Nicolaas Bloembergen (2008) - From Millisecond to Attosecond Laser Pulses

Good morning. I decided that you on the last morning deserve a break from all these powerful Power Point presentations and… (applause). I would use a more old-fashioned method of presentation. It reminds me of my first international meeting in 1948 when I had to carry two boxes of three inch by four inch glass slides, each box weighing a kilogram. Focus … okay thanks. Then came the Kodak slides, two by two inch, much lighter to carry around, then came the Polaroid slides, plastic two by two inches and then came the overhead viewgraph. And I apologise I never mastered the transition to Power Point. But you can transfer information this way. And I was asked by Emil Wolf, who has been the founding editor and is still the editor of Progress in Optics, and for the fiftieth volume in his series Progress in Optics he asked me to make a small contribution and I did an historical overview of the development of ultra short laser pulses. And, an attosecond is ten to the minus eighteenth of a second, and that is a very small number which I have written down here in two ways for this audience who is not scientifically trained. But to give you an idea of a power of eighteen, let’s first go from one second upward to the power ten to the plus eighteen. And that gets you to what is known as an exasecond. Ten to the eighteenth second, and that is longer than the lifetime of our universe. So if you want to ask a profound question, you could ask what happens an exasecond ago, and then you’re really asking what happened before the Big Bang. Of course, we never use these units on the left hand side, kilo, mega, giga, teraseconds. We always use the conventional hours, days, years, centuries and millennia. But let’s now go down from the one second downward. And there we always have to use the scientific notations of milli, micro, nano, pico, femto, atto, because around 1600 Galileo did measurements. I had an office at the Scuola Normale Superiore in Pisa and I could look at the Leaning Tower. And of course I thought that the standard story was that Galileo observed falling objects from the Leaning Tower of Pisa. But I was told that Galileo used an inclined slope and he had little glass balls which he watched falling down and the only clock he had was his own heart beat and after one pulse, the balls had moved this distance. After two pulses, four times as much, and after three heart beats he was at nine times. So he had the uniform acceleration as a precursor to Newton’s development of mechanics. And it is remarkable that we went to shorter and shorter pulses in the last forty years. In 1960 we were at the nanosecond and now we are approaching the atto-seconds. Of course, what people do, they are always optimistic, and as soon as they got shorter than a microsecond, they said we have entered the nanosecond regime. As soon as you get shorter than one nano second, you say I have entered the picosecond regime and so now we say if we are shorter than a femto second, we are in the atto second regime. But we haven’t reached one attosecond. So here are some of the most important landmarks in the development of short pulses. The first laser pulse was the ruby laser of Maiman and that was accidentally about the duration of one millisecond. But before I do that, I want to continue this thing with the attosecond regime and here are some recent important landmark papers which led to the opening up of the attosecond regime. Now, here is the original first operating laser by Theodore Maiman. A very simple device, you have a ruby here with reflecting surfaces on the ends and you excite the chromium ions in the ruby by a xenon high power flash tube used in photography. And that light lasts about a millisecond. You excite the ions in the fluorescent state and then you get stimulated emission in this way and you get a rather irregular pulse of millisecond light out, irregular because of relaxation oscillations between the pumping mechanism from the flash lamp and the stimulated emission of that in various modes in this Fabry-Pérot reflector . But already within one year, in 1961, after the first ruby laser was pointed out, people got into the sub microsecond regime by the method of Q-switching. What you do is you prevent the light oscillation from starting by spoiling the Q, the quality factor of the optical resonator. And this was done by a non linear optical effect, and the main point I want to get across in this lecture is that there was this curious, mutual beneficiary action you see. To get shorter pulses one always uses some kind of non-linear effect but in turn as the pulses get shorter, the energy stored in the optical medium gets emitted in a shorter time. So the shorter the pulses get, you also get higher powers and as you get higher intensities available, you get more non linearities available. And there is this curious mutual development of shorter pulses and higher intensities. What, how this works is, here is the ruby laser and here is a mirror and there is a mirror, but the oscillations cannot build up because there is a Kerr cell which turns the polarization by 45 degrees and then another 45 degrees back and then the polarization is turned by 90 degrees and the light is reflected out of the cavity. So the light oscillation cannot build up as long as I have a voltage on that Kerr cell which is simply a cell filled with a fluid like nitrobenzene and that turned the polarization out. Then you take the voltage off that Kerr cell and suddenly the oscillation can build up and builds up very rapidly because you have all the chromiums, ions in their excited fluorescent state. And indeed one got immediately into the nanosecond regime, light pulses shorter than a microsecond. Incidentally this led to the accidental discovery of stimulated Raman scattering because the people that use research laboratory, where this work was done, found that the stronger they pumped the ruby, the less red light they got out. But they were scientists and they discovered that the light that came out was in the infrared, shifted downward in frequency by the raman active vibration of the nitrobenzene molecules. And so they explained that correctly, too, a stimulated Raman scattering, the shift in the frequency of the ruby light. But in those early days people always tried to Q-switch, by putting a reflecting prism on a dentist’s drill, an air driven dentist’s drill. And only when that mirror on the drill was parallel to the fixed mirror could the oscillations build up. Of course a very poor laser mode control and this method was usually abandoned in favour of the Kerr cell switching. But it worked. Then the next big step which took us to the pico second regime, because it got pulses shorter than a nanosecond was what is known as passive mode locking. You put a film of a fluid consisting of a bleachable dye in the cavity, a very thin film of dye, close to one of the mirrors, and that led to shorter pulses. What does the mode locking mean? It means you have many longitudinal standing modes in the optical cavity and they are spread in frequency by c, the velocity of light over 2L and they can be in phase at a certain time and then they lose, and because they have different frequencies, they get out of phase anywhere else, and what happens is you get a light pulse that goes through the cavity and at time 2L over c later, L is the distance between the mirror, 2L over c later, they again are right in phase and that in phase happens just at the time they cross the dye film. Of course this is just the basis that led to the enormous development, described on the first day of this conference by Professor Hänsch, during the whole. How can you imagine that the light likes to come out in a series of equally timed pulses by simply inserting a dye, an absorbing dye which is bleachable, that is important. Now, what does bleaching mean? That reminds me of my thesis on nuclear magnetic resonance, with Purcell at Harvard in ’46, ’47. You have a spin, a half system of proton here two energy levels. And as you absorb, you put energies in the excited state in the higher energy state and if you have very high intensity, you build it up, so you get equal population in these two levels. At that point you get as many absorption processes as stimulated emission processes and in optics that has the same case, then these are not nuclear spin levels but two optical levels. And you get equal population in the optically excited and in the ground state and then you say the dye is completely bleached. Now, here is how the system works. You have to start off, you have nothing, so you have to start off by spontaneous emission. And the spontaneous emission single is the sort of a random wave. But you see, if accidentally here you have a maximum in that noisy background, that maximum gets amplified more than the rest, because at the maximum the dyes begin to bleach a little bit, and so on a round trip pass you get a little less absorption or more gain. And so this one little region, which happened to have a little larger intensity, grows faster, bleaches the light more etc, etc, until finally all the energy comes out in a very short time. It’s like what happens in a capitalistic society with money. The money goes where there is already some money. And here the light goes where there is already some light, because you get less absorption, more gain, the higher the intensity. That is the simple physical explanation, there is no need to – and it would be wrong to appeal to the boson statistics of protons in this case. People say bosons like to be together but that is hand washing. Then, a decade later, people had more sophisticated ways. One of the problems to get shorter pulses is, you need a large gain bandwidth product. As the pulse gets narrower and narrower, the frequency range that has to be amplified gets larger and larger. And, in electrical engineering, the important term is gain bandwidth product, you have to have gain over a larger and larger frequency range. And in the first experiment in ’64 to get to nanosecond pulses, you couldn’t use ruby but you had to use neodymium glass, which has a larger gain bandwidth product. And then finally people used dyes as a gain medium, rhodopsin, and that has even a larger gain bandwidth product. And then they have the scheme of counter propagating rays and here is the bleachable material and then pulses going clockwise and counter clockwise cross that bleachable material at the same time, and that is only a few microns thick film so you get two counter propagating laser pulses which cross each other exactly at that bleachable dye point. And that is how people first reached pulses shorter than a picosecond and they said they were in the femtosecond regime. Shank and Ippen are the names involved in that development. And then you get the problem, the frequency range gets so large that you have to worry about different frequencies propagating a different speed through some optical elements, and you have to correct for that by putting in a light prism. So to make the optical pass lengths for all the Fourier components in the pulse the same again. That’s a very tricky business but it worked and then people got to delve into the femtosecond regime. Now, around 1990, this generation of femtosecond pulses became as developed enough, so that you could start buying femtosecond pulse generators. And that is based on another way to get short pulses not based on absorption or by bleachable materials, but just based on dispersion. And one had to use a very large gain bandwidth product that you get by replacing the chromium ions in ruby by titanium ions and you call it a ti-sapphire laser material. And like any other material, a crystal, you now start using the intensity-dependent index of refraction. And the higher intensity causes a focusing, because here you have your light wave distribution, highest intensity in the centre and there the index of refraction is highest. So you have a phased lens in the medium itself and if there is a higher intensity like here, indicated by the green waves, which now compared to the lower intensity in the blue wave, the higher intensity gets focused a little more. And if you now have an optical aperture, at just the critical point, then you see that you’ll relatively lose less energy of the high intensity pulse than of the low intensity pulse, and so here again, the higher the intensity, the more the gain. And that leads to shorter and shorter pulses. And with this device, which was then developed commercially, you can get pulses of three femtoseconds which really contain only about three cycles of the light wave, very short pulses. Now, the one thing is how do you know the pulses get that short? In order to measure something, you have to have a measuring stick of about the same size, to measure the lengths, the tallness of persons you have to have a yard stick. But here, you know, you are in a new time regime. You don’t have any clocks there yet. So you have to get the measurement with something comparable to what you want to measure and you do that by splitting a pulse in two. And here you get slightly different optical pass lengths to the bottom half of the optical pulse you have generated and the other. And then you vary the interaction wave length in one of the pass of the two halves. How do you know when the two halves overlap, you take another non-linear effect, second harmonic generation and you can arrange it in such a way that you only get second harmonic generation when the two pulses pass through that little slab at the same time. And you then change the pass lengths in one of the arms and you pluck that and for every picosecond you have a displacement of a third of a millimeter. So it’s easily to measure, and a femtosecond difference corresponds to three tenths of a micron which you can still measure with a micrometer screw. And so by looking that the intensity of the pulse as a function of time, had this curve and was on the half way mark about three femtoseconds. That of course doesn’t describe the whole pulse. In addition to the amplitude, you want to measure the phase and that can be done by a technique which is known as FROG, for Frequency Resolved Optical Gating. You measure separately for different frequency components for the second harmonic generated how they depend on this variable time delay between the two pulses. And then with some mathematical manipulation, you can get the phase variation on a femtoseconds time scale. So these ultra short pulses can be characterized completely on the time scale of femtoseconds. Due to the development of short pulses, it has now been possible to get to extreme highly intensities, here we are at 10 of the 19th watts per square centimeter and you get that by just one milli-dual pulse, if it is ten femtoseconds wide and you focus it on an optical wave length, to the extent to -8 square centimeters, you get 10 to the 19th watt per centimeter. Now, what this means is, a very critical point is the field strengths of the binding of an electron in an atom or a molecule and a measure for that is the field strength of 10 to the 9 volts per centimeter, which is the Bohr orbit of the ground state electron in the hydrogen atom, which is here. And if you exceed that, you just pull various electrons out of any material. And when you are in this region of 10 to the 20th watts per square centimeter, you pull these electrons out and they immediately, in the next quarter of the light cycle, can get accelerated to relativistic velocities. So any material here is changed into a relativistic plasma. But let’s now turn to this region just below the intensity that corresponds to the field strength in a Bohr orbit. We tuned back to 10 to the 13th to 10 to the 14th watt per square centimeter. So our optics field is smaller than the binding field but not much smaller. And then you get the phenomenon of tunneling. Here is the Coulomb field from the nucleus, here is the light field that produces a contribution to the potential energy of the electron this way, and now there becomes a probability for the electrons to go through that potential wall. Maybe a probability of one in a thousand, very sensitive on the field strength you have applied. And then that free electron gets moving in the oscillating field of the light field. It accelerates with the light direction to the amplitude of the electric field in the light turns around, it decelerates and it gets pushed back to the ion it has left. And then it rehits the atom it has just left and it can recombine with the ion to emit radiation. And this is the basis of a new phenomena in the region where this tunneling occurs. And the dimensionless parameter, that is important, is to compare the oscillating energy of a free electron in the field which we denote by the, ponderomotive energy use of P, which is given to the light field strengths by this relation and the light frequency is there. And whether that is larger or smaller than the ionization energy, and if this is larger than the ionization energy, optical tunneling of the electron dominates. And this was already argued theoretically by Keldysh in Moscow in 1964. And when you are in that regime, you observe a new phenomenon like high harmonic generation and this leads to the possibility of attosecond pulses. You see you might argue, you can never have a visible light field pulse shorter than one femtosecond because that corresponds to half an optical light cycle. So to get to the attosecond regime you need higher frequencies. You have to go to the soft x rays or extreme ultra-violet. And that is just what becomes possible with this mechanism of ionization. You see, here you have a pulse that is only three cycles or so and here is the pulse envelope. And let’s look at the red curve. You see that only at this point the tunneling may be effective. And anywhere else you don’t get the tunneling ionization. The tunneling probability is orders of magnitude smaller anywhere else, so you only get tunneling in a very narrow region and near that maximum. Of course you can have another pulse and that depends very sensitively on the phase between the envelope and the wave. Here you have two equal maxima of equal strength. And that makes a lot of difference in the high frequency light you generate. I have here a schematic of what happens, you see the tunneling here. The electron goes and moves back, only if it’s a linear polarized field. If you have circular polarization of the light, the electron orbit, after would be very different, and there is a very strong dependence on polarization in these attosecond phenomena. And then you see that the electron that gets free, gets pushed back in the third half cycle and they can recombine in a re-collision process. And if you look at the highest frequencies that can be generated, they are 3.2 times the ponderomotive force in the field. And if you look at those very high frequencies generated, it makes a lot of difference, what that phase is between the envelope and the field itself. You have only a single line, you can see interference problems, because you had two points in the light cycle in the blue curve. You could equal the number of tunneling here as you have there. So people understand a great deal now of these electron pulses and it’s important to note that the free electron wave function has a phase that is correlated to the phase of the coherent light that created it. And you can steal the phase of the electron wave function by putting in additional light beams and this is a very sophisticated field which I’m not competent and have no time to discuss. But I want to end with a little story that a colleague at Harvard, Dudley Herschbach made after I gave this talk where he was in the audience in Croatia of all places. And he said…Well, a few decades ago there was this very famous book, a Brief History of Light, written by Stephen Hawking. And that was a booklet that I found very difficult to read but you saw it on the coffee tables, especially of non-scientific colleagues. It was a very popular book to show to your friends, a Brief History of Time. He said: “Stephen Hawking wrote that, but you presented a history of brief time.” Thank you very much.

Nicolaas Bloembergen (2008)

From Millisecond to Attosecond Laser Pulses

Nicolaas Bloembergen (2008)

From Millisecond to Attosecond Laser Pulses

Abstract

A historical overview is presented of the experimental development of ever shorter laser pulses from 1960 to the present. Already in the early sixties nanosecond pulses were achieved and the entry into the picosecond domain was reached in the late sixties with a neodymium glass laser. First sub-picosecond pulses were accomplished in 1974 with a broad gain dye-laser medium in combination with a saturable dye-absorber film. A true revolution in femtosecond generation occured with a titanium-aluminium oxide laser crystal. Non-linear effects are essential not only in the generation of picosecond and femtosecond pulses, but also in their measurement and evaluation. In this talk the development from the millisecond to the attoseconds within the last 50 years will be reviewed.

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