Steven Francis Nagle: So today we have flex compute.
Steven Francis Nagle: They are a technology company that specializes in high performance computer or computational software and cloud-based solutions for engineering and scientific simulations. And I think the cloud-based
Steven Francis Nagle: nature is mostly what they're pushing.
Steven Francis Nagle: because otherwise it would just be Ansys. But cloud-based is good.
Steven Francis Nagle: So Thomas Chen Tom Chen is here. He's a senior photonics engineer at flex compute and
Steven Francis Nagle: I wrote here that he received his Phd in physics with a research focus on experimental condensed matter, physics and optics. Is that correct?
Steven Francis Nagle: Good. All right. Currently, he's working on simulation tools and photonic designs at flex compute. Today. He'll be talking about Anderson localization of light in particular, how flex compute software and some of their engineers, perhaps, himself included.
Steven Francis Nagle: helped make that simulation possible.
Steven Francis Nagle: Sound fair.
Steven Francis Nagle: All right, great. I'm going to turn it over to you now.
Steven Francis Nagle: and you can finish your bio
Steven Francis Nagle: and launch right into it. All right. Welcome, Thomas.
Tom Chen: For the invitation. It's always a pleasure coming to Mit.
Tom Chen: So be be before I start. I guess I just want to do a quick background check. So is everyone here from a photonics background.
Tom Chen: No kind of
Tom Chen: okay. Good. So so I used to do research in the condensed measure physics.
Tom Chen: Then, after I graduated, I kind of went into the photonics industry.
Tom Chen: And now I'm working on simulation tools for photonics. So
Tom Chen: so this topic, it's
Tom Chen: Anderson localization of light or electromagnetic waves in general in 3D.
Tom Chen: And
Tom Chen: it's it's really just one example of how we can use modern simulation tools to push the boundary of science discovery.
Tom Chen: right? So
Tom Chen: brief outline of the talk. So today's talk it's kind of divided into 2 parts.
Tom Chen: The 1st part is about Anderson localization of light in 3D. Or to a
Tom Chen: very quick background introduction. In case you are not familiar with the topic.
Tom Chen: Then we'll discuss
Tom Chen: what kind of requirements there are that we we need to have to to really solve this problem.
Tom Chen: And then we'll delve into the technical details of innocent organization and what we covered so
Tom Chen: essentially, the absence of endersonicalization in random dielectric systems
Tom Chen: and the existence of Anderson localization in random metallic systems.
Tom Chen: Then in the last, maybe 5 to 10 min, we would also briefly touch on
Tom Chen: the new world of computing how the computing paradigm is shifting from
Tom Chen: more traditional kind of sequential CPU computing to massively paralyzed Gpu computing and how that can benefit
Tom Chen: photonic simulations. Photonic research.
Tom Chen: So in the fifties Cleo Anderson, originally proposed the idea of Anderson localization
Tom Chen: and and therefore he won a Nobel prize for it
Tom Chen: the the original enderson localization described
Tom Chen: the quantum system. So electrons in a lattice in a periodic lattice.
Tom Chen: If you have a periodic lattice and you have a electron or the wave function. If you have a localized wave pocket
Tom Chen: then if you let it just evolve, you'll see the the way pocket will just spread out to to all the lattice sites.
Tom Chen: But turns out, if you introduce disorder or randomness into the lattice.
Tom Chen: under certain conditions
Tom Chen: you will achieve this local end zone localization
Tom Chen: where the the wave function will will be confined into a certain area.
Tom Chen: And later on people realize that. And this localization is not only applicable in quantum systems, but it's a general wave phenomenon.
Tom Chen: right?
Tom Chen: And so you can do it in acoustic waves. Electromagnetic waves mechanical waves as well.
Tom Chen: And later on in
Tom Chen: early 2 thousands.
Tom Chen: people demonstrated. Experimentally. Let the internal localization of electromagnetic wave or just light.
Tom Chen: can be achieved in 2 decisions.
Tom Chen: So the idea is, you have a
Tom Chen: a 2D waveguide
Tom Chen: with Guy. Let's invariant in one dimension.
Tom Chen: If it's periodic.
Tom Chen: you decided with light, and you will just spread out.
Tom Chen: But if you introduce this order actually, you can you see the light? It's actually confined local.
Tom Chen: However, this long standing debate on whether or not Amazon localization of light
Tom Chen: can exist in three-dimensional systems.
Tom Chen: And the reason why it's a long standing debate is because
Tom Chen: to really simulate this kind of system
Tom Chen: we need a simulation tool that can handle a few things.
Tom Chen: The 1st thing is a large, reflective index contrast.
Tom Chen: So if you have a
Tom Chen: a random system, the the contrast between
Tom Chen: different materials needs to be sufficiently large for Anderson localization to exist
Tom Chen: in the simulation domain
Tom Chen: has to be very large as well. We need to simulate
Tom Chen: up to millions of resonators. In this case
Tom Chen: we'll use Sophiers as resonators, but in principle it can be other geometries as well
Tom Chen: and ideally. We want to simulate the broadband response, though just not one particular frequency, but a range of frequencies.
Tom Chen: and the simulation speed has to be fast
Tom Chen: because you need to verify different geometries, different concentration, different arrangements, different wavelengths.
Tom Chen: and they need to also do the kind of convergence test to make sure your results are reliable. Right? So if the simulation is very slow.
Tom Chen: then that's not really possible to do
Tom Chen: so
Tom Chen: to verify that the Internet localization
Tom Chen: exist or not. So we need to simulate the light transport
Tom Chen: in random resonance systems.
Tom Chen: And one example that we can think about is this randomly placed?
Tom Chen: Sophia's
Tom Chen: can be either dielectrics appears or metallics appears.
Tom Chen: and the the size of those spheres.
Tom Chen: It's particularly chosen such that it's near the 1st me resonance.
Tom Chen: And you really need some kind of resonance to to get the indeson localization.
Tom Chen: So really, we're looking for solving a 3D. Scattering problem.
Tom Chen: right? And there are various tools you can use to solve this kind of scattering problem.
Tom Chen: So just to name a few born theories generalized multi particle B theory, and so on and so forth.
Tom Chen: All these methods can be used to solve the scattering of severe spherical particles.
Tom Chen: But all these methods have some limitations.
Tom Chen: For example, some of some of the methods can only deal with small reflective index contrast. So if you have a severe, with a large reflective index embedded in a background with very low, reflective index.
Tom Chen: Some of these methods will have very, very high computational requirements.
Tom Chen: and generally those methods don't scale very well with the number of spheres. So if you really need to simulate millions of spheres, most of these methods are not really applicable.
Tom Chen: and also you are facing with other limitations, like Sophias, cannot be too close to each other, or overlap with with each other.
Tom Chen: and
Tom Chen: if you want to do a broadband get a broadband response. You need to simulate at various frequencies in independent, and it's very, very time consuming.
Tom Chen: So
Tom Chen: I guess everyone knows
Tom Chen: a general way to solve Mexico's equations it's called the finite difference time, domain method, or Fdpd. Method.
Tom Chen: So fdt. Method solves Maxwell's equations in space and time
Tom Chen: without any approximations. So that's 1 key factor.
Tom Chen: However, so so in principle, it can be used to solve this.
Tom Chen: and there's a localization problem that we are trying to solve.
Tom Chen: But most currently available fdtd, tools
Tom Chen: are built on CPU architecture because just because they were developed kind of a long time ago.
Tom Chen: So scalability is quite limited. So if you want to solve really large problems.
Tom Chen: usually less super time consuming so that's just very difficult to do internally.
Tom Chen: So.
Tom Chen: there are very well known Fdv tools on the marketplace. So you have Ansys numerical that a lot of people use.
Tom Chen: and the famous beep got developed here in Mit.
Tom Chen: All these tools are just based on CPU. So
Tom Chen: they are very good for solving smaller problems. But for our purpose. It's just way too slow.
Tom Chen: So and there's a recent shift in computing paradigm.
Tom Chen: that's essentially from CPU computing to Gpu, computing, thanks to the
Tom Chen: the rapid development of AI and machine learning.
Tom Chen: And we think that's an opportunity for us as well
Tom Chen: to develop
Tom Chen: ultra vast and ultra scalable Fdp, Td platform.
Tom Chen: We'll discuss more about this later on in the talk
Tom Chen: just to show you kind of the benefit of going from CPU to Gpu.
Tom Chen: So here's a speed comparison chart.
Tom Chen: So the horizontal axis of the chart is the size of the stimulation.
Tom Chen: measuring the Fdtv grid point size
Tom Chen: and the vertical axis is the stimulation time.
Tom Chen: So we pick here 4 kind of representative examples of different sizes.
Tom Chen: So what smaller one? You see? If you. So the the black curve represents the CPU Fptd speed.
Tom Chen: The green curve represents essentially the Gpu 50 Td. Speed
Tom Chen: for a smaller one. You see kind of a speed, a factor of 10 speed improvement.
Tom Chen: but for larger ones. You really see hundreds of times faster
Tom Chen: from going going from CPU to Gpu.
Tom Chen: So now, once we take the tool, we can really start investigating
Tom Chen: the Anderson localization 1st in random dielectric systems.
Tom Chen: does it exist?
Tom Chen: So to do that, we set up a simulation that's kind of shown here. So in the middle we have just dialectics of ears
Tom Chen: of radius, 100 nanometer and reflective index of 3.5,
Tom Chen: and we can set a filling fraction
Tom Chen: overloads of years and generate assimilation
Tom Chen: right? So we have closely packed severes, and we excited with a plane wave from the bottom.
Tom Chen: and we monitor
Tom Chen: the transmission to a talk.
Tom Chen: Does your software
Tom Chen: generate
Tom Chen: the not only the the model, but the mesh. Yes.
Tom Chen: so it's a end to end solution. So you can define geometries, materials, it generates mesh.
Tom Chen: run a simulation, and even plug in the results. And does it use home build?
Tom Chen: Modeling? 3D modeling software? Or do you partner with somebody who provided?
Tom Chen: Yeah? So everything is a home built.
Tom Chen: We actually, we use some scientific libraries for the software. But the entire software, and even also the front end, are all home built. And what if somebody had a bunch of things already modeled, and solidworks, or whatever.
Tom Chen: and they wanted to bring it in, how do they get to that same starting point. And then how does your software play nicely in meshing? Because I remember my finite element days? Right? Everything goes to crap and meshing. So you can. So we do support a few
Tom Chen: geometry importing features. So if you have a say a Gds layout, you can import that if you have a cat file. Usually like stl file, you can import that as well.
Tom Chen: And the one benefit of Fdtv method is the measuring is relatively simple.
Tom Chen: So it's kind of it. The Fdt mesh is a rectangular unlike the fem mesh. That's kind of
Tom Chen: Oh, it's not triangular based right? Right? Right? Exactly so. It's relatively straightforward. So we have the measure. And
Tom Chen: but Sdl meshes are grids are usually quite frankly correct, correct. So essentially we kind of interpolate that to
Tom Chen: a permit or refractory index distribution.
Tom Chen: And then we just match, based on that.
Tom Chen: It's relatively straightforward in fem. Usually that you can be quite tricky, especially you have some
Tom Chen: like spiky geometry. Yeah. But but in fdt, usually there's no no problem.
Tom Chen: Yeah, great question.
Tom Chen: So yeah, so the idea is to just
Tom Chen: sending light on the bottom, and we monitor the transmission on top. We also monitor the field distribution within this
Tom Chen: aggregates of softwares.
Tom Chen: So we simulate this
Tom Chen: for a few different feeding fractions. So here is 18%, 29%, 38%, 54%. So it just represents the volume fraction of less of years
Tom Chen: for higher fraction means just more softwares, more densely packed sophias. And they are randomly placed in this region.
Tom Chen: So one kind of
Tom Chen: kind of criteria that we can look at is this so called? Iofi regal criterion.
Tom Chen: and it's given by this K effective times. Rs, roughly equals one. So K, effective is the effective wave vector inside the random medium. And Ls is the mean free pass of scattering. So essentially the
Tom Chen: kind of average distance between 2 scattering events.
Tom Chen: If it's kind of around one or smaller than one, then it's likely that you can see Anderson localization. If it's larger than one oops.
Tom Chen: then it's more of a diffusive transport.
Tom Chen: So use that as a criteria to kind of qualitatively gauge. If we can observe a different localization in the system.
Tom Chen: So here it plus this quantity for various filling fractions from 18% to 54%.
Tom Chen: And you can see. And this, that's that's K effective times. Rs equals one line.
Tom Chen: I can see, can get the reasonably close
Tom Chen: for 38%, for example.
Tom Chen: But does it actually mean? Let's understand localization. The answer is not necessary.
Tom Chen: And
Tom Chen: and the another kind of signature of
Tom Chen: diffusive transport that if we monitor
Tom Chen: the transmitted power
Tom Chen: on the other side of this this random system as a function of time. So we send in a a pulse like a golfing pulse for that, and we monitor the transmit transmitted power as a function of time
Tom Chen: after the initial raise. If if you see a exponential decay of the power
Tom Chen: that indicates the transport is a diffusive. So there's no instant localization
Tom Chen: so turns out in this case
Tom Chen: the decay is exponential for all the filling fractions.
Tom Chen: And from this decay rate we can even extract the diffusion coefficient
Tom Chen: product here. So you can see the diffusion coefficient. That's
Tom Chen: has a minimum around 30%. But
Tom Chen: still it's a diffusive system. Yes, so is it the
Tom Chen: the the part in the middle plot which goes below? One is that Anderson localization? Yeah. So let's say, yeah. So let's say, kind of a a hint that that might be in this localization. But it's really not conclusive. So the the 3rd plot that shows the decay of the power. Okay, if it's exponential decay, then
Tom Chen: it's diffusive transport. So there's no ensem localization. Okay? So even though it seems like here it dips below one slightly, but based on the decay. There's still no signature of any localization. Yeah. Great question. Can I have another question? Yes. Are you saying that it is not possible to observe numerically Anderson localization in 3D. With partial approximation?
Tom Chen: It is not possible or not yet
Tom Chen: observe, because if you really need this and 3.5, and you have to simulate the full master equation, then.
Tom Chen: of course, I understand the need for better numeric method. But I don't understand why
Tom Chen: in person, in principle, you have to simulate
Tom Chen: Maxwell equation. Why don't you just
Tom Chen: nomadic simulates the
Tom Chen: like scalable
Tom Chen: approximation from the bin.
Tom Chen: Yeah. So I think, be because it's a that's a great question. So because it's a complicated system.
Tom Chen: you you really need to make sure you don't use any approximation, of course. But why do you need so complicated system to see under sanitization? Why, I'm asking, is it proven not to be
Tom Chen: possible to standard zone localization with low, effective index.
Tom Chen: Because, for example, this criteria, if you reduce the the factory index and increase the length, then it might be possible to discuss
Tom Chen: simple approximation to get simple solution.
Tom Chen: Yeah, yeah, yeah, that's a, that's a good question. I think. So be before this study. There are other studies using either experimental or other numerical methods.
Tom Chen: but the conclusions are not very conclusive.
Tom Chen: So the goal of this particular study, based on my understanding is essentially we use, we solve the Maxwell's Maxwell's equations. Is there any approximation
Tom Chen: just to verify that? It's
Tom Chen: definitely you can definitely see internal authorization, or you just cannot see the internal organization.
Tom Chen: If you use approximations, then there might be
Tom Chen: debates whether or not what you observe is due to the approximation or or not.
Tom Chen: Yeah. But but yeah, that's a that's a good question.
Tom Chen: So yeah, so turns out, let's know in the sum localization in this particular case.
Tom Chen: then, some people might say, well, this, 3.5 effective index might not be sufficiently large. And to verify that we tried a even lot, even higher
Tom Chen: effect reflective index up to 10
Tom Chen: and
Tom Chen: turns out in this case this criteria is not met either.
Tom Chen: So even at you can try various filling fractions, and it's always above one.
Tom Chen: And if we look at the same transmitted power sponge of time
Tom Chen: after the pulse, just, they all still follow this exponential decay.
Tom Chen: So the authors draw the conclusion that the Amazon localization
Tom Chen: does not exist in
Tom Chen: random dielectric systems, at least within random dielectrics of years of ears.
Tom Chen: Then,
Tom Chen: then the question becomes, does indecent localization exist in random metallics?
Tom Chen: So previous studies suggest that the reason why you cannot observe enderson localization in dielectric systems
Tom Chen: might be because light can couple to
Tom Chen: longitudinal modes in a pilot shift.
Tom Chen: So then, then people might think, oh, if we, if we have a metallic system where the
Tom Chen: electric field is perpendicular, always perpendicular to a surface.
Tom Chen: might lead to indeson authorization.
Tom Chen: So to test that
Tom Chen: we essentially do the same simulation. But this time with Sophia, is made of pec, so perfect electric conductors
Tom Chen: and reaches 50 nanometers.
Tom Chen: And here you can see also various failing fractions from 8% all the way to 48%.
Tom Chen: So if we look at this flux flux transmitted flux plot. We can notice that the
Tom Chen: above certain fraction value
Tom Chen: the decay becomes the the decay deviates from the exponential decay.
Tom Chen: Right? Very notes from the red curve and the green curve.
Tom Chen: It kind of follows exponential decay, and it kind of deviates fine.
Tom Chen: And then we can also calculate this K. Times L.
Tom Chen: And
Tom Chen: turns out a higher filling fraction. They do dip below one as well.
Tom Chen: and I just keep decreasing
Tom Chen: with with the concentration.
Tom Chen: So from this this curve we can extract again the diffusion coefficient. So
Tom Chen: here you can do a a sliding window feeling to to get the diffusion coefficient as a function of delay time.
Tom Chen: So we can see for lower concentration. It's constant, just means it's exponential decay
Tom Chen: for higher concentration noticeably above 30%.
Tom Chen: Yeah, it's really
Tom Chen: deviates from a constant right drops into this one over P relation, which also it's also a signature of decentralization
Tom Chen: happens. Do you start to see the diffusion to happen faster or slow. So.
Tom Chen: okay, that's fine. And did you encryption in general? Correct, correct
Tom Chen: either 2 or hold on.
Tom Chen: So there is a kink correct. So what's the finish line?
Tom Chen: Shorter than certain amount of time?
Tom Chen: Right? Right? Right? Right? So so that's a great question. So so maybe the next slide will cover it. So so let's kind of
Tom Chen: not super intuitive calculation results
Tom Chen: to to really visualize the initialization. I think.
Tom Chen: it's easiest to just look at the real space simulation.
Tom Chen: Right? So if I if I if I may answer so I I was gonna ask before.
Tom Chen: So these are what you're showing right here are
Tom Chen: that's directly from quantities that you're calculated within material. When you're done with answering Towel's question, could you explain
Tom Chen: how you take what was calculated from flexible view to turn it into the plots we saw. Yeah, yeah, sure, that's a great question. Yeah. So in a real space. It's a signature of indeson localization. It's much more obvious. So the idea is, we
Tom Chen: half
Tom Chen: a again, this random pec severes and we
Tom Chen: inject a focus Gaussian beam into this system
Tom Chen: right? If it's if he follows the diffuse, diffusive transport.
Tom Chen: we will see the beam will spread out as it propagates. And it's evident in this plot.
Tom Chen: So here the feeding fraction is 15%. So let's
Tom Chen: essentially this blue curve. So there's no innocent localization.
Tom Chen: and we see the beam spreads out as it propagates. Right? So here, you see, from this axis is time. So from 0 to 2 picosecond.
Tom Chen: it just spreads out right?
Tom Chen: And but a higher feeding fraction. So 48%, for example, that's where we think, let's understand localization indicated. Here.
Tom Chen: we see the beam. It's just stays concentrated right? Even after 20 picoseconds. It doesn't. It doesn't get spread out. And what exactly is measured on the color bar? Is it like numbers of photons? Is it? Yeah, exactly. That's essentially the intensity of the field.
Tom Chen: Yeah.
Tom Chen: we plot the size of the the beam as a function of time.
Tom Chen: In the lower concentration case we see this square root of P dependent, which also indicates a diffusion spreading.
Tom Chen: But for the higher concentration you can see it's kind of stays constant
Tom Chen: for for a very long time. So let's
Tom Chen: a direct evidence for instant localization
Tom Chen: pieces.
Tom Chen: One propagation of incident or
Tom Chen: sample for like a hundred measurement simulation. Yeah, every person that's 1 simulation.
Tom Chen: Yes, we just fix the position of all these particles.
Tom Chen: sending a Gaussian ping and see how it propagates within the the this this random
Tom Chen: one.
Tom Chen: Supposedly
Tom Chen: spherical wavefront
Tom Chen: the times, as that is correct, correct, correct, correct.
Tom Chen: And let's show. Yeah, exactly. The time and distance are the same. So we can
Tom Chen: watch a animation of how this spreading occurs. So a lower, free, lower concentration where there's no instant localization. Instead of being
Tom Chen: it's just gradually spreads out as it propagates. So the time is indicated here.
Tom Chen: so you can see from 0 to 2 picoseconds
Tom Chen: it just spreads into this very large area
Tom Chen: in comparison
Tom Chen: with Anderson localization. You see.
Tom Chen: notice the time here is much longer compared to this case
Tom Chen: it just stays concentrated as it propagates.
Tom Chen: You say this was continuously single frequency correct, correct.
Tom Chen: Even after 20 picoseconds. The the beam size doesn't really change. Yes, you, you said, this is a suspension of of metal. So they are just moving around. And you're also monitoring their
Tom Chen: movement in the fluid. No, so so the positions of the severes are fixed. Okay? So they are randomly generated initially. Then they are fixed. Oh, I mean, as as good as yeah. It's I just want to know, is it random? Right? Right? Right? Randomly correct, correct. Correct.
Tom Chen: So going back, what was the
Tom Chen: so to answer the question, essentially.
Tom Chen: So here, to to calculate this quantity, you need to calculate the effective wave vector, and the mean free pass of scattering right? So the effective wave vector is essentially can be calculated. So if you have a random system.
Tom Chen: we can use effective median theory.
Tom Chen: So effective Median theory tells you, if you have a random system with certain fit infraction.
Tom Chen: what's the effective index of the of this random system?
Tom Chen: And from the effective index, you can calculate the effective way. Vector.
Tom Chen: alternatively, you can just simulate this system
Tom Chen: and you can plot the field inside the building.
Tom Chen: Inside a meeting. You'll see the the propagation of the of the of the field.
Tom Chen: and even though it's random, you can still see, identify the period or wavelength.
Tom Chen: and from that you can also determine the effective wave factor.
Tom Chen: how much does it deviate from?
Tom Chen: For lambda? Yeah, yeah, so that, yeah, so essentially, the effect of the index, it's we can think of as say.
Tom Chen: feeling fraction, times, effective, index of less of fear plus one minus filling fraction times, effective, reflective index of the background. Just one. So it's kind of like averaging between the 2. So are you, or is it averaged over each of the nodes into properties, or groups of nodes to simulate
Tom Chen: like, how are you managing right over the whole volume? Yeah, so yeah, I actually, I'm not super familiar with all these details. But I think essentially, you can plot the field distribution right? Then you can do a fitting
Tom Chen: to. Essentially so it's a it's a wave. Let's decay as it propagates. Well, I guess then it's a similar question, then, is, is the software calculating this particular quantity for us? Or did someone have to do a lot of post processing to get to that. Yeah, someone has to do some post-processing to get there.
Tom Chen: Correct? Correct? Correct? Yeah, exactly. That's why this quantity is more of a kind of a qualitative thing. So
Tom Chen: the the exact value doesn't really matter that much.
Tom Chen: and the scattering length can be calculated also based on the
Tom Chen: the decay of the field. Inside the inside is a random system, so you can do a a fit to the decay, and from the fitting you can also extract the schedule index.
Tom Chen: This transmitted flux that's directly from the simulation. There's no post processing involved. We we calculate
Tom Chen: 1 1 rectangle in
Tom Chen: correct, correct, correct, correct? Exactly
Tom Chen: another question.
Tom Chen: He's still there.
Tom Chen: 48%. But that means it's keeping Christine to 100%. You will becomes better, or the best number is around 50%. Yeah, yeah, great question, could you summarize this question for the microphone?
Tom Chen: Yeah, yeah. So essentially, the question is, here we show up to 48%. But what if we go even higher? Right? Right? 90%. Would that be a ratio? Something similar to this? As well, I I actually don't know
Tom Chen: I think it should, but the the issue with a super high filling fraction is, the field decays very fast.
Tom Chen: and the transmission becomes very low. So you really need to have
Tom Chen: tons of accuracy to really determine.
Tom Chen: You can imagine right if you have a random, Sophia, if it's very, very densely packed.
Tom Chen: The percentage of transmission becomes very low.
Tom Chen: right? So to kind of
Tom Chen: you know, you get to a numerical noise level things like that, it becomes more complicated. Right? So I I think that should be the case. But
Tom Chen: I'm not totally sure. Actually
Tom Chen: so what can we learn from all this
Tom Chen: results.
Tom Chen: So the conclusion from the paper, it's Anderson. Localization doesn't occur in random dielectric systems. But it does occur in random metallic systems.
Tom Chen: and the ability to solve Maxwell's equations in this brute force way.
Tom Chen: which often is considered not super elegant in research
Tom Chen: that can lead to some discoveries that were not possible previously.
Tom Chen: Okay, so now we will be shifting gears a little bit to discuss
Tom Chen: computing. And
Tom Chen: and so here we have a chart, a chart that shows the
Tom Chen: speed of the processing
Tom Chen: for CPU, and this this curve
Tom Chen: and Gpu in this group.
Tom Chen: So for CPU, we know we. It's, you see, this exponential increase
Tom Chen: in the
Tom Chen: like nineties up to early 2 thousands.
Tom Chen: But in a recent decade also, it really throw it really slow down right
Tom Chen: now. It's kind of a plateau, even though we're still making some progress. But
Tom Chen: it's not this exponential growth anymore.
Tom Chen: On the other hand, if we look at Gpu performance in the past, decade
Tom Chen: it it nicely follow this exponential increase. Right? So over the past 10 years the speed of Gpu has
Tom Chen: becomes a thousand times faster compared to 10 years ago.
Tom Chen: and this momentum is largely fueled by AI.
Tom Chen: as everyone knows, because people think it's promising. So we just keep developing this and give users. It's getting better and better.
Tom Chen: But besides, AI we can also utilize Gpu for other computing right? Like scientific computing simulations for you.
Tom Chen: So in a recent paper that we published with a media, we discussed how
Tom Chen: Gpu acceleration can be very beneficial for simulations.
Tom Chen: If you're interested, you can take a look at this.
Tom Chen: And essentially what we find is if we look at the Fdt simulation speed this kind of denoted by the color of this plot.
Tom Chen: The horizontal axis is the memory bandwidth of the hardware. The vertical axis is the compute speed of the hardware.
Tom Chen: If you look at cpus they are kind of
Tom Chen: located around this corner. See? It's much slower. But if we look at Gpus, really the commercial grade Gpu's that people use to train AI models.
Tom Chen: The speed is orders of magnitude higher.
Tom Chen: And it's largely because Cfd
Tom Chen: Speed, it's a memory bandwidth limited. So so we use higher memory bandwidth components like Gpus.
Tom Chen: The speed can really be largely, greatly boosted.
Tom Chen: And
Tom Chen: why is it important to have this kind of tool.
Tom Chen: 1 1 reason is because they are widely used right in both research and industry, right? So people from different research and in engineering fields like meta materials, meta services.
Tom Chen: optical sensors integrated photonics optical displays. They all need to do simulations to design components, right.
Tom Chen: And also because of AI. Now, a lot of people have interest in
Tom Chen: Optical interconnect in data center. So that's also kind of
Tom Chen: fueling this exponential growth of integrated photonics.
Tom Chen: And we think at this point we are
Tom Chen: capable of
Tom Chen: doing chip design where you have
Tom Chen: a layout, as I just shown here. You'll then kind of drop in the layout through a tool.
Tom Chen: It runs the simulation and tells you the performance of the
Tom Chen: of the of the circuit prices now
Tom Chen: it.
Tom Chen: This on the flex compute module. Correct? Correct.
Tom Chen: So this this kind of dovetails into a question.
Tom Chen: I remember back in the early days of people just trying to do anything different than single CPU to multi CPU. There was a paradigm shift in how you had to code the problem you're trying to solve had lend itself to parallelize computing.
Tom Chen: It's a similar thing with Gpu correct. So
Tom Chen: how do you guys deal with those edge cases that aren't
Tom Chen: particularly suited to parallel computing. Are you still able to offer some kind of speed up using Gpus? Yeah, yeah, even though the person doing it might. But I didn't think it's possible. But then you come in and say, Well, you could. And here's how do you decouple the the linear stuff from the stuff that can go in parallel. Yeah, yeah, that's a that's a good question. So yeah, for
Tom Chen: various reasons, some computation are not suitable to be paralyzed. For example, if you look at the fem, for example, right?
Tom Chen: Solve this.
Tom Chen: But an element method problem. Usually you don't see much benefit for going from CPU to Gpu, because you have this large matrix inversion process is kind of hard to paralyze. Right?
Tom Chen: Same. For for example, most obvious in in photonics, right? You know, software with Guy mode
Tom Chen: or optical fiber mode. That's also kind of a matrix inversion problem. So for that, we still use CPU at the moment.
Tom Chen: So essentially, it's not like everything is better with Gpu. Only the Fdtv method itself that's particularly suitable to be paralyzed. And we use Gpu for that.
Tom Chen: Then
Tom Chen: there are other- other
Tom Chen: class of problems that are just not particularly suitable.
Tom Chen: there are other methods that kind of can speed up Gpu computing for, say, basically, immersion or other processes. But they usually have some constraints. It's not not a general method. Yeah. So
Tom Chen: right? Well, so that's that's kind of the heart of what you know. What flex compute seems to offer
Tom Chen: primarily in terms of the engineering
Tom Chen: moving the needle, you know, through through clever engineering, utilizing Gpus and utilizing parallel for it. So I wonder if you guys are trying to
Tom Chen: take some of those other problems where they are seemingly not very paralyzable because it's matrix inversion and everything's coupled. Are you trying to find ways of decoupling, just doing perturbational type analysis where you can come back and couple it. Go off. Do something fast. Come back up and see if it still works right? Right? Yeah, that's that's a great question. So we also have a product that's designed for computation of weight dynamics
Tom Chen: where that's kind of a fem type setting.
Tom Chen: And for that, I think
Tom Chen: we also achieved a very significant speed benefit
Tom Chen: compared to the traditional method.
Tom Chen: I'm not very familiar with the details of how they implemented the algorithm or augmentation
Tom Chen: but I think in in general. There are definitely things you can do
Tom Chen: still. And nowadays, especially with this
Tom Chen: super rapid growth of gpu efficiencies. Eventually, it might be the case that even for certain problems that
Tom Chen: traditionally people think might not be the best, for Gpu
Tom Chen: turns out, maybe a few years afterward Gpu can still be faster. And
Tom Chen: there are a lot of details that you need to pay attention to, to really make
Tom Chen: Gpu faster. What is the problem, for example, how you manage the data communication between different Gpu notes. Well, yeah, that. So that was gonna be kind of my last question before I shut up and let anybody else ask questions but
Tom Chen: in a prior life we were doing a lot of this kind of thing to to be able to take bright field images and then find features within them that we had previously previously trained towards all deep learning stuff. And I recall what
Tom Chen: what one of the biggest cruxes was how to manage all of the spinning up of workers and spinning them down and transferring the data back and forth. And so it
Tom Chen: it really came down to almost the speed of your data center as much as your cleverness, and breaking the problem up, just break it up and be the smartest guy in the world. But
Tom Chen: if the data center can
Tom Chen: spin up a new node quickly enough, we'll transfer the data around and you screw. So correct.
Tom Chen: do you guys have your own data center? That is purpose built? Or you just working with the aws.
Tom Chen: a passion.
Tom Chen: Yeah, yeah. Great question.
Tom Chen: we do have our own cluster. It's actually hosted by a commercial data center. But we have our own hardware. But they hosted actually also here. It's it's local here. And it is.
Tom Chen: I need to be a bit careful, too, and not
Tom Chen: mean if
Tom Chen: yeah, yeah. But but there are definitely a lot of engineering to make sure it works efficiently. We have some particular algorithms that we patent to make sure the communication is more efficient.
Tom Chen: But
Tom Chen: obviously it's still limited. Yeah. So that's why, for if you have a smaller simulation.
Tom Chen: you don't really get benefit from running a small simulation on, say a hundred gpus, right? Right?
Tom Chen: Might be best if you just have 3 Gp. For example.
Tom Chen: So we have also this intelligence scheduling thing like try to determine if all this simulation, what's the optimal amount of hardware that we should use? Right?
Tom Chen: So a lot of details there.
Tom Chen: And that's also why, now, there's this huge interest in doing optical interconnect between Gpu's in Data center to kind of increase the bandwidth.
Tom Chen: And
Tom Chen: I think we we as this, the speed improves. We will focus get a benefit in our simulations.
Tom Chen: Yeah, it seems like, you guys should be partnering with people who help you build that thing on the right hand side there to using your own data centers.
Tom Chen: Yeah, yeah, it's really kind of a kind of a positive feedback. Yeah, look, we provide a tool so they can design components faster. They can make this progress. Then you can have better interconnect, then feeds back to our simulation scheme.
Tom Chen: But yeah, that's a that's an interesting question.
Tom Chen: So we we only 5 min in in regulation time. I wanna make sure everybody else got to.
Tom Chen: So here, if we interrupt the video itself, we just need to manually tell each layer 400.
Tom Chen: Yeah. So essentially, we have
Tom Chen: a sort of technology stack file. So essentially, you spy specify which layer is which I see then you import a Gds. It automatically detects all all the ports of the wave guys for the layer stacks and just sets up the simulation for you. So we call
Tom Chen: correct, correct, correct, correct. So we work with a lot of foundry
Tom Chen: to get their technology stack. But if you work with a particular foundry, likely that we already support it directly.
Tom Chen: purchase
Tom Chen: should usually require a different
Tom Chen: right? Right? Right?
Tom Chen: Thanks. So much
Tom Chen: correct. Correct?
Tom Chen: Right?
Tom Chen: Chip steps. Yeah. Yeah. Great great question. Yeah. So the question is, whether or not we? When we simulate the entire chip? Do we all use Gpu for all the computation?
Tom Chen: So the short answer is, no. For example, if you have a super large circuit. Right? You don't want to run Fd. For the entire circuit
Tom Chen: usually break it down into different components, right? So for each component, the fdt. Simulation runs on gpus.
Tom Chen: then you get a compact model out of the simulation, right? So essentially, the S matrix of the component.
Tom Chen: Then for the circuit simulation. You have various compact models for different components. Then you do a circuit simulation based on the compact models, and that computation is done in CPU, so that's usually put in light.
Tom Chen: But but, like, say, if we want to do this, do we have to
Tom Chen: tell the the program like, which part of you want to run like Ftd, which part we don't or like the when we like, pull the chip in like the software itself will help you to decide like which part. So we hope to get there at some point right now, you still have to manually decide
Tom Chen: which component that you want to simulate.
Tom Chen: Some. Some components can be simulated. Some components can be
Tom Chen: like analytical model. But if you just have a long wave guide, you can say the propagation is to do the most of it. Just just
Tom Chen: publication.
Tom Chen: So
Tom Chen: correct? Correct?
Tom Chen: Yeah, also.
Tom Chen: specifically, since you mentioned can do chip scale simulation. Can you also include like a 3D. Structure of like a cavity to like a customized CAD model in order to run fttd simulation.
Tom Chen: but
Tom Chen: ftl. 5, option 3 Sto 5 can import it into the Fttd software and run a simulation that way. And then you specify how that essentially element might get plugged into a correct. Correct? Correct.
Tom Chen: Yeah. Gds, as well. Yes.
Tom Chen: So city
Tom Chen: sure.
Tom Chen: Site like profile office 3D. And just put the cat model
Tom Chen: and just quickly closing here. So the other class of problems that we are very good at is the inverse design optimization. So this I guess all of you already know.
Tom Chen: topology optimization. You can do local shape optimization as you define
Tom Chen: your design area, you say, oh, I want the device to perform
Tom Chen: in a specific way. For example, you can say
Tom Chen: I have a fundamental mode coming in, and I want to get a higher order mode coming out right then it just automatically optimizes the the shape. And you can get the resource. Yeah.
Tom Chen: occasionally.
Tom Chen: That's exactly this slide.
Tom Chen: So we have fabrication awareness kind of features. So
Tom Chen: patternization minimum feature, size, minimum curvature or maximum curvature things like that. We have building features to help with that.
Tom Chen: So we can say.
Tom Chen: I want to have a certain minimum feature size.
Tom Chen: Yeah, yeah, exactly. And it just automatically calculates that.
Tom Chen: Okay? And yeah, with that, I think I'm running out of time. So it's very
Tom Chen: I mean, it costs a lot of credits. Right? Great question. So the benefit of the inverse design or just adjoint methods is that you can get the
Tom Chen: the gradient of the objective function with respect to all the design parameters in just 2 simulations.
Tom Chen: right? So you do a sort of forward simulation and the adjoint simulation that you post process the field distribution to get a greeting.
Tom Chen: So if you, a typical azure simulation, might take, you say, 15 iterations
Tom Chen: each. Iteration requires 2 simulations. So in total, you probably need like 100 simulations.
Tom Chen: and usually the inverse design models are very small.
Tom Chen: so you don't really need a lot of simulation time to to do that.
Tom Chen: Are you actually quoting everything
Tom Chen: in pytorch like? Oh, no, no, but you just call it
Tom Chen: no, no. So yeah. So the idea is that that we provide this platform. So just like a pytorch. Right? If you want to do a neural network.
Tom Chen: you don't really want to specify all this back propagation or this gradient tracking thing. Right? So we we do essentially the same thing. You just define your objective function
Tom Chen: and your parameters. We take care of all the ingredient calculation all this kind of thing for you
Tom Chen: design? I guess I'm not exactly familiar, but like, say, for like a 2D. Cavity, I know you can design a pattern. But does it also come. Is it possible also to do like a 3D. University that, for example, I can also customize certain depths of
Tom Chen: partially actually into your cavities.
Tom Chen: So that's also.
Tom Chen: yeah. So okay.
Tom Chen: I guess because you want to make sure you don't have
Tom Chen: floating structures
Tom Chen: right?
Tom Chen: Eventually, the Ftd result makes quite a bit difference. I see. I see. I see. Yeah, 3D, yeah. 3D problems are a bit a bit trickier. But can be done inclusively.
Steven Francis Nagle: Good.
Tom Chen: All the things. But like, I guess, numerical or yes, in terms of accuracy. Yeah, we we did a lot of benchmarking, just to make sure the accuracy is good.
Tom Chen: Yeah, yeah, if, yeah, if the accuracy is not good, then all the speed is useless.
Steven Francis Nagle: Is that your speaker, or is that ours?
Steven Francis Nagle: I thought I turned it off. Sorry.
Steven Francis Nagle: I just wanted to say Thank you for
Steven Francis Nagle: for coming, and thanks for all that, I thought it was very informative, and as much as you say? Oh, I don't know how that's made. I appreciate the depth of knowledge you did bring. That's very, very nice.
Steven Francis Nagle: So let's just give a nice round of applause.
Steven Francis Nagle: And we hope to hear from you guys again, and maybe even hear more about
Steven Francis Nagle: how flex computers approaching some of those problems that
Steven Francis Nagle: aren't necessarily custom built for Gpus, but you've managed to speed them up anyway, like that.
Steven Francis Nagle: That fluid dynamics problem. And I'm sure there's others that are like that
Steven Francis Nagle: all right. Great, nice to have you thanks again, Thomas.