 So, far we have focused our attention on a time correlated single photon counting which allows us to make measurements of lifetime from hundreds of picoseconds well maybe tens of picoseconds if you can have a very good instrument like we do and up to say hundreds of nanoseconds in some cases you might be able to go beyond that as well. Today we talk about a technique which allows you to go down further to hundreds of picoseconds at least if not better and this technique is called time resolved fluorescence up conversion or the name I like better is femtosecond optical gating the reason why I do not like the term fluorescence up conversion is that there are many people working in the area of material science who want to make up conversion materials materials in which two photons of smaller energy would join up to give you one photon of higher energy and the moment they see fluorescence up conversion technique they come and ask me is it possible for us to test our samples on your equipment of course it is not possible to test their sample on our equipment so I like femtosecond optical gating better just to avoid trouble. But then fluorescence up conversion technique is an absolutely valid commonly used name and we will see where this term up conversion comes from in this technique and how is it that we get accuracy in time up to femtosecond scale before proceeding further it is important to point out that none of these slides are made by me I do not know how to make such beautiful slides they are all prepared by my colleague for the Shobhan Shen from school of physical sciences Javalaner University he has kindly agreed to allow me to use these slides as many times as I want wherever I want. So let me start thanking Shobhan for these slides that are made with a lot of care as you will see so first of all let me show you a photograph of the up conversion spectrometer this is what it looks like this is actually photograph taken from top this is not our instrument it is the instrument that is there in JNU but then our instrument is pretty much the same and next day we are going to go to the lab and we are going to show you our instrument in real time and we will show you how the data is recorded so the idea is in this module we are going to tell you and try to make you understand without actually going to the lab how the data is recorded and what are the underlying principles and all and next day you will come to the lab and you will see what exactly is actually done right. So what you see here is this black flat surface with a lot of holes is a breadboard and if you go to any optics lab you will see breadboard like this in fact if you look carefully you will see that this black surface with holes is sitting on a shiny surface with holes that is an optical table top of the top of the optical table and the reason why we have so many screws the so many holes there is that it is possible to use bolts and screws and fix pieces of optics on this surface. Now whatever you see here is a piece of optics it may not be very clear from this photograph because it might be for many of us that we are seeing such apparatus for the first time but when you go to the lab and we see everything in front of our eyes I hope it will become clear and today's exercise is going to help us understand things that are there as well to start with let me try to give you from this figure a description of what is there in this spectrometer. So first thing that you have is what is written as SHG crystal SHG means second harmonic generation crystal we are going to have a couple of modules on nonlinear optical on nonlinear optics later on and there will learn that there are materials that allow two photons of they may be same energy they may be different energy but they allow two photons to combine and produce a photon of larger energy it is pretty much like two drops of water falling on a table coming together and forming a bigger drop it is just that the drops here are not drops of water they are drops of energy drops of light but not everything allows combination of photons there are very stringent conditions that have to be satisfied for a material to act as a nonlinear optical material and it that in itself is a very active field of research. So without going into that at this time just believe me when I say that the first thing we have here is a second harmonic generation crystal what is the purpose we will see in a while. Now why are we saying second harmonic because in this crystal at least what happens is you make incident laser light nominally of 800 nanometer but whatever laser light you might want to use and two photons of the same laser join up to produce a photon of double the energy this photon of double the energy that is called second harmonic or if I put it in another way suppose the frequency of the incident light is omega then two photons of frequency omega join up to produce another photon of 2 omega this 2 omega is a second harmonic of omega it is as simple as that. So what we do here is that you make incident this red light which is from a laser in our case it is a femtosecond pulsed titanium sapphire laser later on we will have occasion to talk a little more about what is there in the laser and how femtosecond pulses are produced for now let us just accept that this red light is the output of a femtosecond pulsed second harmonic sorry femtosecond pulse titanium sapphire laser and wavelength of this laser that the one that we have can be tuned from say 700 nanometer to 1000 nanometer or so let us say that this red light that we are showing you here is has a wavelength of 800 nanometer of course if I say wavelength of 800 nanometer it is not very difficult for you to work out what the frequency is because frequency and wavelength are related by lambda nu equal to c. Now what happens in the second harmonic generation crystal is that as I said two photons join up to give you one photon so suppose I am using 800 nanometer light what will be the wavelength of the some frequency photon this one is very easy it is going to be half right 800 by 2 400 but while doing this thing please remember one thing that you have to add frequencies not wavelength wavelength is actually in reciprocal scale. So the right way of doing it is to convert whatever you have to frequency at the frequencies and then go ahead you will see when we talk about some frequency generation later on rather than second harmonic generation that will become a little important second harmonic generation is easy because the wavelength of the output is just the half of the wavelength of input light. Now here let me tell you something it is a little easier to produce second harmonic of femtosecond pulse laser short pulse lasers why because when you do second harmonic generation what are you doing the first photon takes the material from its ground state to what is called a virtual state a virtual state is a non stationary state associated with the lifetime of 0 and it is usually described as a linear combination of these stationary states of the system. So requirement for second harmonic generation is that you take the system from the ground state to the first stationary state then there must be another photon of the same energy which will take it to another virtual state okay. So first frequency takes it to an energy of say nu well I am stating energy in terms of frequency here omega second one second photon also of omega frequency takes it to a virtual state whose energy gap between whose energy gap with the ground state is equivalent to a frequency of 2 omega and now there is no memory the system does not remember that it had gone up in two steps and it cannot stay in virtual state for any finite amount of time. So it has to emit a photon and comes down and since the energy gap between that virtual state and the ground state is equivalent to frequency of 2 omega it actually emits a photon of 2 omega and that is what you see as the sum frequency or in this case second harmonic it may be a little difficult to follow it in this way when I speak but then later on when we talk about non-linear optics will actually draw diagrams and then I hope it will become a little easier for now all we need to understand is that this red light falls on the second harmonic generation crystal SHG crystal and blue light is produced and what you have seen is the path of the blue light I will go back a little and I show you the path of the blue light but before that let me tell you you could see what happened right blue light gets produced here at the second harmonic generation crystal it hits what we have here is a dichroic beam splitter dichroic beam splitter means it reflects one color and transmits another color in this case you use a dichroic beam splitter which reflects blue light but transmits red light it could be the other way round as well you have dichroic beam splitter of both the variety then having been reflected from this dichroic beam splitter the blue light comes to another dichroic beam splitter this one dumps the residual red light residual red light goes through and blue light gets reflected in this way where it gets focused on the sample which is kept here by a mirror by a lens alright that is the path of blue light I will just show you the animation once more blue light is produced at second harmonic generation crystal it is the first beam splitter second one and now is focused on to the sample using a lens in our case we use a lens but there is a better option as we will come to later on now then the sample fluoresces and this is why you need blue light as we have discussed in one of the first modules fluorescence spectrum always comes at a lower energy compared to the excitation light unless you have an up conversion material right but normally when you talk about normal fluorescence emission always has emission is always at a lower energy because you cannot have more energy than what you put in unless something like this is going on that is why you need blue light because suppose you excite using 800 nanometer light where is it going to emit the only hope is NIR in fact materials emitting NIR are very useful but most of the things do not most of the things actually emit invisible range sometimes in UV range for that you need higher energy light and that is what is produced by the second harmonic generation crystal. So red light second harmonic generation crystal is sized to blue light that is deflected through a lens onto the sample and then from the sample you get a fluorescence that is shown by this line. Now fluorescence occurs in all directions the fluorescent light is sort of like the light that comes out of the regular lamps that we have it is in all directions and what we do here is that we collect the fluorescence by using this lens so you can understand this is the sample this is the lens. So the only fluorescence it can collect is something that comes from this point on the sample on which the excitation light has been focused and is within this solid angle that can be captured by the lens. So here something that becomes very important is numerical aperture ratio between the focal length of the lens and the diameter of the lens. If your focal lens is large in this case is it good or is it bad do I want to use a large focal length lens or a small focal length lens definitely small focal length lens in fact there are instruments in which they use a microscope objective you want the lens to be as close to the sample as possible because the further away you go more is the loss of light if you are here then you are catching say this solid angle if this is suppose this is your lens cross section of your lens you keep it here this is the solid angle that you catch you go here this line goes in this direction this way goes in this direction so you end up catching a much smaller solid angle right that means light collection is less efficient and fluorescence in any case the number of photons emitted is not all that great especially when you are talking about femtosecond time scale your lifetime is small and what we learned in the previous module is that lifetime is proportional to the fluorescence intensity pi f is equal to k r into tau f. So small lifetime would usually imply a small quantum yield as well now out of that if you are going to reject most of it then what will you see so that is why you want to capture as much of the solid angle as possible if you can capture 180 360 is never possible if you could capture 180 degrees it would be great but 180 is not possible so you want a lens with high numerical aperture so that you can go as close as possible and capture as much of the fluorescence light as possible are you clear about that and the other thing that is also implicit here is that the sample is kept at the focus of the collecting lens that is the configuration for best collection so you told me you do not want a long focal length lens and we discussed why do you want a small wider lens or do you want a narrower lens I mean diameter of the actual optic should it be small should it be large it should actually be as large as possible but there is a practical problem to that because your focal length is small if you want a very large lens then it is going to be a very huge curved surface like that cannot be very large actually right so there is a limitation that is why numerical aperture is the quantity that determines what kind of lens you are going to use alright so let us see what is happening here we have some labels here omega 2 is the frequency of fluorescence as we are denoting here what is omega 1 will come to that shortly so this fluorescent light is captured by the lens with small focal length then here we have a filter what is the purpose of this filter you see you are doing a collinear collection you are collecting in the same direction as the direction of propagation of the incident light so of course there will be not only this fluorescence light a lot of excitation light will also be there in the same path but then you do not want it right because if excitation light gets into the detection channel then your instrument is going to get messed up so you want to cut out an excitation light cut out the excitation light and you want only the fluorescence light to reach wherever it is going to reach later so now tell me how do I cut out the excitation light and allow only fluorescence to go through what should I use I we should use a filter that is right what kind of a filter a filter that cuts out high frequency high energy short wavelength light and transmits low frequency low energy long wavelength light what is that kind of a filter called it is called a long pass filter that is right so in equipment like this you have to actually use many different kinds of filters here you use a long pass filter and the purpose of that filter is to cut the excitation light while allowing the fluorescence to go through here you if you look carefully you will see there is another something here also you have some filters these are a different kind of filter they are called neutral density filter what is the meaning of a neutral density filter something that ideally cuts down a lot of the light going through irrespective of wavelength so if you plot absorbance or rather percentage transmittance against wavelength then you expect to see a flat line in case of neutral density filters a flat line that is at 50% 20% 10% 1% depending on your need why do you have neutral density filters here because we do not want too much of light to fall on the sample they are using a 100 femtosecond pulse so that is putting a lot of energy in to the sample in a very very small time so sample is going to burn that is why you always want to work at minimum excitation energy possible if you put in more excitation energy perhaps you will get stronger fluorescence but that comes at a cost and the cost is your sample might get damaged and if you are not careful you might not even understand that your sample is getting damaged so the problem with that is that once we are done with this discussion we can come back to it the problem with that is actually get incorrect result the lifetime you record can actually be different from what it what it is that problem is not there in TCSPC in TCSPC first of all not much of damage is there if you use diode less as an all secondly it does not matter if the sample degrades even during the experiment unless another fluorescence species is produced lifetime will remain unaffected not so in up conversion not so in optical gating in this case if the sample degrades even if it becomes something that is not fluorescent then your measurement can be affected and we will discuss why once we are done with the remaining part of the experiment of the discussion all right so what do we have we have this fluorescence going through the long pass filter then that cuts out all the blue light only fluorescence light goes through here you have a lens perhaps you will understand better when we show it to you in three dimensions next day here you have a lens and this lens focuses the fluorescence light on to another nonlinear crystal but here you see this one was SHG crystal the first one the second one is called SFG crystal because here it means some frequency generation crystal not second harmonic generation crystal why do we need on nonlinear crystal what is it doing there what is the function how does it help we will come to that shortly but for now we need to remember that this is a some frequency generation crystal now you see here when I say long pass filter you might actually have to use a different filter for a different sample that is why in this kind of an instrument you always need a set of filters what you see here you can see some color there they are all colored glass a set of filter mostly long pass which allow only the fluorescence light to go through but actually not all are long pass some short pass filters also there we will come to that all right so are we all okay with this path fundamental red light getting frequency double producing blue light which is directed on to the sample focused on to the sample then fluorescence light goes through a long pass filter whereby the excitation light is eliminated and then the fluorescence is focused by a lens on to a some frequency generation crystal are you okay with this arm but this is only one arm of the instrument only half of the story the remaining half of the story and that is where omega one comes in is in this side remember what is this optic here is it a plain is a simple mirror it is actually a dichroic right and dichroic reflects blue light and transmits red light what you see now is the path of the red light which is omega one I will show you the animation once again but then I am afraid I cannot speak fast enough to keep up with the animation after all we are trying to animate light which is the fastest thing in the in well in the universe so let us see so red light goes through the dichroic it is a mirror another mirror goes to and if retro reflector comes back see I could not keep up with it so now let me try to do it in a static mode so this is where your red light goes through where is it produced in the laser outside the spectrometer it is there if you see carefully you can see two beams one blue and one red the red light goes to the dichroic it is this mirror then this mirror comes back and here you have a retro reflector retro reflector means it can even be a pair of mirrors something that turns light back okay light does an about turn at the retro reflector what we have in our lab and in these instruments which are marketed by CDP corporation what they always have is they have a three sides of a cube front coated with gold there are some advantage with having three sides of a cube the advantage is that the light that comes out from the retro reflector is exactly parallel to the light that goes in that helps it alignment so if light goes in like this it will come out like this if it goes in like this it will come out like this so having a retro reflector which is three sides of a cube helps us in the alignment a little bit but after that again you have another mirror which takes the light to this mirror which focuses it through the same lens on to this some frequency generation crystal and we are saying that this red light has a frequency of omega 1 okay and this light also goes by the name of gate light remember one of the names is femtosecond optical gating this omega 1 serves as the gate before going any further let us make sure that we have not forgotten what kind of a light is that red light is it continuous light or is it pulse light it is pulse light right where remember it is the output of femtosecond pulse titanium sapphire laser it is pulse light full width of maximum of the pulse would be something like 100 femtosecond in our case it can be even smaller okay pulse light omega 1 is pulsed so what does it look like if the x axis time it looks something like this what about omega 2 if I look at it in time domain what is the time evolution of omega 2 is from fluorescence right so it is a decay okay this is a point that we are going to come back to shortly right but before that let us think in a little simple manner not worrying about time at the moment now you see what we have done we have focused light of two different frequencies omega 1 and omega 2 onto the some frequency generation crystal what should happen it is a non-linear crystal it is called a some frequency generation crystal so it would better give rise to some frequency what is the meaning of some frequency omega 1 plus omega 2 right so the some frequency is generated here and actually it is this some frequency that is detected how do we ensure that after here what we have not shown is we have a monochromator like the ones that we have discussed earlier while talking about steady state measurement but generally here you use a double monochromator there are two great things because you need very high precision in this case and then you have a regular photomultiplier tube or some other photodiode detector like what you have in your say fluorescence spectrometer okay so you are going to see omega 1 plus omega 2 and if you just measure the photo current out of the photomultiplier tube then you can get an idea about the intensity of the some frequency omega 1 plus omega 2 are we clear but what does all this have to do with femtosecond time resolution femtosecond optical gating we have understood the optical gating part perhaps because we said that this omega 1 light is called optical gate but why is it called a gate and we have understood femtosecond upconversion because here we are doing upconversion so this crystal is also called the upconversion crystal okay but how does that give us femtosecond time resolution that is what we are going to discuss in the next module before that let us do simple arithmetic I have 800 nanometer light right that is omega 1 okay and 600 nanometer light here of course fluorescence is broadband let us say we are focusing on the 600 nanometer fluorescence light okay so what wavelength is obtained upon mixing 600 nanometer and 800 nanometer light so what I have written is 800 nanometer and 600 nanometer light can we work it out of course maybe I can do a little bit of mental arithmetic it is upconversion right so you have to add 600 plus 800 1400 nanometer is the wavelength of the are we going to get 1400 nanometer when we combine 600 and 800 nanometer light in some frequency generation crystal why not because see 1400 nanometer is actually lesser energy than both 600 and 800 right and let us not forget that when you so go back to the fusion of drops analogy when 2 drops fuse 2 drops of water their masses add up when 2 drops of light when 2 photons fuse their energies should add up right E equal to h nu or E equal to hc by lambda so what you need to do is E 1 plus E 2 you cannot do lambda 1 plus lambda 2 right so E 1 plus E 2 would be hc 1 by lambda 1 plus 1 by lambda 2 so lambdas are you cannot add lambdas just like that you have to add frequencies so who can tell me what is the wavelength will obtain when we mix 800 nanometer with 600 nanometer yet work it out I do not think you are so good at mental arithmetic that you will be able to do it just like that I am not what you actually have to use is 1 by lambda equal to 1 by lambda 1 plus 1 by lambda so if you do not believe in taking LCM and all it is 600 plus 800 divided by 600 to 800 but reciprocal of that it turns out to be 344 nanometer now tell me this 344 nanometer light is it UV is it visible is it ultraviolet is infrared what is it UV right so now suppose your 800 nanometer is a nominal value for omega 1 if omega 2 is less than 600 nanometer it will be even more higher energy some frequency will have even higher energy more into UV what is the best case scenario if this is 800 the second one can be at most 800 actually cannot it has to be longer than 800 nanometer right so if it is 800 nanometer no what am I saying it can be anything actually because you are exciting by 400 nanometer sorry my mistake but suppose it is 800 nanometer then it will be 400 so typically well the point I am trying to drive at is that now when you choose at the monochromator and you choose the detector you want a monochromator and a detector that work well in the ultraviolet range we have not had the scope of discussing the blazing of monochromators unless you are using monochromators that use your holographic grating they are usually blazed at some wavelength or the other that means they are optimized the performance is based at that wavelength if you have grating that is blazed at 600 nanometer that means you will get maximum light coupling at 600 nanometer if you have something that is blazed at 300 nanometer that is what it means okay so typically and same is true for detectors and you do not have one ring to rule them all usually so you have a detector that works well in a particular range so when you do the up conversion measurement you might think that you need a rate sensitive detector you do not because you are looking at some frequency higher energy you will always need a higher energy you will need a detector that works well in UV region so that is another point to remember that you are actually detecting UV so the instrument would better be such that it can detect UV nicely okay but we are still not answered the question where is femtosecond in all this where is the question of grating that is what we want to do in the next module when instead of using the photograph we are going to use this schematic and we will show you where femtosecond time resolution comes from.