Laser Fundamentals I | MIT Understanding Lasers and Fiberoptics

the following content is provided under a Creative Commons license your support will help MIT OpenCourseWare continue to offer high quality educational resources for free to make a donation or view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu good morning everyone wherever you are I'd like to welcome you to this short course entitled understanding lasers and fiber optics and before I do anything I'd like to tell you what sort of topics I'll be covering I will start with the many reasons why we're all interested in lasers today then I would like to talk about the key properties of lasers that make all these applications possible then once we understand these key properties then I would like to discuss how these properties come about and then we'll go describing the operation of a simple laser and even show your demonstration how a simple laser works well what you need to make things happen and then we look at variety of properties of this simple laser then we go look at other issues and problems to do with with lasers lasers are not perfect and if you don't treat them right you know they can give you give you some problems and in some cases you can get rid of these problems in some cases well you try to minimize them then I'll discuss the variety of lasers and what makes them tick because we have all kinds of lasers today and it's nice to get a feel for the variety of them and how they work how they get pumped and so on then I'm going to change topics and I will switch to the basics of fiber optics and to to familiarize you with what's going on in fiber optics what are the issues and but mainly the emphasis on on on basics and then finally I'll have a few words to say about future developments in in lasers and fiber optics now the how will I present the material well I will be using a very simplified treatment and the reason is so that people without specialized background can can follow I will emphasize only fundamentals and not not the details so that the the understanding can be made very easy and I will use very little math I will certainly not emphasize mathematics because I would like to make it very understandable and I don't want to switch people off and most important I'll be using lots of demonstrations to to illustrate some of the fundamental phenomena in lasers and also in in fiber optics so now I think we're ready to to start the course and the first topic that I had is why is there so much interest in in lasers well the the reason why there's so much interest is because lasers have these unique properties that we're going to discuss and it and it's these unique properties that make all these applications happen now these properties have created all sorts of new devices will mention a few of them briefly and also have improved many existing devices so the laser has been very nice in lots of lots of fields just to give you some example of just a few applications well let's just look at it just briefly the barcode readers everybody's familiar today with barcode readers now laser suddenly make that possible and of course the compact discs computer printers laser color copiers all these depend on on some of these properties of lasers that we we discuss then of course you've seen the laser shows and that suddenly uses a specific laser property then there is holography as the 3d imaging the hologram that you see on on credit cards that's all due to lasers then lasers are also used for precise control of position and in motion are for example sensors lasers today can measure all kinds of things with fiber optics without fiber optics or what have you the the big area of today and the future is fiber optic communication and again it involves not only fiber optics but also lasers so we'll see how the properties of lasers are used for fiber optic communication then we have topics like materials processing like cutting drilling welding and so on in materials there is a whole slew of techniques for non-destructive testing this is the destruction this the testing of systems without without having to destroy them and lasers are quite sensitive and they can do that without the need to damage the systems then we go to spectroscopy and the variety of spectroscopic techniques have been opened up by by the laser chemical process ah then we get to the military application military systems and we hear a lot about the laser the use of lasers in in the military and finally least last but not least we have medical procedures medical diagnostics using using lasers and all these applications come about because of very few unique properties of lasers and suddenly this course we want to make sure that that we understand those and how they come about fact the we find lasers all over the place today we find them in the home with the factory and hospitals in laboratory in the the military wherever it is in even in space in the ocean and even in the in the theater there you can see lasers are playing a very important role in our lives today all right so now I would like to go and to the next to the next topic and that is the the unique properties of lasers all right so what are these unique properties well let's start with property number one now some people refer to it as high mano chromaticity what is mano chromaticity well that means it's one color and we have to see what what people mean by that others refer to it as as a source of light that has very narrow spectral width again we want to see what what what it means and and and others may refer to this property as high as something that has a high temporal coherence and we want to understand what all what the meaning of all these things are so let's start first with with with the narrow spectral width on the single color here what I have and I hope you can see it the colors of the spectrum I did the coloring myself and it's pretty close to to the spectrum with whatever colors I had now the visible range as we all know extends from about 4500 angstroms to about 6,500 angstroms in the in the red which is about what 2,000 answers are so and that's that's the visible essentially that's the visible range now when we compare a light sources to this to this range for example the spectral lamp that has a very narrow line width or spectral width here it is here's the typical output of a spectral lamp let's say here in the yellow and the width over which there's this radiation could be as low as one tenth of an Langstrom okay 0.1 angstroms or in terms of frequency it's 10 10 gigahertz and then you can get the some lamps that have smaller line widths or you can even get them with broader line width depending on on the conditions of the discharge and so on then when when we come to two lasers the line width is extremely narrow the spectral width is extremely narrow and it can be in the megahertz but can also be in the micro Hertz now remember this is ten to the minus six thirds or even smaller so the laser is an incredible kind of device when it comes to the spectral width the line width can be extremely narrow now I know in practice that's not what one measures but but if you get rid of some of the effects we'll talk about external effects then you should be able to see line width as narrow as narrow is that all right so the laser then is is extremely extremely narrow the let's see how now let's see how you might measure the spectral width so you don't have to take my word for it let's see how you might measure well if you took a typical spectral lamp here and then collect some of the light from it and put it into a spectrometer or some other device that device that measures the spectrum then what you get you get a plot like this intensity versus wavelength and here you can either plot wavelength or you can plot frequency depending on the kind of work you do and then you'll see some blob like this and it has a certain width over which the the the source radiates and we call it either Delta Lambda for the width or or Delta f now when we compare it with a with a laser again we do the same thing we'll take the laser and feed it into a spectrometer or some other device the width here can be very narrow and just like I said before can be even as narrow as micro Hertz but these only under special conditions but even if it's megahertz or tens of megahertz it's way narrower then you get from from a from a lab so again if you're not sure then you have to do the experiment and check indeed that the laser does give you an extremely narrow narrow line with all right so that's basically then the line width of the of the laser now the next thing is what about high temporal coherence what has that got to do with the line with the delays all right so now we need to explain that topic now let's start first with with a wave with a sine wave and now the sine wave let's say starts from minus infinity in terms of time and goes all the way to plus infinity completely uninterrupted a pure sine wave now if you had a wave like this that has a constant frequency in a constant amplitude then when you look at its spectrum on the in the Freak on the free in the frequency domain what you see you see something that's let's say centered at F 0 F sub 0 with a width Delta F here very close to to 0 all right now this is a source of radiation it's like a sine wave like this that has that has what we call perfect temporal coherence or time coherence and that's the best essentially the best that what can happen now in in in practice light sources do not radiate for such a long for a long long time without any phase interruption so let's say we have a light source like this that that radiates only for a time town and then shuts off for exam now this one because it's it only radiates for a time tau it's going to have aligned with in the frequency domain it's gone it's not going to be a delta function like we had before and this width if you do the calculation this width in terms of frequency is proportional to 1 over the the length of this wave train tau again I put approximate so that I don't get into trouble about the exact numbers but it's very close to Delta F is one over tau so that if tau is very long if tau is very long in Delta F is small as we've shown you before but if tau is short then the line width here will will grow now atoms for example because this is where we get our radiation from from atoms they radiate in bursts bursts like like this now if they radiate in bursts like this then then tau can be sometimes can be quite short which means that the width of the radiation will be will be broader so the shorter this is then the broader this this width and here I show bursts from other atoms and when you put them all together essentially that's what you get you get a certain width that's characteristic of the time of the uninterrupted radiation of Van and here we get an interruption therefore the tau then is only when the wave is is uninterrupted now some other atoms will radiate in in decaying sinusoids exponentially decaying sine so it doesn't matter the calculation is a little bit trickier but again you get a sort of width and for the purpose of this course all I'm after is is the is the is the dominant width and I'm not worried about all the side bands down here just just the width and again you can say that the width here is of the order of 1 over tau whether it's exponentially decaying or it's looks like this or what have you all right then then to summarize now high temporal coherence means that the radiation time of the atoms without phase interruption is very long because the line width is 1 over town would be very small and when you have a something that has a high temporal coherence which means to have very long it means that you can predict the amplitude and the phase of the wave at at any time every time because it's a pure wave in fact if I go back to to this plot over here so this is where you have infinite coherence it means that if I know the amplitude and phase of the wave at this time I can only with using a clock I can predict exactly what the amplitude and phase of the wave would be at some other time later and the separation in the time can be can be very long when when we get to when we get into into sources that radiate like this then obviously within this time I can predict the the amplitude phase of the wave but if I stretch the time little further bigger than than this towel then I cannot predict anymore the applet in the face because this is like another another waveform that is completely uncorrelated with the first one so what we call the coherence time now is going to be limited only to this time during which the the the wave is uninterrupted then you might ask what what are typical applications of of this of this unique property well the the fact that it has narrow line width can be used in in communication so that's a key key property here in spectroscopy especially in high resolution spectroscopy in interferometry holography and a variety of sensors so that's a that's a key property for for many many applications now what I'd like to do is discuss the second part or the second unique property of of lasers now here it is the many ways of describing it one way is that the laser is has a highly collimated beam and we've seen that in laser shows or what have you that the laser has a highly collimated beam other people may use most better scientific language I would call it diffraction limited collimation and we want to know what that means to some the fact that the laser has a very small focus spot is a is this meaning of this property and others may call it again in a better scientific language it's a diffraction-limited focus all right so whether it's diffraction-limited collimation diffraction-limited focusing or even as others might call it laser has high spatial coherence they all mean essentially the same thing and let's find out now what what we mean by by all these words alright let's go back and look at a typical a typical light source let's say let's spectral lamp we have electrodes here plus and minus we have an arc here and then we collect the light from the arc with a lens and that's placed at the at the focus of the lens here this distance here F is the focal length of the lens so now we try to collimate this this light source well what sort of collimation do we get you can see here that this point this one end of the of the of the discharge or is that you collect these two arrays from here and you create a collimated beam in this direction at the other end of this arc for example the other extreme will give you a collimated beam in this direction and when you put them together you have this this widely diverging beam now you can easily estimate the angle of this beam in fact the angle of the divergence of this beam theta is given by H which is half the size of the source here in this case it's an arc it could be discharge lamp or whatever half the size of the of the source divided by the focal length of the lens and so so the so if if you don't like if this angle is too big then the only thing you can do is either reduce the size of the source or increase the focal length of the lens now if you let's look at increasing the focal length of the lens if you increase the focal length of the lens means you've got to put it way far from from the source if you do that you're going to lose a lot of light so you may get a better collimation but it's not going to be much lightining the other thing to work on is h the size of the source and clearly if you make it small and smaller then the collimation will be better and better and that's how pre laser days that's how one got our collimated beams with a lot of light in them because you try to generate sources that have that very small socks now let's see what's the best one can do here well the best one can do is called diffraction limited color mesh and here if you do the physics of it if you have a beam let's have diameter D then the best you can do this is now a perfect optical beam light beam or what have you beam electromagnetic radiation a diamond at D I don't care what it's microwave optical UV or whatever whatever then the best you can do in terms of divergence angle is lambda divided by D lambda being the wavelength of the light dividing by D as simple as that and I make it approximate here because it's just a small factor here which I'm not going to worry about in this in this course the critical thing it depends on the ratio of lambda the wavelength over D the short of the lambda the better the collimation the larger d the better the collimation or this the smaller is the divergence angle and it doesn't depend on any source size or anything because this is this is due to basic physics of of electromagnetic radiation that's what we call the diffraction limited collimation that's the best you can do so keep that keep that in mind now let's compare the the output of a laser with this with this diffraction limited beam here's a laser source and with some optics and what have you I can create a beam that's diameter D and if I go check this it's size further down I indeed see that the angle here the angle of divergence is very close to lambda over D just like the the perfect light source that we talked about before so you can say that laser is indeed diffraction-limited and and again the divergence is just limited by the wavelength divided by D while in the case of the light source we had to worry about the size of the source and then the other important thing here is that all the laser light all the laser light can be put into into that beam so we don't need to lose any any light because we're not collecting you know so it's another fantastic kind of kind of property now the applications of this of this property at let's start with the collimation part the high degree of collimation can be used of course for alignment you can do large distances without the beam expanding too much certainly you see these barcode with the lights flashing if there was too much divergence you'll be able to to scan the bars because the spacing is very small between them and certainly if you want to do long distance communication especially in space radar and what-have-you high degree of collimation is is very very important now the next thing here is that I mentioned before is the very small focus spot or the diffraction limited focus now what is that is that come from and and how does it compare with what we can do without lasers well let's go back to basics back to our arc lamp here and then we collect the light as we did before but now instead of just collimating let's put another lens and focus it down and that's normally how we get intense spots high-intensity focus spots by again taking light from a source and and refocusing now it turns out that because the source has a certain size you're not going to be able to create anything here that's going to be brighter than the source and again if you don't believe me you have to go look up basic physics and any sort of makes sense that it's very difficult it's impossible to make this brighter than here so you cannot increase the brightness as as dictated by by the source all right now what about lasers or before we get to lasers what's the best one can do let's go back to our collimated beam of diameter D that that was our perfect ideal beam now if we take that put a lens here with a focal length F and focus it down it'll focus down to a very small spot now this is the smallest spot that you can get and the spot size is given by our lambda over D which we'll remember from before multiplied by F the focal length of the lens now if F is approximately D if you can choose F proximity D then we have a spot size here that's of the order the wavelength of light so again without having to study hard or remember hard then we have two things the collimation is just given the best collimation you can get is lambda over D and the focus spot size is lambda and this is then assumes that it's a perfect perfect light source all right so that now let's compare with with what the laser with the weather laser can do all right so now we bring the laser up so here's our laser giving us a beam a collimated beam of diameter d put a lens here focus it down and i go measure the spot size and it turns out of the spot size if I'm careful is very close to the wavelength of the of the light so this means that the laser beam is as ideal and it's close to perfect as one can get both in collimation as well as in focus while with a well with a light source it was difficult to to get something that is that is extremely bright you can make this of course the spot size small here by putting apertures by putting apertures here you can make this spot size small but you cannot have a small spot size with with very high intensity like you can here in this case you can put all that laser line and will talk about all kinds of outputs very soon and you can put all that into this tiny spot and that's how you can get these huge intensity well you might say what are the applications of some of these small focused spots with high intensities well there are all kinds of application there's compact discs for example that rely on a on a tiny small spot for the for the resolution is certainly for laser printers and again for materials processing is it's a for cutting and welding and drilling and so on and also in medical surgery where the the spot size you know for cutting and what-have-you has to be has to be pretty small you don't want to make a huge huge cut and also because you have to deliver so much intensity you need the spot size to be small okay especially like for example look at the example of retinal surgery when a retinal welding we try to well the retina the spot size is a key is a key issue because you can almost get any light source to to spot well the retina the only problem is its what well the entire retina but here with a tiny with a tiny beam tiny focused beam you can you can only well just just small areas of course they're damaged areas and you hopefully you can still see with the rest of the retina so the the small spot size is is a key thing to a lot of these applications now I mentioned earlier that that some people refer to this property of high collimation or small focus spot to high spatial coherence so let's see what the what is meant by by that the here is a high spatial coherence and and then what we mean by that is that the wave is well behaved in space now before we talked about waves that are well behaved with respect to time remember we showed that the wave continues uninterrupted for for a long of time that's very well behaved wave into in time now we're talking about a well behaved wave in in space which means that we can predict its amplitude and phase at any position at the given time while before it was at the same position at a different time but here at any and any position now any spatial position as a function of time and also of course of space so let's look at it now an ideal point source of radiation is over here and then it puts out you know these spherical waves that we probably used to seeing if the source is very small then you have perfect spherical waves if I don't like a diverging beam and I put a lens here then I can make this into a collimated beam and this will be perfectly collimated beam which means that for for what we call high spatial coherence means that if I know the amplitude and phase of the wave here in this position in space I can also predict the amplitude and phase of the wave in another position in in space and and and and that's great so whether this is diverging beam or a collimated beam or so on if you tell me what the amplitude and phase of the wave here I can tell it I can tell you what it's going to be over here because the wavelength is is stable and the the spatial be here behavior is stable well if this doesn't mean much to you let's look at what a what a light source puts out and it's back to our spectral lamp here or an arc lamp now because we have so many atoms in the source here that's their radiating then we get a mess of a waveform that's that's coming out so even so if I know the amplitude and phase over here it's pretty impossible for me to predict what the amplitude and phase going to be at a different location in space and even as a function of time because I really have no control over these light sources over here while in the in the case of the laser I can get pretty close to perfect prediction anywhere I want in space but in a in a in a non laser light source it's very difficult now I can improve things by making the light source very small as we showed you before I take lenses of focusing down put small apertures and can sort of create a tiny focus spot the only problem is there's not much light by the time I do that while the laser you can put all the laser light into let's say collimated beam with diverging beam that has perfect spatial spatial coherence all right so these are two very key properties now what I'd like to do is is talk about few more a few more properties all right now here is the next one which is high-power the laser as we know lasers have incredible power all right so let's let's see with that where that comes from here's again picture of a laser and putting out a beam of light now there are two kinds of lasers is what we call CW or continuous-wave laser and is also pulse so if the output is not continuous and it's possibly call it pulse laser and some of them can be very short and so on alright now let's see what sort of power levels that we can get from from lasers and these these numbers if you're not familiar with them they're going to really open your eyes out too to what's going on now in terms of continuous lasers well we're all familiar I suppose with the helium neon laser or semiconductor lasers that put a few milli watts alright some of us work with bigger lasers that put out sort of watts and not that many people work with kilowatt lasers today these are you can buy these lasers for all kinds of applications and you can also generate even mega watts of continuous lasers that's ten to the power six watts that's huge huge continuous power that comes out from these lasers now in terms of pulse lasers Wow the numbers get really very big here we're talking about in continuous docking with tenders six watts here we're talking about anywhere from ten to the nine watts which is a or gigawatt depending where you come from and then we also have can produce pulse lasers with with the peak pulse power of 10 to the 12 watts terawatts and even 10 to the 15 watts and I don't know if you've heard of this word here petawatt and Pitta watt means 10 to the 15 this case 10 to the 15 was and also recently we read that some people have produced xor peak power which is 10 to the 10 to the 18 watts it is fantastic fantastic power levels and we'll see how they generate it soon and and what we can use them for but for here I'll just mention just a few applications of these peak powers certainly in materials processing where you want to do welding cutting and what-have-you for fusion today as we know there's a big fusion program for many years now that uses that's based on on lasers called laser fusion and the military of course would love to use these high-power lasers with a pulsed or or CW and certainly a lot of nonlinear optics application are based on the fact that we have a lot of a lot of power in these in these lasers because it depends on the on the intensity now the next property that I want to mention is the tuning range of of lasers lasers again are sources of radiation and can have incredible tuning range now let's see over this spectrum of electromagnetic radiation where lasers are first of all we have the visible lasers you know the ones we we see are basically basically over here and and you they may have a certain tuning let's say from here to here and and we'll discuss them later I mean here this is just in a pictorial form I want to show you where the lasers are and then maybe as we get into the infrared maybe other lasers like this one here some laser here let's say over here is in the firing getting close to the fire infrared some lasers that have large large tuning range we go from the visible we can go to the ultraviolet or even to the vacuum ultraviolet and today we've gone all the way to two x-rays so lasers are found all over the spectrum all over the electromagnetic spectrum but their tuning range or their widths over with the spectrum or the spectral width of the lasers or the tuner range of the lasers can be can be quite broad and then then we'll discuss them later but today we have lasers all over the electromagnetic spectrum sure we may have some gaps here and there but there are techniques of filling these gaps by by mixing techniques and so on that will fill these gaps and today we read I have no excuse to say that I don't have a laser at a specific wavelength because all sorts of techniques to to create lasers there if they aren't any lasers they already now the applications of of Y tuning range could be in the interaction with specific atoms and molecules where you need to tune the light sources to be able to interact with specific atoms and molecules to reach their resonances and so on in studying structure of atoms molecules solids and so on you need a widely tunable source it's an area of spectroscopy and then for propagation sometimes you know if you want to dodge certain molecules in the atmosphere and the water and so on you need to tune the laser away from the absorption of these molecules or atoms and in in in medical applications sometimes you need to to tune the laser so that it's at the right wavelength for interacting with tissue or or what-have-you and and it's nice to have lasers that are tunable now I have one more key property and that's it it's going to be just the fifth one and and here it is that lasers can produce very short pulses now these these are incredibly short pulse with much shorter than any any electronic circuit can can generate and here we are is a laser pulse that one can generate and the pulse width can be well this is big ten to the minus nine second was called nanosecond certainly we can produce these on a routine basis picosecond or 10 to the minus 12 seconds and today we're very close the record is that we're very close to 10 to the minus 15 seconds excuse me which is a femtosecond that's incredible because because even ten to the minus twelve seconds very difficult is impossible to reach with electronic source so already from from below ten to the minus twelve that's a ten and once eleven or so this is all lasers because you can't do it electronic all right so again this this is fantastic property of lasers and and let's mention at this stage what are some some applications of very short pulses we can certainly use them to study very fast phenomena where the let's say the relaxation time is so fast that normal techniques don't work they cannot be used to observe them because it's too long alright so in order to study fast phenomena you need very short pulse lasers then of course the exciting thing about optical computers if they will ever come about is to take advantage of these very short pulses so you can have can have faster clocks and and so on and for high-resolution radar and imaging these very short pulses can give you again incredible resolution and so so there are lots of applications of these short pulses and will have something to say about them later now I would like to to switch to to the my my next topic which is how these properties how these properties are come about and and again we'll start with with the first with the first property which is this monochromatic narrow spectral width and high temple coherence which I hope you still remember from from earlier the question is how does this property where does this property come from okay so the answer is that the laser is an optical oscillate and so some people might say well what's an optical oscillator I know it comes out like a sine wave but what's an optical oscillate well he what's an optical oscillator is the first you know to understand an optical oscillator you have to understand what an oscillator so now we're ready to talk about the properties of an oscillator and we hope then we can extend it to an optical oscillator and then we can appreciate with that first property of lasers comes from so here we are let's review the basic properties of oscillators I know a lot of you know about oscillators but I have to start at some level so I'm going to start right here so if we have here black box that puts out this sinusoidal oscillation this perfect sinusoidal oscillation where the length of this wave train as we've seen before goes all the way from minus infinity plus infinity very long uninterrupted constant amplitude then in the frequency domain that as we've done before that is that delta function centered at some frequency here that depends on the wavelength of this of this radiation source all right so that's what we generally call an oscillator and especially electrical oscillators we see them on a sillas cope we see this beautiful sine wave on the oscilloscope and and the the the source of the oscillation well we'll have to see how that comes about in case of lasers and this spectral width is is extremely narrow and we see that Electrical oscillators all the time and we don't even think about now now I would like to tell you a little bit about how an oscillator is made and once we understand oscillate is made then we extend it to to the optical and be able to explain how laser works ok so let's review some background here in oscillators well there are all kinds of oscillators I'm going to start with it with a pendulum here's a simple pendulum length length D and I let it I let it swing what does it do when I let it swing well it'll go backwards and forwards just like this will generate an oscillation here of the pendulum which will die down and the frequency of this oscillation is given by 1 over 2 pi the square root of G the acceleration of gravity divided by D the length of the the pendulum now the so the the longer D is the smaller the frequency of oscillation but but as we can see this oscillation dies down and the question why does it die down well why does it die down because there are some losses and the losses for example come in this pivot here comes pushing air around and so on but basically it will die down because we difficult to get rid of all these losses so we don't have that constant oscillation I showed you before now we go to the frequency domain reminding you what we did before because I have a dying oscillation like this then if the time constant is is tau then the line width is going to be approximately Delta F which is approximately 1 over tau and that is proportional directly proportional to the losses the higher the losses the larger larger is the line width and the shorter is the the decay time all right so that if I improve the losses if I reduce the losses then I can get this to narrow down and I can get this to last to last longer now the if I as I just mentioned just now this is in pictorial form if I reduce the losses if I'm clever in reducing the friction in this pivot and so on I can make the wave last longer and this width gets gets now but in order to make it constant amplitude I have to do something else all right this is what I have to do I have to call on this fellow here to to push on this pendulum to push on this pendulum so that it stops it from from dying down in a way what this fellow is doing by doing he's pushing at the right time it's really overcoming the losses whether at the the pivot here or pushing around and and so on so in order instead of having just the dying oscillation like this where I end up with a constant amplitude because if this fellow here is putting energy into this system and compensating for so as the amplitude here becomes becomes constant then the line width here starts Delta F starts to shrink and goes close to zero so in this way I produce a an oscillator and in this case of course it's a it's a pendulum oscillator that's used like a clock and and so on but I do need this energy source this person here to overcome to overcome the losses now this is not the only type of oscillator I have all kinds of let's say I have a mass spring system I can make that into oscillator let's say here I have a spring and is it mass connected to it and then if I pull the mass away it's going to wobble backwards and forwards going to oscillate again it's going to be a dying oscillation like this because of well friction mass friction it has a friction between the friction between the mass and and the stable and losses in the spring and so on the frequency here will be determined by the square root of the of the spring constant K and divided by the mass if I change the mass I change the frequency end and so on and so so again just like in the pendulum it's a dying oscillation and has a in the frequency domain that has a certain width and the width is proportional to 1 over 1 over tau and that's again proportional to the losses if I look at a stretched string here straight string if I hit it then it Bob's up and down here in the middle and then the frequency will be determined by the speed of sound in the material divided by by twice the separation which in the ends and again it dies down okay this bobbing up and down will die down because again of losses and also will have a level width and then finally here if I have an LC circuit inductor and capacitor again if I if I inject a pulse into it I see that again I get an oscillation if I look let's say the voltage across the capacitor here I have this oscillation that dies down and the frequency is given by in this case by the square root of 1 over LC L being the inductor sees the is the value of the capacitance and the this decay is due to losses now in electrical circuit where the losses come from where they come from Oh make loss is essentially dissipation in the in the wires according to Ohm's law so that the all these kinds of oscillators whether pendulum or mass spring a vibrating string or electrical oscillator they essentially they all have specific frequencies all right they oscillate at and but they all have lost and to make them into into an oscillator you have to overcome these losses and as we as we saw that in the indicates that the pendulum you need somebody to push here you may also need somebody to push over here you again you you have to you have to keep vibrating these things to maintain oscillation and of course in electrical one we add a an amplifier to overcome to overcome the losses now to then then summarize then we need to make an oscillator then we need a resonator that will determine the frequency for us and we need a means of overcoming the loss so if we have that then we can then we can get this oscillation this nice oscillation that that comes out from that black box I showed you earlier now what about the laser okay how does the laser work well in in in lasers because if the laser is an oscillator we need a resonator first of all so let's look at how we can create electromagnetic resonator well just like this is very similar to the to the straight string we need we need two ends we need two nodes and here we have to create this we have two mirrors here the two mirrors em and they're spaced a certain distance L apart now the the lowest frequency that can fit between these two modes and oscillate backwards and forth between these two modes is the one where half the wavelength where L is half half this wavelength because the wave would be will be about this size now such a way would be able to bounce backwards and forwards between the two mirrors and and will be at that frequency determined by in this case will be determined by F equals C over 2l because lambda x times the frequency equals the velocity of light so either that the wavelength is 2l all right or its frequency is just C over 2l okay so this is then the the lowest frequency that will be supported in this kind of a structure with two reflectors or two nodes at the ends just like in the vibrating string now this oscillation will die down if I injected some light in here and I get it to oscillate like this who will die down because of losses and again in the frequency domain this will have a width question is what where are the losses in this case well the losses come from the reflection in the in the mirrors if the reflectivity of the mirror is not perfect then then every time the light bounces from one mirror to the other then the amplitude will go down and very quickly it will die down altogether so in order to to make this then oscillate or essentially lays we need to overcome these losses but before I get to this I want to talk about other other modes in in this kind of resonate the so far I've talked about this one way only half the wavelength fits between the two mirrors but I can also get a condition where a full wavelength foot fits between the two mirrors these are sort of normal modes of of these resonators now where lambda 1 was here was equal to 2 L and f1 was C over 2 L in this case lambda 2 is is essentially L or I like to write it as 2 L over 2 but I can cancel to do the twos not get L and the frequency is just 2 C over 2 L so here we had one time C over 2 L here is to C over 2l and and so here I'm spacing it along in the frequency along the frequency scale here's my f1 and here's f2 and the seperation is C over 2l and each one has a width because of the of the losses now we can go a little further here and consider few more of these oscillations in this case well I have one and a half waves it will fit between the the cavity between the two mirrors and or within the cavity and then the wavelength will be 2 over 3 instead of 2 L over 2 and the frequency will be 3 over 2 L instead of - C over 2 L here so now again you can see I'm going to stack them up F 1 F 2 M 3 and the separation is equal between them which is C over 2l and we can go to many more and I'm jumping here to to the what we call the Q's mode lambdas some Q and just because the way I was doing it previously you can see that the wavelength will be 2 L divided by Q this is the the Q number just like in here this was 3 2 to 1 and now in this case will be the Q's mode and the frequency will be just QC over 2l just like here we have 3 C over 2l to 0 to L and so on so on the on the frequency scale then we have all these resonances that come from that I can excite in one resonator and can we can be as high as as you want and the width each one will have a width because of the losses now not all the widths will be the same because because not all the losses will the some losses will depend on the wavelength or the frequency you're at so since the mirrors can have loss but the loss can depend on the wavelength and so so the these widths can can vary so now this explains the the resonator and and and just the let me summarize the the information here we have a typical now laser cavity which again two mirror spaced by L in this case I'm going to take L as a hundred centimeters one meter if I choose for the wavelength to be half a micron or five times ten to the minus five centimeters then Q comes out to be this Q this integer we talked about comes out to be two L of a lambda from from the from this formula here and it's 200 divided by five times 10 minus 5 which comes out to be about 4 times 10 to the 6 which means that Q has the value of few million all right which means there lots of little waves in here in a in a cavity of a hundred centimeters separation the frequency associated with that is against F sub Q from here is six times comes out to be six times into 14 Hertz and the width will depend on the losses which are mainly due to let's say mirror losses and and so on which we'll get into into later so so the so then to make a optical oscillator or like a laser we need the resonator that we with it we have talked about but it has not just one frequency but has many frequency and it has we have to have a means of overcoming the loss and and that is is that comes about with with a light with a light amplifier so the the light amplifier is the is the key element in a lays in a laser because without the amplifier you can have all these cavities empty cavities that do absolutely nothing for you but in order to make create lasers out of them then you have to put an amplifier okay so here is then then the laser is the cavity that we talked about and then we have to insert this this amplifier and this amplifier which we will talk about later in more depth this amplifier then provides gain for the light that goes backwards and forwards between these two mirrors to overcome the losses whatever the losses come from and the whole idea is to make the losses as small as possible so you don't you need to use a big amplifier because - in order to generate this gain which we'll talk about later it costs a lot of effort a lot of money and so on so so we want to minimize the the gain that's needed but we certainly have to have enough gain to overcome the losses and and here for example I have this this amplifier this this gain of this amplifier located at this particular frequency and over here I have all the modes of the cavity that we talked about before but if there is one of these cavity modes under the bandwidth of this amplifier then if there is enough gain to overcome the loss then I can get this to to oscillate and in fact here it is as we know that this width of the of the cavity comes about because of the losses in the cavity but if I have enough gain to overcome the losses then I collapse this width to this Delta function that we had before and and the output that comes out from this mirror if I put some transmission in this mirror here I leak a little bit of light out then that light will will have this spectrum that's very narrow spectral width or in terms of the time domain I have a this lovely oscillation here that has a constant frequency determined by this cavity mode and a constant amplitude so I think the this will be a very fitting time to stop for this first session because because I brought you just to the stage where I think now you want to know where this where this gain comes from that makes lace as possible so when we come back we'll start exactly with that with that topic

Channel: MIT OpenCourseWare

Views: 248,421

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Keywords: lasers, fiberoptics, fundamentals, unique properties, simple laser, problems, types of lasers, basics

Id: saVE7pMhaxk

Length: 58min 14sec (3494 seconds)

Published: Wed Mar 21 2012