Thank you very much everybody for coming to this talk. I actually work for two institutions, University of Southampton and NTU Singapore. And I will be giving you a talk on picophotonics.
Essentially, the purpose of my talk is to show that it is now possible to see and study picometric scale events. optically. So to start with, I will show you this line of sizes and technologies for imaging.
And we know that together electron and optical microscopy ends somewhere at the level of a few tens of picometers. And the most advanced cryo transmission electron microscopes equipped with a very very considerable computational power can get to this level of optical resolution of resolution while optics perhaps is finishing at the level of a few tenths of nanometers so beyond that there's a no man's land and i my talk will aim to show that actually we can enter now the no man's land, applying new ideas of imaging and metrology using light and electron beams. I will start with picometer imaging with free electron beams. This idea came to us a few years ago, and since then we will be exploiting it in various applications.
But let me first introduce the idea. If you have a nanoscale object, for instance, a typical element of a nanotechnology, a cantilever, and put it into a scanning electron microscope, a very conventional scanning electron microscope, and focus a beam of electrons at the edge of such structure, so then if the structure moves, the rate of production of secondary electrons, which is normally detected in SEM, will depend on the position of the structure. And if you focus on a sharp cliff of such a structure, so the rate of electrons will be proportional to the gradient of the profile of the structure.
You can very easily see... that in a conventional microscope with this conventional rate of electrons coming and secondary electrons generated, one picometer displacement amplitude can be detected in one second. And one picometer is essentially 1% of atomic size diameter. So how do we make an imaging technology out of that? So I show you with using this cartoon.
This is a fly with moving wings. And what you do in conventional electron microscopy, you scan the electron beam across the structure, across the subject, and detect secondary electrons. What we are doing, we are doing something slightly different.
We fix our electron beam at a particular point, or in this case, of the moving wing. and detect secondary electrons for some time. And once they are detected for some time, we can calculate the spectrum of modulation of the secondary electrons, which will be relevant to the spectrum of movement of the structure. As a result of that, we can then represent a hyperspectral image of the object at the given frequency. And as I said, this can be done with...
with incredible resolution. So these are a couple of examples of this technique. For instance, this is an iconic image of a flea which was observed by Robert Hooke with his first microscope.
We took exactly the same type of flea and put it into an electron microscope and then focusing on a particular set of the flea. we can see that the elements of the setae actually move when the flea is slightly shaken by a piezoelectric transducer. And you can see that, for instance, at the frequency of 50 kHz, you can see the amplitude of induced motion and the phase of that using this technique. as imaging techniques. This is not that impressive because here the amplitude of motion is the scale of nanometers.
It's considerably more impressive if you start doing this for the sake of detecting Brownian motion in the structures. The amplitude of Brownian motion in nanostructures is anything in between a few picometers to a few hundredth of a picometer. And this is a scanning electron microscope image of the of the cantilever made on a thin membrane.
And nearby you see an image of this cantilever in terms of its Brownian motion amplitude at the main frequency of out of plane oscillations of the cantilever. So therefore this image represents the picture of motion. on the cantilever. And the amplitude here, you can see, if I put, for instance, my measuring point somewhere here, this would be the spectrum of the motion. This is the main mode we are presenting here.
And the flow level is at about one picometer per square hertz. And therefore, in one second, you can detect amplitude of motion about one picometer. So this opens an incredible opportunity to look much more closely into thermal motion of nanoscale objects, say, like MEMS and NEMS, biological objects and many others. We were in particular interested in that because we thought that there's an opportunity to study different regimes of thermal motion.
in an scale object. And again, look, this is a silicon atom which has a Van der Waals diameter of about 200 picometers. So we are detecting here motions, movements with amplitude of one picometer and above. Okay, let's come to the nature of Brownian motion, of thermal motion rather.
in a nanoscale object. I give you an example of a very simple thing and a cantilever. And normally when you say thermal or Brownian motion, what you think about is that the object is colliding with ambient molecules, and as a result of this random collision, you see a random Brownian motion.
Yeah, this is true, but in many cases of nanotechnology, what is important is not the collision, with the external molecules, but rather collision with annihilation and creation of the phonons in the structure. So here we are talking about flexural phonons, so the coherent flexural phonon mode is responsible for the movement of the cantilever. And the phonon impact and momentum transfer related to that creates the Brownian motion.
However, if you are able to look at this process with much higher temporal resolution, you perhaps would be interested to see what happens between individual collisions, individual acts of releasing momentum from the annihilation or creation of flexor ophonum. And we did exactly that. So we created a cantilever, focused our beam at the end of the cantilever, used our technology for detecting amplitude of motion and traced the motion in time.
So this is a characteristic trace of the end of the cantilever. You see that it has a haute component corresponding to the thermal motion. The spectrum of this motion is presented here, and you see that the main amplitude, as it follows from the Langevin theory, of Brownian motion and resonance system is at the fundamental resonance of the structure.
And again, you see noise equivalent displacement again about one picometer squared second. So, however, if you now do these measurements with high time resolution, which of course you can do by simply employing a high-speed secondary electron detector, You will see a very interesting regime of movement. This regime is called ballistic regime.
So if you look for the displacement of the cantilever in short period of time, the beginning of this coordinate axis, you will see that the... the mean square displacement of the cantilever is not proportional to the time, which would be characteristic for a diffusive regime. It's actually proportional to the time square.
And this means that for some time the cantilever moves ballistically. And if this period of time is about few microseconds, you see ballistic movements of the cantilever. And then after that, for longer periods of time, the multiple collisions mess up the ballistic motion and it's becoming random. So you can see here, for instance, in the velocity autocorrelation functions for about few microseconds, the velocity measured at this particular moment of time and a microsecond later is exactly the same. The system moves ballistically.
There's a lot of interesting physics behind that. I don't have time and I would like to move now from here to applying actually optical techniques to measure picometric movements and events in metham. Right, let us start with metamaterials, which is very topical for this particular conference. We have been working on what we call nano. optomechanical metamaterials for many years.
And the typical characteristic structure there is a membrane which is cut into beams containing either plasmonic elements or dielectric resonators. And mutual movements of the beam create a change of optical properties of such an array. And this is demonstrated here.
So I show two two nanowires in the array, which are decorated with plasmonic elements. And because the plasmonic metamolecule is split between two nanowires, their mutual movements create change of the optical properties of the structure. So the mechanical and the optical properties in the structure are highly correlated.
So as a result of that, one can see brownie motion in such metamaterial. Indeed, if you have an array of beams and they thermally oscillate, so for a typical metamaterial of this type, the characteristic displacement or amplitude of oscillation at the resonance frequency would be about 100-200 picometers. This is not much, this is only half of silicon atom diameter, but nevertheless, because of the plasmonic enhancement, the change in the reflectivity or transmission of such metamaterial is reaching a good fraction of a percent, which is of course quite easy to detect. You simply put your metamaterial into a beam of light, and as a result of that, if you detect the Fourier spectrum of the transmitted or reflected light, you will see peaks of oscillation, of a peak of haotic modulation of the optical properties of the material by detecting light.
So what is important here is that by simply detecting transmission and reflection of the metamaterial, you have access to movements in the metamaterial which are only fraction of atomic size. So picometric scale events may be very easily here to be detected by light. So you can of course get into much more complex set of measurements and ideas, and since these elements have non-linearity and can be controlled in various ways through heat and applied light, you can create a variety of very interesting phenomena.
And I will be actually giving shortly, on another session, a talk on how this can be applied to create new types of metamaterial structures and new types of metamaterial functionalities, in particular parametric and floccular systems. If you are interested, come to the next talk. So, but I promised you to talk about picometric metrology and the study of the event with light.
So, this looks like a crazy proposition. We all know that It should be extremely difficult to do anything on the picometric scale with light for the very simple reason. So if you have, for instance, an atom, this is a sodium atom, its main D-line emission wavelength is in the visible part of the spectrum, and the atom itself is 3,000 times smaller. than the emission wavelength.
So if the atom changes position, for instance, this would have absolutely no effect on the, or very little effect on the emission scattering of such atoms. And this is true. So if you try to do metrology with, or imaging with conventional plane waves, it is very, very, very, very difficult to get beyond.
the diffraction limit. However, the idea which we are pursuing is that not using the plane waves, but using what we call structured, topologically structured light. As you perhaps know, the light can be structured, coherent light, on a very, very small scale.
And this is an example which was first given by Michael Berry about 10 years ago when he did show analytically that if you have a few beams propagating in slightly different directions but nevertheless coherent at the same frequency, you can create a complex field which would contain singularities. So, discontinuities of the phase, area of energy backflow where predominant energy direction is opposite to the main direction of the propagation of light energy and zones of high value of gradient of phase, which are called local k-vectors areas. All of them are significantly smaller than the wavelength of light, orders of magnitude. In particular, singularity is located as a delta function.
And so the idea is to use this sort of light in improving resolution. A couple of years ago, we have demonstrated and actually experimentally measured an example of a light field which would have such structures. This is a so-called super-acrylid light field.
It doesn't really matter what is the nature of the field, but what is important is that it has singularity pointed out by green circles, areas of high gradients of phase. high local chi-vector value and zones of energy backflow. All of them are on the deeply sub-webland scale.
So, as a result of that, we came to the idea that if we can visualize that energy of areas of, for instance, singularities or areas of high values of local chi-vector, we can use it in metrology. And very much the same as you use a conventional ruler and apply it for metrology of objects, your resolution will be limited to the halfway length of light if you use a conventional microscope to apply to this ruler. However, if you use so-called optical ruler, a structure which creates high-light localizations, and these localizations and singularities are much smaller than the wavelength of light.
So then you can improve the rule accordingly. And we have demonstrated exactly that. So we created a very simple system consisting of a laser, a metasophis, and which creates highly structured, topologically structured light, a simple device to recover positions of the singularities.
And then... use it as an optical ruler on two mutually moving platforms. In a very, very simple experiment, you immediately have a resolution of about one nanometer. But this is a metrology rather than imaging. It is a metrology of macroscopic objects.
So, can you actually use it for the metrology of the microscopic object? So, this is the idea, again, of the same nature. So, you have your… this artistic impression of a small object, you put it into a topologically structured light, and you then detect scattering. and you detect scattering while changing position of the object.
And the idea is that detecting scattering at various positions of the object, you should be able to get some information about the object. And the best way of treating that is actually reconstructing the object by using artificial intelligence. And I'll give you an example of that in a second. But let me just show you that actually this looks very, very promising.
So, for instance, this is a phase profile of a topological structure, a superacidatory hotspot, and this is its intensity profile. And now I start moving a small particle across this area and study what happens in the scattered light. at various directions, designated here by the position of the detector, and for various positions of the particle. And you see that scattered light becomes seriously changing when the particle passes through the singularity area. So this actually is a mathematically proven thing, and we now have a considerable amount of analytical theory to explain details of that.
But let me go into the experiments first. So I said that artificial intelligence is a way of doing that, and this is a great area where artificial intelligence can be applied. You know that detecting shape or size of the object through scattered light is an ill-posed mathematical problem.
And if you apply conventional analytical techniques, you actually cannot get better than resolution equal to lambda by two roughly. The solutions become unstable at this level. However, artificial intelligence, it was found in recent years, is an absolutely perfect algorithm, a perfect approach, using neural networks and deep learning to tackle this problem, because in the deep learning process, you can have access to really very large amount of information. which will then help to improve the revolution of the system. So we started with something which is not structured light, but simply an object illuminated by light, and then we studied the scattering pattern of this object in the limited angular direction.
So what we have done, we applied this to measure a width and position of a small slit, a subwavelength slit in a metallic film. So in order to do that, we created a training set, which was what we called a physical training set. Essentially, we created a few wafers in which a metallic layer was perforated with slits of different position and different widths. And then we created diffraction patterns corresponding to the slits.
And this is a typical example of the diffraction. pattern and then we use it to train a convolutional neural network with this data. As a result of that, the trained network can recognize a diffraction pattern, you can see it here, and associate the diffraction pattern with the size and position of the slit.
It actually can be done under conventional microscopy, but gives an amazingly nice result. For instance, if you plot the actual ground truth value of the width of the slit against optically measured, you get a resolution which is comparable to that of fabrication with focused-iron beam milling and detection with scanning electron microscope. I don't want to go into details of that, but we did a series of experiments, which allow you at the end of these experiments to have a true dispersion of measurements using scanning electron microscope, focused on the milling system, and optical measurements.
And you can see that all of them give values of the same ballpark, a few nanometers of resolution. The teaching here is twofold. The first thing is that you can actually detect optical object parameters, parameters of the object optically, with much, much higher resolutions than lambda by two. And the second thing is that your quality and actual resolution is determined by the quality of the training set.
And here the training set is created by Folkstein-Bemilling of the slits, and it has its own accuracy. And this actually is what's limiting. in this particular experiment, resolution of the optical technique, accuracy of the optical technique. So therefore, as usual in artificial intelligence, the quality of the training set is the main thing which determines accuracy of the neural network. And with this knowledge, we came to the idea of improving our training set.
Here, as I said, the training set is made by milling a large number, a few hundred of elements used for training of the neural network. But can we do better than that? And this brings me to the last section of this presentation, in which I am I'm extending this beginning of my talk where we used electron beams to use optical beams. What about replacing the electron beam with a topologically structured light? And instead of detecting secondary electrons, detecting scattered photons?
And then measuring displacement of the beam using light. This is exactly what we did, but because we were targeting much, much higher resolutions than one or a few nanometers, we created what we call an institute training set. It's a very elegant solution in which we created a nanowire sitting in the gap between two in a channel between these two sides. And this nanowire can be electrostatically controlled to bend either towards that direction or towards that direction.
You simply apply this nanowire, it's metallized, and you can apply electrostatic voltage to slightly move the position of the nanowire. So this then becomes the same type of experiment as with the slit. You eliminate your nanowire with light, you see diffraction pattern. You create a training set now by controlling the voltage, different value of voltage to the nanowire, and training your neural network with that.
And actually this little video shows how you can actually change the position of the nanowire electrostatically. So once this process is done, and the training has been performed in situ on the same object you are going to measure, you can hope for really very, very good results by black artificial intelligence. So we now show the network a diffraction pattern which corresponds to the unknown position of the wire and see what position of the wire was as far as the network is concerned.
And here are the results. So this is the result for plane wave illumination. And the training set, as I said, was considerably improved.
And we vertically plot error in optical measurement displacement with respect to the ground truth value. So if your displacement is anything between 10 and 100 picometers, So the typical error is 76 picometers, right? With the increase of the size, it's becoming slightly bigger, but relative error actually diminishes, but the absolute error increases. But if you then go to topologically structured light elimination, you get to the remarkable level of 20. eight picometers when your displacement is between 10. and 100 picometers, and it's becoming 63 at high level of displacement.
So this is, as I said, this is a remarkable thing. The average displacement here is a small fraction, 10% of the silicon atom diameter. I would...
You should probably go to conclusions, Nikolay, now. Yeah, I'm concluding, Jeremy. I don't want to scare horses, but so these results I just presented there on public domain, these are results which are not yet in public domain, but we made considerable improvements in the laser system and mechanics of that. And this is the latest result.
We can now measure just under two picometers displacement of the nanowire. Watch this space. So I will skip this slide and come to conclusions. So the first thing is why it doesn't work so well.
First of all, I already said that the inverse scattering problem, which is essentially a Fred Golem integral equation solving problem, can be done very, very efficiently by a well-trained network. So highly congruent with the experiment training sets, as demonstrated here, can give absolutely miraculous results. And of course, topological illumination and sensitivity to small repositioning of the object against singularities gives access to very, very high value of k vectors in the system. And this helps the process.
The last slide I have here is the same nanowire. And I said, actually, I can measure 28 picometer displacement, which I do. I now can measure 2, right?
Okay, say 28. But I already told you that its Brownian oscillation is about 100 picometers at the resonance frequency. So what does it mean? It means a very simple thing.
We actually integrate the photodetector signal in the Zist DRA for a period of time which is much longer than the damping time of the Brownian motion. So we integrate and therefore detect the mean value. And this is obvious.
But what does also give you an opportunity to think about is that if you actually can do this diffraction pattern measurement with high frame rate, which is, say, a higher frame rate than the damping time of Brownian motion, you can have access to the dynamics of Brownian motion using optical techniques. So, this is exactly what we are doing. We are now having high frame rate cameras, which will soon allow us to study the Brownian motion dynamics and fundamental physics at that level in nanostructures and opening the dynamics of the picometric world.
This is the end of my slide. I think this is the first cut into the field of picophotonics in the sense of detection of a pigometric scale event. And these open opportunities for metrology and various forms of optical imaging, which we are working on, study of Brownian motion, studying of new mechanisms of switching, various optical and optically assisted forces.
and the dynamics of light-driven machines and many, many other things. In particular, actually, we hope that at some stage we will be able to see things like movements of the spikes of the viruses and apply this to biological imaging. Thank you very much.
And there's quite a lot of people involved here in Southampton, where I'm currently now, and in Singapore in this work. And thank you, Jeremy, for your patience. Thank you, Nicola.
So we have time for just maybe a few questions. So if people in the hall want to ask any questions, I can repeat them. Yes, please, down here. Just speak and I'll repeat.
Jeremy, you need to repeat the questions. I will, but do we have a microphone? But I don't know what the collision time corresponds to.
So the question I think, Nikolai, is what does the collision time correspond to for internal Brownian motion? What is the typical collision time? Yeah, what does the collision time correspond to?
You can imagine it for molecules against a beam, but what does it correspond to in the internal degrees? Yeah, so if you have internal collisions with molecules, this is simply an act of collision and momentum transfer to the object, say a brownie particle. Here, the rate of creation and death of flexural photons is equivalent to the collision time.
This regulation and creation of the phonons has the same meaning as collisions with external molecules. Maybe we should... Sorry, Jamie. Details of the times involved are in the archive. It will be published anytime soon at Science Advances.
But there is already an archive on the web about it. Okay, any other questions that people would like to ask? There's one online question, but I don't know how we get this person.
Can they unmute themselves? Or do we have to do that? I don't think so. You can read the questions, I guess. It's not in the chat.
So maybe this person can put the question in the chat. In question and answer. Sorry.
Okay, yes. I think they're all about fixing the slides. Yeah. The first talk. Any other questions?
I have a question, Nikolai, about the relation to this and, for instance, work on x-ray interferometry, which uses x-ray beams. So in some ways, this is an advanced version of interferometry, or do we think about it differently to that? Yeah, well, so the argument I quite often hear is that, well, I don't know. 10 picometers or 50 picometers is impressive, but advanced interferometers can do that.
And in fact they do. But say, look at the complexity of the LIGO system, which operates at this level, or high-end advanced interferometers, which are used in optical technology. These are hugely complex machines. But here, you, in a single shot, under conventional microscope, get the same level of resolution and can do it very, very fast.
And this ability to do it in a simple setting and with very high frame rate actually is extremely important. So you would like us to change the gravitational wave detector to use more structured light, is that right? I have had approach from light people. all together. Yeah, that sounds interesting.
Okay, well I think with that people would like to go and get coffee, so let's thank Nikai again for his talk. Thank you very much for your attention.