 Hello. Welcome to the last module of this course. Well, in the previous module, you might remember, we have said that we are going to have two more. But then taking stock of how much ground we have covered and how much time we have, it appears to dent that we call it a day with this module itself. Because if you want to discuss 2D IR spectroscopy or data hard spectroscopy or non-linear spectroscopy for that matter in any more detail, we will need at least 10 more modules. We do not have scope for doing that. Secondly, let me apologize for the quality of this video because right now this is being recorded from my home because of this deadly disease worldwide. Like most of the people, we are also locked down. And so the quality that you see here is nothing like what you have experienced so far. So apologies for that. Please bear with us in this difficult time. And that's another reason why I thought, let us not prolong it any further. Let's call it a day here. So today we will complete our discussion with a brief introduction to the techniques of 2D IR spectroscopy. And once again, before I begin the module, let me acknowledge my friend, Dr. Shukendu Nath of BRC, from whom I have learned whatever little I know about 2D IR spectroscopy. So what we have said so far is that in 2D IR spectroscopy, it's all about coupling. If you have coupled vibrational modes, then they show up as off-diagonal peaks in the 2D IR spectrum. Very much like NMR spectroscopy, for example. There also in 2D NMR, off-diagonal peaks show up when there is coupling between nuclear spins. Here, instead of nuclear spins, we're talking about coupling between vibrational and normal modes of polyatomic molecules. We have also said that one can perform studies of time evolution of these off-diagonal peaks. And that gives us an idea of dynamics of coupling or decoupling. For dynamics of coupling, we see an emergence of the off-diagonal peaks with time. For decoupling, we see a disappearance of these off-diagonal peaks with time. Now the question is how are we going to do on this? There are three techniques that we want to talk about very briefly. The first is very simple. It is called frequency-frequency domain 2D IR spectroscopy, or frequency-frequency double resonance 2D IR spectroscopy. And the setup here is very simple and it's absolutely same, well, almost absolutely same as something that we are very familiar with, the pump flow spectroscopy. So what we have here is that we have an ultra-short IR pulse, let us say of 150 second time duration and of a spectral width of 200 centimeter inverse or so. This beam is split into two parts. One is pump. The pump pulse goes through reflective optics and is made incident on the sample after which it is stopped, blocked. And the probe pulse goes through a retroreflector which can be moved by a computer-controlled delay stage. And then it is also focused using a parabolic mirror onto the same spot of the sample where the pump is made incident. And the probe pulse goes through a spectrograph on an array detector to give the probe spectrum. So, so far it's exactly the same as broadband pump probe spectroscopy. How do we get the second dimension? The second dimension, remember, is pump frequency. We get pump frequency by introducing one more piece of optics here. And the piece of optics that is introduced is very fundamental to lasers. It is called a Fabry-Perot filter. A Fabry-Perot filter is nothing but a pair of almost parallel partially reflecting plane mirrors. So whoever has gone this far in this course would know for sure what happens when we have two partially reflecting plane mirrors. Well, they form a cavity. Remember laser cavity? That is a very fundamental discussion that we performed here. So we have studied that when we have this kind of a cavity, the cavity length determines which frequencies can be sustained in it. And if we change the cavity length a little bit by tweaking the mirrors a little bit, then one can have tune ability. So remember we are working with femtosecond pulses here. So the spectrum is always broadband. But what we can do is that out of this broadband, we can select a narrower band. Say a 5 to 15 centimeter inverse spectral width by introducing this Fabry-Perot filter. So by tweaking it, of course, the tweaking is not on my hand. Everything is computer controlled. One can choose a narrow range of pump frequencies as well. Now the job becomes very simple. Beside which range of pump frequency we want, set the Fabry-Perot filter accordingly, and then scan TW. TW is the W is for weight. TW is the weight time that is the conventionally used term for the time associated with the delay of the probe beam in 2-discotroscopy. So the probe here is subjected to a variable delay TW. So for every value of TW, one gets a 2-dir spectrum. So very simple. Now what is the limitation of this technique? Limitation is how small a band you can generate out of this Fabry-Perot filter. That is what will determine the spectral resolution. Otherwise it's a very simple technique. But then towards the beginning of this course, we spend a significant amount of time talking about why time domain spectroscopy is more advantageous. We actually did it in a bit more detail in the NPTEL course on molecular spectroscopy that we have offered a couple of semesters ago. So as we know, when we do IR spectroscopy, nobody does frequency domain anymore. I mean, I'm talking about regular IR spectroscopy that you do for sample characterization, run of the mill. Even then, the spectrometers that are used are always FTIRs, Fourier transform IRs. Which means the data are recorded using a Richardson interferometer in time domain and Fourier transformation takes us over to the frequency domain. For further understanding, please refer to lectures from the earlier NPTEL course on molecular spectroscopy. So the question is, can we do it here? Can we use, say, time frequency domain 2D IR here? Actually we can. And it gives, there are some advantages associated with it. But the moment we try to do it, the experiment becomes a little more complex. So let us see what we have in a setup in which we want to do time frequency domain 2D IR spectroscopy. We start with a similar ultrafast IR pulse, split it into two parts as usual. One part is probe shown in black lines. The probe is focused by a parabolic mirror onto the sample and is routed through a spectrograph onto an annotator. That part is exactly the same. The pump is different. The pump, what we have is, we have a beam splitter. 50% of the pump pulses are sent in this direction to hit a plane mirror in normal incidence. Because the incidence is normal, it retraces its path and comes in this direction. And if that's the only thing that is there, then you get this pump pulse coming here. But then remember, this bit of optics here is really a beam splitter. So it sends 50% of the beam in this direction. It transmits 50% of the beam. And that 50% is incident normally on another plane mirror, 100% reflecting mirror. And this plane mirror is mounted on a variable delay. So since, once again, the incidence is normal, the beam retraces its own path and comes back. Now see, if the path difference is zero. If the path length is exactly the same on the two arms, then the two pulses combine and we get one pulse here. If, however, there is a non-zero path difference. That means the path lengths in the two arms. Two arms means one generated by reflection from the beam splitter, the other because of the transmission. If the path difference is non-zero, then what happens? Then the pump does not consist of one pulse anymore. Rather, it consists of a pulse pair, two pulses separated in time. So why would you want to do that? You want to do that because if you take a pulse pair with variable time separation between them tau, then Fourier transformation of such a pulse pair turns out to be a sinusoidal spectrum in frequency domain. So what we have done is we have generated a lot of colors at the same time. So now we do not need that February filter anymore. We do not have to look at individual pump frequencies one by one. Rather, we generate a whole range of pump frequencies with varying amplitudes, varying electric peaks. Moreover, the periodicity, what is periodicity? The separation between the two peaks. The periodicity turns out to be one by tau. I am avoiding all the mathematics here. All the mathematics involved here. Please bear with me for that. Unfortunately, I have written the name of the book a little wrongly. It is not Ham and Zany and Ham. That is one Ham too many. The book Concepts and Methods of 2D IR Spectroscopy is written by Zany and Ham. It is considered to be the textbook for people who want to study 2D IR. Please study this book if you want to know more about these techniques. So coming back, what happens if I increase tau? If I increase tau, then the periodicity changes because periodicity is a reciprocal of the time difference between the pulses. So as we change tau, we get different shapes, different sinusoidal shapes. So we basically get different, maybe the same range of frequency, but the contribution of each frequency changes depending on tau. So suppose we now use the same spectrograph and diode array detector. And record the spectra as function of tau. Then what happens? Then we get a plot like this. On x-axis, we have the probe wavelength. On y-axis, we have tau, the separation between the pulses. And z-axis is the feet. So now what one can do is one can Fourier transform the y-axis, the tau axis. And that will give us the 2D IR spectrum with which we are now familiar. So the good thing about using it is that this time frequency domain 2D IR technique is associated with all the advantages of time domain measurement. You do not need to work with a small range of frequencies at a time. The entire range of frequencies is incident at the same time. I talk about pump frequencies. So all those techniques, all those advantages that are there for the time domain technique, jacking on advantage, throughput advantage. All these advantages are there in this kind of a technique. So this is a more elegant method than frequency-frequency domain 2D IR. However, this is not all because 2D IR spectroscopy actually has many facets, which unfortunately we do not have time to discuss in this course anymore. But it is not just recording spectra. Polarization, coherence, these are very important things that come up here. Because you excite, you pump, let us say, using a vertically polarized pass. Then you generate all these vibrations that are all coherent. And then decoherence takes place. What is the time for this decoherence? What is the time for this defacing? That is something that can be followed very elegantly using the time-time domain 2D IR technique. This is also called photon echo technique. Once again, photon echo itself would require maybe four or five modules if you want to discuss in detail. The technique as such is discussed in our regular textbook. So whoever is interested, please go through that book. And to put it very simply, once again, we resort to what I hope most of us would know from our earlier experience with NMR spectroscopy. In NMR spectroscopy, one technique that is used very frequently is to measure the relaxation times. One uses pulse radio frequencies. One uses pulse radio frequencies to record spectra as well. But to record relaxation times, one uses pulse sequences. So let us do a quick recap of NMR spectroscopy without showing any slide. Whoever wants a more detailed treatment, please refer to the lectures on this topic in the earlier NPTEL course on molecular spectroscopy. So what happens is, if one wants to measure, let us say, transverse relaxation time. Then first, in 90 degree pulse, I'm talking about NMR right now. A 90 degree pulse is made incident on the sample. The purpose of this 90 degree pulse is to flip the bulk magnetization into the XY plane from the Z plane. And then if you wait for some time, the fanning out effect takes place, defacing. Then a 180 degree pulse is applied to turn this fan exactly by 180 degrees, to flip the fan. Then what happens is, if you wait for an equal amount of time, then the defacing effect is exactly nullified. And then we see what is the extent of decrease in magnetization due to the spin lattice relaxation. That is how spin echo works, and we can explain it by using classical analogs. Unfortunately, photon echo does not have a classical analog, so it is not very easy for us to explain it without resorting to quantum mechanics and mathematics. Of which, as I said, we do not have the time. So let me just tell you what is there in this setup. So this is only, well, it's not even the tip of the iceberg. It's only an introduction. I sincerely hope that you will be encouraged to read further and understand this technique in much more detail. So what we have here is this. As you see, there are more retro reflectors, more tau, let us see one by one. We have the femtosecond higher pulse. It goes through a beam splitter, which sends a part of the beam in this direction. We have not shown it yet. It will come. The other part is transmitted. Of the transmitted beam, one part is reflected by another beam splitter. We call this beam number one. This another beam splitter, which produces beam number two. And the beam number three is the beam that is finally transmitted to this third beam splitter that is shown. So let's go one by one. What is the path of beam number one? It goes up, it's this mirror, it's this mirror, falls on this parabolic mirror and is focused onto a point on the sample. And then see that beam is blocked. This horizontal black thing that is shown here, that is basically a beam stop. So pulse number one goes to the sample and is stopped, not detected. What about pulse number two? It's this mirror, comes this way, it's this mirror, here, here. Well, there may be more optics in between actually. We are not showing everything here. It is just a schematic. Then the same parabolic mirror focuses it onto the same point on the sample as beam number one. And then it goes through and even beam number two is stopped, not detected. As you see, beam number two can be associated with a delay time of tau, which is variable. Beam number three similarly is associated with another delay time, T w. So this is really the problem. So beam number three falls on the same parabolic mirror and is focused onto the same spot on the sample. And then beam number three, remember beam number three is the probe beam that is also stopped. So now that's a very strange situation. We have two pump beams. They are stopped, understandable. The probe beam is also stopped. So what is it that we detect? That may be a question. Well, before answering that question, well, what we detect is this dashed line. This dashed line goes, hits this mirror and is directed to the spectrograph. In fact, you do have a spectrograph here. I've not shown it here, but you do have a spectrograph CCD array here. Because the spectrograph, what it essentially does is that it performs a Fourier transformation that gives you the data in frequency domain. But the question is, what is this dashed line? That is the photon equal. If we're going there, let me show you another figure which is of utmost importance. Well, the figure is taken from a paper on not 2D IR spectroscopy, but 2D UV spectroscopy, well, 2D electronic spectroscopy that I've referred to a little later. See, looking at the schematic here, you might think that everything is in the same plane. What happens is that these beams are aligned in the so-called box-cars geometry. Think of the square and think of this point. It's as if the three beams propagate from the three points of the square. See, the number one, two and three, all coming from these corners of the square. There are four corners. These three come from three corners. The good thing about box-cars geometry is that if three ultrafast beams are made incident on a sample in this way, then we have studied a little bit of nonlinear spectroscopy, nonlinear effects take place. And we get a fourth beam emerging along this dotted line. The fourth line from the fourth point of the square drawn to the same point on the sample. That is the vector sum, well, linear combination of the k vectors. Well, that is associated with light whose k vector is a linear combination of the k vectors of beam numbers one, two and three. That is the photon Ecosignal. So what happens here is that beam number one is sort of like the 90 degree paths of NMR. It comes and creates a coherence. Over a period tau, decoherence takes place. And then the second beam comes and flips it sort of. That's like the 180 degree paths. And then once again, coherence takes place. And what you have is a photon Ecosignal. Very similar to spin Ecosignal in NMR. And it is a photon Ecosignal that is detected by the detector. Now there's a problem here. If you go through, in the same Helen Abramov's book, if you see the expression for photon Ecosignal, what you find there is not intensity but the field. And you might be wondering already what this LO is. The thing is this, we need to know the field and not the intensity. If you look at intensity, intensity is the mod square of field. The moment you do mod square, the phase information is completely lost. In fact, we need phase information here in order to proceed. So to do that, now comes the role of this beam splitter here. What this beam splitter does is that it creates another pathway for yet another beam. And this beam number 4 is called the local oscillator. What the local oscillator does is that, okay, this is the path from here to here, here, here. Now it is combined with the photon Ecosignal and goes into the detector along with the photon Ecosignal. And when this mixture goes in, heterodyning takes place. We will not discuss heterodyning in any great detail here. Just believe me when I say that by virtue of heterodyning, we get information of electric field and not just the intensity. And this is something that we need for the subsequent Fourier transformation. Without heterodyning, we cannot really do it. Heterodyning is a technique that makes use of the local oscillator. For want of time, unfortunately, we will not be able to get into this any further. But I will refer to some other work where heterodyning is discussed in some detail. So this oscillator is associated with its own delay time. So what you have is a little more complex Fourier transformation involving all these delay times. That is what finally gives you the 2D IR spectrum. So why would we do it? Because as I said, there is more to 2D IR. We talked about polarization. We have not talked about polarization rather. But polarization is an important thing. Decoherence is an important thing. So all these things can be understood when we incorporate this little bit of complication in this technique. Right. So to conclude this discussion, let me show you an example. I will not tell you what the sample is. But this here is the, this here are 2D IR spectra of the same sample recorded by three different techniques. As you see, they are qualitatively similar. Wanted to give me, they may be a little different because every technique is associated with its own strengths and own weaknesses. So that is all I wanted to say about 2D IR. Unfortunately, we did not get time to talk about applications. I suggest that in addition to reading Zani and Ham's book, please go through this paper published in Chemical Reviews. Here there is an ample discussion of how one can study the dynamics of, well, movement of chains of proteins, for example, using 2D IR spectroscopy. And this chemical review issue itself is very special because it is a special issue on ultrapass processes in chemistry. I'm going to refer to another paper of this in a moment. So what I suggest is that, in fact, read all the papers published in this particular issue of Chemical Reviews published in 2017. So much for 2D IR. Let me tell you that, well, this is the book of Ham and Zani. Please go through this book. Let me tell you that this 2D spectroscopy is not limited to IR. In fact, there's a lot of promise in 2D electronic spectroscopy. A lot of people like Shol Mookamel and others have done, well, Tokmakov, they have done a lot of good work on different kinds of 2D spectroscopies. This perspective article is a good reading material for 2D electronic spectroscopy. So this is what we could say and actually we could not say in this course. I'd love to talk more about 2D IR spectroscopy. I'd love to discuss data IR spectroscopy, which has become very, very interesting over the last maybe decade and a half. Not only from the point of view of fundamental studies, but also for applications like exposure. Whoever is interested, please do read reviews and papers on 2D IR spectroscopy. And finally, I would like to refer to this paper by Tahara and co-workers on ultrafast dynamics at water interfaces studied by vibrational sun frequency generation spectroscopy. Nonlinear spectroscopy at surfaces using heterodyne so that they can talk about phase. So they don't only have to talk about intensities. From that, they have generated a wealth of information about many kinds of interfaces. Unfortunately, we could not discuss all this in any great detail because that would be too much. Maybe later on, if NPTEL agrees, we can have a half semester NPTEL course on these advanced asteroids of ultrafast spectroscopy. There we can talk more about multi-dimensional 2D spectroscopy. We can talk about data IR spectroscopy. We can definitely talk about surface nonlinear spectroscopy. But let that be the story for another day. For now, I hope that we have learned something new in this course. And I hope that it has been a pleasurable experience for all of us. So with this, we come to an end of this course and it is time for us to say goodbye.