 So, we are discussing time-resolved fluorescence upconversion technique and once again let me state that the slides are all from Shobhansen of JNU. So, this is where we had stopped in the previous module and what we have here is we have a schematic of the optics that are there in upconversion. Now, we want to use this use some animation to show you how the decay is actually recorded. Now, before that let us just quickly remind ourselves what we have. You have a titanium sapphire laser right now you do not have to worry about anything else but typically we have a 100 femtosecond pulse we have 100 femtosecond pulses at 80 megahertz then this is directed into the spectrometer this is the part that we had discussed earlier the spectrometer. A lens L1 focuses the red light on to the second harmonic generation crystal and the second harmonic generation crystal that is used is typically a BBO crystal what is BBO? Beta-variant borate that is usually the non-linear optical material that is used everywhere now then what this one does is that it converts some of the red light into blue light both are collected by this lens. So, see the thing is in order to get best result you have to focus your light but then the output of that is a diverging beam you cannot work with the diverging beam you want to collimate it once again. So, this combination of two lenses one focusing lens and one collecting lens is ubiquitous in when you work with optical instruments why do we need to focus because let me write now rather let me draw what we have discussed in the previous module without drawing anything I think it is better to draw otherwise it may not be very simple to visualize is that we said let us say this is the ground state of your BBO or whatever it is. So, first you have this first photon coming and it is omega 1 in keeping with the terminology we have used later it causes a promotion and usually the promotion is not to a stationary state it is to a virtual state we have discussed that already for second harmonic generation you require the presence of another photon omega 1 which promotes the system to another virtual state and then as we said there is no memory when the system is here it does not remember whether it came there by one step or 500 steps. So, the light that comes out is like this 2 omega this is second harmonic generation would very very simply for you now for this to happen what is the requirement is that when you promote up to here another photon must be there and when I say there I might clarify a little bit saying the second photon must be there and must be there at that instant. Let us say this is the cross section of your crystal and let us say you have promoted to this virtual state at this spot it makes no sense if you have another omega 1 available here it has to be here and it makes no sense if the second omega 1 comes 2 years after the first one 2 years of course is an exaggeration it must be there at that instant that is why first of all you have to focus using the optics that we have shown earlier. So, that you have lot of photons here and when you use a pulse this is the typical shape of a pulse intensity versus time all the energy is packed in this short time. So, within this 100 femtoseconds you can expect that there will be a large number of photons that will be there to serve as a second omega 1 that is why it is convenient to get second harmonic generation if your laser is pulsed. So, this is why we need to focus as well. Now let us return to our presentation. So, this lens collects it straight this is a dichroic mirror dm means dichroic mirror blue light is sent in this side and if your alignment is perfect then it goes as a collimated beam it goes to some other optics we have discussed neutral density filter which is ND what this is will come to this in this module or the next then you have m 5 which is actually another dichroic mirror residual red goes this way blue light goes here again you have a lens which focuses the light on to the sample and one thing I forgot to say in the previous module is that if you are working with liquid sample then you want to rotate it. So that the same point does not get illuminated always and if it is a solid sample then you want to translate it and typically translation is like this is a name for this kind of a scanning what is it called it is called raster scanning right you go like this in the same spot is never hit by light twice. So, possibility of damage is minimized. So, once again we have this familiar focusing and collecting optics arrangement once again if your alignment is perfect then what comes out of this lens is a collimated beam but in this collimated beam it is nothing it is anything but monochromatic you have blue light as well as fluorescence and in fact blue light is more intense that is why you use F2 which if you remember is the long pass filter which cuts out the blue light excitation light laser light allows only fluorescence to go through and then this lens focuses it on to these some frequency generation crystal. Here what happens is on the other arm red light which is called gate light omega 1 as we have put it goes to this mirror m3 then to m4 it is a retrofactor is turned back and the retrofactor is actually mounted on a one foot long screw which is which can be moved using a what is called a step motor. Step motor means something that does not turn continually but goes in steps. So, if you step motors are quite common in day to day use they are used in printers for example and there are many other applications. So, from m6 it goes to m7 same lens is used to focus it on to the some frequency generation crystal if everything is perfect then you get omega 1 plus omega 2 some frequency and then you detect this some frequency and here when I say everything is perfect what does it mean one very important parameter two parameters one is that both the spots must have been focused both the light beams must have been focused on the same spot and you understand why the diagram we drew a little while earlier the two lights have to be specially overlapped otherwise they cannot combine if one spot is here one spot is here how will they combine. Second thing that we have not discussed so far because we are going to have a little more discussion when we talk about talk formally about non-linear optics is that the phase angle of this crystal has to be right. Basically some frequency is very strongly dependent on the angle of the crystal with respect to the incident light it typically works in a very narrow range of orientation. So, what you do is in order to get good some frequency generation or good second harmonic generation you have to angle tune the crystal turn the crystal until you get a good some frequency or good second harmonic light and you detect it. Now we come back after 10 minutes of recapitulation of what we said in the previous module we come back to the question we asked what does all this have to do with femtosecond time resolution remember we are doing this because you cannot have electronics that can do a real time femtosecond measurement all electronic components have the response time which makes them slow a microsecond is something electronics can handle quite comfortably not femtosecond. So essentially we are trying to overcome this limitation of electronics by using something that is faster than anything else if you leave out things like tachyon and human mind what is the fastest thing you know especially as is a spectroscopic course light right light since electronics is too slow we have to use the fastest thing at our disposal that is light to get the resolution and what I will do is first of all I will draw and then we are going to show you an animation. So let us go back to the drawing board let me draw omega 1 in blue sorry omega 2 in blue and omega 1 in black all right. Now if I want to plot intensity versus time for omega 1 what does it look like intensity versus time plot of omega 1 something like this yeah it is a pulse to the finite bit 152 second or whatever if I want to make the same plot for omega 2 what would it look like so this is decay right it would go up and come down something like this it can come down completely it can be incomplete whatever it is. Now see if you go back to the schematic of the instrument what we have essentially is that drawing it very simply this is your omega 1 I am not drawing the bits of optics I am just drawing the path one thing I cannot avoid drawing is the some frequency generation crystal what about omega 2 omega 2 well there is some path before this and omega 2 also has some path before this and then it comes straight it would better overlap with omega 1 exactly at a subject which it does not so what I will do is I will just make the subject order in real life I cannot do it it would better fall on the same spot. Now see omega 1 has travelled some path omega 2 has travelled some path right and if you remember omega 1 retro reflector is mounted on a one foot long screw which I said is operated by a step motor which can move forward and back what does it mean that means omega 1 has a variable path length omega 2 has a fixed path length and I can move omega 1 so that the path difference between omega and omega 2 can be altered alright let us say the path difference is something like this and this is at the crystal right at the some frequency generation crystal the path length is such that this is a scenario remember black is omega 1 blue one is omega 2 I will not write that anymore now in this situation do you think there will be any some frequency generation yeah omega 1 has come too soon okay omega 2 is not even there so there will be nothing right so if I now want to plot intensity of some frequency as a function of I will write delta what is delta the path difference what will the intensity be 0 you might see where we are going because we have done a very similar discussion when we talked primary well in a very hand waving manner when we talked about pump probe spectroscopy earlier on okay same thing now suppose I change the path length of omega 1 and it comes here path difference is smaller will I get any some frequency generation here no so once again some frequency intensity is 0 now suppose it has come here now this is the best possible situation okay so what will happen to intensity of some frequency provided the angle is right it will go up it shoots up now if I change the path length of omega 1 a little more and bring it here then what will happen intensity of omega is same intensity of omega 2 has fallen off exponentially or whatever and intensity of omega 1 plus omega 2 intensity of some frequency what will it be it will be something like intensity of omega 1 multiplied by intensity of omega 2 and there can be some factor something kappa okay so what we are doing here is that always intensity of omega 1 is constant but intensity of omega 2 first of all is 0 then it rises sharply to some value and then it falls off so if you keep changing the path length what will happen is intensity of some frequency will also change accordingly so if it comes here even though intensity of omega 1 is the same intensity of omega 2 is a little less as the fluorescence has decayed a little bit will come down accordingly if you change keep on changing the path length then the intensity of some frequency will fall off and it is important to understand that the shape of this curve is exactly the same as the shape of the decay of omega 2 so what we have generated here is a map of the fluorescence decay we have generated a map of the fluorescence decay and here it is important to not get confused about one point the way it works is that the screw moves so the retroreflector moves and as long as the retroreflector moves no measurement is done then it stops at some particular position delta 1 it stays there for some time half a second one second two second five second whatever you set it to be that is when the measurement is done alright so two things first is movement of the retroreflector second is actual recording or intensity of intensity they do not take place simultaneously when one happens the other does not so when you make a measurement actually then everything else is fixed mirrors are not moving delta 1 value is fixed so we are making essentially a steady state measurement and we are integrating for one second two second five second whatever so the good thing about this is that you do not need a fast detector we are actually get off using relatively inexpensive simple detectors like a regular photomultiplier tube which you would use in a steady state fluorescence measurement because you are performing steady state measurements here and that is the beauty of the technique you are using what is at your disposal the fastest thing at your disposal that is light just by moving this retroreflector little you are giving different path difference and that is what can give you femtosecond time resolution before coming to that let us show you the animation alright this is your back to the projection once again so this is what it is and remember what we are doing now is this is the same diagram that I just drew red is omega 1 green is omega 2 what you are doing essentially is that you are changing the delay like this and therefore the path differences are changing omega 1 samples different parts of the decay and that is how the plot is generated it is important to understand that what you generate is the map of the fluorescence spectrum and this is exactly why I do not try to use my presentation are you like to use so once because it takes a lot of time to make animation like this but now now that you have seen the nice presentation it is important to go back to the chalkboard once again and see whether what I see makes and what I say makes any sense or not so let us go back and do a little bit of calculation once again right you told me light is the fastest thing that we have right what is the speed of light 3 into 10 to the power 8 meters per second what does this mean the rule of thumb that I like to use is light travels 1 foot approximately 1 foot in 1 nanosecond ok so that is what it means how much does the translation stage have to move if I want to give a if I want to change the path length a path difference by 1 point 2 second very simple let us say so this is your retro reflector right this is omega 1 I am saying that I move it to this position right and there I am going to neglect this part of course the only thing that matters is this length so suppose I move it by delta rather let us say I move it by s s is better right in class 9 10 physics also we say distance is s so I move it by a distance s what is the change in path length well what is the change in time involved if I move it by s by how much is how much more distance is light moving s while going s while coming so 2 s 30 centimeter is equivalent to 10 to the power 9 second is equal to how many femtosecond this is that 10 to the minus 9 seconds 10 to the power 6 femtosecond ok how many micrometers is centimeter 10 to the power 4 right 4 so 30 into 10 to the power 4 micrometer is equivalent to 10 to the power 6 femtosecond so if I want 1 femtosecond that will be equivalent to 3 into 10 to the power 5 divided by 10 to the power 6 micrometer and that is equal to 2 s so from here you can see what it will be something like 1 micrometer or something like that so basically you have you must have the precision of moving this retro reflector by a micron is it possible it is possible because you use a screw it is very easy to get a pitch of less than a millimeter and it is not difficult to move it by a fraction of a degree that way you can get femtosecond resolution so this is how femtosecond time resolution comes ok what do you need you need you need to have a suitable pitch of the screw and you need to have a step motor that is sufficiently accurate ok it should be able to move in milli degrees or something like that that is not very difficult to get so this is how you can get the femtosecond time resolution ok this we have already answered and I think now you have understood how we get time resolution here we get time resolution because we can move this retro reflector in very small steps so we can actually give very small differences in path length and then we make a steady state measurement now you might remember that I told you that we use lenses to focus but there is a better way of doing it the reason why I said it is that again we are going to elaborate upon this point in one of the later modules when short pulse when ultra short light pulses go through any dispersing medium they get broadened and in fact it is used to our advantage in some application later on but then if you want to make a measurement with a very good time resolution your laser pulse and everything else must be very very short so then you cannot use any optics through which the light goes you have to use all reflector optics in that case what you do is in fact even here to focus the light on second harmonic generation you want to use instead of a lens you want to use a curved mirror and then actually even this is not correct you do not want to use a lens here you replace all the lenses by parabolic mirrors like this that gives you better time resolution typically in our instrument we have a hundred femtosecond pulse coming out of the laser but when we measure instrument response function it is no longer hundred femtosecond it is close to 300 femtosecond so if you do not want that if you want that your suppose you want to use a 50 femtosecond pulse and you want your instrument response function to be no more than say 70 femtosecond then you want to use all reflective optics like this in fact initially everybody made all reflective optics they did not use lens for the fear of losing out on resolution the problem here is that to get the first signal if you build your instrument and you do it with parabolic mirror getting the first signal is a complete nightmare it is much easier to use a lens because with the lens you have only one control you have to move it forward or backward and you already know what the focal length is so you already know the approximate position it is much easier to get the first signal when you set up the instrument using a lens that is why usually people are happy sacrificing some of the time resolution by using a lens because that would give better collection efficient right now this is an example of up conversion data you can see this is the data and this is a fitting curve we talked about fitting curve in the previous module and you might be able to recognize here that the data quality here is definitely not as good as what we get in a TCSPC TCSPC gives unparalleled data quality that is why it is so popular worldwide but then if you want better time then you have to use something like up conversion you can also use something else called stick camera we will talk about it in very brief next point of discussion is why do you want to take care of polarization and what are the things that can go wrong in an up conversion measurement that is what we will take up in the next module.