:15:28.080 So we have demonstrated that the intrinsic line 00:15:28.080 --> 00:15:31.720 width, the fundamental line width of a laser 00:15:31.720 --> 00:15:35.200 must be pretty small, certainly smaller, quite a bit smaller 00:15:35.200 --> 00:15:37.580 than 30 Hertz. 00:15:37.580 --> 00:15:41.210 So remember here is the beat we looked at the spectral width 00:15:41.210 --> 00:15:44.560 of the beat note of two lasers. 00:15:44.560 --> 00:15:49.240 So each one must be quite a bit smaller than 30 Hertz. 00:15:49.240 --> 00:15:53.600 If we had a better technique for doing the spectrum analysis, 00:15:53.600 --> 00:15:58.600 we would have shown you an even narrower spectral width. 00:15:58.600 --> 00:16:00.970 Now just as a footnote, what I'd like to do 00:16:00.970 --> 00:16:05.440 is calibrate the electronic spectrum analyzer for you 00:16:05.440 --> 00:16:11.620 by bringing in a good stable oscillator around 557 megahertz 00:16:11.620 --> 00:16:15.610 or so and indeed demonstrate that the 30 Hertz is really 00:16:15.610 --> 00:16:20.230 the resolution limit of the electronic spectrum analyzer. 00:16:20.230 --> 00:16:23.170 So when you come back, we'll have that set up for you. 00:16:26.110 --> 00:16:29.670 So here is the stable oscillator over here. 00:16:29.670 --> 00:16:31.320 It's an HP stable oscillator. 00:16:31.320 --> 00:16:35.970 And the output at 557 megahertz or so, 00:16:35.970 --> 00:16:39.090 we're going to feed it into the electronic spectrum analyzer 00:16:39.090 --> 00:16:42.770 to see what the width is. 00:16:42.770 --> 00:16:46.600 So here I pressed the single sweep button. 00:16:46.600 --> 00:16:48.690 And here is the output. 00:16:48.690 --> 00:16:51.720 And you can see that the width here 00:16:51.720 --> 00:16:55.650 is very similar to what we saw for the beat between the two 00:16:55.650 --> 00:16:57.280 laser frequencies. 00:16:57.280 --> 00:17:00.180 And this shows that, indeed, the resolution limit 00:17:00.180 --> 00:17:06.609 is 30 Hertz of the electronic spectrum analyzer. 00:17:06.609 --> 00:17:10.180 So, in summary, the laser spectral width 00:17:10.180 --> 00:17:15.060 depends on the stability of the laser cavity. 00:17:15.060 --> 00:17:19.079 If the laser cavity jitters and shakes, 00:17:19.079 --> 00:17:21.329 or the refractive index fluctuates, 00:17:21.329 --> 00:17:24.270 then we would expect that the laser spectral 00:17:24.270 --> 00:17:26.700 width would be quite broad. 00:17:26.700 --> 00:17:29.280 So in order to reduce the laser spectral width, 00:17:29.280 --> 00:17:34.560 we need to design a stable laser cavity. 00:17:34.560 --> 00:17:38.640 Now, in terms of typical numbers, a simple helium neon 00:17:38.640 --> 00:17:42.110 laser like the one we used in this demonstration, 00:17:42.110 --> 00:17:47.480 the line width would be around 50 kilohertz or so. 00:17:47.480 --> 00:17:51.980 The recently developed CW neodymium YAG lasers 00:17:51.980 --> 00:17:54.770 have a line width of the order of 1 kilohertz. 00:17:54.770 --> 00:17:57.770 But other lasers like semiconductor lasers, dilasers, 00:17:57.770 --> 00:18:03.030 and what have you can have line widths of many, many megahertz. 00:18:03.030 --> 00:18:05.370 Now remember, the intrinsic line width 00:18:05.370 --> 00:18:08.603 is only a small fraction of a Hertz, 00:18:08.603 --> 00:18:11.020 or, as I mentioned before, of the order 10 to the minus 3, 00:18:11.020 --> 00:18:13.830 10 to the minus 4 or even smaller. 00:18:13.830 --> 00:18:15.540 Now, there are not many applications 00:18:15.540 --> 00:18:22.410 that require such narrow line width, except one. 00:18:22.410 --> 00:18:24.560 And that is the ring laser gyroscope 00:18:24.560 --> 00:18:26.750 that's used for navigation. 00:18:26.750 --> 00:18:30.460 Now, for this application, the intrinsic line width 00:18:30.460 --> 00:18:33.910 of the laser is at present the limit 00:18:33.910 --> 00:18:38.200 on the ability of this device to measure inertial rotation. 00:18:38.200 --> 00:18:40.900 But many other applications, at present, 00:18:40.900 --> 00:18:44.830 do not require that super narrow spectral width 00:18:44.830 --> 00:18:48.300 that is inherent in the laser.