 So, so far we have discussed about titanium sapphire laser and how it gets modulocked by itself by something called carb lens modulocking. Now we are not so lucky in all lasers, not all lasers would behave like at isophire laser and get self modulocked, especially when you want to produce picosecond pulses and nanosecond pulses, you have to put in some effort and get the pulses prepared. And one method by which as we have discussed you can get short pulses is modulocking. There are 2 ways in which one can achieve modulocking, one is active modulocking, one is passive modulocking. Active modulocking means we put in some device and by applying a voltage or doing something we try and modulock the pulses. In passive modulocking we put in an element to which we do not do anything but by virtue of some property of this element itself modulocking takes place. So, in this module we are going to perform a brief discussion of both these forms of modulocking. So, active modulocking is based on what is called device airs effect and device airs effect was something that was known decades before the first laser was made. So, you can see this paper 1932 PNAS is where this was published. Now device airs effect essentially means this you take a glass of water and put it on a transducer and then apply some sound wave. What you see in the diagram is sound waves have been applied from the top and light goes through in a perpendicular direction. So, what you see in device airs effect is you see something like a diffraction. You do not see one spot going through when the sound wave is applied rather you see several along the vertical axis in this kind of a setup. Not only that the beams that are displaced from the mean position above or below are frequency modulated and the amount by which the frequency is modulated is an integral multiple of omega where omega is the frequency of angular frequency of the sound wave. So, you can think like this you see in this diagram we have alternate layers of light and dark you have some layers that are white and some are not white. What does this mean? Why have you drawn it like this? No, not constructively interferes yet even before that. All we have done is we have put in some sound wave, remember sound wave is a little different from your electromagnetic wave. What kind of, so there are two kinds of waves, transverse wave and longitudinal wave. What kind of wave is sound, it is longitudinal wave which means it propagates by alternate compression and rarefaction of the medium through which it propagates. So, in this diagram the dark region stands for an amount of medium which has been compacted and the light one is where the medium is rarefied. So, it is very easy to understand in case of a gas of course but then this same mechanism happens in liquids and solids and that is how sound propagates. So, this is essentially depiction of the sound wave that has been applied. Now see if you have something like this, a cylinder in which you have alternate regions of high and low density, does it remind you of something that we have discussed earlier something that you know about, well it is like a grating right or you can think it is like a series of slits, wherever the medium is rarefied you can think it is a slit where if it is compacted you can think that it is a stop. So, what happens when light goes through even two slits you get diffraction do not you and what is the meaning of diffraction, so that is what happens here, so essentially it is diffraction but then since you are applying sound wave which has a particular frequency it is not just diffraction, frequency modulation also takes place. Of course device here is effect is a lot of mathematics which you are not going to go into that is too much of optics, too much of physics but we need to know the end result at least. This is actually an undergraduate experiment in physics nowadays, one can buy apparatus like this, so what you see in the apparatus in the top right panel in the slide is like an aquarium in which you can fill water, on top of the aquarium you have a transducer and at 90 degrees laser goes in, in the setup that we have shown here you can use a red laser or a green laser and in the bottom panel you can see the spots that you can get if you hold a piece of paper or a photographic film on the other side. And you can see as you change the intensity of the sound you get more or less number of spots and what you can perhaps not see here is that the spots are all of different color and you see the different color of the spots you can I cannot and I will be surprised if you see I suspect that is that white and red is intensity because see what is the frequency of say red light okay say it in hertz forget about angular frequency how much hertz 10 to the power 4 centimeter inverse right 10,000, 20,000 10 to the power 4 centimeter inverse multiplied by speed of light in centimeter 10 to the power 8 or 10 to the power 10. So 10 to the power 14 and what is the frequency of sound wave typically mega hertz right. So 10 to the power 14, 10 to the power 6 we are doing 10 to the power 14 plus minus 10 to the power 6 may not be so easy to see at least I cannot see you might be able to see I cannot but there are instruments that can okay. So this is very roughly what device here effect is and this is the beginning of or attempt to do active mode locking nothing why do we see this frequency modulation why do we have not only refraction but also phase modulation first of all light is going in from air into whatever that medium is it can be quartz it can be piece of glass it can be something some transparent medium. So that is definitely a denser medium quartz or glass or water or whatever it is right. So what will happen at denser medium frequency will change is that right why will frequency change because what is lambda nu lambda multiplied by nu that is equal to what actually C by n is not it we write C because you always take n to be 1 but it is not the complete statement C by n right. So since n is changing your frequency and all else have to change everything changes. So now suppose I change this n periodically what am I doing in this transducer I am applying a sound wave right and it is not just a block of glass it is not just a block of quartz it is a block of glass or quartz in which I am applying a sound wave okay. So as an application of sound wave the frequency is also going to your sorry the refractive index is also going to change periodically because you are applying a sound wave that is periodic right. So that is what leads to phase modulation the output in time since you have periodic variation of n1 by applying a frequency some kind of frequency the output gets phase modulated okay. Now when you want to do mode locking you have to work in what is called Raman Nath regime Raman is the well known CV Raman Nath was one of his students Raman Nath regime means L should be much lesser than capital lambda square by divided by 2 pi lambda where capital lambda is the wavelength of sound small lambda is the wavelength of light and L is the thickness of the mode locking medium that you want to use. Now once again lot of mathematics will not go into we are not going to go into it right whoever is interested there are lot of discussions about Raman Nath Raman Nath regime in say max bonds optics book for example if you are interested you can read it but it is a non-trivial exercise if you want to read that book you need to understand all that math okay. So in Raman Nath regime this mode locking phenomenon is observed later on in the next module perhaps we are going to come across some other regime is absolutely opposite well L is much larger than capital lambda square by 2 pi small lambda that is called Bragg regime and what we will discuss is in Bragg regime you do not get this kind of an effect you get something else is close but not the same okay that is what is used in what is called cavity damping right now we are discussing mode locking and remember mode locking can only take place in Raman Nath regime. Now what is the only thing that I have control on I have not only thing only thing perhaps I did not say it correctly. So I know that when I want to make a mode locker I have to be in Raman Nath regime so what are the parameters in my control first of all capital lambda wavelength of sound right I can use whatever wavelength it is very easy to produce all wavelengths of sound second thing is L so construction of a mode locker these things have to be taken into construction into consideration it is not as if you can take any piece of quartz and apply some frequency you will get mode locking it is not the case okay. Now what happens in mode lockers is that you work with not travelling waves but standing waves and at this point let me ask what is the standing wave yes. So I got this animation unfortunately in the web the animation is endless here it is not let us see it with trans you see. So basically you have this red and blue did you see two waves red and blue propagating in opposite directions right and when they superimpose they give rise to a standing wave in which the position of the maxima and minima do not change. In fact the position of the node also does not change okay it just goes up and down maximum becomes minimum minimum becomes maximum node remains the same I will do it once again see carefully. So it is red and blue are travelling waves and the standing wave is in black right yeah a big wave blue cannot be blue blue red and what is the other color last color you saw green okay not black green. So look at the green wave that is a standing wave see how it changes with time. So what I have here is that I have one I have a red wave going from one direction to the other I have an equivalent blue wave travelling in the opposite direction see what happens to the green one is oscillating in such a way that the nodes remain where they are the maximum displacement if you do not worry about sign those positions are also the same. So this is the kind of wave that you have okay. So this is what you generate because what you do is you take quartz crystal or something like that you have a transducer at one end and polish the other end. So the sound waves go back and forth and they set up a standing wave right. Now the next question to ask is very often it is easy for us to understand transverse wave sometimes we get confused when we talk about longitudinal waves. What is a standing longitudinal wave? This is what the situation would be at different times. Let us say this here is your mode locker you have applied sound wave from this direction. So at first instance this is the rarefied portion this is the dense portion compressed portion rarefied dense like that. After sometime it becomes homogeneous after some other time what happens is what was white now becomes black what was black becomes white that is the other extreme where maxima and minima change maxima and minima interchange right. Now tell me look at this line in time suppose a light goes through the middle then what will the refractive index it experience be as a function of time to start with refractive index is high very high then it will go down then it will be very high in the other direction then it comes to mean position and then it becomes very high again. So this is how it will change right. Of course refractive index will never become negative right it will oscillate between a maximum and a minimum value periodically and the point to understand here is that the period of oscillation is it has some relation with period of oscillation with sound wave also. What is the time period associated with sound wave whose angular frequency is omega angular frequency is omega what is the time period. So from this graph can you tell me what the relationship is between angular frequency of refractive index and angular frequency of this sound wave or the time periods if that helps essentially same right. So it makes the refractive index change periodically that is what it does and this is the experimental setup in an ancient spectrophysics laser. So I have given only this book reference but this is discussed a little better in EW Smalls chapter 1 chapter 2 in topics in fluorescence spectroscopy volume 1 right. So this is an actual diagram of a spectrophysics laser from 3, 4 decades ago. The way they did mode locking is that right in front of the high reflector mirror they put in this prism okay. So this is a prism light is incident from this direction the triangular faces of the prism are polished and on one side you apply a transducer. So I hope you can see in the diagram that these circles denote these regions of differing refractive index that is the direction in which the sound wave is applied okay. So what will happen the omega beam will go in a particular direction that direction is aligned with the axis of propagation of laser is omega plus minus n delta go in other directions. So these directions are not sustained propagation in these directions are not sustained in the lasing action. So you only have omega that can participate in lasing right and since the refractive index varies sinusoidally well periodically that is what causes mode locking wherever refractive index is the least that is when light propagates most and see intense light is what will propagate with the highest probability and intense light comes from mode locking not only that the period of oscillation of the refractive index in a mode locker is said to be exactly equal to the period of oscillation of a pulse in the cavity okay. So it acts as a gate it lets a pulse through and then when the pulse does a round trip and comes back there it finds a gate open anything that comes in between is not allowed to go through that is how a that is how mode locking is achieved. You cannot use this technique to make femtosecond pulses because second is where this works most efficiently right. So this is active mode locking and it is achieved by using what are called acoustic modulators AOMs in short and acoustic modulators are used in other applications related to lasers as well we will come to that. Now let us talk about passive mode locking what is the meaning of passive mode locking in passive mode locking what you do is you introduce an element in which you do not apply sound do not apply voltage do not apply anything there is some property of the medium by which mode locking is achieved. And the simplest passive mode locking device is a die cell very highly concentrated solution of some die over the die has to have some property will come to that this is called the saturable absorber can someone tell me what the meaning of saturable absorber is it has some maximum absorbance no see anything will have a spectrum anyway maximum threshold actually that is right that is called non-linear absorption that it will absorb the light until what is the meaning of threshold threshold of what is the other way around low intensity light will be blocked and high intensity light will be allowed to pass through and we will see very schematically what we mean by that. But before we go that this would be the typical arrangement of getting mode locking using passive mode locker so you keep a solution of die and when I say solution of die I mean very highly concentrated solution of die it should be so dark that if you hold it up in front of the light you should not see any light that is usually kept right in front of a mirror and we will see what you can use other than dies also. But that is not the active medium active medium is something else okay see right now what you see is a schematic a very general schematic of a laser with a saturable absorber passive mode locker and this is a schematic of an actual laser once again from many years ago you can see the year of this paper it was published in 1972 applied physics letters 1972 so here see carefully what the beam is it is a die laser right and the die that is used as an active medium is rhodamine 60 where does it absorb where does it emit rhodamine 60 yes so it absorbs green and it emits in red okay. So this is the cavity here you have the high reflector well you here you have one of these is the high reflector here you have the two concave mirrors and here this is where the argon ion laser is switched into the cavity by using a prism and then this here is a cavity in the other end of the cavity you have do DCI do DCI is a sign in die you do not need to know the full name there is a sign in die and which has rather interesting photo physics very short lifetime so and in fact lifetime of the saturable absorber is also very important it should be short if you want a short pulse. So now what happens is this you see this is the emission spectrum you can say and emission spectrum rhodamine and absorption spectrum of dot C there is a strong overlap so dot C would absorb the light that comes out from rhodamine the emission of rhodamine okay. Now see let us consider two levels in do DCI two levels involved in absorption process and let us say population of the lower one is n1 population of the higher level is n2. So if you have a small intensity then what will happen that will you absorb right when does absorption take place when does transmission take place absorption will take place as long as n1 is less than n2 if you somehow achieve n2 n1 equal to n2 then you get what is called bleaching okay. So if there if you have a weak beam of light it will just get absorbed and then the molecule comes down from its ground state to x sorry xr is set to ground state and then it is reset once again once again n1 is very large number n2 is practically 0 however what happens when there is a strong beam if you have a strong beam then it is possible to almost achieve population inversion right almost but not quite almost and as you know and as you worked out yourself pulse light is really very intense. So let us say we have this laser cavity in which we have CW light propagating and pulse light propagating as well CW light will be absorbed by the saturable absorber and therefore stopped since propagation will be hindered pulse light because it is intense will cause bleaching and will get transmitted okay. So this saturable absorber is going to select pulse light over CW light okay so let me show you something this is the actual data of pulse with how we measure pulse with we come to that sometime later but this was a pulse fit measured in 1972 using this absorber using this apparatus using this laser that you see what is the pulse fit written there yeah 2.3 picosecond. So in this laser you can get almost 2 picosecond was reported in 1972 right. So here in this setup what is happening is the argon ion acts only as a pump if there is no saturable absorber you are going to get a CW operation of the dye laser. Since the saturable absorber has been inserted that is the only mode locking device there there itself you can get a pulse fit that is as narrow as about 2 picosecond what happens is you can do better than this you can do better if you have pulsing already and you use the saturable absorber only as a selector but not as the primary mode locking device. One thing that I want to say before closing this part of the discussion is and I was actually hoping that you are going to say it will you agree with me if I say that the pulse gets narrowed as a result of this. See let us consider that there is a pulse somehow mode locking has taken place that always happens some amount of mode locking will take place. So that mode locked pulse is there. Now if you have a saturable absorber while going through the leading edge of the pulse is going to be absorbed is not it do you agree you have a pulse something like this in time right initially at the onset of the pulse intensity is 0 then it goes up gradually well quickly to a maximum and then it falls again. So what will happen to the leading edge of the pulse that will be absorbed and that light will be used to produce to increase N2 more and more then there will we will reach a time when bleaching will take place and from that instant onward the pulse will go through do you agree. So this induction time for which the population of the excited state is being prepared that is a time when even the pulse will not be transmitted it will be absorbed. So that portion of the pulse is cut off so you end up so let me give you some example let us say I have a 20 picosecond pulse 20 picosecond full width half maximum and let us say to keep the discussion simple it takes 20 picosecond for bleaching to happen what does that mean what was full width at half maximum of the pulse now becomes a base of the pulse. So full width at half maximum perized becomes 2 picosecond 3 picosecond something like that okay. So it is important to understand that passive mode locking leads to narrowing of pulses as well okay we will stop here and we will continue the discussion in the next module.