 In the last module, we stopped with a very brief discussion of chart pulse amplification. As you know, for many applications like pump probe, which is one of the more simple applications of lasers, we cannot work with the output of a titanium sapphire oscillator because the pulse energy of nanodules is attacked too low. So, we have to find a way of amplifying the pulse and the way it is done is called chart pulse amplification. We are going to try to discuss chart pulse amplification in the next two or three modules. This is the scheme of chart pulse amplification. I think this was the last slide more or less of the last module anyway. So, there we said that last year's Nobel Prize in Physics was in two parts. One for optical tweezers. The second one was for Gerard Moreau and Donna Strickland's work on chart pulse amplification. So, I strongly recommend you to read these or see these videos or do both. The YouTube videos that are listed here, they are the Nobel lectures of Moreau and Strickland. This optics communications paper is one of the original, one of the very few original papers of these two Nobel audience published together on this technique and well these two actually. Optics Communications and IEEE Journal of Quantum Electronics, these are two papers which reported for the first time their work in this field and these two papers on reviews of modern physics published earlier this year, they contain, they are basically the paper form of the Nobel lecture they delivered last year. So, two and one more paper that you should read is this one on chart pulse amplification this is very nice review by our high power ultrafast lasers by Captain Murnen and other workers it was published way back in 1998 in review of scientific instruments but it provides a good idea of what we are going to discuss now. In fact it provides a good idea of what we are going to discuss now and also things that we are not going to discuss. So, what we will do is we will keep it very qualitative we will try to draw pictures and show how things happen and try to develop a physical insight rather than stressing too much on the math rather than stressing the math at all in the next two, three modules but there is actually lot of calculation, lot of physics, lot of optics that is required you do not have to study all but you should be aware that it is not just heat and go trial and error nothing like that a lot of design a lot of theory has gone into this kind of work right. So, when we say we want to amplify from nanojoule to Mirageau we can think very simplistically that we have an oscillator which we have discussed in one of the earlier modules titanium sapphire oscillator or some other oscillator that gives you femtosecond pulses we are going to maybe feed it into something like an amplifier which will give us the desired ultra short but amplified pulse but it is not so easily done it is not so easily done because in the amplifier typically what one would try to do as we are going to discuss later in the next module definitely not this one is the way you try to do it is you try to feed the output of an oscillator into a gain medium say another Tysaphire crystal which is pumped by a green laser. Now if you are going to put in the ultra short pulse then as you yourselves have calculated few weeks ago a lot of energy goes into the system in a very small amount of time and then we have talked about thermal lensing it is the intense part of the beam that gets focused. So, in a very short amount of time a lot of energy impinges on a very small region of space. So, if you try to do direct amplification like what is sort of shown in the scheme then it is very highly unlikely that you are not going to cause damage to the optics and say optics the piece of optics that I have in my mind more than anything else is that Isaphire crystal in the amplifier itself that is going to burn. So, you have to somehow find a way of spreading out the energy of the oscillator before you can feed it into the amplifier. So, the way it is done following the method of the Nobel laureates is that you have the output of an oscillator first of all try and stretch it and we know already what is an easy way of stretching a pulse because it was already there right remember when we discussed at the time sapphire laser we had said that when you produce an ultrashot pulse by thermal lensing the good thing is that thermal lensing gives you an ultrashot pulse. The bad thing is since you have a special variation of refractive index it acts as a lens you also have something called chirping different wavelengths travel at different speeds and that causes a broadening of pulse so that is something is already there and so far we have seen it as a hindrance. The beauty of charge pulse amplification is that this apparent hindrance has been made use of converted to an advantage and it has been used in amplification. So, first of all in a stretcher what you do is you produce a charped pulse so now see if you look at of these are all schematic but then if you look at this ultrashot pulse on the oscillator and if you look at this stretched pulse output of a stretcher even visually what is the difference that you see it can be a little confusing because I have drawn this in red but here you can see that this part is blue and this part is red right and x axis is time which means away what I have done is I have made red light travel shorter distance somehow so it leads and the blue light trails right that is one aspect what is another aspect you see the other obvious relationship between the uncharped pulse and the charped pulse typically this would be some tens of femtosecond and the charped pulse would be something like 200 picosecond will you agree with me if I say that the area under this pulse and this pulse should be the same what is area number of photons is not it. So number of photons is the same it is just that I spread it out over a longer time then what happens that then in a very small amount of time a lot of energy does not engage on the crystal right. So if I can stretch the pulse by introducing chirp then the resultant chirp pulse which is long is not going to damage the crystal so much. So what you do is you feed this into an amplifier and then the amplified pulse is also chirped now the areas are of course not the same this area is many times more than the area under this curve but the property that is conserved is the chirping see the leading edge is still red the trailing edge is still blue and then when this chirp pulse is compressed then you get the desired ultra short chirp free pulse okay this is the scheme of things so our job in the next 2 or 3 modules is to understand how this is done. So to start with in this module we are trying to discuss how stretching and compressing is done actual amplification will come in the next module. So if I have a pulse of light and I want different colors in the pulse to spread out what is the easiest way of doing it okay forget about time if I want to have a mixture of colors of course by now you know that the pulse consists of many modes that are locked together right. So that is why an ultra short pulse is always a broadband pulse shorter the pulse broader is the band and then that transform limiting factor is there. My question is what happens or how do you make this different how do you separate these different colors from each other forget about time let us talk in space that is very easy isn't it use a grating then different colors will go different ways and then if I put a mirror in such a way that path length of red is more than that of blue or path length of blue is more than that of red then my job is done. So there are several designs that one can think of I will start with this pulse stretcher or pulse compressor using a single grating a concave mirror and a plane mirror okay this is the design of the laser that I had used as a post doc long ago but more or less this design is still used in many places and as we will see in the next few minutes it does get more complicated from here okay. So let us say we have this and then this pulse goes in this part is very simple okay the red on in red and red on in blue and see this angle of grating is also important whether you put it this way or that way okay by selecting the parameters the generally in this kind of a setup what you do is you introduce a negative chart negative chart means smaller frequencies lesser energies trail and larger frequencies lead that means blue has a shorter path length red has a longer path length and if you just look at the length of the arrows that is achieved already okay but the problem now is that it is dispersed in space it will be difficult to handle you have to somehow get it back and make a beam how do you do that you do that with the help of the plane mirror so the way it is placed is that this grating is at the focus of the concave mirror okay this point is in the focal plane of the concave mirror so now what will be the fate of this diverging beam which is specially dispersed after hitting the concave mirror the blue as well as the red both the beams have come from the focus of the concave mirror what will be the path after hitting the concave mirror points from a focus after hitting concave mirror what happened to them raised from a focus sorry raised from the focal point yeah then become a parallel beam the only difference between this parallel beam and the parallel beams that we usually study is that in the usual parallel beams the color is same throughout here it is not the case this is what will happen then you put in this plane mirror okay now how do you put the plane that is important you can put like this normal incident if you do it in normal incidence the good thing is that the rays will retrace their paths okay and then they will get focused on the grating again and it will go out in the same direction as the incoming beam right people do that but then there is a problem the problem is how do you separate the outgoing beam from the incoming beam so you have to use in that case something called an optical isolator will not discuss optical isolator right now because there is an easier way of circumventing this problem and the way is this what you see here is the top view right it is in top view now let us see the side view right earlier we are looking from here now we look from this side how do the beams hit the plane mirror like this like this the two beams hit like this so what will be the direction of the beams that come out like this okay of course I am it is not so easy maybe this is easier I can make these two fingers parallel hit like this and go like this okay this is how they will go so if you look from the top what will happen looking from the top this is input this is output it look like the same direction but the good thing is they are vertically separated so you do not need any optical isolator okay so they come back from the top you think that it is retracing its path but actually it is not all right I hope you understand the color code the stretched beam is chart so that is what is shown in gradation of colors red trailing blue leading and again if you take a side view in this region then it is like this do you see the incoming beam incoming beam is lower outgoing chart beam is higher now it is very it is a very simple matter to take the beam out right I put a mirror like this a mirror that does not block the path of the incoming beam okay so put a mirror here and the chart stretch beam can go in whatever direction you need it to go so this is the design of a pulse stretcher using a single grating do you have any question simple right now let me ask something what kind of chart is this this is negative chart right suppose my input beam a same input beam is a positively chart beam then what will happen here the discussion is that the input beam is an uncharped ultra short pulse now I am saying the input beam is not an ultra short uncharped pulse it is a chart pulse with positive chart then what will happen provided the amount of charting induced is exactly equal in magnitude to the amount of charting that was there in the incoming beam so in the same design one could make a compressor it all depends on what is going in but see it is easier said than done it is very easy for me to draw this and say that this is what it is going to happen stretching okay you can still do it but the moment you try to compress then you have to be very careful that you should compensate exactly for the amount of charting induced in the stretcher that is where a very intricate and careful calculation comes in because if you compensate too less there is still be some chart left and if you compensate too much then will then what will happen then again you will have a chart beam is it not it is just a positive chart chart will change to negative chart is it understood so you have in the stretcher let us say blue is going first blue is leading and red is trailing now I put in a compressor which will make blue go through a bigger path distance that path distance has to exactly compensate for the lead it had taken on red if it the if that compensation is too little you will still have some chart left if you overcompensate then it will now turn head on now red will lead and blue will follow and you still not have an ultra short pulse in fact sometimes it happens and it all depends on what kind of application your work is on if you need a very short output for our kind of experiments we are happy with the 50 femtosecond pulse but there are applications where you might need say 10 femtosecond pulse there it is not so easy to get an exact compensation by using a stretcher compressor combined in that case you will see in those experiments if you see a block diagram of their apparatus you will see they use additional prism pairs outside the cavity to compensate for whatever residual chart is there of course you have to know what amount of chart is there then only you can compensate for it so sometimes just what is there in the box is not sufficient you might have to do a little more okay so this is the simplest possible design I can think of suppose you want a greater pulse what kind of path difference will we need I have a 10 femtosecond pulse I want to make it 200 picosecond 200 picosecond translates to what length 1 nanosecond that we all remember right 1 nanosecond 1 foot 1 nanosecond is equivalent to 30 centimeter so 0.2 nanosecond is equivalent to what kind of 0.2 into 30 how much is that 6 centimeter right so see it is not very small if you really want a 200 picosecond pulse this one round trip may not be enough because you want a path difference between this blue and red beam you want the path difference of 6 centimeter so that means your stretcher has to be really very long right only if these beams travel at least a couple of meters can you think about having a path difference of 6 centimeter is it not so then the stretcher has to be really very long and usually space is always at premium so many times what you do is you introduce additional optics by which you make multiple passes and each pass introduces some additional chart so multiple passes are often required to get a pulse stretching to a desired extent okay so with that we will close this module and we will come back in the next one and start from this slide