Publikationen
Monografien

U.W. Pohl, A. Strittmatter, A. Schliwa, M. Lehmann, T. Niermann, T. Heindel, S. Reitzenstein, M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Chapter 3: StressorInduced Site Control of Quantum Dots for SinglePhoton Sources, in Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Heidelberg, 2020, pp. 5390, (Chapter Published), DOI 10.1007/9783030356569_3 .
Abstract
The strain field of selectively oxidized A10x current apertures in an A1GaAs/GaAs mesa is utilized to define the nucleation site of InGaAs/GaAs quantum dots. A design is developed that allows for the selfaligned growth of single quantum dots in the center of a circular mesa. Measurements of the strain tensor applying transmissionelectron holography yield excellent agreement with the calculated strain field. Singledot spectroscopy of sitecontrolled dots proves narrow excitonic linewidth virtually free of spectral diffusion due to quantumdot growth in a defectfree matrix. Implementation of such dots in an electrically driven pin structure yields singledot electroluminescence. Singlephoton emission with excellent purity is provided for this device using a Hanbury Brown and Twiss setup. The injection efficiency of the initian pin design is affected by a substantial lateral current spreading close to the oxide aperture. Allpying 3D cariertransport simulation a ppn doping profile is developed achieving a substantial improvement of the current injection. 
S. Rodt, P.I. Schneider, L. Zschiedrich, T. Heindel, S. Bounouar, M. Kantner, Th. Koprucki, U. Bandelow, S. Burger, S. Reitzenstein, Chapter 8: Deterministic Quantum Devices for Optical Quantum Communication, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Heidelberg, 2020, pp. 285359, (Chapter Published), DOI 10.1007/9783030356569_8 .
Abstract
Photonic quantum technologies are based on the exchange of information via single photons. The information is typically encoded in the polarization of the photons and security is ensured intrinsically via principles of quantum mechanics such as the nocloning theorem. Thus, all optical quantum communication networks rely crucially on the availability of suitable quantumlight sources. Such light sources with close to ideal optical and quantum optical properties can be realized by selfassembled semiconductor quantum dots. These highquality nanocrystals are predestined singlephoton emitters due to their quasi zerodimensional carrier confinement. Still, the development of practical quantumdotbased sources of single photons and entangledphoton pairs for applications in photonic quantum technology and especially for the quantumrepeater scheme is very demanding and requires highly advanced device concepts and deterministic fabrication technologies. This is mainly explained by their random position and emission energy as well as by the low photonextraction efficiency in simple planar device configurations. 
M. Kantner, Th. Höhne, Th. Koprucki, S. Burger, H.J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Chapter 7: MultiDimensional Modeling and Simulation of Semiconductor Nanophotonic Devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Heidelberg, 2020, pp. 241283, (Chapter Published), DOI 10.1007/9783030356569_7 .
Abstract
Selfconsistent modeling and multidimensional simulation of semiconductor nanophotonicdevices is an important tool in the development of future integrated light sources and quantumdevices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically exploretheir optimization potential. The efficient implementation of multidimensional numerical simulationsfor computeraided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in devicescale modeling of quantum dot based singlephotonsources and laser diodes by selfconsistently coupling the optical Maxwell equations with semiclassical carrier transport models using semiclassical and fully quantum mechanical descriptionsof the optically active region, respectively. For the simulation of realistic devices with complex,multidimensional geometries, we have developed a novel hpadaptive finite element approachfor the optical Maxwell equations, using mixed meshes adapted to the multiscale properties ofthe photonic structures. For electrically driven devices, we introduced novel discretization andparameterembedding techniques to solve the driftdiffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on variousapplications, including verticalcavity surfaceemitting lasers, grating couplers and singlephotonsources. 
M. Kantner, Electrically Driven Quantum Dot Based SinglePhoton Sources: Modeling and Simulation, Springer Theses, Springer, Cham, 2020, XVII, 180 pages, (Monograph Published), DOI 10.1007/9783030395438 .
Abstract
Semiconductor quantum optics is on the verge of moving from the lab to real world applications. When stepping from basic research to new technologies, device engineers will need new simulation tools for the design and optimization of quantum light sources, which combine classical device physics with cavity quantum electrodynamics. This thesis aims to provide a holistic description of singlephoton emitting diodes by bridging the gap between microscopic and macroscopic modeling approaches. The central result is a novel hybrid quantumclassical model system that selfconsistently couples semiclassical carrier transport theory with open quantum manybody systems. This allows for a comprehensive description of quantum light emitting diodes on multiple scales: It enables the calculation of the quantum optical figures of merit together with the simulation of the spatially resolved current flow in complex, multidimensional semiconductor device geometries out of one box. The hybrid system is shown to be consistent with fundamental laws of (non)equilibrium thermodynamics and is demonstrated by numerical simulations of realistic devices.
Artikel in Referierten Journalen

H. Wenzel, M. Kantner, M. Radziunas, U. Bandelow, Semiconductor laser linewidth theory revisited, APPS. Applied Sciences, 11 (2021), pp. 129, DOI 10.3390/app11136004 .
Abstract
More and more applications require semiconductor lasers distinguished not only by large modulation bandwidths or high output powers, but also by small spectral linewidths. The theoretical understanding of the root causes limiting the linewidth is therefore of great practical relevance. In this paper, we derive a general expression for the calculation of the spectral linewidth step by step in a selfcontained manner. We build on the linewidth theory developed in the 1980s and 1990s but look from a modern perspective, in the sense that we choose as our starting points the timedependent coupledwave equations for the forward and backward propagating fields and an expansion of the fields in terms of the stationary longitudinal modes of the open cavity. As a result, we obtain rather general expressions for the longitudinal excess factor of spontaneous emission (Kfactor) and the effective Alphafactor including the effects of nonlinear gain (gain compression) and refractive index (Kerr effect), gain dispersion and longitudinal spatial hole burning in multisection cavity structures. The effect of linewidth narrowing due to feedback from an external cavity often described by the socalled chirp reduction factor is also automatically included. We propose a new analytical formula for the dependence of the spontaneous emission on the carrier density avoiding the use of the population inversion factor. The presented theoretical framework is applied to a numerical study of a twosection distributed Bragg reflector laser. 
S. Amiranashvili, M. Radziunas, U. Bandelow, K. Busch, R. Čiegis, Additive splitting methods for parallel solutions of evolution problems, Journal of Computational Physics, 436 (2021), pp. 110320/1110320/14, DOI 10.1016/j.jcp.2021.110320 .
Abstract
We demonstrate how a multiplicative splitting method of order Pcan be utilized to construct an additive splitting method of order P+3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourthorder additive method, which is yielded by the LieTrotter splitting. We provide error estimates, stability analysis of a test problem, and numerical examples with special discussion of the parallelization properties and applications to nonlinear optics. 
A. Pimenov, S. Amiranashvili, A. Vladimirov, Temporal cavity solitons in a delayed model of a dispersive cavity ring laser, Mathematical Modelling of Natural Phenomena, 15 (2020), pp. 47/147/18, DOI 10.1051/mmnp/2019054 .
Abstract
Nonlinear localised structures appear as solitary states in systems with multistability and hysteresis. In particular, localised structures of light known as temporal cavity solitons were observed recently experimentally in driven Kerrcavities operating in the anomalous dispersion regime when one of the two bistable spatially homogeneous steady states exhibits a modulational instability. We use a distributed delay system to study theoretically the formation of temporal cavity solitons in an optically injected ring semiconductorbased fiber laser, and propose an approach to derive reduced delaydifferential equation models taking into account the dispersion of the intracavity fiber delay line. Using these equations we perform the stability and bifurcation analysis of injectionlocked continuous wave states and temporal cavity solitons. 
I. Franović, S. Yanchuk, S. Eydam, I. Bačić, M. Wolfrum, Dynamics of a stochastic excitable system with slowly adapting feedback, Chaos. An Interdisciplinary Journal of Nonlinear Science, 30 (2020), pp. 083109/1083109/11, DOI 10.1063/1.5145176 .
Abstract
We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noiseinduced spiking, noiseperturbed oscillations, or stochastic busting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance, or effectively control the features of the stochastic bursting. The setup can be considered as a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noiseinduced fluctuations by a corresponding stationary FokkerPlanck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noiseinduced switching between a stationary and an oscillatory regime gives rise to stochastic bursting. 
U. Gowda, A. Roche, A. Pimenov, A.G. Vladimirov, S. Slepneva, E.A. Viktorov, G. Huyet, Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold, Optics Letters, 45 (2020), pp. 49034906, DOI 10.1364/OL.397840 .
Abstract
We report on the formation of novel turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold. Experimentally, the laser emits a series of power dropouts within a roundtrip, and the number of dropouts per series depends on a set of parameters including the bias current. At fixed parameters, the drops remain dynamically stable, repeating over many roundtrips. By reconstructing the laser electric field in the case where the laser emits one dropout per roundtrip and simulating its dynamics using a timedelayed model, we discuss the reasons for longterm sustainability of these solutions. We suggest that the observed dropouts are closely related to the coherent structures of the cubic complex GinzburgLandau equation. 
A.V. Kovalev, P.S. Dmitriev, A.G. Vladimirov, A. Pimenov, G. Huyet, E.A. Viktorov, Bifurcation structure of a sweptsource laser, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 101 (2020), pp. 012212/1012212/5, DOI 10.1103/PhysRevE.101.012212 .
Abstract
We numerically analyze a delay differential equation model of a shortcavity semiconductor laser with an intracavity frequencyswept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrowband filter, there exist two bursting cycles determined by different parts of a continuouswave solutions branch. 
O. Melchert, C. Brée, A. Tajalli, A. Pape, R. Arkhipov, S. Willms, I. Babushkin, D. Skryabin, G. Steinmeyer, U. Morgner, A. Demircan, Alloptical supercontinuum switching, Nature Photonics, 3 (2020), pp. 146/1146/8, DOI 10.1038/s42005020004141 .
Abstract
Efficient alloptical switching is a challenging task as photons are bosons and cannot immediately interact with each other. Consequently, one has to resort to nonlinear optical interactions, with the Kerr gate being the classical example. However, the latter requires strong pulses to switch weaker ones. Numerous approaches have been investigated to overcome the resulting lack of fanout capability of alloptical switches, most of which relied on types of resonant enhancement of lightmatter interaction. Here we experimentally demonstrate a novel approach that utilizes switching between different portions of soliton fission induced supercontinua, exploiting an optical event horizon. This concept enables a high switching efficiency and contrast in a dissipation free setting. Our approach enables fanout, does not require critical biasing, and is at least partially cascadable. Controlling complex soliton dynamics paves the way towards building alloptical logic gates with advanced functionalities. 
M. Tlidi, E. BerríosCaro , D. PintoRamo, A.G. Vladimirov, M.G. Clerc, Interaction between vegetation patches and gaps: A selforganized response to water scarcity, Physica D. Nonlinear Phenomena, 414 (2020), pp. 132708/1132708/12, DOI 10.1016/j.physd.2020.132708 .
Abstract
The dynamics of ecological systems are often described by integrodifferential equations that incorporate nonlocal interactions associated with facilitative, competitive interactions between plants, and seed dispersion. In the weakgradient limit, these models can be reduced to a simple partialdifferential equation in the form of a nonvariational Swift?Hohenberg equation. In this contribution, we perform this reduction for any type of kernels provided that their Taylor series converge. Some parameters such as linear and nonlinear diffusion coefficients are affected by the spatial form of the kernel. In particular, Gaussian and exponential kernels are used to evaluate all coefficients of the reduced model. This weak gradient approximation is greatly useful for the investigation of periodic and localized vegetation patches, and gaps. Based on this simple model, we investigate the interaction between twowell separated patches and gaps. In the case of patches, the interaction is always repulsive. As a consequence, bounded states of patches are excluded. However, when two gaps are close to one another, they start to interact through their oscillatory tails. The interaction alternates between attractive and repulsive depending on the distance separating them. This allows for the stabilization of bounded gaps and clusters of them. The analytical formula of the interaction potential is derived for both patches and gaps interactions and checked by numerical investigation of the model equation. 
A. Boni, H.J. Wünsche, H. Wenzel, P. Crump, Impact of the capture time on the series resistance of quantumwell diode lasers, Semiconductor Science and Technology, 35 (2020), pp. 085032/1085032/9, DOI 10.1088/13616641/ab9723 .
Abstract
Electrons and holes injected into a semiconductor heterostructure containing quantum wellsare captured with a finite time. We show theoretically that this very fact can cause a considerableexcess contribution to the series resistivity and this is one of the main limiting factors to higherefficiency for GaAs based highpower lasers. The theory combines a standard microscopicbasedmodel for the captureescape processes in the quantum well with a driftdiffusion description ofcurrent flow outside the quantum well. Simulations of five GaAsbased devices differing in theirAlcontent reveal the rootcause of the unexpected and until now unexplained increase of theseries resistance with decreasing heat sink temperature measured recently. The finite capturetime results in resistances in excess of the bulk layer resistances (decreasing with increasingtemperature) from 1 mΩ up to 30 mΩ in good agreement with experiment. 
J.P. Köster, A. Putz, H. Wenzel, H.J. Wünsche, M. Radziunas, H. Stephan, M. Wilkens, A. Zeghuzi, A. Knigge, Mode competition in broadridgewaveguide lasers, Semiconductor Science and Technology, 36 (2020), pp. 015014/1015014/12, DOI 10.1088/13616641/abc6e7 .
Abstract
The lateral brightness achievable with highpower GaAsbased laser diodes having long and broad waveguides is commonly regarded to be limited by the onset of higherorder lateral modes. For the study of the lateralmode competition two complementary simulation tools are applied, representing different classes of approximations. The first tool bases on a completely incoherent superposition of mode intensities and disregards longitudinal effects like spatial hole burning, whereas the second tool relies on a simplified carrier transport and current flow. Both tools yield agreeing powercurrent characteristics that fit the data measured for 5 to 23 µm wide ridges. Also, a similarly good qualitative conformance of the near and far fields is found. However, the threshold of individual modes, the partition of power between them at a given current, and details of the near and far fields show differences. These differences are the consequence of a high sensitivity of the mode competition to details of the models and of the device structure. Nevertheless, it can be concluded concordantly that the brightness rises with increasing ridge width irrespective of the onset of more and more lateral modes. The lateral brightness 2W · mm¯¹ 1mrad¯¹ at 10MW · cm¯²2 power density on the front facet of the investigated laser with widest ridge (23 µm) is comparable with best values known from much wider broadarea lasers. In addition, we show that one of the simulation tools is able to predict beam steering and coherent beam 
U. Bandelow, S. Amiranashvili, S. Pickartz, Stabilization of optical pulse transmission by exploiting fiber nonlinearities, Journal of Lightwave Technology, 38 (2020), pp. 57435747, DOI 10.1109/JLT.2020.3003447 .
Abstract
We prove theoretically, that the evolution of optical solitons can be dramatically influenced in the course of nonlinear interaction with much smaller group velocity matched pulses. Even weak pump pulses can be used to control the solitons, e.g., to compensate their degradation caused by Ramanscattering. 
M. Kantner, Th. Koprucki, Beyond just ``flattening the curve'': Optimal control of epidemics with purely nonpharmaceutical interventions, Journal of Mathematics in Industry, 10 (2020), pp. 23/123/23, DOI 10.1186/s13362020000913 .
Abstract
When effective medical treatment and vaccination are not available, nonpharmaceutical interventions such as social distancing, home quarantine and farreaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptibleexposedinfectiousrecovered) model and continuoustime optimal control theory, we compute the optimal nonpharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of diseaserelated deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socioeconomic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a singleintervention scenario that goes beyond heuristically motivated interventions and simple ?flattening of the curve?. Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socioeconomic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID19 pandemic in Germany. 
M. Kantner, Generalized ScharfetterGummel schemes for electrothermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient, Journal of Computational Physics, 402 (2020), pp. 109091/1109091/24, DOI 10.1016/j.jcp.2019.109091 .
Abstract
Many challenges faced in today's semiconductor devices are related to selfheating phenomena. The optimization of device designs can be assisted by numerical simulations using the nonisothermal driftdiffusion system, where the magnitude of the thermoelectric cross effects is controlled by the Seebeck coefficient. We show that the model equations take a remarkably simple form when assuming the socalled Kelvin formula for the Seebeck coefficient. The corresponding heat generation rate involves exactly the three classically known selfheating effects, namely Joule, recombination and ThomsonPeltier heating, without any further (transient) contributions. Moreover, the thermal driving force in the electrical current density expressions can be entirely absorbed in the diffusion coefficient via a generalized Einstein relation. The efficient numerical simulation relies on an accurate and robust discretization technique for the fluxes (finite volume ScharfetterGummel method), which allows to cope with the typically stiff solutions of the semiconductor device equations. We derive two nonisothermal generalizations of the ScharfetterGummel scheme for degenerate semiconductors (FermiDirac statistics) obeying the Kelvin formula. The approaches differ in the treatment of degeneration effects: The first is based on an approximation of the discrete generalized Einstein relation implying a specifically modified thermal voltage, whereas the second scheme follows the conventionally used approach employing a modified electric field. We present a detailed analysis and comparison of both schemes, indicating a superior performance of the modified thermal voltage scheme. 
A.G. Vladimirov, K. Panajotov, M. Tlidi, Orthogonally polarized frequency combs in a modelocked VECSEL, Optics Letters, 45 (2020), pp. 252255, DOI 10.1364/OL.45.000252 .
Abstract
We introduce a spin?flip model for a verticalexternalcavity surfaceemitting laser (VECSEL) with a saturable absorber. We demonstrate the possibility, due to the spin?flip dynamics, to generate two orthogonally linearly polarized frequency combs in the modelocked regime. The two combs are shifted in wavelength due to the birefringence in the VECSEL gain and/or saturable absorption mirror. We show that the polarization degree of freedom may also lead to several pulses being generated per roundtrip in the two orthogonal linear polarizations and to more complicated dynamics with both linear polarizations excited.
Beiträge zu Sammelwerken

A. Roche, U. Gowda, A. Pimenov, A.V. Kovalev, M. Marconi, M. Giudici, E.A. Viktorov, A.G. Vladimirov, G. Huyet, S. Slepneva, Turn on transient in a long cavity laser, in: Physics and Simulation of Optoelectronic Devices XXVII, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 11274 of Proceedings of SPIE, SPIE Digital Library, 2020, pp. 112740L/1112740L/6, DOI 10.1117/12.2545965 .
Abstract
In this paper we study, both experimentally and theoretically, the turn on transient dynamics observed in a long (20m) cavity laser. The laser consists of a ring cavity based on a single mode fiber with unidirectional propagation of light. The gain is provided by a semiconductor optical amplifier (SOA) centered around 1300nm and wavelength selection is provided by a tunable narrow transmission bandwidth FabryPerot filter. At high bias current and when the filter transmission sets the laser to operate in an anomalous dispersion regime, the laser exhibits only chaotic oscillations, while in a normal dispersion regime, the laser can exhibit stable operation. At a bias current close to the threshold the laser always exhibits multiple dropouts. In order to record the lasing build up dynamics, the bias current driven to the SOA is periodically switched from the offstate to a high current level. The lasing build up occurs at each roundtrip via a stepwise increase of the laser intensity. The laser intensity is widely oscillating during the first steps and approaches a stationary state after a large number of roundtrips. Recording of the phase evolution of the electric field during each step demonstrates the linewidth narrowing at each subsequent roundtrip. Theoretically, we describe the system by a set of delay differential equations and observe similar behavior. While typically a semiconductor laser exhibits relaxation oscillations before reaching the stable lasing regime, which is associated with class B lasers, our study shows that the long cavity laser demonstrates a different mechanism of lasing build up. 
G. GarreWerner, J.J. MontielPonsoda, V. Raab, G. Safont, C. Brée, M. Radziunas, C. Cojocaru, K. Staliunas, 1 kW cw fibercoupled diode laser with enhanced brightness, in: HighPower Diode Laser Technology XVIII, M.S. Zediker, ed., 11262 of Proceedings of SPIE, SPIE, San Francisco, 2020, pp. 1126202/11126202/9, DOI 10.1117/12.2546086 .
Abstract
We developed a 1kW cw fibercoupled diode laser at 9XX nm by using beam combining of eight high power diode laser bars. To achieve beam combining, we employ Lyotfiltered optical reinjection from an external cavity, which forces lasing of the individual diode laser bars on intertwined frequency combs with overlapping envelopes and enables a high optical coupling efficiency. Unlike other spectral beam combining techniques that are based on the use of grating elements, this technique is insensitive to the thermal drift of the laser diodes. In addition to this, the FWHM spectral width at 1 kW output power is only around 7 nm, which is convenient for wavelength sensitive applications such as pumping. 
U. Gowda, A. Roche, S. Slepneva, A. Pimenov, E.A. Viktorov, A.G. Vladimirov, G. Huyet, Stability of a long cavity laser, in: Realtime Measurements, Rogue Phenomena, and SingleShot Applications V, D.R. Solli, G. Herink, S. Bielawski, eds., 11265 of Proceedings of SPIE, SPIE Digital Library, 2020, pp. 112650F/1112650F/6, DOI 10.1117/12.2545916 .
Abstract
In this paper, we will discuss the properties of long cavity frequency sweeping lasers and demonstrate various scenarios of coherence deterioration in such lasers. The long cavity lasers are known to demonstrate a rich variety of dynamical regimes including the formation of localised structures and transition to turbulence. The interest to frequency sweeping long cavity lasers has recently increased due to their application for imaging and sensing. For these applications, the stability of the laser is an important parameter as it directly influences its coherence and therefore, the quality of the obtained images.1 Our laser consists of a fiber based ring cavity resonator including a semiconductor optical amplifier as a gain medium and a FabryPerot tunable filter. Experimentally, we considered different laser configurations which has allowed us to study the influence of the cavity length, frequency sweeping speed and the detuning. We considered the dynamical regimes of the laser operating at a static (fixed output frequency) and quasi static regimes. The study shows that the laser can be stable or unstable and demonstrate localised structures stable over multiple roundtrips. We also show the connection of the dynamics observed in the static, quasistatic and synchronisation regimes of long cavity lasers. Numerically, we used a model based on a system of delayed differential equations. The numerical simulation showed excellent agreement with the experimental data. We also show the formation of dark pulses, both periodic and nonperiodic, and showed that they are closely connected to NozakiBekki holes previously predicted in the complex GinzburgLandau equation. 
M. Kolarczik, F. Böhm, U. Woggon, N. Owschimikow, A. Pimenov, M. Wolfrum, A.G. Vladimirov, S. Meinecke, B. Lingnau, L. Jaurigue, K. Lüdge, Coherent and incoherent dynamics in quantum dots and nanophotonic devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Cham, 2020, pp. 91133, DOI 10.1007/9783030356569_4 .
Abstract
The interest in coherent and incoherent dynamics in novel semiconductor gain media and nanophotonic devices is driven by the wish to understand the optical gain spectrally, dynamically, and energetically for applications in optical amplifiers, lasers or specially designed multisection devices. This chapter is devoted to the investigation of carrier dynamics inside nanostructured gain media as well as to the dynamics of the resulting light output. It is structured into two parts. The first part deals with the characterization of ultrafast and complex carrier dynamics via the optical response of the gain medium with pumpprobe methods, twocolor fourwave mixing setups and quantumstate tomography. We discuss the optical nonlinearities resulting from lightmatter coupling and charge carrier interactions using microscopically motivated rateequation models. In the second part, nanostructured modelocked lasers are investigated, with a focus on analytic insights about the regularity of the pulsed light emission. A method for efficiently predicting the timing fluctuations is presented and used to optimize the device properties. Finally, one specific design of a modelocked laser with tapered gain section is discussed which draws the attention to alternative ways of producing very stable and high intensity laser pulses. 
J.P. Köster, M. Radziunas, A. Zeghuzi, H. Wenzel, A. Knigge, Traveling wave modelbased analysis of tapered broadarea lasers, in: Physics and Simulation of Optoelectronic Devices XXVIII, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 11274 of Proceedings of SPIE, SPIE, San Francisco, 2020, pp. 112740I/1112740I/10, DOI 10.1117/12.2537015 .
Abstract
We present simulation results showing the impact of a longitudinal linearly varying electrical contact width on intracavity intensity, carrier density and temperature distributions of broadarea lasers. In addition, the impact of index guiding trenches on these internal distributions is investigated. The simulations were performed using a timedependent traveling wave model which takes all relevant physical effects into account. We show that a tapered contact area results in a reduced longitudinal intensity inhomogeneity as well as longitudinal spatial hole burning, at the cost of an increased temperature towards the front facet. Index guiding trenches were found to effectively prevent lateral intensity modulation as well as lateral carrier accumulation near the contact edges at the front facet. 
U. Bandelow, M. Radziunas, A. Zeghuzi, H.J. Wünsche, H. Wenzel, Dynamics in highpower diode lasers, in: Semiconductor Lasers and Laser Dynamics IX, M. Sciamanna, R. Michalzik, K. Panajotov, S. Höfling, eds., 11356 of Proceedings of SPIE, 2020, pp. 113560W/1113560W/14, DOI 10.1117/12.2559175 .
Abstract
Highpower broadarea diode lasers (BALs) exhibit chaotic spatiotemporal dynamics above threshold. Under high power operation, where they emit tens of watts output, large amounts of heat are generated, with significant impact on the laser operation. We incorporate heating effects into a dynamical electrooptical (EO) model for the optical field and carrier dynamics along the quantumwell active zone of the laser. Thereby we effectively couple the EO and heattransport (HT) solvers. Thermal lensing is included by a thermallyinduced contribution to the index profile. The heat sources obtained with the dynamic EOsolver exhibit strong variations on short time scales, which however have only a marginal impact on the temperature distribution. We consider two limits: First, the static HTproblem, with timeaveraged heat sources, which is solved iteratively together with the EO solver. Second, under short pulse operation the thermally induced index distribution can be obtained by neglecting heat flow. Although the temperature increase is small, a waveguide is introduced here within a fewnslong pulse resulting in significant near field narrowing. We further show that a beam propagating in a waveguide structure utilized for BA lasers does not undergo filamentation due to spatial holeburning. Moreover, our results indicate that in BALs a clear optical mode structure is visible which is neither destroyed by the dynamics nor by longitudinal effects. 
M. Kantner, Th. Koprucki, Nonisothermal ScharfetterGummel scheme for electrothermal transport simulation in degenerate semiconductors, in: Finite Volumes for Complex Applications IX  Methods, Theoretical Aspects, Examples  FVCA 9, Bergen, June 2020, R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., 323 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 173182, DOI 10.1007/9783030436513_14 .
Abstract
Electrothermal transport phenomena in semiconductors are described by the nonisothermal driftdiffusion system. The equations take a remarkably simple form when assuming the Kelvin formula for the thermopower. We present a novel, nonisothermal generalization of the ScharfetterGummel finite volume discretization for degenerate semiconductors obeying FermiDirac statistics, which preserves numerous structural properties of the continuous model on the discrete level. The approach is demonstrated by 2D simulations of a heterojunction bipolar transistor. 
M. Radziunas, D.M. Kane, Semiconductor laser with delayed optical feedback  What simulations tell us that we didn't know, in: 14th Pacific Rim Conference on Lasers and ElectroOptics (CLEO PR 2020), OSA Technical Digest, Optical Society of America, Washington, 2020, pp. C4C_4/1C4C_4/2, DOI 10.1364/CLEOPR.2020.C4C_4 .
Abstract
Comprehensive numerical simulations of a semiconductor laser with optical feedback system showing the impact of key laser parameters on dynamical mapping are reported. These raise new opportunities for optimising such systems for their key applications. 
M. Radziunas, J. MontielPonsoda, G. GarreWerner, V. Raab, Simulation of cascaded polarizationcoupled systems of broadarea semiconductor lasers, in: Proceedings of the 20th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2020, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2020, pp. 9798, DOI 10.1109/NUSOD49422.2020.9217764 .
Abstract
We present a brightness and powerscalable polarization beam combining scheme for highpower, broadarea semiconductor lasers. To achieve the beam combining, we employ Lyotfiltered optical reinjection from an external cavity, which forces lasing of the individual diodes on interleaved frequency combs with overlapping envelopes and enables a high optical coupling efficiency. We demonstrate how repeatedly introduced new stages of the external cavity allow efficient coupling of 2 n emitters. We simulate the operation of twofoureightsixteen coupled emitters, analyze beam coupling efficiency, and discuss possible limiting factors of this coupling scheme.
Preprints, Reports, Technical Reports

A.G. Vladimirov, S. Suchkov, G. Huyet, S.K. Turitsyn, A delay differential equation NOLMNALM modelocked laser model, Preprint no. 2858, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2858 .
Abstract, PDF (2904 kByte)
Delay differential equation model of a NOLMNALM modelocked laser is developed that takes into account finite relaxation rate of the gain medium and asymmetric beam splitting at the entrance of the nonlinear mirror loop. Asymptotic linear stability analysis of the continuous wave solutions performed in the limit of large delay indicates that in a classB laser flip instability leading to a period doubling cascade and development of squarewave patterns can be suppressed by a short wavelength modulational instability. Numerically it is shown that the model can demonstrate large windows of regular fundamental and harmonic modelocked regimes with single and multiple pulses per cavity round trip time separated by domains of irregular pulsing. 
A. Zeghuzi, J.P. Koester, M. Radziunas, H. Christopher, H. Wenzel, A. Knigge, Spatially modulated broadarea lasers for narrow lateral farfield divergence, Preprint no. 2857, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2857 .
Abstract, PDF (397 kByte)
A novel laser design is presented that combines a longitudinallateral gainloss modulation with an additional phase tailoring achieved by etching rectangular trenches. At 100 A pulsed operation, simulations predict a farfield profile with 0.3degree full width at half maximum where a 0.4degreewide main lobe contains 40% of the emitted optical output power. While farfield measurements of these structured lasers emitting 10 ns long pulses with 35 W peak power confirm a substantial enhancement of radiation within the central onedegree angular range, the measured farfield intensity outside of the obtained central peak remains high. 
A. Hajizadeh, A. Matysiak, M. Wolfrum, P.J.C. May, Auditory cortex modelled as a dynamical network of oscillators: Understanding eventrelated fields and their adaptation, Preprint no. 2854, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2854 .
Abstract, PDF (857 kByte)
Adaptation, the reduction of neuronal responses by repetitive stimulation, is a ubiquitous feature of auditory cortex (AC). It is not clear what causes adaptation, but shortterm synaptic depression (STSD) is a potential candidate for the underlying mechanism. We examined this hypothesis via a computational model based on AC anatomy, which includes serially connected core, belt, and parabelt areas. The model replicates the eventrelated field (ERF) of the magnetoencephalogram as well as ERF adaptation. The model dynamics are described by excitatory and inhibitory state variables of cell populations, with the excitatory connections modulated by STSD. We analysed the system dynamics by linearizing the firing rates and solving the STSD equation using timescale separation. This allows for characterization of AC dynamics as a superposition of damped harmonic oscillators, socalled normal modes. We show that repetition suppression of the N1m is due to a mixture of causes, with stimulus repetition modifying both the amplitudes and the frequencies of the normal modes. In this view, adaptation results from a complete reorganization of AC dynamics rather than a reduction of activity in discrete sources. Further, both the network structure and the balance between excitation and inhibition contribute significantly to the rate with which AC recovers from adaptation. This lifetime of adaptation is longer in the belt and parabelt than in the core area, despite the time constants of STSD being spatially constant. Finally, we critically evaluate the use of a single exponential function to describe recovery from adaptation. 
V.V. Klinshov, S.Y. Kirillov, V.I. Nekorkin, M. Wolfrum, Noiseinduced dynamical regimes in a system of globally coupled excitable, Preprint no. 2853, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2853 .
Abstract, PDF (2811 kByte)
We study the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. Performing a numerical bifurcation analysis of the nonlocal nonlinear FokkerPlanck equation for the thermodynamic limit, we identify a complex bifurcation scenario with regions of different dynamical regimes, including collective oscillations and coexistence of states with different levels of activity. In systems of finite size this leads to additional dynamical features, such as collective excitability of different types, noiseinduced switching and bursting. Moreover, we show how characteristic quantities such as macroscopic and microscopic variability of inter spike intervals can depend in a nonmonotonous way on the noise level. 
A. Vladmirov, M. Tlidi, M. Taki, Dissipative soliton interaction in Kerr resonators with highorder dispersion, Preprint no. 2843, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2843 .
Abstract, PDF (1126 kByte)
We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized LugiatoLefever equation with fourth order dispersion We use an asymptotic approach to derive interaction equations governing the slow time evolution of the coordinates of two interacting dissipative solitons. We show that Cherenkov radiation induced by positive fourthorder dispersion leads to a strong increase of the interaction force between the solitons. As a consequence, large number of equidistant soliton bound states in the phase space of the interaction equations can be stabilized. We show that the presence of even small spectral filtering not only dampens the Cherenkov radiation at the soliton tails and reduces the interaction strength, but can also affect the bound state stability. 
M. Nizette, A.G. Vladimirov, A generalized Haus master equation model for modelocked classB lasers, Preprint no. 2840, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2840 .
Abstract, PDF (893 kByte)
Using the multiscale technique we develop a generalized version of the classB Haus modelocking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the standard classB Haus modelocked model, our model is able to describe not only Qswitched instability of the fundamental modelocked regime, but also the appearance of harmonic modelocked regimes with the increase of the pump power. 
S. Slepneva, A. Pimenov, Nonlinear dynamical properties of frequency swept fiberbased semiconductor lasers, Preprint no. 2839, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2839 .
Abstract, PDF (3636 kByte)
We investigate dynamics of semiconductor lasers with fiberbased unidirectional ring cavity that can be used as frequency swept sources. We identify key factors behind the reach dynamical behaviour of such lasers using stateoftheart experimental and analytical methods. Experimentally, we study the laser in static, quasistatic and synchronisation regimes.We apply experimental methods such as optical heterodyne or electric field reconstruction in order to characterise these regimes or study the mechanisms of transition between them. Using a delay differential equation model, we demonstrate that the presence of chromatic dispersion can lead to destabilisation of the laser modes through modulational instability, which results in undesirable chaotic emission. We characterise the instability threshold both theoretically and experimentally, and demonstrate deterioration of the FDML regime near the threshold. 
L. Mertenskötter, K. Busch, R. DE J. LeónMontiel, Entangled twophoton absorption spectroscopy with varying pump wavelength, Preprint no. 2837, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2837 .
Abstract, PDF (647 kByte)
In virtualstate spectroscopy, information about the energylevel structure of an arbitrary sample is retrieved by Fourier transforming sets of measured twophoton absorption probabilities of entangled photon pairs where the degree of entanglement and the delay time between the photons have been varied. This works well for simple systems but quickly becomes rather difficult when many intermediate states are involved. We propose and discuss an extension of entangled twophoton absorption spectroscopy that solves this problem by means of repeated measurements at different pump wavelengths. Specifically, we demonstrate that our extension works well for a variety of realistic experimental setups. 
S. Yanchuk, M. Wolfrum, T. Pereira, D. Turaev, Absolute stability and absolute hyperbolicity in systems with discrete timedelays, Preprint no. 2824, WIAS, Berlin, 2021, DOI 10.20347/WIAS.PREPRINT.2824 .
Abstract, PDF (425 kByte)
An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete timedelays. In the case of a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. Similarly, for multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions are crucial for determining whether a system can have stabilizing or destabilizing bifurcations by varying time delays. 
S. Amiranashvili, M. Radziunas, U. Bandelow, K. Busch, R. Čiegis, Additive splitting methods for parallel solution of evolution problems, Preprint no. 2767, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2767 .
Abstract, PDF (312 kByte)
We demonstrate how a multiplicative splitting method of order P can be used to construct an additive splitting method of order P + 3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourthorder additive method, which is yielded by the LieTrotter splitting. We provide error estimates, stability analysis, and numerical examples with the special discussion of the parallelization properties and applications to nonlinear optics. 
M. Kantner, Th. Koprucki, Beyond just ``flattening the curve'': Optimal control of epidemics with purely nonpharmaceutical interventions, Preprint no. 2748, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2748 .
Abstract, PDF (3116 kByte)
When effective medical treatment and vaccination are not available, nonpharmaceutical interventions such as social distancing, home quarantine and farreaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptibleexposedinfectiousrecovered) model and continuoustime optimal control theory, we compute the optimal nonpharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of diseaserelated deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socioeconomic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a singleintervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve". Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socioeconomic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID19 pandemic in Germany. 
U. Gowda, A. Roche, A. Pimenov, A.G. Vladimirov, S. Slepneva, E.A. Viktorov, G. Huyet, Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold, Preprint no. 2724, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2724 .
Abstract, PDF (2735 kByte)
We report on the formation of novel turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold. Experimentally, the laser emits a series of power dropouts within a roundtrip and the number of dropouts per series depends on a set of parameters including the bias current. At fixed parameters, the drops remain dynamically stable, repeating over many roundtrips. By reconstructing the laser electric field in the case where the laser emits one dropout per round trip and simulating its dynamics using a timedelayed model, we discuss the reasons for longterm sustainability of these solutions. We suggest that the observed dropouts are closely related to the coherent structures of the cubic complex GinzburgLandau equation. 
A.V. Kovalev, P.S. Dmitriev, A.G. Vladimirov, A. Pimenov, G. Huyet, E.A. Viktorov, Bifurcation structure of a swept source laser, Preprint no. 2681, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2681 .
Abstract, PDF (602 kByte)
We numerically analyze a delay differential equation model of a shortcavity semiconductor laser with an intracavity frequency swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrowband filter, there exist two bursting cycles determined by different parts of a continuouswave solutions branch.
Vorträge, Poster

M. Kantner, Mathematical modeling and optimal control of the COVID19 pandemic (online talk), Mathematisches Kolloquium, Bergische Universität Wuppertal, April 27, 2021.

M. Kantner, Noise in semiconductor lasers (online talk), MATH+ Spotlight Seminar, MATH+, July 14, 2021.

W. Matthias, Temporal dissipative solitons in systems of delaydifferential equations, SIAM Conference on Dynamical Systems (Online Event), Minisymposium 184 ``Traveling Pulses in Delay and Lattice Differential Equations'', May 27, 2021, Portland, Oregon, USA, May 27, 2021.

U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Dynamics in Lasers, Photonics and Quantum Light sources'', Macquarie University, Sidney, Australia, February 18, 2020.

U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Photonics and Optoelectronics'', University of New South Wales, Sydney, Australia, February 17, 2020.

U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Nanoscience, Nanotechnology, Fibre optics'', University of Sydney, Australia, February 17, 2020.

U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ''Optical fiber technology, glass development, nonlinear fibers, biophotonics'', University of South Australia, Adelaide, Australia, February 12, 2020.

U. Bandelow, Applied mathematical research in photonics at WIAS Berlin, Workshop ``Biomedical engineering, lightmatter interactions'', Australian National University, Canberra, Australia, February 14, 2020.

U. Bandelow, Dynamics of highpower diode lasers (online talk), SPIE Photonics Europe (Online Event), April 3  7, 2020, April 6, 2020.

U. Bandelow, Modeling of nonlinear dynamical effects in photonics, Colloquium of the School of Mathematics and Physics, University of West Australia, Perth, Australia, February 19, 2020.

M. Kantner, Nonisothermal ScharfetterGummel scheme for electrothermal transport simulation in degenerate semiconductors, Finite Volumes for Complex Applications IX (Online Event), June 15  19, 2020, University of Bergen, Bergen, Norway, June 16, 2020, DOI 10.1007/9783030436513_14 .

M. Kantner, Nonisothermal ScharfetterGummel scheme for electrothermal transport simulation in degenerate semiconductors (online talk), Finite Volumes for Complex Applications IX (Online Event), June 15  19, 2020, NORCE  Norwegian Research Centre, Bergen, Norway, June 16, 2020.

M. Radziunas, Efficient modeling and simulation of dynamics in highpower broadarea semiconductor lasers, final EffiLas/HoTLas project meeting, Jenoptik Berlin, March 4, 2020.

M. Radziunas, Simulation of cascaded polarizationcoupled systems of broadarea semiconductor lasers, 20th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2020), September 14  25, 2020, Politecnico di Torino, Italy.

M. Wolfrum, Dynamics of a stochastic excitable system with slowly adapting feedback, Workshop on Control of SelfOrganizing Nonlinear Systems 2020, September 2  3, 2020, TU Berlin, September 3, 2020.

M. Wolfrum, Temporal dissipative solitons in systems with time delay, Séminaire Orléans, Institut Denis Poisson, Orléans, France, January 23, 2020.
Forschungsgruppen
 Partielle Differentialgleichungen
 Laserdynamik
 Numerische Mathematik und Wissenschaftliches Rechnen
 Nichtlineare Optimierung und Inverse Probleme
 Stochastische Systeme mit Wechselwirkung
 Stochastische Algorithmen und Nichtparametrische Statistik
 Thermodynamische Modellierung und Analyse von Phasenübergängen
 Nichtglatte Variationsprobleme und Operatorgleichungen