Modeling, simulation, and analysis of dynamics in semiconductor lasers: a brief overview of the WIAS-FBH collaboration
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Leibniz MMS Days 202322 / 23
00:00
Berlin (carriage)Narrow gauge railwayScoutingFinger protocolMode of transportPiston ringOpticsToolFinger protocolGas turbineSpare partTypesettingToolMode of transportHawkins Brown ArchitectsBraun, FerdinandPiston ringSeparation processCartridge (firearms)Narrow gauge railwayOpticsAutomatic watchShip of the lineHot workingPaperEngineAircraft carrierLecture/ConferenceComputer animationEngineering drawingDiagram
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WinterreifenMode of transportOpticsAircraft carrierScoutingShip of the lineSemi-trailer truckFinger protocolPunt (boat)MopedMultiple birthHose couplingMaterialPaperAircraft carrierFinger protocolScoutingCartridge (firearms)ToolTypesettingCooper (profession)Photographic processingSpantVolumetric flow rateHose couplingEngineShip of the lineHot workingPaperWind waveScrew threadComputer animationEngineering drawingDiagram
Transcript: English(auto-generated)
00:00
In this talk, I would like to talk about modeling simulation analysis of dynamics of semiconductor lasers in our research group, which is called Laser Dynamics, and also about collaborations
00:20
with Ferdinand Braun Institute, which is another Leibniz Institute, and some representatives are sitting here. OK, so first of all, I will give a brief overview of what we're doing in our research group. So it's brief overview, not full overview. And then I will touch three different lasers which were studied in collaboration with Ferdinand
00:46
Braun Institute, within different research programs. OK, this is actually a naive diagram, so it's my understanding. So how Ferdinand Braun Institute and our research group at Ferris-Truss Institute are collaborating
01:02
on what they are doing. I say naive because so Ferdinand Braun colleagues maybe could say that they are doing something different or much more. But anyway, so they are concentrating more or less on these processes, so they're doing technology, characterization of prototypes, semiconductor lasers, but also they're doing
01:22
mathematical modeling, simulations, and kind of analysis. We at our research group are doing also such kind of works. We're doing mathematical modeling, simulations, analysis, maybe different type of analysis, but anyway analysis, and also we're doing efficient algorithms and software.
01:43
As you can see from this diagram, so we are a step behind of applications. They are, of course, much closer because they are, OK, engineers, physicists, and they're much closer. But anyway, so our contribution reaching real-world applications are significant and required,
02:01
which leads to many collaborative projects between our institutions. OK, now what we're doing at our research group, so it's very brief overview, not full. So OK, at least we're dealing with hierarchy of models, which in many cases can be written
02:25
in such ways. So these are dynamical models, so what I'm indicating by putting time derivative here, so and OK, these are equations of optical fields for carrier density, so they are coupled. And in many cases, they can describe different laser devices.
02:43
And this is hierarchy of models because this can be ordinary differential equations models, these can be delayed differential equations model, these can be partial differential equation models in one and two spatial dimensions. So it depends on the demand, so we select a suitable model.
03:02
What we do next, we actually with these models, we can study a variety of different dynamical states. Study states, pulsing, particle operating semiconductor laser systems with different and these states are used for different applications actually.
03:23
Next of course, we as mathematicians, we analyze model equations, we are performing different types of analysis, some of them written here. We are developing effective numerical algorithm, implementing them into the software tools, several software tools I mentioned here, so.
03:42
And least but not last, so we are exchanging our ideas and experience with partners, with engineers who are doing real world stuff. OK, and in this case, for example, Ferdinand Braun Institute. So by doing this task actually, so during the last 15 years, we had together with Ferdinand
04:04
Braun Institute, we had about 20 peer reviewed papers, about 20 conference papers. And the work was done within about 10 smaller or larger projects. OK, so first type of lasers which we're considering and first type of models which we're doing,
04:23
so we're considering a narrow waveguide semiconductor lasers. So with a narrow waveguide, that means that for description, it is enough to have one plus one dimensional partial differential equation model. That means it is PDE, you're having time derivative and having space derivative.
04:42
Yeah, so and there are again two equations which are coupled in a linear manner, so. And these models actually are sufficient to investigate different types of laser. It could be coupled laser system, master slave laser system, a schematic illusion here. It could be laser with optical feedback.
05:01
It could be also some fancy lasers including ring structures or several ring structures if these rings are relatively long. All of these devices in some concerns can be described with such type of models. So our tool which we have developed, so we can of course simply take these equations
05:23
and can just integrate in time, solve these equations and just analyze the output. Do some post-processing probably and analyze. But this is pretty simple and kind of not very clever because we can do more.
05:40
For example, we can do already with this model, we can do kind of path following, automatic path following. So that means tuning parameters, we can look what kind of response we have and analyze it and do some conclusions. It's already better. But still we can do even better. So we can, for example, compute optical modes. We can compute mode spectra of this equation.
06:04
And to decompose computed fields and to look what contribution of moles is in the general computed output. This allows us to understand so more structure of computed fields, which is sometimes helpful. Further, for some type of models, we can do even more analysis.
06:22
We can derive reduced models or the differential equations, which can be either just integrated numerically, but it is not very hard to say simple. But they can be analyzed by path following and bifurcation analysis tools for ODEs. So which gives some more deeper information about bifurcations, about loss of stability,
06:44
and so on and so on. OK, so this is our first part of model. And this model could be applied in collaboration with Vernon Brown Institute at this kind of project made together. So for analysis of so-called external cavity diet laser, which consists of diet and some
07:04
externally placed volume Bragg rating, which provides frequency filter and feedback to the laser. So in experiments, OK, this laser was created in order to have steady states, stable lasing
07:20
with good properties. And in experiments, they had several jumps. When tuning some control parameters, so injected current, in experiments, they have a jump. And depending on the direction in which this control parameter was tuned, they have either these red jumps, either black jumps of going back.
07:42
So depending on the direction, these are emitted power. And this is wavelength of the emission. So we could reproduce something similar in our simulations. And since we have something similar, we could analyze in details what is there and why these jumps occur.
08:01
And we could clarify that there are many steady states in the system. So these are black points. And tuning control parameters, so they are moving along these lines in the phase space. And the same figure represented in this way, so a standard one-dimensional diagram. So this is control parameter.
08:22
And when tuning this control parameter, we see that calculated points, spots, are lying on the analytically computed black curves, which indicate steady states. So in this case, we see that depending on the geometry of laser, we can have positions where we can simultaneously operate in several stable steady states, which is not very good
08:46
in application. So if they want to have the single one stable state. This investigation, again, was done in the frame of some research project. Sorry, wrong.
09:02
OK. A bit later, we had another project. There are, oh, sorry. I'm jumping quietly. OK, a bit later, recently, we had another project devoted to a bit deep analysis of these lasers, external cavity-dial lasers.
09:23
Now they are considering a bit shorter lasers, monolithically-integrated lasers consisting of active sections and dispersive reflective sections, which have grating, which provide this filter rate feedback.
09:40
And engineers at Ferdinand Braun Institute were interested in the line width of the emission, which is some special property which cannot be computed directly with our models. They were suggested some models, so we have implemented them in our tool and used it to
10:02
characterize wavelengths. OK, here, for example, two similar lasers are compared, so violet and green. So they are corresponding to two lasers of similar type. In one case, we have only one active section, and another section is fully passive. That means active zone is removed there.
10:22
In other laser, both these sections have the same active section, just second section is not pumped. And it can be pumped only optically. So in that case, so for high pumpings, as you can see from three upper diagrams, both lasers provide pretty similar, how to say, behavior up to wavelength.
10:44
And here, we can see that wavelength is significantly different. And that's the case, because wavelengths in these lasers are not wavelength, sorry. So because a line within these lasers are strongly dependent on carrier densities in all active zone of this laser.
11:02
OK, next project was related to the high power broad area lasers, which have extra lateral dimension. So in the first hour version, so the model equations were similar, just we had to take
11:21
into account another x dimension, which makes this model much more complicated to calculate. So because we have extra dimension, so everything is much slowly. And in order to have result in reasonable time, so we had to go parallel.
11:41
And it was kind of success, because instead of waiting until some computation, some necessary computations will be done from a single device, say three hours, so we can do this in 10 minutes using 28 processors. Much more drastic numbers are if we're considering, how to say, array of lasers.
12:02
So each such tapered structure represents single lasers. It is difference between more than a day and one and a half hour in that case. And the parallelization was successful, so we had about 80% speed up of calculations.
12:21
OK, these projects and this work actually was motivated by Vernon Brown Institute again, they were using this tool for investigating of so-called tapered lasers. So these are calculated optical fields, forward propagating field, backward propagating field
12:43
in this kind of tapered structure, and these are average carrier densities. And again, we could compare experiments with theory, so we could get pretty good comparison. But in the second stage, it was clear that that model which we had, so it is not sufficient.
13:03
So because we had to take into account extra effects which were neglected first, so therefore we had to develop version two of our scroller, and we had to extend our traveling wave model with another models for describing current spreading, which shows how currents are spreading
13:26
from the contact, which is more or less here, towards the active zone, which is more or less here. And we have to extend the model with a heat flow model. That means while temperature is very important when looking for the quality of the emission.
13:46
OK, and these challenges when developing these models and when coupling them so where, first of all, these models are defined in different domains, whereas our previous model is defined in x and z directions.
14:03
It is just this active zone. It is our previous model. Now we have to account the cross-sections of the laser, which are in the y and x domains, and there are multiple cross-sections such that we have quasi-3D modeling.
14:21
And another challenge is strongly different time and space scales, which is drastic when looking for temperature specialists, because that means that due to this difference of time scales, so we cannot do simultaneously proper dynamic temperature and dynamic optoelectronic
14:44
model simulations. So for this case, so we are coupling electro optical model, which is here, so with our thermal model, which is here, so doing several iterations. OK, so going to the end.
15:02
OK, this is about the same stuff. Going to the end, recently we have started a new project that is Leibniz Association's cooperative excellence program, project within Leibniz Association, actually. And within this project, we are looking for another type of laser, so it is laser which
15:25
emits in vertical direction, in contrast to the pre-evaluation cases. And again, so the model equations can be written in this manner, more or less the same type as earlier, just now, so we are looking for different dimensions. So it's again, it has two spatial dimensions, at least, but now there are, how to say, somehow
15:47
different dimensions. Earlier it was z and x, and now are x and y, so we are looking what happens in this cross-section. And what is interesting in this device is that one layer consists of the photonic crystal.
16:01
So photonic crystal, so it can have different features there, so and by designing vertical structure, by designing photonic crystal, it is hope that one can design the laser which emits a very nice beam in vertical direction, which at the same time has high power.
16:23
And the advantage of such laser, comparing to the etch emitters, which we discussed before, so is that the quality of the beam could be much better. Okay, so concluding, we have a brief overview of fruitful cooperation of the Wehrstrass
16:43
Institute Research Group, Laser Dynamics, and Ferdinand Braun Institute during the last 15 years. It was kind of win-win cooperation, allowing to improve the diet lasers at the Ferdinand Braun Institute and develop new algorithms and software tools at Vias.
17:00
And the results of this cooperation were published in multiple peer-reviewed and conference papers and were reported in various meetings. Okay, that's it.