 So, this is where we had left off in the previous class with a something called magic angle. What is that? Once again we want to deal with it briefly because we intend to come back to the issue of polarization of fluorescence in a little more detail later on. To keep it very, very brief generally you excite using a linearly polarized light and you do that because first of all the laser that you use is usually linearly polarized. If you are talking about a Ticephal laser, Ticephal laser is very nicely linearly polarized. If you are working with diode laser of course you cannot work with diode laser for up conversion for TCSPC diode laser usually is elliptically polarized which means there is a mixture of horizontal and vertical polarizations. There you put in another polarizer and generate one kind of polarization. So, when you excite with polarized light then what happens is photo selection. Photo selection means only molecules that have a component of whose dipole moment has a component along this direction is going to get excited. We come back to this in little more detail later on but the issue is this when you excite and then when fluorescence takes place even though you excite with linearly polarized light this one the fluorescence that comes out is actually depolarized to different extent depending on your sample medium and so on and so forth. And I hope it is not very difficult to understand what these jumping targets are what it means is that generally not generally always when light polarized light is incident on a nonlinear medium then the harmonic that is generated undergoes a 90 degree shift of polarization. What you see here what you see here in the red double arrow here the polarization is in the plane of the breadboard the blue light has polarization in perpendicular direction okay. So, the problem is this you have depolarized fluorescence coming out but then depolarization can take place by many different mechanisms rotation of the fluorophore while in the excited state being a major one and that brings something like a rise time in the decay unless you are careful. So, after all when you excite the molecule has this kind of polarization when it emits it has say this kind of polarization then this state was not even there so it has grown over time after excitation that can show up as a rise time. In fact if you measure at 90 degree polarization with respect to the excitation polarization you do get a rise time distinctly. And then if you measure at parallel polarization then also you are not safe because this state the state with this kind of polarization undergoes an additional decay because this one is being formed and that decay is not the decay of the excited state that decay is just because of rotation of the molecule. So if you measure along parallel polarization then you are going to get a very fast decay. So crux of the matter is because of rotation of the molecule while in the excited state you are going to have additional fast decay or rise in your decay in your transient rise in decay sounds foolish how do we eliminate that we are going to do the math in a little more detail later on. But for now let me just tell you that there is this angle 54.7 degrees which is called a magic angle you might want to be wondering why I am saying 54.7 when the magic angle written on the slide is 35.3 to understand that do a very simple bit of math subtract 54.7 from 90 degrees what do you get you get 35.3. So 35.3 because 35.3 is what you maintain with respect to the fundamental red light. So that the angle with the blue light is 54.7 degree. What happens at this magic angle so once again skipping the math for now let me just tell you that this rotation thingy has a 3 cos square theta minus 1 term and when theta equal to 54.7 degrees 3 cos square theta minus 1 is 0. So this is the angle and that is why it is called a magic angle where the fast decay or fast rise due to rotation is not observed. So what you see in your transient is just the time evolution of the electronic excited state irrespective of orientation that is why when you record lifetime by TCSPC or by up conversion you always have to measure at magic angle otherwise you are going to get additional spurious components and rotation is only one thing if there is homo freight you are going to get a rise. So magic angle is what you have to maintain and magic angle does not mean angle between the beams it is the angle between polarization that is usually achieved by something called a Berek plate once again we will not go into that at the moment later on if there is time for discussing optics in a little more detail we will come back to that. Let us just say that Berek plate is something that rotates the polarization and you can rotate it to 35.3 degrees with respect to blue well you rotate the polarization of the blue light by 35.3 degrees so that you only look at fluorescence of this polarization magic angle to the fundamental. Next let us move on a little bit and talk about something we do not have in our lab see in the experiment that we have discussed so far you have to suppose you want to know how the fluorescence spectrum evolves with time we have had a discussion of that in the one of the previous modules already. So then you have to go wavelength by wavelength emission wavelength by emission wavelength right and every time you have to record a decay stop then go and change the angle of the SFG crystal start the experiment again so all this can be made a little simpler if you do what is called 2D up conversion 2D up conversion also comes in two different forms we are discussing this the simpler form now if there is time we will talk about the more interesting form later on but for that we will need some knowledge of nonlinear optics so we are postponing that discussion. So especially Marget Chebu is group in Switzerland what they have done is that they have attached a computer control to the some frequency generation crystal. So now remember this is only thing that one thing that changes about the some frequency generation crystal is that you have to change the angle so in this instrument first of all it is calibrated and the angle for all different wavelengths is determined that what is the angle for 600 nanometer what is the angle for 605 nanometer so everything is calibrated and fed into the computer and then the rest is simple start the instrument and say that you are going to measure at every position of the BBO crystal for a certain amount of time. Now understand what is happening first your computer sets this BBO crystal the SFG crystal at a particular angle that means your omega 2 is selected omega 1 is constant anyway there now you scan the delay so you get a transient. Next you go back and change the position of the BBO crystal so instead of omega 2 A your system is tuned for omega 2 B you record a transient once again for the same amount of time when I say same amount of time I do not mean integration time I mean total acquisition time half an hour 1 hour 20 minutes 5 minutes whatever so for every angular position of the SFG crystal you record a transient but the trick is you record the transient for a given amount of time you program it in such a way that all decays are recorded for say 5 minutes each or 20 minutes each or something all of them so now some decay will be like this some decay will be bigger depending on the emission wavelength right so now the intensities are believable since you are recorded for the same amount of time. So now you get this kind of a plot you see this is a 3D plot here it is color coded x axis is time y axis unfortunately is cut but y axis is well wave number of emission so if you take a cut along this direction what do you get if you get a horizontal cut then you are keeping the emission frequency constant and you are looking at time evolution you get the decays and that is what you are measuring actually anyway if you take a vertical cut then what do you get you get the spectrum when you take a vertical cut what am I doing this is 0 time right you go from bottom to up you get the 0 time spectrum now when you are at 0.2 picosecond you go from bottom to up you get the spectrum at 0.2 femtosecond okay so from this plot you can take this cut or this cut and get either decay at a particular emission wavelength or emission spectrum at a particular time the problem here of course is deconvolution if your pulse is not so small if it is 300 femtosecond or so then at least for the first 1 or 2 picosecond you get a spectrum that is converted alright so that is a little bit of an issue but otherwise this is a convenient way of doing it if nothing else this allows you to get the decays across the entire spectrum and after that if you are if you want to include convolution you do what we did earlier convolute well deconvolute get the lifetimes using the lifetimes and steady state spectrum to generate the time resolved emission spectrum and in fact even the setup we have or the setups that are there in different labs of India can in principle be converted into this 2D up conversion it is not such a big deal you need a lab view program which is going to drive this and we will interface with the existing program or write a lab view program for the entire thing okay the other way so if you read this paper in Anju camp published in 2006 by Marith Chaguri this is what you see but then if you read the work of Therazima and co-workers what they do is that they use a very thin some frequency generation crystal and it is such that this angle tune is not even required so there you actually record the entire spectrum in one shot you use a spectrograph CCD kind of arrangement to detect the entire spectrum at different positions of delay that is a smarter way of doing it but we would like to come back to it later on if you have gained sufficient understanding of your non-linear optics and all that. Now before concluding this discussion it is important to understand where we can make mistakes okay first mistake that can come and this is something that one needs to be very very worry about is if the gate beam is not horizontal okay let us go back to the schematic remember this decay that you are generating this map of the fluorescence decay is actually raw values of intensity it is not a relative value or anything okay and remember what we had said earlier that this intensity of some frequency is sort of a product of intensities of omega 1 and omega 2 beams. One thing that we have not brought into the discussion so far and now we should is that we now need to worry about the actual spots on the Bivio crystal of course they showing you a very enlarged picture here but let us say that this red circle is the spot of omega 1 on the Bivio crystal and let us say that this one is omega 2 okay here the way I have drawn it the special overlap is perfect right all of intensity of omega 2 is in a region where omega 1 intensity is there and of course these spots are usually if you think specially they are Gaussian which means that the intensity would be maximum in the center and fall off to the sides now let us say this is the situation okay I do not if you understood what went on I will go back let us say that this is omega 2 beam this is omega 1 beam that is coming in instead of coming horizontally let us say it comes like this okay what will happen as I change the path length as I change the path length this is what will happen it is moving like this if it is horizontal it does not matter okay let us say the pulse is here well for the sake of discussion let us say I am talking about one pulse which is here okay it does not matter moves like this if it is like this then what will happen special overlap will get worse right that is what we are shown here you start with perfect special overlap but let us say omega 1 is not coming like this it is not horizontal then as it moves the overlap will become poorer and poorer okay so effectively intensity of omega 1 does not remain constant okay and effectively always unless you start from a very bad special overlap always what will happen is that as the stage moves the special overlap will become bad it will go from bad to worse so what does that mean suppose you are recording from 0 time to some time t dash okay special overlap keeps on getting worse at every step so you can think that intensity of omega 1 is decreasing for every measure so that adds another spurious component to the decay of the some frequency intensity you are going to get always so your decay is always going to look faster than it what it should look and it is not essential that you are going to be able to resolve it it is not essential that it is very fast compared to what you are looking for it may be something that is close and that is the most dangerous situation you would not even know it what you are not going to get the correct result so it is absolutely important to ensure that what we say the stage is flat which means this omega 1 light beam is flat how do you do that and that is where the role of M3 and M4 come in all mirrors have two controls horizontal and vertical if you touch one the beam moves horizontally if you touch the other the beam moves vertically okay so what you do is by playing around with the controls of M3 and M4 you ensure that the beam is horizontal how do you ensure the beam is horizontal the crude measurement is user ruler and ensure that it is at the same height from the base plate everywhere that is what you should do first secondly what you can do is you can put an additional mirror somewhere here and take your beam to a distance and put it on a wall and then move this delay forward and backward look at the spot on the wall see if it is moving vertically or not it should not move so you should keep on playing around with M3 and M4 until for delay being here at the minimum position and here at the maximum position your spot on the wall does not move that is the best way and the most strenuous way of doing and bigger the stage you work with worse it becomes okay now let me ask a question this previous first component I am talking about does it show up for smaller times or longer times shorter times or longer times definitely longer times so it is a long component that is going to be effective if it is okay that you work within 2 picosecond if your decay gets over in 2 picosecond of course the other problem for a decay that gets over in 2 picosecond is that there will be hardly an intensity that is a different issue but suppose it gets over in 2 picosecond then even if it is a little away from the alignment it will not matter but if you have to move your delay line over a length of 15 centimeter 15 centimeter is 1 nanosecond then it is so in my opinion the best way of doing it is to put it on the wall but now with advent of technology you can do other things what you could do is remove this BBO crystal or if you are scared to remove the BBO crystal at least put a lens put a mirror here and use a webcam put this of course before putting it on the webcam if you value it put a lot of neutral density filter so that intensity is as low as possible you are working with the laser after all so just put it on a webcam look at the output good thing about this method is that if you put a spot how what is the thickness of the spot the millimeter less right about a millimeter let us say that spot if you use a webcam on your computer screen will look this big alright so you look at the spot it will look like a white spot white circular spot and move the delay line and see whether the spot is going up and down since your spot is being magnified so much there is no need to put it on the wall the reason why we put it on the wall is that remember this L equal to r theta the distance that you see if this is an arc the length of the arc is equal to radius multiplied by theta right so we need a long distance so as to have a an observable value of L it is like lamps lamp and scale arrangement galvanometers that you might have used during a BSC or something in physics labs okay but you might as well use a webcam it is not advisable to use your iPhone you can use your mobile phone actually but then we are using a laser phone camera might go bad so just exercise caution but no matter what you do you have to ensure always that the beam is horizontal and you cannot think that I saw it horizontal that it is horizontal today therefore it is going to remain horizontal one year later you do not have to be so paranoid as to check every day or once every two weeks is good practice right you have to ensure that this gate light beam is horizontal otherwise all your measurements are going to be wrong especially when you are talking about longer times okay so that is the biggest thing that can give you a wrong result non horizontal gate beam second thing is magic angle if your magic angle is not setting properly and setting the magic angle is a bit of a bother because this berik plate is a little tricky thing but you have to learn it and you have to do it because if it is not at magic angle now which component will be affected the short component has to get magic third thing is something that usually we do not have a problem with is laser stability and power generally ties up our lasers of the present generation are extremely stable in their output if you keep them on for 3 days the output does not change but if your laser is fluctuating then you actually cannot do the experiment it is very important that your laser is stable throughout the experiment because do not forget you are working with actual intensities here not relative intensities so that is it that completes our discussion of femtosecond optical gating we have talked about TCSPC already there is a go between there is something called streak camera which gives you time resolution which is better than up the better than TCSPC but not as good as up conversion it is very expensive but very convenient unfortunately we do not have one in IIT Bombay but there is one in I think now IZR Pune it used to be NCBS IZR Pune has one TIFR might have had one I am not very sure there was one in Katindor so next day what we do is we briefly talk about how streak camera works and or maybe we leave it for a little later next day let us go back a little bit to the basics there is all this while we are saying that we are going to use a laser that has 100 femtosecond pulse and so on and so forth how does one produce 100 femtosecond pulse or 6 femtosecond pulse that is what we need to learn to do that we have to go back even further to the basics it is always good to start at the very beginning so in the next module we will start talking about the absolute basics of lasers we will start with Einstein's formulation of the problem of absorption and stimulated emission and spontaneous emission and from there we will try to see what are the components required to make a laser and what kind of systems can give you lasing after that we are going to learn about what are called modes of lasers there are two kinds of modes transverse modes and longitudinal modes we will learn about the modes and then we will learn how one can lock the modes together to produce pulses so that is all theory then we are going to learn about pieces of equipment that can actually do this mode locking for us actually for femtosecond lasers you need nothing they get mode locked by themselves because of a magical phenomenon called thermal lensing curr effect but if you want picosecond pulses you have to work a little harder we will learn so you have to do what is called active mode locking we will learn active mode locking because there some devices are used which are used later on when you talk about amplified lasers so we will learn about things called mode lockers and Q switches when we are done with all this then we come back and talk about what is there inside a titanium sapphire oscillator and how do you amplify pulses then we hope to go on to optical parametric amplification okay so that is quite a bit of work cut out for us but before we do all that next step is to go to our lab and have a look at this femtosecond optical gating instrument that we have there that is what the next module will be about okay we are done for today thank you very much.