 Today we are going to talk about how to generate femtosecond pulses of different wavelengths for applications like pump probe spectroscopy. As we have talked about the amplifiers earlier, the reason why we want to use amplifiers is that for many applications you want to use a laser pulse that is really very intense. And the way you do it as we have discussed is first you use a seed laser an oscillator you feed it into another laser which is an amplifier and we have learned different techniques of elongating the laser pulse feeding it into the cavity of amplifier by using Pockel cell then switching it out using another Pockel cell or maybe the same Pockel cell and then compressing it once again to get an amplified pulse which is short as well. Now the issue with this sharp pulse amplification method that we have discussed earlier is that you can only get one modal wavelength of course we know that femtosecond pulse by itself is broadband we are not talking about that. But if you think of the modal wavelength there is no way in which you can tune it because the seed pulse has to have exactly the same frequency as the one that will come out well when I say frequency I mean modal frequency as the one that will come out of the amplifier. So if you try to tune the seed then you have to play around with the amplifier laser cavity and all that and then alignment becomes problematic I am not saying that tunable amplifiers are not there they are there but alignment there is a non-trivial process. So what one needs to do is one needs to work on the pulses post production if you want to generate pulses with different central frequencies and the way it is done is called optical parametric generation and optical parametric amplification. So these once again are non-linear optical techniques and as we are going to see they are exactly the opposite of what we have studied earlier second harmonic generation and some frequency generation some frequency generation to be more general. So as you know in some frequency generation what we do is we take light of two different frequencies and we have in our previous discussion we have developed this concept of signal and idler we have talked about the relative frequencies of signal idler and pump and there what we said is that the pump is the highest frequency right the pulse with highest frequency is called the pump pulse and that time it might have sounded a little counter intuitive because there you are actually producing the pump but when we say pump we think of something that is going in right the reason why we introduce it at that time is what we are going to use now. So earlier we have studied some frequency generation not very difficult to understand by considering virtual states we said it is sort of like two droplets of water joining up to giving you a droplet of to give you a droplet of bigger mass. Similarly you have two photons of smaller energy which join up to give you a single photon of a higher energy and what we explained was that you have this material in ground state then let us say omega s comes in the signal frequency the system gets promoted to a virtual state and then at the same instant if omega i comes in it will get promoted to higher virtual state frequency of the energy gap between which and the ground state would be a say h omega p where omega p equal to omega i plus omega s and then when since it is a virtual state it is 0 lifetime so relaxation takes place within 0 lifetime the light that comes out has frequency of omega p which is omega s plus omega i and that is not very difficult to understand right omega s plus omega i combining to give you omega p what we want to talk about now is whether it is possible to do the reverse we have omega p which is a higher frequency is it possible to break it down into two photons one with frequency omega p omega s and another with frequency omega i and the answer is yes but this is not as efficient a process as it is inverse it is much easier to combine omega i and omega s to give you omega p then to take omega p and break it down into omega s and omega i that is point number one and we are not going to get into the detailed quantitative treatment of this that itself can be a course but what we are trying to do here is that we are trying to develop the general idea of how this is done now can you just looking at this expression does it occur to you that there is a potential problem or potential issue or potential feature associated with breaking up omega p into omega s and omega i that problem is not there when you start with omega s and omega i and produce omega p which is a sum of the frequencies when I want to break down into constituents there is something that should strike us what is that feature I am thinking about see when we do some frequency you start with omega s and omega i there some can be only one quantity there is no problem with that but you start with omega p there can be a in principle infinite combinations of omega s and omega i right so there is no predetermined value at least at this moment we will see later on whether it is possible to bring in some predetermined value but as of now all that is required is omega p must be omega s plus omega i right so that reminds me of a story that I did as a child that there was an arithmetic problem in which it was said that 10 pens cost 50 rupees how much does one pen cost and a student wrote we cannot say and when he was asked why you cannot say he said see I mean nowhere is it written that they all cost the same so I can buy one pen for 5 rupees one pen for 10 rupees and I have some kind of a combination and there are many different combinations that are possible so actually that student was right so you have to say that they each pen cost the same here we cannot say each pen cost the same okay or maybe we can as we will see later right but this is what it is now this thing takes place and it is actually a complicated process when you produce these photons they are correlated and the science of this goes beyond our requirement of producing light of different frequencies actually what you produce here is correlated photons and that opens up a different branch altogether in our institute we had this talk by Professor Mukhamal couple of weeks ago you might remember that he did mention in the passing correlated photons right so this is where it starts now when you do it let us say we can do it that a pump light gets into a non-linear crystal and gets broken up into signal and idler first thing that we want to say is you cannot have infinite combinations little while ago we said at least at that point I could write any value of omega s any value of omega i as long as they add up to omega p that is not necessarily correct because not only do you need energy conservation momentum has to be conserved as well as we had discussed for some frequency generation the moment you say momentum has to be conserved the number of possibilities goes down right yeah and also directionality has a role to play now it is just splitting now I can combine this case and Ki and the vector sum can be k pump but you can see that if I have a longer case going higher up and I have a longer Ki then again you can have the same vector sum right if you change the angle so once again it is going to depend on the angle at which the photons propagate right and for a completely collinear geometry the equation that you get is once again you might remember that we had discussed that those polar plots and all and we said that the condition for production of second harmonic was that the refractive indices had to match for the fundamental second harmonic here also refractive index multiplied by omega p np multiplied by omega p equal to ns multiplied by omega s plus ni multiplied by omega i is the conservation of momentum condition the moment you bring this in it is sort of bringing in quantization right not all combinations of omega s and omega i are going to be now allowed but still there will be many okay there can be many of course we have already brought in some restriction here remember we are talking about collinear geometry that is what will restrict things a little bit now why am I not saying that there will be only one combination why am I still saying that there can be several combinations np omega p equal to ns omega s plus ni omega i so if np is defined ns is defined ni is defined then I should think that only one pair of values of omega s and omega i should satisfy this condition why am I still saying there can be several pairs yes yeah what do they depend upon ns and ni are not constant that is the answer even np may not be constant what would they depend upon sorry wavelength is frequency right omega i omega p the automatically wavelengths are defined it cannot be wavelength something else something simpler something you studied when you are younger before you studied wavelength yeah yes maybe but then I am working with the same medium I will not change the medium so that is one way of course you change the crystal you can have different kind of optical parametric generation suppose I work with the same medium what can I change to change the refractive indices what about temperature yeah temperature so you can have temperature control refractive index so therefore using changing temperature as we are going to demonstrate later on you are you can actually get different combinations of omega s and omega i okay so temperature tuning becomes very important here right okay so this would be the simplest geometry in this case so what we have here is we have this omega p coming in focused on to z 1 then here we have the non-linear crystal okay here is the optical optic axis let us say we do not know what omega i and omega s are at the moment we only know omega p but let us say they have been produced so what do you have your mixture of omega s omega i omega p okay and now suppose you want to take the idler out idler is typically the lowest frequency lowest frequency means longest wavelength the shortest wavelength longest wavelength so use a long pass filter if you use a long pass filter you can choose to get only the idler out or you could use a long pass filter which will allow the idler as well as the signal to go out and then by using a dichroic mirror you can get the idler as well as the signal going in different paths that is what is done in a commercial OPO or OPA okay you can actually generate both I mean will generate everything but you can actually use both if you want what is the problem the problem is intensity very very small so first of all what you can do is like earlier you can do angle tuning for phase matching that way you can decide omega s omega i and you can optimize the condition by which they come out this we have to remember that signals are very very low see even some frequency we said typical efficiency is like 20% here typical efficiency would be 2% or 1% or less depending on what kind of material it is very low and then depending on the NLO material you can have type 1 phase matching or type 2 phase matching type 1 type 2 phase matching we have discussed in the previous modules now what is the application the major application in this case is what is the range that is available to us most easily what is the range of wavelengths that is available to us suppose you are using a ticep ion laser the range of wavelength that is available to us very easily is red right from red we have learnt how to create blue or even UV by second or third harmonic generation here we have learnt how to create IR right and also how to create single photons so one application that we are not really going to talk about here today but it is a very important application of optical parametric generation is that many times you want to do experiments in which you generate only one photon that is done very easily here okay you can do it by angle tuning you can do it by modulation of intensity and all that you do it in such a way that at an instant only one photon is produced and then you do whatever you want to do with it okay do you know what is a very good detector for a single photon yeah yes or I can actually see a single photon if you are in a dark room and one photon comes in and it is if it impinges on your eye that will generate a signal I is good enough right now let me show you the schematics of construction of an optical parametric oscillator where does this oscillation thing comes we have a later slide where the schematic oscillation is shown briefly see we have said that the efficiency is very less right so if efficiency is less how do we increase the efficiency one is by amplification which we will study later the other is if you make sort of a laser cavity and if you make the signal beam go around in the cavity several round trips then you can have some amplification right so and note the date physical review let us find what which year was this published 1965 so these experiments started more or less along with the invention of laser the moment lasers were invented people started thinking what can you do with them perhaps I do not know whether they even thought that we are going to do bumpers spectroscopy and all that at that time they just wanted to create single photon they wanted to create correlated photon pairs they wanted to have a mean of tuning the wavelength so as far back as 1965 before any of us here were born this thing was there okay and here is the schematic again the active medium here is new medium ion the different substrate it gives you 1058 nanometer 1.058 micron that is let us say omega 0 so what they did was first of all they put in a lithium niobidate crystal they called it T1 crystal and the work of this crystal is actually to do what we already know to generate the second harmonic 2 omega 0 now the moment you create second harmonic you know very well that the efficiency of conversion is only 20% or 15% 10% 8% something like that so there you have 2 wavelengths already omega 0 and 2 omega 0 which one is omega p which one is omega s how have you defined it what is the highest frequency what is the largest frequency what is it called pump signal or idler no highest frequency is a pump so this 2 omega 2 omega 0 is actually equal to omega p that is your pump and omega 0 is the signal of course in this case idler will also have frequency omega 0 if you are going to use it like that so then here after that they had this infrared absorbing filter which one will get removed omega 0 is gone you only have 2 omega 0 here omega p okay then they had this second lithium niobidate crystal T2 from which you are going to generate omega s and omega i okay how can you do it we have discussed already that if you change temperature then all these refractive indices will change so even for collinear geometry you can get different frequencies for idler different frequencies of signal if you simply change the temperature and that is the experiment they actually did unfortunately the 1965 many many years ago so that time drawing graphs and all perhaps did not capture so much of attention like what we do nowadays but you can see what is there on the x axis what is there on the y axis x axis is temperature degrees centigrade right and it goes from 46 degrees to 66 degrees about 20 degrees and y axis what is y axis yeah it is wavelength in micron okay so what you get is you get two branches you see these dots these are the experimental points the two branches this one is the signal this one is the idler is it right did I say the right thing why not idler is longer wavelength look at the y axis shorter values on the top longer values at the bottom the top one is 0.96 micron then this is 0.981 and the lowest one is 1.16 in 1965 people used to think differently what can I do so what they have done is they have plotted from the lowest value of wavelength is on the top or you can think like this they have written wavelength that is the issue highest value of frequency is on the top right so in this parabola that we have the points on the top are the signal points at the bottom are the idler okay and many times you see there are more points I do not know if you can see that you see there are more points in the top than in the bottom so many times they could not even detect the idler the idler got absorbed or intensity was too small they could not detect something like that signal is a little better that is why it is called the signal okay lower the frequency more difficult it is to detect okay I have no idea why it is called idler of all things because I mean it is as idle as in the signal I guess but signal is a little easier to observe okay so by changing the wavelength sorry changing the temperature here different omega s and omega i were prepared of course you understand that for a particular value of omega s frequency of the signal frequency of the idler gets automatically determined right because frequency of pump is known that is 2 omega 0 1058 multiplied by 2 in nanometer right that is of course wavelength the frequency corresponding to that. So at a particular temperature you get omega p is the same at all temperatures omega s and omega i values vary with the condition that omega s plus omega i is always equal to omega p that is 2 omega 0 next that this silicon filter which cuts out visible light and only omega s and omega i are transmitted okay so this is one of the first examples of optical parametric oscillator I have not shown the entire diagram here the entire diagram would look something like this where this non-linear crystal is actually put inside sort of a laser cavity a cavity so that the resonant signal beam gets amplified a little bit and signal and idler output typically travel in the same direction and then you can further separate them by using no that is not that is in the next one by using a separation optics like dichroic mirrors okay. So the problem is that the intensity is very small so when intensity is very small you want to amplify it and that brings us to the principle of optical parametric amplifier and when we discuss optical parametric amplifier actually two phenomena come to my mind when we discuss this one is Raman effect the other is stimulated emission and you see why I am saying this so what you see in this diagram here is you have a stationary state ground state and you have a virtual state at higher energy compared to the ground state okay let us say that the pump frequency promotes the system to this excited to this virtual state okay so omega p takes the system to this virtual state here now let us say and that is why this reminds me of stimulated emission let us say by some means I already have a little bit of omega s in the system okay now what will happen sort of stimulated emission okay so if you sort of stimulated emission would take the system from this higher energy virtual state to a lower energy virtual state difference in energies between which would correspond to the frequency omega s right so this is what you would get instead of one now you get two photons the photon that part of the virtual state with higher energy and the photon that is generated as a result of lowering the energy from the higher to lower energy virtual states this is why it reminds me of stimulated emission and you can see where amplification comes in here right one pump photon sorry one signal photon came in and two were produced right now what happens to the remaining energy omega p-omega s what would that be equal to omega i idler that would also come out automatically right this is how this is the very basic principle of optical parametric amplifier now if you think practically where will we get omega s now and then I want a tunable source right so I might want as many possible values of omega s as possible the best way of trying to do that is to generate white light yeah now we are familiar with this concept of the white light generation we know that if you focus an intense femtosecond pulse on a substrate like calcium fluoride or your sapphire earlier experiments are done by focusing because second pulse on water D2O mixtures then you get something called self phase modulation and white light is generated of course white light intensity will be nothing compared to the laser light but we do not need a high intensity we only need some photons that are going to cause this downward transition so a good strategy of building an OPA would be you take your light laser light say 800 nanometer light out of an amplified out of an amplifier tie sapphire amplifier split it into two parts focus one part on to some substrate there sapphire filter okay generate white light okay then of course you need optics to collimate the white light and all then on the nonlinear crystal focus that white light and focus the residual part of the output of the amplifier now what will happen output of the amplifier is going to serve as omega p all the components of white light can in principle contribute can act as omega s but by angle tuning the crystal and of course we are maintaining the some temperature you can select preferentially which of these frequencies of white light is going to act as omega s right so by angle tuning that is what happens in an OPA by angle tuning you can select the signal frequency and the idler is generated any okay so you have actually generated two different colors already now you decide whether you want to work with the signal or the idler generally you prefer to work with signal sometimes due to some problematic combinations of optics and all the signal may not be all that accessible and if you are fortunate that the idler frequency idler intensity is large enough then you might actually end up working with the idler that is point number one point number two is sometimes you want to work with idler when do you want to work with idler what is the output of your tie sapphire amplifier 800 nanometer model wavelength so that is red what is the constitution of the white light it is all visible isn't it so typically your omega s would be in the visible range suppose you want IR light how will you get it using all this if you want for some application suppose you want to do an IR probe experiment or suppose you want to do an IR pump IR probe experiment something like that 2D IR then the only hope of generating IR from this essentially visible light giving system is to work with the idler right so the frequency of the idler is essentially the difference of frequencies of pump and signal isn't it so this process is called optical parametric amplification OPA it is also called difference frequency generation DFG okay so what it essentially does is that if you have the right optics then in fact it gives you tunability from anywhere to anywhere so what you could do and what is done in commercial amplifier a commercial OPA is as we might discuss in the next module is that first of all you have nonlinear crystals by which you do second harmonic generation that gives you access to blue and maybe even UV you do third harmonic generation 800 by 3 how much is that the magic numbers you have to know 800 by 3 you neither do arithmetic quickly or you have to know 267 right 266 that is a magic number third harmonic say third harmonic second harmonic fourth harmonic this when you are into lasers these things will occur to you automatically 1064 is a magic number in the fundamental 532 second harmonic then third harmonic of that fourth harmonic of that all these numbers will come to us automatically so on one hand by higher harmonic generation you can access UV right and not only that you do not have to be restricted to only the harmonics now you can do this and generate signal in blue or maybe even UV on the other hand if you use the fundamental of the amplifier 800 nanometer as omega p then you can get things in red and the difference frequency can give you IR so that is why an optical parametric amplifier a single optical parametric amplifier which is properly equipped with the right crystals and right optics and in good shape can give you tunability from 200 nanometer all the way to IR that is the strength of this piece of instrument okay and the principle if you do not go into very deep of it the qualitative discussion of the principle is quite simple okay so again this is an example of a of one stage of an OPA typically OPAs would have several stages but this is something that is there and this is from the usual textbook that we use so let us say this is omega p 1047 nanometer and this is omega s 1.1 to 1.8 micrometer as a 1.1 micrometer means how many nanometer 1100 nanometer so first of all I do not understand why this is 1047 nanometer and why that is 1.1 micrometer I do not know but we should not think that this is 1000 that is 1 that is why I wanted to make this so here in this system that we are discussing actually your pump and signal have not very different energies now the thing to note is the difference in polarization and that has a role to play later the pump is vertically polarized the signal is horizontally polarized okay and the idler you will produce you are using lithium new update if you remember what we discussed in at the earlier ones in LINB O3 we have EOO kind of situation if you take pump signal and idler so the idler that will be produced will have the same polarization as the signal not the pump so you change the temperature you angle tune it do whatever you want until you get signal and idler right signal and idler have the same polarization pump has perpendicular polarization now it is very easy to take the pump out just use a polarizer here they have used a Rokon polarizer you can look up what a Rokon polarizer is it is basically the same as Wallaston polarizer you have calcite or something which is cut into 2 and then joined again the regular stuff that you have been studying in organic chemistry rotation of polarization that kind of thing so first of all when you use a polarizer the pump gets cut out and then depending on what you want you want the signal or you want the idler you are going to use a filter the filter that is shown here is a germanium filter which will allow the idler to go through the smallest energy and it will not let the signal to go through okay you can always use a dichroic mirror to send the idler one way and the signal the other way that way you have access to both okay so this is the principle of optical parametric generator and optical parametric amplifier what we have in our lab is an OPA not an OPO OPO's generally operate at much higher frequencies similar frequencies as your tricep higher oscillators so OPO's are very good for things like up conversion experiments femtosecond up conversion femtosecond optical gating because they can give you a continually tunable range of wavelengths at high frequency 80 megahertz that is what you need for your fog kind of experiments but in pump probe generally one wants to use OPA because you need higher intensities right and OPA's once again they are limited by the frequency that goes in and OPA's also have their own limitation not all OPA's can work at all frequencies typically you want to use an OPA which can work at the frequency of the output of the amplifier which in our case is 1 kilohertz right so typically OPA's are associated with higher intensities higher number of photons I want to say I do not want to say energy because we will get confused with h nu higher number of photons let us say and lower frequencies whereas OPA's are usually associated with lower number of photons but higher rates okay both have their own advantage both have their own applications and both are equally costly actually an OPA is I think more costly than OPA as you know amplifier of course is more costly than oscillator because it contains an oscillator it has to cost more but if you want an OPA that is why you will see OPA's everywhere OPA's are not all that common because OPA's are actually very expensive and if you have a short enough pulse for a tricepher oscillator with this sealed tricepher oscillators that we now have and with continuous tunability very often people do not care for OPA anymore but in some applications it might be required okay so that is what I wanted to say about OPA's in the next module we will briefly discuss the construction of the OPA that we use and then we have discussed instruments for a long time we want to discuss some actual experiments classical experiments that have been done we will next go on to two experiments one is Amidstuel's experiments that we got in Nobel prize in 1999 how much time does it take for a bond to break and how does a bond breaks what you what you call snapshots of bond breaking we will discuss that in the module then I want to talk about water a little bit because water is my favorite subject and in any case our life is based on water so two things one is solvation dynamics in water ram flaming spark the other is how a vibration energy is transferred from one mode to the other in associated water molecules that is Eric Nibering's work and perhaps we will stop with stop this section with Eric Nibering's work on visible pump IR probe experiments then depending on how much time we have I want to talk a little bit about pulse shaping and I want to talk about 2D experiments if you get time we will talk about Terahertz experiments as well the purpose of this course is that we want to have an overview of all the kinds of different ultrafast experiments that chemists across the world are doing at the moment we are not going to talk about at a second experiments because until now I believe that there is no chemistry in at a second it may be a little atrocious statement to me but then after all the reason why I am saying this is that it takes 100s of femtoseconds for a bond to break and chemistry starts with bond breaking so faster than that there are interesting phenomena there can be state to state dynamics but at least in this course we are not going to talk about at a second spectroscopy because that requires a different level of understanding but these are the experiments which we want to discuss and while doing that we will have to come back to instrumentation a little bit after this because I want to talk about pulse shaping because many of you might end up in laboratories where you have to do pulse shaping if you want to do a 2D experiment pulse shaping becomes extremely important so we will talk about that a little bit so much for today.