Publications
Articles in Refereed Journals

S. Amiranashvili, E. Tobisch, Extended criterion for the modulation instability, New Journal of Physics, 21 (2019), published online on 28.03.2019, DOI 10.1088/13672630/ab0130 .
Abstract
Modulation instability, following the classical Lighthill criterion, appears if nonlinearity and dispersion make opposite contributions to the wave frequency, e.g. in the framework of the onedimensional nonlinear Schrödinger equation (NLSE). Several studies of the wave instabilities in optical fibers revealed four wave mixing instabilities that are not covered by the Lighthill criterion and require use of the generalized NLSE. We derive an extended criterion, which applies to all four wave interactions, covers arbitrary dispersion, and depends neither on the propagation equation nor on the slowly varying envelope approximation. 
S. Amiranashvili, M. Radziunas, U. Bandelow, R. Čiegis, Numerical methods for accurate description of ultrashort pulses in optical fibers, Communications in Nonlinear Science and Numerical Simulation, 67 (2019), pp. 391402, DOI 10.1016/j.cnsns.2018.07.031 .
Abstract
We consider a onedimensional firstorder nonlinear wave equation (the socalled forward Maxwell equation, FME) that applies to a fewcycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard secondorder wave equation under assumption of weak nonlinearity. We compare FME to the commonly accepted generalized nonlinear Schrödinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to fewcycle pulses. We analyze and compare pseudospectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization. 
C. Brée, V. Raab, J. MontielPonsoda, G. GarreWerner, K. Staliunas, U. Bandelow, M. Radziunas, Beamcombining scheme of highpower broadarea semiconductor lasers with Lyotfiltered reinjection: Modeling, simulations, and experiments, Journal of the Optical Society of America. B, 36 (2019), pp. 17211730, DOI 10.1364/JOSAB.36.001721 .
Abstract
A brightness and powerscalable polarization beam combining scheme for highpower, broadarea semiconductor laser diodes is investigated numerically and experimentally. 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. Unlike conventional spectral beam combining schemes with diffraction gratings, the optical coupling efficiency is insensitive to thermal drifts of laser wavelengths. This scheme can be used for efficient coupling of a large number of laser diodes and paves the way towards using broadarea laser diode arrays for costefficient material processing, which requires highbrilliance emission and optical powers in the kWregime. 
S. Eydam, I. Franović, M. Wolfrum, Leapfrog patterns in systems of two coupled FitzHughNagumo units, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 99 (2019), pp. 042207/1042207/9, DOI 10.1103/PhysRevE.99.042207 .
Abstract
We study a system of two identical FitzHughNagumo units with a mutual linear coupling in the fast variables. While an attractive coupling always leads to synchronous behavior, a repulsive coupling can give rise to dynamical regimes with alternating spiking order, called leapfrogging. We analyze various types of periodic and chaotic leapfrogging regimes, using numerical pathfollowing methods to investigate their emergence and stability, as well as to obtain the complex bifurcation scenario which organizes their appearance in parameter space. In particular, we show that the stability region of the simplest periodic leapfrog pattern has the shape of a locking cone pointing to the canard transition of the uncoupled system. We also discuss the role of the timescale separation in the coupled FitzHughNagumo system and the relation of the leapfrog solutions to the theory of mixedmode oscillations in multiple timescale systems. 
S. Eydam, M. Wolfrum, The link between coherence echoes and mode locking, Chaos. An Interdisciplinary Journal of Nonlinear Science, 29 (2019), published online on 08.10.2019, DOI 10.1063/1.5114699 .
Abstract
We investigate the appearance of sharp pulses in the mean field of Kuramototype globally coupled phase oscillator systems. In systems with exactly equidistant natural frequencies self organized periodic pulsations of the mean field, called mode locking, have been described re cently as a new collective dynamics below the synchronization threshold. We show here that mode locking can appear also for frequency combs with modes of finite width, where the natu ral frequencies are randomly chosen from equidistant frequency intervals. In contrast to that, so called coherence echoes, which manifest themselves also as pulses in the mean field, have been found in systems with completely disordered natural frequencies as the result of two consecutive stimulations applied to the system. We show that such echo pulses can be explained by a stimula tion induced mode locking of a subpopulation representing a frequency comb. Moreover, we find that the presence of a second harmonic in the interaction function, which can lead to the global stability of the modelocking regime for equidistant natural frequencies, can enhance the echo phenomenon significantly. The nonmonotonous behavior of echo amplitudes can be explained as a result of the linear dispersion within the selforganized modelocked frequency comb. Fi nally we investigate the effect of small periodic stimulations on oscillator systems with disordered natural frequencies and show how the global coupling can support the stimulated pulsation by increasing the width of locking plateaus. 
M. Kantner, Generalized ScharfetterGummel schemes for electrothermal transport in degenerate semiconductors using the Kelvin formula for the Seebeck coefficient, Journal of Computational Physics, (2019), published online on 07.11.2019, 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 (nonlinear) 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. Pimenov, A.G. Vladimirov, Dynamics of an inhomogeneously broadened passively modelocked laser, The European Physical Journal B. Condensed Matter and Complex Systems, 92 (2019), published online on 22.05.2019, DOI 10.1140/epjb/e2019906428 .
Abstract
We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively modelocked laser. We demonstrate numerically using travelling wave equations the formation of a Lambdip instability and suppression of Qswitching in a laser with large inhomogeneous broadening. We derive simplified delaydifferential equation model for a modelocked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model. 
S. Slepneva, B. O'Shaughnessy, A.G. Vladimirov, S. Rica, E.A. Viktorov, G. Huyet, Convective NozakiBekki holes in a long cavity OCT laser, Optics Express, 27 (2019), pp. 1639516404, DOI 10.1364/OE.27.016395 .
Abstract
We show, both experimentally and theoretically, that the loss of coherence of a long cavity optical coherence tomography (OCT) laser can be described as a transition from laminar to turbulent flows. We demonstrate that in this strongly dissipative system, the transition happens either via an absolute or a convective instability depending on the laser parameters. In the latter case, the transition occurs via formation of localised structures in the laminar regime, which trigger the formation of growing and drifting puffs of turbulence. Experimentally, we demonstrate that these turbulent bursts are seeded by appearance of NozakiBekki holes, characterised by the zero field amplitude and ? phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model. 
P. Kravetc, D. Rachinskii, A.G. Vladimirov, Periodic pulsating dynamics of slowfast delayed systems with a periodic close to the delay, European Journal of Applied Mathematics, 30 (2019), pp. 3962, DOI 10.1017/S0956792517000377 .
Abstract
We consider slow?fast delayed systems and discuss pulsating periodic solutions, which are characterised by specific properties that (a) the period of the periodic solution is close to the delay, and (b) these solutions are formed close to a bifurcation threshold. Such solutions were previously found in models of modelocked lasers. Through a case study of population models, this work demonstrates the existence of similar solutions for a rather wide class of delayed systems. The periodic dynamics originates from the Hopf bifurcation on the positive equilibrium. We show that the continuous transformation of the periodic orbit to the pulsating regime is simultaneous with multiple secondary almost resonant Hopf bifurcations, which the equilibrium undergoes over a short interval of parameter values. We derive asymptotic approximations for the pulsating periodic solution and consider scaling of the solution and its period with the small parameter that measures the ratio of the time scales. The role of competition for the realisation of the bifurcation scenario is highlighted. 
CH. Schelte, A. Pimenov, A.G. Vladimirov, J. Javaloyes, S.V. Gurevich, Tunable Kerr frequency combs and temporal localized states in timedelayed GiresTournois interferometers, Optics Letters, 44 (2019), pp. 49254928, DOI 10.1364/OL.44.004925 .
Abstract
In this Letter, we study theoretically a new setup allowing for the generation of temporal localized states (TLSs) and frequency combs. The setup is compact (a few centimeters) and can be implemented using established technologies, while offering tunable repetition rates and potentially high power operation. It consists of a vertically emitting microcavity, operated in the Gires?Tournois regime, containing a Kerr medium strong timedelayed optical feedback, and detuned optical injection. We disclose sets of multistable dark and bright TLSs coexisting on their respective bistable homogeneous backgrounds. 
K.R. Schneider, The point charge oscillator: Qualitative and analytical investigations, Mathematical Modelling and Analysis. Matematinis Modeliavimis ir Analize. The Baltic Journal on Mathematical Applications, Numerical Analysis and Differential Equations, 24 (2019), pp. 372384, DOI 10.3846/mma.2019.023 .
Abstract
We determine the global phase portrait of a mathematical model describing the point charge oscillator. It shows that the family of closed orbits describing the point charge oscillations has two envelopes: an equilibrium point and a homoclinic orbit to an equilibrium point at infinity. We derive an expression for the growth rate of the primitive perod Τ_{α} of the oscillation with the amplitude α as α tends to infinity. Finally, we determine an exact relation between period and amplitude by means of the Jacobi elliptic function cn. 
S. Yanchuk, S. Ruschel, J. Sieber, M. Wolfrum, Temporal dissipative solitons in timedelay feedback systems, Physical Review Letters, 123 (2019), pp. 053901/1053901/6, DOI 10.1103/PhysRevLett.123.053901 .
Abstract
Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, autosolitons, spot or pulse solitons, these states play an important role in data transmission using optical pulses, neural signal propagation, and other processes. While this phenomenon was thoroughly studied in spatially extended systems, temporally localized states are gaining attention only recently, driven primarily by applications from fiber or semiconductor lasers. Here we present a theory for temporal dissipative solitons (TDS) in systems with timedelayed feedback. In particular, we derive a system with an advanced argument, which determines the profile of the TDS. We also provide a complete classification of the spectrum of TDS into interface and pseudocontinuous spectrum. We illustrate our theory with two examples: a generic delayed phase oscillator, which is a reduced model for an injected laser with feedback, and the FitzHughNagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudocontinuous spectrum develops a modulational instability. 
M. Krüger, V.Z. Tronciu, A. Bawamia, Ch. Kürbis, M. Radziunas, H. Wenzel, A. Wicht, A. Peters, G. Tränkle, Improving the spectral performance of extended cavity diode lasers using angledfacet laser diode chips, Applied Physics B: Lasers and Optics, 66 (2019), published online on 01.04.2019, DOI 10.1007/s003400197178z .
Abstract
We present and compare theoretical and experimental results on the electrooptical performance of extended cavity diode lasers (ECDLs) that employ two ridge waveguide designs for the singletransverse mode GaAs laser diode chip. One facet of the laser diode chips serves as a partially reflective output coupler for the laser cavity. The other facet constitutes an intracavity interface which introduces spurious optical feedback to the laser diode chip. The waveguide designs differ with respect to the suppression of this spurious feedback. The first design employs a straight ridge waveguide intersecting both facets at normal incidence. The intracavity facet is antireflection coated and features a residual intensity reflectivity of the order 10?4. The second design employs a bent ridge waveguide intersecting the antireflectioncoated intracavity facet at an appropriate angle. This provides an additional suppression of the spurious intensity reflection to a value estimated to be less than 10?6 . We compare the electrooptical performance of both designs theoretically and experimentally. The utilization of a bent waveguide results in an improved spectral stability and purity, specifically a higher side mode suppression and a small intrinsic spectral linewidth over the whole investigated current range, of the external cavity diode laser without sacrificing other parameters such as the output power. The external cavity diode lasers under study exhibit no degradation of the measured frequency noise power spectra and intrinsic linewidths even if there is a drop of the side mode suppression ratio provided that it is not reduced to a very small value. Thus, the usage of a more readily accessible straight waveguide chip in an ECDL could be sufficient if only a limited tuning range and a particularly compact assembly are needed. For spectroscopic applications requiring a small intrinsic spectral linewidth over a large frequency range a bent waveguide chip could be the better choice. 
A. Zeghuzi, M. Radziunas, H.J. Wünsche, J.P. Koester, H. Wenzel, U. Bandelow, A. Knigge, Traveling wave analysis of nonthermal farfield blooming in highpower broadarea lasers, IEEE J. Quantum Electron., 55 (2019), pp. 2000207/12000201/7, DOI 10.1109/JQE.2019.2893352 .
Abstract
With rising current the lateral farfield angle of highpower broadarea lasers widens (farfield blooming) which can be partly attributed to nonthermal effects due to carrier induced refractive index and gain changes that become the dominant mechanism under pulsed operation. To analyze the nonthermal contribution to farfield blooming we use a traveling wave based model that properly describes the injection of the current into and the diffusion of the carriers within the active region. Although no preassumptions regarding the modal composition of the field is made and filamentation is automatically accounted for, the highly dynamic timedependent optical field distribution can be very well represented by only few modes of the corresponding stationary waveguide equation obtained by a temporal average of the carrier density and field intensity. The reduction of current spreading and spatial holeburning by selecting proper design parameters can substantially improve the beam quality of the laser. 
J.P. Koester, M. Radziunas, A. Zeghuzi, H. Wenzel, A. Knigge, Simulation and design of a compact GaAs based tunable dualwavelength diode laser system, Optical and Quantum Electronics, 51 (2019), pp. 334/1334/12, DOI 10.1007/s1108201920502 .
Abstract
We present our design of a compact, integrated and tunable dualwavelength diode laser system emitting around 785 nm, which is of interest for several applications like Raman spectroscopy and the generation of THz radiation. To achieve a more compact device compared to previous GaAs based designs two etch depths are realized, leading to shallowly etched ridge waveguides in regions were optical gain is applied and deeply etched waveguides used to enable compact integrated waveguide components. The device parameters are optimized using a numerically efficient simulation tool for passive waveguides. Subsequently, the entire laser system is further analyzed applying a sophisticated travelingwave equation based model for active devices giving access to internal intensity and carrier density distributions. It is shown that active laser simulations are crucial to deduce critical and performance limiting design aspects not accessible via an allpassive simulation. 
A. Zeghuzi, H.J. Wünsche, H. Wenzel, M. Radziunas, J. Fuhrmann, A. Klehr, U. Bandelow, A. Knigge, Timedependent simulation of thermal lensing in highpower broadarea semiconductor lasers, IEEE J. Select. Topics Quantum Electron., 25 (2019), 1502310, DOI 10.1109/JSTQE.2019.2925926 .
Abstract
We propose a physically realistic and yet numerically applicable thermal model to account for short and long term selfheating within broadarea lasers. Although the temperature increase is small under pulsed operation, a waveguide that is formed within a fewnslong pulse can result in a transition from a gainguided to an indexguided structure, leading to near and far field narrowing. Under continuous wave operation the longitudinally varying temperature profile is obtained selfconsistently. The resulting unfavorable narrowing of the near field can be successfully counteracted by etching trenches. 
M. Radziunas, D.J. Little, D.M. Kane, Numerical study of optical feedback coherence in semiconductor laser dynamics, Optics Letters, 44 (2019), pp. 42074210, DOI 10.1364/OL.44.004207 .
Abstract
The nonlinear dynamics of semiconductor laser with coherent, as compared to incoherent, delayed optical feedback systems have been discussed and contrasted in prior research literature. Here, we report simulations of how the dynamics change as the coherence of the optical feedback is systematically varied from being coherent to incoherent. An increasing rate of phase disturbance is used to vary the coherence. An edge emitting, 830nm, Fabry Perot semiconductor laser with a long external cavity is simulated. Following this study, consideration of prior and future experimental studies should include evaluation of where on the continuum of partial coherence the delayed optical feedback sits. Partial coherence is a parameter that will affect the dynamics. 
M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.J. Wünsche, Th. Koprucki, C. Brée, H. Wenzel, U. Bandelow, Efficient coupling of electrooptical and heattransport models for highpower broadarea semiconductor lasers, Optical and Quantum Electronics, 51 (2019), published online on 22.02.2019, DOI 10.1007/s1108201917921 .
Abstract
In this work, we discuss the modeling of edgeemitting highpower broadarea semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple verticallateral laser crosssections with a fast dynamic electrooptical (EO) model determined on the longitudinallateral domain that is a projection of the device to the active region of the laser. Whereas the HTsolver calculates temperature and thermallyinduced refractive index changes, the EOsolver exploits these distributions and provides timeaveraged field intensities, quasiFermi potentials, and carrier densities. All these timeaveraged distributions are used repetitively by the HTsolver for the generation of the heat sources entering the HT problem solved in the next iteration step. 
A.G. Vladimirov, A.V. Kovalev, E.A. Viktorov, N. Rebrova, G. Huyet, Dynamics of a classA nonlinear mirror modelocked laser, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 100 (2019), pp. 012216/1012216/7, DOI 10.1103/PhysRevE.100.012216 .
Abstract
Using a simple delay differential equation model we study theoretically the dynamics of a unidirectional classA ring laser with a nonlinear amplifying loop mirror. We perform analytical linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turingtype instabilities, as well as by a bifurcation leading to the appearance of squarewaves. We investigate the formation of squarewaves and modelocked pulses in the system. We show that modelocked pulses are very asymmetric with exponential decay of the trailing and superexponential growth of the leading edge. We discuss asymmetric interaction of these pulses leading to a formation of harmonic modelocked regimes.
Contributions to Collected Editions

C. Brée, V. Raab, D. Gailevičius, V. Purlys, J. Montiel, G.G. Werner, K. Staliunas, A. Rathsfeld, U. Bandelow, M. Radziunas, Genetically optimized photonic crystal for spatial filtering of reinjection into broadarea diode lasers, in: 2019 Conference on Lasers and ElectroOptics Europe and European Quantum Electronics Conference, OSA Technical Digest, IEEE, Piscataway, 2019, DOI 10.1109/CLEOEQEC.2019.8871622 .
Abstract
Modern highpower broadarea semiconductor laser diodes (BASLDs) deliver optical output powers of several ten Watts at high electrooptical conversion efficiencies, which makes them highly relevant for numerous industrial, medical and scientific applications. However, lateral multimode behavior in BASLDs due to thermal lensing turns out highly detrimental, as it results in poor focusability and decreased laser beam brightnesss. Approaches to overcome this issue include improved epitaxial layer design, the optimization of evanescent spatial filtering by tailoring the emitter geometry and facet reflectivity, or Fourier spatially filtered reinjection from an external resonator [1]. 
C. Brée, V. Raab, J. Montiel, G.G. Werner, K. Staliunas, U. Bandelow, M. Radziunas, Lyot spectral filter for polarization beam combining of highpower, broadarea diode lasers: Modeling, simulations, and experiments, in: 2019 Conference on Lasers and ElectroOptics Europe and European Quantum Electronics Conference, OSA Technical Digest, IEEE, Piscataway, 2019, DOI 10.1109/CLEOEEQEC.2019.8871911 .
Abstract
Summary form only given. Recent improvements in design and development have significantly increased the relevance of highpower, broadarea laser diodes and laser diode bars in the market for industrial, highbrightness materials processing applications, like welding, soldering and cutting. Here, we present, experimentally [1] and, for the first time, in direct simulations [2], a polarization beam combining scheme, which maintains the linear polarization of the individual sources, and, unlike common wavelength multiplexing schemes, is insensitive to spectral drifts caused by variations of temperature or injection current. In our setup, two laser diodes are operated with optical reinjection from a common external cavity containing a Lyot spectral filter; cf. the setup shown in Fig. 1a). Our timedomain direct numerical simulations take into account both, the lateral, and longitudinal dimensions of the laser emitters [3]. The optical reinjection from the common external resonator was modeled by suitable Fresnel integrals in the paraxial regime, accounting for the different phase and group retardations of ordinary and extraordinary beam components within the birefringent crystal (calcite) [4]. Using a halfwave plate for polarization rotating the emission of diode 2, the spectrally filtered feedback enforces lasing of both diodes on interleaved frequency combs. The spectrum of each diode is then localized in the respective transmission window of the Lyot filter, determined by cos 2 ??nL/? (diode 1) and sin 2 ??nL/? (diode 2), where ?? is the phase birefringence of the crystal. In consequence, both beams can be combined with maintained linear polarization and high optical coupling efficiency. Simulated and experimental results for two coupled laser diodes are shown in Figs. 1b) and c). Indeed, simulations and experiments show that the usable output power in the combined beam is 86% (simulations) and 80% (experiment). 
M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo, Mathematical modeling of semiconductors: From quantum mechanics to devices, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 269293, DOI 10.1007/9783030331160 .
Abstract
We discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantumclassical model that selfconsistently couples van Roosbroeck's driftdiffusion system for classical charge transport with a Lindbladtype quantum master equation. The coupling is shown to obey fundamental principles of nonequilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of socalled GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy. 
M. Kantner, Th. Koprucki, H.J. Wünsche, U. Bandelow, Simulation of quantum dot based singlephoton sources using the SchrödingerPoissonDriftDiffusionLindblad system, in: Proceedings of the 24th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2019), F. Driussi, ed., 2019, pp. 355358, DOI 10.1007/9783030221160_11 .

M. Kantner, A generalized ScharfetterGummel scheme for degenerate and nonisothermal semiconductors, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 78, DOI 10.1109/NUSOD.2019.8806839 .
Abstract
We present a highly accurate generalization of the ScharfetterGummel scheme for the discretization of the currentdensities in degenerate semiconductors under nonisothermalconditions. The underlying model relies on the Kelvin formula forthe Seebeck coefficient, which has the intriguing property that the?Tterm in the electrical current density expressions vanishesexactly when passing to the driftdiffusion form ? even thoughthe thermoelectric crosscoupling is fully taken into account. 
M. Kantner, Hybrid modeling of quantum light emitting diodes: Selfconsistent coupling of driftdiffusion, SchrödingerPoisson, and quantum master equations, in: Proceedings of ``SPIE Photonics West'', San Francisco, USA, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 10912 of Physics and Simulation of Optoelectronic Devices XXVII, SPIE Digital Library, Bellingham, 2019, pp. published online on 26.02.2019, DOI 10.1117/12.2515209 .
Abstract
The devicescale simulation of electrically driven solid state quantum light emitters, such as singlephoton sources and nanolasers based on semiconductor quantum dots, requires a comprehensive modeling approach, that combines classical device physics with cavity quantum electrodynamics. In a previous work, we have selfconsistently coupled the semiclassical driftdiffusion system with a Markovian quantum master equation in Lindblad form to describe (i) the spatially resolved current injection into a quantum dot embedded within a semiconductor device and (ii) the fully quantum mechanical lightmatter interaction in the coupled quantum dotphoton system out of one box. In this paper, we extend our hybrid quantumclassical modeling approach by including a Schroedinger?Poisson problem to account for energy shifts of the quantum dot carriers in response to modifications of its macroscopic environment (e.g., quantum confined Stark effect due to the diode's internal electric field and plasma screening). The approach is demonstrated by simulations of a singlephoton emitting diode. 
M. Kantner, Simulation of quantum light sources using the selfconsistently coupled SchrödingerPoissonDriftDiffusionLindblad system, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 1516, DOI 10.1109/NUSOD.2019.8806839 .
Abstract
The devicescale simulation of electrically drivenquantum light sources based on semiconductor quantum dotsrequires a combination of the (classical) semiconductor deviceequations with cavity quantum electrodynamics. In this paper, weextend our previously developed hybrid quantumclassical modelsystem ? where we have coupled the driftdiffusion system witha Lindbladtype quantum master equation ? by including a selfconsistent Schrödinger?Poisson problem. The latter describes the(quasi)bound states of the quantum dot carriers. The extendedmodel allows to describe the biasdependency of the emissionspectrum due to the quantum confined Stark effect 
A. Pimenov, A.G. Vladimirov, S. Amiranashvili, Analysis of temporal dissipative solitons in a delayed model of a ring semiconductor laser, in: Extended Abstracts Spring 2018, A. Korobeinikov, M. Caubergh, T. Lázaro, J. Sardanyés, eds., 11 of Trends in Mathematics, Birkhäuser, Cham, 2019, pp. 712, DOI 10.1007/9783030252618_2 .
Abstract
Temporal dissipative solitons are short pulses observed in periodic time traces of the electric field envelope in active and passive optical cavities. They sit on a stable background, so that their trajectory comes close to a stable steady state solution between the pulses. A common approach to predict and study these solitons theoretically is based on the use of Ginzburg?Landautype partial differential equations, which, however, cannot adequately describe the dynamics of many realistic laser systems. Here, for the first time, we demonstrate the formation of temporal dissipative soliton solutions in a timedelay model of a ring semiconductor cavity with coherent optical injection, operating in anomalous dispersion regime, and perform bifurcation analysis of these solutions. 
S. Slepneva, U. Gowda, A. Pimenov, A.G. Vladimirov, E. Viktorov, G. Huyet, Complex dynamics of long cavity lasers, in: 2019 21st International Conference on Transparent Optical Networks (ICTON), M. Jaworski, M. Marciniak, eds., IEEE, Piscataway, 2019, DOI 10.1109/ICTON.2019.8839990 .
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 rich variety of dynamical regimes including formation of localised structures and transition to turbulence. The interest to frequency sweeping long cavity lasers has also 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, for example, the quality of the obtained images. We investigated static, quasi static and synchronisation regimes of such lasers and analysed possible instabilities in such system. Experimentally, we considered different laser configurations which has allowed us to study the influence of the cavity length, frequency sweeping speed and the detuning. Numerically, we used a model based on a system of delayed differential equations. The numerical simulation of our model showed excellent agreement with the experimental data. In particularly, we studied 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. 
N. Akhmediev, A. Ankiewicz, S. Amiranashvili, U. Bandelow, Generalized integrable evolution equations with an infinite number of free parameters, in: Workshop on Nonlinear Water Waves, S. Murashige, ed., 2109 of RIMS Kôkyûroku Bessatsu, RIMS, Kyoto, 2019, pp. 3346.
Abstract
Evolution equations such as the nonliear Schrödinger equation (NLSE) can be extended to include an infinite number of free parameters. The extensions are not unique. We give two examples that contain the NLSE as the lowestorder PDE of each set. Such representations provide the advantage of modelling a larger variety of physical problems due to the presence of an infinite number of higherorder terms in this equation with an infinite number of arbitrary parameters. An example of a rogue wave solution for one of these cases is presented, demonstrating the power of the technique. 
U. Gowda, S. Slepneva, A. Pimenov, A. Vladimirov, E. Viktorov, G. Huyet, Stable and unstable NozakiBekki holes in a long laser, in: Proceedings of ``SPIE Photonics West'', San Francisco, USA, 02.02.2019  07.02.2019, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 10912 of Physics and Simulation of Optoelectronic Devices XXVII, SPIE Digital Library, Bellingham, 2019, pp. published online on 26.02.2019, DOI 10.1117/12.2510300 .
Abstract
Long cavity fibrebased wavelength sweeping lasers are promising devices with a wide range of potential applications ranging from communications to life sciences. For example, Fourier Domain ModeLocked (FDML) lasers, which are commonly used for Optical Coherence Tomography (OCT) imaging applications are long cavity lasers incorporating an intracavity resonator driven in resonance with the cavity round trip time. The coherence properties of such swept sources are of major importance as they define the image quality. The purpose of this work is to analyze the mechanism that deteriorates the coherence of long lasers. In our experiment, the laser included a 100nm wide semiconductor optical amplifier at 1310nm and a fibre cavity that could vary from 20m to 20km. the laser emission wavelength was controlled using a fibre based intracavity filter with a bandwidth of 10GHz. Near the lasing threshold and/or for fast carrier decay rate, we observed the appearance of periodic power dropouts with stable NozakiBekki holes (NBH) that circulate in the laser cavity. As a function of the injection current, the laser could operate in various regimes including bistability between NBH and stable (cw) operation, unstable NBH or chaotic operation. Such behavior indicates that the interplay between the injection current and carrier decay rate can lead to highly coherent emission of a long cavity laser. 
J.P. Köster, M. Radziunas, A. Zeghuzi, H. Wenzel, A. Knigge, Traveling wave model based simulation of tunable multiwavelength diode laser systems, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 7576.
Abstract
We show simulation results of a compact, integrated and tunable multiwavelength diode laser emitting around785 nm. The presented design was optimized using passivewaveguide simulations and then further analyzed by performingactive laser simulations. The latter enables deducing criticaldesign parameters not accessible via an allpassive simulation. 
U. Bandelow, S. Amiranashvili, S. Pickartz, Control of solitons in the regime of event horizons in nonlinear dispersive optical media, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 141142.
Abstract
We describe the propagation of nonlinear pulses indispersive optical media on base of our generalized approach [1].It is known, that intense pulses, such as solitons, can mimic eventhorizons for smaller optical waves. We prove that such strongpulses can be dramatically influenced in the course of nonlinearinteraction with the proper dispersive waves. Moreover, it will bedemonstrated, both numerically and more efficiently by a newanalytic theory [2], that small optical waves can be used to controlsuch solitons [3], [4]. In particular, the typical pulse degradationcaused by Ramanscattering can be completely compensated bythese means [4], which is supported by recent experiments [5].
Preprints, Reports, Technical Reports

M. Heida, M. Kantner, A. Stephan, Consistency and convergence for a family of finite volume discretizations of the FokkerPlanck operator, Preprint no. 2684, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2684 .
Abstract, PDF (2376 kByte)
We introduce a family of various finite volume discretization schemes for the FokkerPlanck operator, which are characterized by different weight functions on the edges. This family particularly includes the wellestablished ScharfetterGummel discretization as well as the recently developed squareroot approximation (SQRA) scheme. We motivate this family of discretizations both from the numerical and the modeling point of view and provide a uniform consistency and error analysis. Our main results state that the convergence order primarily depends on the quality of the mesh and in second place on the quality of the weights. We show by numerical experiments that for small gradients the choice of the optimal representative of the discretization family is highly nontrivial while for large gradients the ScharfetterGummel scheme stands out compared to the others. 
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. 
I. Franović, S. Yanchuk, S. Eydam, I. Bačić, M. Wolfrum, Dynamics of a stochastic excitable system with slowly adapting feedback, Preprint no. 2678, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2678 .
Abstract, PDF (1974 kByte)
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. 
M. Kantner, Th. Koprucki, Nonisothermal ScharfetterGummel scheme for electrothermal transport simulation in degenerate semiconductors, Preprint no. 2664, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2664 .
Abstract, PDF (1331 kByte)
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 Scharfetter? Gummel finite volume discretization for degenerate semiconductors obeying Fermi?Dirac 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. 
U. Bandelow, S. Amiranashvili, S. Pickartz, Stabilization of optical pulse transmission by exploiting fiber nonlinearities, Preprint no. 2661, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2661 .
Abstract, PDF (3800 kByte)
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. Höhne, Th. Koprucki, S. Burger, H.J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Multidimensional modeling and simulation of semiconductor nanophotonic devices, Preprint no. 2653, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2653 .
Abstract, PDF (9836 kByte)
Selfconsistent modeling and multidimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multidimensional numerical simulations for computeraided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in devicescale modeling of quantum dot based singlephoton sources and laser diodes by selfconsistently coupling the optical Maxwell equations with semiclassical carrier transport models using semiclassical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multidimensional geometries, we have developed a novel hpadaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multiscale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameterembedding techniques to solve the driftdiffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including verticalcavity surfaceemitting lasers, grating couplers and singlephoton sources. 
CH. Schelte, A. Pimenov, A.G. Vladimirov, J. Javaloyes, S.V. Gurevich, Tunable Kerr frequency combs and temporal localized states in timedelayed GiresTournois interferometers, Preprint no. 2650, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2650 .
Abstract, PDF (478 kByte)
In this Letter we study theoretically a new setup allowing for the generation of temporal localized states and frequency combs. The setup is compact (a few cm) and can be implemented using established technologies, while offering tunable repetition rates and potentially high power operation. It consists of a vertically emitting microcavity, operated in the Gires?Tournois regime, containing a Kerr medium with strong timedelayed optical feedback as well as detuned optical injection. We disclose sets of multistable dark and bright temporal localized states coexisting on their respective bistable homogeneous backgrounds. 
K.R. Schneider, A. Grin, Global bifurcation analysis of limit cycles for a generalized van der Pol system, Preprint no. 2639, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2639 .
Abstract, PDF (189 kByte)
We present a new approach for the global bifurcation analysis of limit cycles for a generalized van der Pol system. It is based on the existence of a DulacCherkas function and on applying two topologically equivalent systems: one of them is a rotated vector field, the other one is a singularly perturbed system. 
K.R. Schneider, A. Grin, Lower and upper bounds for the number of limit cycles on a cylinder, Preprint no. 2638, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2638 .
Abstract, PDF (295 kByte)
We consider autonomous systems with cylindrical phase space. Lower and upper bounds for the number of limit cycles surrounding the cylinder can be obtained by means of an appropriate DulacCherkas function. We present different possibilities to improve these bounds including the case that the exact number of limit cycles can be determined. These approaches are based on the use of several DulacCherkas functions or on applying some factorized Dulac function. 
S. Pickartz, The role of the selfsteepening effect in soliton compression due to crossphase modulation by dispersive waves, Preprint no. 2585, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2585 .
Abstract, PDF (33 MByte)
We consider the compression and amplification of an ultrashort soliton pulse through the interaction with a weaker velocitymatched dispersive wave, in the socalled optical event horizon regime. We demonstrate that in this interaction scheme the selfsteepening effect plays the key role in producing a strong soliton compression. While the interaction between the two pulses is mediated through cross phase modulation, the selfsteepening effect produces an energy exchange, which enhances soliton compression. We provide numerical results and an analytical expression for energy transfer and compression rate. 
A. Pimenov, S. Amiranashvili, A.G. Vladimirov, Temporal cavity solitons in a delayed model of a dispersive cavity ring laser, Preprint no. 2581, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2581 .
Abstract, PDF (1614 kByte)
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 CW states and temporal cavity solitons.
Talks, Poster

S. Amiranashvili, Controlling light by light, Waves Côte d'Azur, June 4  7, 2019, Universié Côte d'Azur, Nice, France, June 4, 2019.

S. Amiranashvili, Controlling light by light, Seminar for theoretical physics, Technische Universität Wien, Austria, January 23, 2019.

C. Brée, V. Raab, D. Gailevičius, V. Purlys, J. Montiel, G.G. Werner, K. Staliunas, A. Rathsfeld, U. Bandelow, M. Radziunas, Genetically optimized photonic crystal for spatial filtering of reinjection into broadarea diode lasers, CLEO/EuropeEQEC 2019, Munich, June 23  27, 2019.

C. Brée, V. Raab, J. Montiel, G.G. Werner, K. Staliunas, U. Bandelow, M. Radziunas, Lyot spectral filter for polarization beam combining of highpower, broadarea diode lasers: Modeling, simulations, and experiments, CLEO/EuropeEQEC 2019, Munich, June 23  27, 2019.

S. Eydam, A. Gerdes, Extensive chaos, cluster and chimera states in globallycoupled StuartLandau systems, SFB 910: Workshop on ''Control of SelfOrganizing Nonlinear Systems'', Lutherstadt Wittenberg, August 20  22, 2019.

S. Eydam, Modelocked solutions in systems of globallycoupled phase oscillators, XXXIX. Dynamics Days Europe, September 2  6, 2019, University of Rostock, September 6, 2019.

S. Eydam, Modelocked solutions in systems of globallycoupled phase oscillators, WIAS Workshop ,,Optical Solitons and Frequency Comb Generation'', September 18  20, 2019, WIAS Berlin, September 18, 2019.

M. Kantner, A generalized ScharfetterGummel scheme for degenerate and nonisothermal semiconductors, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), July 8  12, 2019, University of Ottawa, Canada, July 8, 2019.

M. Kantner, Devicescale simulation of quantum light emitting diodes, International Symposium ,,Semiconductor Nanophotonics'', November 4  5, 2019, Technische Universität Berlin, November 4, 2019.

M. Kantner, Hybrid modeling of quantum light emitting diodes: Selfconsistent coupling of driftdiffusion, SchrödingerPoisson, and quantum master equations, SPIE Photonics West, February 5  7, 2019, San Francisco, USA, February 6, 2019, DOI 10.1117/12.2515209 .

M. Kantner, Simulation of quantum dot based singlephoton sources using the SchrödingerPoissonDriftDiffusionLindblad system, International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2019), September 4  6, 2019, Università degli Studi di Udine, Italy, September 6, 2019.

M. Kantner, Simulation of quantum light sources using the selfconsistently coupled SchrödingerPoissonDriftDiffusionLindblad system, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), July 8  12, 2019, University of Ottawa, Canada, July 8, 2019.

A. Pimenov, Temporal solitons in a delayed model of a semiconductor laser, Waves Côte d'Azur, Nice, France, June 4  7, 2019.

U. Bandelow, Control of solitons in the regime of event horizons in nonlinear dispersive optical media, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), July 8  12, 2019, University of Ottawa, Canada, July 11, 2019.

U. Bandelow, Hybrid modeling and simulation of electrically driven quantum light sources, 12th Annual Meeting Photonic Devices, ZuseInstitut Berlin, February 15, 2019.

U. Bandelow, Modeling and simulation of electrically driven quantum dot based singlephoton sources, Seminar NATEC II, Technical University of Denmark, Kgs. Lyngby, Denmark, June 7, 2019.

U. Bandelow, Selfconsistent thermaloptoelectronic model for the dynamics in highpower semiconductor lasers, European Semiconductor Laser Workshop (ESLW), September 27  28, 2019, University College Cork, Ireland, September 28, 2019.

U. Bandelow, Ultrashort solitons and their interaction with dispersive waves in the regime of event horizons in nonlinear optical media, 2nd International Conference on Photonics Research, November 4  9, 2019, Kocaeli University, Antalya, Turkey, November 8, 2019.

M. Radziunas, Efficient modeling and simulation of dynamics in highpower semiconductor lasers, 24th International Conference on Mathematical Modelling and Analysis (MMA2019), May 28  31, 2019, Tallinn University of Technology, Estonia, May 31, 2019.

M. Radziunas, Modeling of thermal effects in BALs, HoTLas project meeting, WIAS Berlin, February 20, 2019.

M. Radziunas, Modeling parameter dependence on temperature in highpower broadarea semiconductor lasers, Hotlas/Effilas project meeting, FerdinandBraunInstitut, Berlin, September 4, 2019.

A.G. Vladimirov, Nonlinear wave phenomena in delay differential models of multimode lasers, Waves Côte d'Azur 2019, June 4  7, 2019, Faculté des Sciences de l'Université de Nice, France, June 6, 2019.

M. Wolfrum, Patterns in discrete media, Fundamentals and Methods of Design and Control of Complex Systems Introductory Lectures 2019/20 of CRC 910, Technische Universität Berlin, December 2, 2019.

M. Wolfrum, Phasesensitive excitability of a limit cycle, SFB 910: Workshop on ''Control of SelfOrganizing Nonlinear Systems'', August 20  22, 2019, SFB 910, Lutherstadt Wittenberg, August 21, 2019.

M. Wolfrum, Phasesensitive excitability of a limit cycle, XXXIX Dynamics Days Europe, September 2  6, 2019, University of Rostock, September 3, 2019.

M. Wolfrum, Temporal dissipative solitons in a DDE model of a ring laser with optical injection, Equadiff 2019, July 8  12, 2019, Leiden University, Netherlands, July 9, 2019.

M. Wolfrum, Temporal dissipative solitons in systems with time delay, 11th Colloquium on the Qualitative Theory of Differential Equations, University of Szeged, Bolyai Institute, Hungary, June 20, 2019.

M. Wolfrum, The relation of Chimeras, bump states, and Turing patterns in arrays of coupled oscillators, School and Workshop on Patterns of Synchrony: Chimera States and Beyond, May 6  17, 2019, International Centre for Theoretical Physics, Trieste, Italy, May 16, 2019.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations