Publikationen
Artikel in Referierten Journalen

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. 
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 .

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, R. Mindaugas, 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), 334 (12pp).
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. 
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. 
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 (published online on 23.07.2018), 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, D. Gailevičius, V. Purlys, G.G. Werner, K. Staliunas, A. Rathsfeld, G. Schmidt, M. Radziunas, Chirped photonic crystal for spatially filtered optical feedback to a broadarea laser, Journal of Optics, 20 (2018), pp. 095804/1095804/7, DOI 10.1088/20408986/aada98 .
Abstract
We derive and analyze an efficient model for reinjection of spatially filtered optical feedback from an external resonator to a broad area, edge emitting semiconductor laser diode. Spatial filtering is achieved by a chirped photonic crystal, with variable periodicity along the optical axis and negligible resonant backscattering. The optimal chirp is obtained from a genetic algorithm, which yields solutions that are robust against perturbations. Extensive numerical simulations of the composite system with our optoelectronic solver indicate that spatially filtered reinjection enhances lowerorder transversal optical modes in the laser diode and, consequently, improves the spatial beam quality. 
A. Pimenov, J. Javaloyes, S.V. Gurevich, A.G. Vladimirov, Light bullets in a timedelay model of a wideaperture modelocked semiconductor laser, Philosophical Transactions of the Royal Society A : Mathematical, Physical & Engineering Sciences, 376 (2018), pp. 20170372/120170372/14, DOI 10.1098/rsta.2017.0372 .
Abstract
Recently, a mechanism of formation of light bullets (LBs) in wideaperture passively modelocked lasers was proposed. The conditions for existence and stability of these bullets, found in the long cavity limit, were studied theoretically under the mean field (MF) approximation using a Haustype model equation. In this paper we relax the MF approximation and study LB formation in a model of a wideaperture three section laser with a long diffractive section and short absorber and gain sections. To this end we derive a nonlocal delaydifferential equation (NDDE) model and demonstrate by means of numerical simulations that this model supports stable LBs. We observe that the predictions about the regions of existence and stability of the LBs made previously using MF laser models agree well with the results obtained using the NDDE model. Moreover, we demonstrate that the general conclusions based upon the Haus model that regard the robustness of the LBs remain true in the NDDE model valid beyond the MF approximation, when the gain, losses and diffraction per cavity roundtrip are not small perturbations anymore. 
I. Bačić, S. Yanchuk, M. Wolfrum, I. Franović, Noiseinduced switching in two adaptively coupled excitable systems, European Physical Journal Special Topics, 227 (2018), pp. 10771090, DOI 10.1140/epjst/e20188000846 .
Abstract
We demonstrate that the interplay of noise and plasticity gives rise to slow stochastic fluctuations in a system of two adaptively coupled active rotators with excitable local dynamics. Depending on the adaptation rate, two qualitatively different types of switching behavior are observed. For slower adaptation, one finds alternation between two modes of noiseinduced oscillations, whereby the modes are distinguished by the different order of spiking between the units. In case of faster adaptation, the system switches between the metastable states derived from coexisting attractors of the corresponding deterministic system, whereby the phases exhibit a burstinglike behavior. The qualitative features of the switching dynamics are analyzed within the framework of fastslow analysis. 
I. Omelchenko, O.E. Omel'chenko, A. Zakharova, E. Schöll, Optimal design of the tweezer control for chimera states, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 97 (2018), pp. 012216/1012216/9, DOI 10.1103/PhysRevE.97.012216 .
Abstract
Chimera states are complex spatiotemporal patterns, which consist of coexisting domains of spatially coherent and incoherent dynamics in systems of coupled oscillators. In small networks, chimera states usually exhibit short lifetimes and erratic drifting of the spatial position of the incoherent domain. A tweezer feedback control scheme can stabilize and fix the position of chimera states. We analyse the action of the tweezer control in small nonlocally coupled networks of Van der Pol and FitzHughNagumo oscillators, and determine the ranges of optimal control parameters. We demonstrate that the tweezer control scheme allows for stabilization of chimera states with different shapes, and can be used as an instrument for controlling the coherent domains size, as well as the maximum average frequency difference of the oscillators. 
A. Ankiewicz, U. Bandelow, N. Akhmediev, Generalized SasaSatsuma equation: Densities approach to new infinite hierarchy of integrable evolution equations, Zeitschrift für Naturforschung A, 73 (2018), pp. 11211128, DOI 10.1515/zna20180377 .
Abstract
We derive the new infinite SasaSatsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Laxpair technique, this approach does not involve ponderous 3 x 3 matrices. Moreover, it allows us to explicitly obtain operators of many orders involved in the time evolution of the SasaSatsuma hierarchy functionals. All these operators are parts of a generalized SasaSatsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multiparameter dynamical system. 
O. Burylko, A. Mielke, M. Wolfrum, S. Yanchuk, Coexistence of Hamiltonianlike and dissipative dynamics in chains of coupled phase oscillators with skewsymmetric coupling, SIAM Journal on Applied Dynamical Systems, 17 (2018), pp. 20762105, DOI 10.1137/17M1155685 .
Abstract
We consider rings of coupled phase oscillators with anisotropic coupling. When the coupling is skewsymmetric, i. e. when the anisotropy is balanced in a specific way, the system shows robustly a coexistence of Hamiltonianlike and dissipative regions in the phase space. We relate this phenomenon to the timereversibility property of the system. The geometry of lowdimensional systems up to five oscillators is described in detail. In particular, we show that the boundary between the dissipative and Hamiltonianlike regions consists of families of heteroclinic connections. For larger chains with skewsymmetric coupling, some sufficient conditions for the coexistence are provided, and in the limit of N → ∞ oscillators, we formally derive an amplitude equation for solutions in the neighborhood of the synchronous solution. It has the form of a nonlinear Schrödinger equation and describes the Hamiltonianlike region existing around the synchronous state similarly to the case of finite rings. 
I. Franović, O.E. Omel'chenko, M. Wolfrum, Phasesensitive excitability of a limit cycle, Chaos. An Interdisciplinary Journal of Nonlinear Science, 28 (2018), pp. 071105/1071105/6, DOI 10.1063/1.5045179 .
Abstract
The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear thresholdlike behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear thresholdlike response appears only after perturbations applied within a certain part of the periodic orbit, i.e the excitability happens to be phase sensitive. As a paradigmatic example of this concept we employ the classical FitzHughNagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase sensitive nonlinear thresholdlike response to perturbations, which can be explained by the nonlinear behavior in the vicinity of the canard trajectory. Triggering the phase sensitive excitability of the relaxation oscillations by noise we find a characteristic nonmonotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this nonmonotone dependence as a result of an interplay of two competing effects of the increasing noise: the growing efficiency of the excitation and the degradation of the nonlinear response. 
M. Khoder, M. Radziunas, V. Tronciu, G. Verschaffelt, Study of wavelength switching time in tunable semiconductor microring lasers: Experiment and travelling wave description, OSA Continuum, 1 (2018), pp. 12261240, DOI 10.1364/OSAC.1.001226 .
Abstract
We report in this paper the wavelength switching features of semiconductor ring lasers that are wavelength tunable based on filtered optical feedback. The filtered feedback provides a wavelength dependent loss mechanism in these devices with which a particular longitudinal mode, and thus a particular wavelength, can be selected by changing the filter characteristics of the feedback channel. We investigate how the wavelength switching speed depends on the amplitude of the modulation of the switching driving signal and on the different phase factors within the filtering branches of the SRL. We compare qualitatively the experimental results with numerical simulations based on a travelling wave model. We also investigate the dynamical behavior of the lasing and nonlasing longitudinal modes in the two channels of the clockwise and the counterclockwise directions. We show the crucial importance of various phase relation factors on the wavelength switching behavior. Finally, we discuss what limits the switching speed and how we can accelerate it. 
O.O. Omel'chenko, M. Wolfrum, E. Knobloch, Stability of spiral chimera states on a torus, SIAM Journal on Applied Dynamical Systems, 17 (2018), pp. 97127, DOI 10.1137/17M1141151 .
Abstract
We study destabilization mechanisms of spiral coherenceincoherence patterns known as spiral chimera states that form on a twodimensional lattice of nonlocally coupled phase oscillators. For this purpose we employ the linearization of the OttAntonsen equation that is valid in the continuum limit and perform a detailed twoparameter stability analysis of a $D_4$symmetric chimera state, i.e., a fourcore spiral state. We identify fold, Hopf and paritybreaking bifurcations as the main mechanisms whereby spiral chimeras can lose stability. Beyond these bifurcations we find new spatiotemporal patterns, in particular, quasiperiodic chimeras, $D_2$symmetric spiral chimeras as well as drifting states. 
V.Z. Tronciu, H. Wenzel, M. Radziunas, M. Reggentin, J. Wiedmann, A. Knigge, Investigation of redemitting distributed Bragg reflector lasers by means of numerical simulations, IET Optoelectronics, 12 (2018), pp. 228232, DOI 10.1049/ietopt.2018.0025 .
Abstract
The authors report theoretical and experimental results on the properties of distributed Bragg reflector semiconductor lasers. Using the traveling wave equation model, they show that a proper choice of coupling coefficient and front facet reflectivity allows an optimisation of the laser operation, such that for wide range of injected current into the active region the laser emits a temporally stable output power. The numerical results are in a qualitative agreement with the measured characteristics. 
A. Zeghuzi, M. Radziunas, H.J. Wünsche, A. Klehr, H. Wenzel, A. Knigge, Influence of nonlinear effects on the characteristics of pulsed highpower broadarea distributed Bragg reflector lasers, Optical and Quantum Electronics, 50 (2018), pp. 88/188/12, DOI 10.1007/s1108201712978 .
Abstract
We theoretically analyze the influence of nonlinear effects such as spatial holeburning, twophoton absorption and gain compression on the power?current and beam characteristics of a highpower broadarea distributed Bragg reflector laser with a stripe width of 50 ?m operated in pulsed mode and compare them with simulations of a similar Fabry?Pérot laser. On the one hand, spatial holeburning leads to a higher mean intensity within the cavity for a Fabry?Pérot laser and resulting higher losses in combination with twophoton absorption and gain compression, on the other hand, excitation of higher order lateral modes leads to losses through the Bragg grating. In combination with spatiotemporal power variations resolved by the utilized timedependent traveling wave model twophoton absorption leads to higher power losses compared to those models using averaged powers. 
U. Bandelow, A. Ankiewicz, S. Amiranashvili, N. Akhmediev, SasaSatsuma hierarchy of integrable evolution equations, Chaos. An Interdisciplinary Journal of Nonlinear Science, 28 (2018), pp. 053108/1053108/11, DOI 10.1063/1.5030604 .
Abstract
We present the infinite hierarchy of SasaSatsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the SasaSatsuma equation that includes thirdorder terms. Up to sixth order terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higherorder terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly. 
O.E. Omel'chenko, The mathematics behind chimera states, Nonlinearity, 31 (2018), pp. R121R164, DOI 10.1088/13616544/aaaa07 .
Abstract
Chimera states are selforganized spatiotemporal patterns of coexisting coherence and incoherence. We give an overview of the main mathematical methods used in studies of chimera states, focusing on chimera states in spatially extended coupled oscillator systems. We discuss the continuum limit approach to these states, OttAntonsen manifold reduction, finite size chimera states, control of chimera states and the influence of system design on the type of chimera state that is observed. 
M. Radziunas, M. Khoder, V. Tronciu, J. Danckaert, G. Verschaffelt, Semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation, Journal of the Optical Society of America. B, 35, pp. 380390, DOI 10.1364.JOSAB.35.000380 .
Abstract
We study experimentally and theoretically a semiconductor ring laser with four filtering channels providing filtered delayed optical feedback. To describe and analyze the wavelength selection and tuning in this device, we exploit the travelingwave model determining the evolution of optical fields and carrier density along the ring cavity and filtering branches. The numerical results agree with the experimental observations: we can reproduce the wavelength tuning, the multiple wavelength emission, and the wavelength switching speed measured in these devices. The travelingwave model allows us to study in detail the effect of the different laser parameters and can be useful for designing the future devices. 
M. Radziunas, Modeling and simulations of broadarea edgeemitting semiconductor devices, Int. J. High Perform. Comput. Appl., 32 (2018), pp. 512522, DOI 10.1177/1094342016677086 .
Abstract
We present a (2+1)dimensional partial differential equation model for spatiallateral dynamics of edgeemitting broadarea semiconductor devices and several extensions of this model describing different physical effects. MPIbased parallelization of the resulting middlesize numerical problem is implemented and tested on the blade cluster and separate multicore computers at the Weierstrass Institute in Berlin. It was found, that an application of 2530 parallel processes on all considered platforms was guaranteeing a nearly optimal performance of the algorithm with the speedup around 2025 and the efficiency of 0.70.8. It was also shown, that a simultaneous usage of several inhouse available multicore computers allows a further increase of the speedup without a significant loss of the efficiency. Finally, an importance of the considered problem and the efficient numerical simulations of this problem were illustrated by a few examples occurring in real world applications. 
A.G. Vladimirov, S.V. Gurevich, M. Tlidi, Effect of Cherenkov radiation on localizedstate interaction, Physical Review A, 97 (2018), pp. 013816/1013816/6, DOI 10.1103/PhysRevA.97.013816 .
Abstract
We study theoretically the interaction of temporal localized states in all fiber cavities and microresonatorbased optical frequency comb generators. We show that Cherenkov radiation emitted in the presence of third order dispersion breaks the symmetry of the localized structrures interaction and greatly enlarges their interaction range thus facilitating the experimental observation of the dissipative soliton bound states. Analytical derivation of the reduced equations governing slow time evolution of the positions of two interacting localized states in a generalized LugiatoLefever model with the third order dispersion term is performed. Numerical solutions of the model equation are in close agreement with analytical predictions.
Beiträge zu Sammelwerken

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.

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.
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.
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 
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]. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, in: Proc. SPIE 10526, Physics and Simulation of Optoelectronic Devices XXVI, B. Witzigmann, M. Osiński, Y. Arakawa, eds., SPIE Digital Library, 2018, pp. 1052603/11052603/6, DOI 10.1117/12.2289185 .
Abstract
The design of electrically driven quantum light sources based on semiconductor quantum dots, such as singlephoton emitters and nanolasers, asks for modeling approaches combining classical device physics with cavity quantum electrodynamics. In particular, one has to connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems. We present a first step in this direction by coupling the van Roosbroeck system with a Markovian quantum master equation in Lindblad form. The resulting hybrid quantumclassical system obeys the fundamental laws of nonequilibrium thermodynamics and provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantum optical figures of merit (e.g. the second order intensity correlation function) together with the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, Modeling and simulation of electrically driven quantum light sources: From classical device physics to open quantum systems, in: 14th International Conference on Nonlinear Optics and Excitation Kinetics in Semiconductors, September 2327, 2018, Berlin, Germany (Conference Program), 2018, pp. 135.

A. Pimenov, S. Amiranashvili, A.G. Vladimirov, 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 cavity 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 CW solution between the pulses. A common approach to predict a nd study these solitons theoretically is based on the use of GinzburgLandautype partial differential equations, which, however, cannot adequately describe the dynamics of many realistic laser systems. Here for the first time we demonstrate formation of temporal cavity 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. 
M. Khoder, M. Radziunas, V. Tronciu, J. Danckaert, G. Verschaffelt, Tuning the emission of micro ring lasers using integrated optical feedback: Experiments and traveling wave simulations, in: Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF), OSA Technical Digest (Online), Optical Society of America, 2018, pp. JTu5A.10/1JTu5A.10/2, DOI 10.1364/BGPPM.2018.JTu5A.10 .
Abstract
We investigate the tuning of the wavelength of a microring laser using onchip feedback. We demonstrate tuning experimentally and numerically. The results also show that travelingwave model is suitable for simulating complex laser configurations. 
A.V. Kovalev, E.A. Viktorov, N. Rebrova, A.G. Vladimirov, G. Huyet, Theoretical study of modelocked lasers with nonlinear loop mirrors, in: Proc. SPIE 10682, Semiconductor Lasers and Laser Dynamics VIII, K. Panayotov, M. Sciamanna, R. Michalzik, eds., SPIE Digital Library, 2018, pp. 1068226/11068226/6.

V.Z. Tronciu, H. Wenzel, M. Radziunas, M. Reggentin, J. Wiedmann, A. Knigge, Numerical and experimental studies of a distributed Bragg reflector laser, in: Proceeding of the 6th International Conference ``Telecommunications, Electronics and Informatics'', Chisinău, Moldova, May 2427, 2018, S. Andronic, ed., Technical University of Moldova, 2018, pp. 105108.
Abstract
We report in this paper theoretical and experimental results on the dynamical properties of a distributed Bragg reflector (DBR) semiconductor lasers. Using the traveling wave equation model, we show that a proper choice of coupling coefficient and front facet reflectivity allows an optimization of the laser operation, such that for a wide range of currents injected into the active region the laser emits a continuouswave beam. The numerical results are in a qualitative agreement with measured characteristics. 
A. Zeghuzi, M. Radziunas, H. Wenzel, H.J. Wünsche, U. Bandelow, A. Knigge, Modeling of current spreading in highpower broadarea lasers and its impact on the lateral far field divergence, in: Proc. SPIE 10526, Physics and Simulation of Optoelectronic Devices XXVI, B. Witzigmann, M. Osiński, Y. Arakawa, eds., SPIE Digital Library, 2018, pp. 105261H/1105261H/10, DOI 10.1117/12.2289803 .
Abstract
The effect of current spreading on the lateral farfield divergence of highpower broadarea lasers is investigated with a timedependent model using different descriptions for the injection of carriers into the active region. Most simulation tools simply assume a spatially constant injection current density below the contact stripe and a vanishing current density beside. Within the driftdiffusion approach, however, the injected current density is obtained from the gradient of the quasiFermi potential of the holes, which solves a Laplace equation in the pdoped region if recombination is neglected. We compare an approximate solution of the Laplace equation with the exact solution and show that for the exact solution the highest farfield divergence is obtained. We conclude that an advanced modeling of the profiles of the injection current densities is necessary for a correct description of farfield blooming in broadarea lasers. 
U. Bandelow, S. Amiranashvili, S. Pickartz, Ultrashort solitons and their control in the regime of event horizons in nonlinear dispersive optical media, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 8788.

M. Radziunas, U. Bandelow, C. Brée, V. Raab, H. Wenzel, A. Zeghuzi, Modeling and simulation of highpower broadarea semiconductor lasers with optical feedback from different external cavities, in: 2018 IEEE International Semiconductor Laser Conference (ISLC 2018), Santa Fe, New Mexico, USA, 1619 September 2018, Institute of Electrical and Electronics Engineers, Inc. (IEEE), 2018, pp. SuA4/1SuA4/2.

M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.J. Wünsche, Th. Koprucki, H. Wenzel, U. Bandelow, Efficient coupling of heat flow and electrooptical models for simulation of dynamics in highpower broadarea semiconductor devices, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), J. Piprek, A.B. Djurisic, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 9192.

M. Wolfrum, Enumeration of positive meanders, in: Patterns of Dynamics. PaDy 2016, P. Gurevich, J. Hell, B. Sandstede, A. Scheel, eds., 205 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2018, pp. 203212, DOI 10.1007/9783319641737_13 .
Abstract
Meanders are geometrical objects, defined by a nonselfintersecting curve, intersecting several times through an infinite straight line. The subclass of positive meanders has been defined and used extensively for the study of the attractors of scalar parabolic PDEs. In this paper, we use bracket sequences and winding numbers to investigate the class of positive meanders. We prove a theorem about possible combinations of bracket sequences to obtain a meander with prescribed winding numbers and present an algorithm to compute the number of positive meanders with a given number of intersection points.
Preprints, Reports, Technical Reports

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. 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. 
M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo, Mathematical modeling of semiconductors: From quantum mechanics to devices, Preprint no. 2575, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2575 .
Abstract, PDF (3500 kByte)
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. 
N. Akhmediev, A. Ankiewicz, S. Amiranashvili, U. Bandelow, Generalized integrable evolution equations with an infinite number of free parameters, Preprint no. 2529, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2529 .
Abstract, PDF (1005 kByte)
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. 
S. Amiranashvili, E. Tobisch, Generalized Lighthill criterion for the modulation instability, Preprint no. 2512, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2512 .
Abstract, PDF (1138 kByte)
An universal modulation instability is subject to Lighthill criterion: nonlinearity and dispersion should make opposite contributions to the wave frequency. Recent studies of wave instabilities in optical fibers with the minimum chromatic dispersion revealed situations in which the criterion is violated and fast unstable modulations appear due to the four wave mixing process. We derive a generalized criterion, it applies to an arbitrary dispersion and to both slow and fast unstable modulations. Since the fast modulations depend on nonlinear dispersion, we also demonstrate how to describe them in the framework of a single generalized nonlinear Schrödinger equation.
Vorträge, 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.

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 .

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.

S. Amiranashvili, How to manipulate ultrashort optical solitons to remove their selffrequency shift, 4th International Conference on Wave Interaction (WIN2018), April 3  7, 2018, Johannes Kepler Universität Linz, Austria, April 6, 2018.

S. Eydam, Bifurcations of modelocked solutions, Workshop ,,Dynamics in Coupled Oscillator Systems", WIAS, Berlin, November 19, 2018.

S. Eydam, Mode locking in systems of globally coupled phase oscillators, Dynamics Days Europe, Loughborough, UK, September 3  7, 2018.

S. Eydam, Modelocking in systems of globally coupled phase oscillators, International Conference on Control of SelfOrganizing Nonlinear Systems, Warnemünde, September 9  13, 2018.

M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, SPIE Photonics West 2018: Physics and Simulation of Optoelectronic Devices XXVI, January 29  February 1, 2018, The Moscone Center, San Francisco, USA, January 29, 2018.

M. Kantner, Hybrid quantumclassical modeling of quantum dot based singlephoton emitting diodes, Workshop Applied Mathematics and Simulation for Semiconductors, WIAS Berlin, October 10, 2018.

M. Kantner, Modeling and simulation of electrically driven quantum light emitters, Leibniz MMS Days, Leibniz Institut für Oberflächenmodifizierung (IOM), Leipzig, March 2, 2018.

M. Kantner, Thermodynamically consistent modeling of electrically driven quantum dot based light emitters on a device scale, Workshop ,,Nonlinear Dynamics in Semiconductor Lasers (NDSL2018)'', June 18  20, 2018, WIAS, Berlin, June 18, 2018.

A. Pimenov, Analysis of temporal localized structures in a delayed model of a semiconductor laser, Interdisciplinary Workshop on Multiple Scale Systems, Systems with Hysteresis and Trends in Dynamical Systems (MURPHYSHSFS2018), May 28  June 1, 2018, Centre de Recerca Matemàtica, Bellaterra, Spain, July 30, 2018.

A. Pimenov, Analysis of temporal localized structures in a time delay model of a ring laser, 675. WEHeraeus Seminar: Delayed Complex Systems 2018, Bad Honnef, July 2  5, 2018.

A. Pimenov, Effect of chromatic dispersion in a delayed model of a modelocked laser, Workshop ,,Nonlinear Dynamics in Semiconductor Lasers (NDSL2018)'', June 18  20, 2018, WIAS, Berlin, June 20, 2018.

U. Bandelow, Control of ultrashort solitons in the regime of event horizons in nonlinear dispersive optical media, XX Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL 2018), December 3  7, 2018, Universidad de los Andes, Universidad de Mar del Plata, Hospital Italiano de Buenos Aires, Santiago, Chile, December 6, 2018.

U. Bandelow, Hierarchies of integrable NLStype equations and selected solutions, 4th International Conference on Wave Interaction (WIN2018), Johannes Kepler Universität Linz, Austria, April 4, 2018.

U. Bandelow, Semiconductor laser instabilities and dynamics emerging from mode degeneracy, International Workshop ''Synthetic NonHermitian Photonic Structures: Recent Results and Future Challenges'', August 13  17, 2018, Max Planck Institute for the Physics of Complex Systems, Dresden, August 14, 2018.

U. Bandelow, Ultrashort solitons and their control in the regime of event horizons in nonlinear dispersive optical media, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), WA6, November 5  9, 2018, The University of Hong Kong, China, November 7, 2018.

U. Bandelow, Ultrashort solitons and their control in the regime of event horizons in nonlinear dispersive optical media, George Stegeman Symposium, University of Central Florida, Orlando, USA, March 13, 2018.

M. Radziunas, Efficient coupling of heat flow and electrooptical models for simulation of dynamics in highpower broadarea semiconductor devices, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), WB2, November 5  9, 2018, The University of Hong Kong, China, November 7, 2018.

M. Radziunas, Impact of longitudinallateral periodic modulation of BALs to the quality of emitted beam, Project meeting of the BMBFEffiLas/HotLas project, DILAS Diodenlaser GmbH, Mainz, September 25, 2018.

M. Radziunas, Intelligent solution for complex problems, Research Seminar of the Faculty of Science and Engineering, Macquarie University, Sydney, Australia, July 4, 2018.

M. Radziunas, Modeling and simulation of highpower broad area lasers with PWC filtering element within an external cavity, Eurostars HIP Lasers project meeting, Monocrom S. L., Vilanova, Spain, December 10, 2018.

M. Radziunas, Modeling and simulation of highpower broad area lasers with PhC filtering element, EUROSTARS project E!10524 HIPLasers meeting, May 22  23, 2018, Femtika, Vilnius, Lithuania, May 22, 2018.

M. Radziunas, Modeling and simulation of highpower broadarea semiconductor lasers with optical feedback from different external cavities, 26th International Semiconductor Laser Conference (ISLC 2018), September 16  19, 2018, IEEE Photonics Society, Santa Fe, USA, September 16, 2018.

M. Radziunas, Modeling of heat and current spreading effects in dynamic simulations of broadarea semiconductor lasers, HotLas project meeting, Jenoptik Diode Lab GmbH, Berlin, February 27, 2018.

M. Radziunas, Modeling, simulation, and analysis of nonlinear dynamics in semiconductor lasers, Research Seminar of the Faculty of Science and Engineering, Macquarie University, Sydney, Australia, July 24, 2018.

A.G. Vladimirov, Delay models in nonlinear laser dynamics, Dynamics Days Europe 2018, September 3  7, 2018, Loughborough University, UK, September 6, 2018.

A.G. Vladimirov, Timedelay modeling of short pulse generation in lasers, Annual International Conference ,,Days on Diffraction 2018'', June 4  8, 2018, Steklov Mathematical Institute, St. Petersburg, Russian Federation, June 6, 2018.

A.G. Vladimirov, Timedelay systems in multimode laser dynamics, 675. WEHeraeusSeminar ,,Delayed Complex Systems'', July 2  5, 2018, Physikzentrum Bad Honnef, July 4, 2018.

M. Wolfrum, Dynamics of coupled oscillator systems and their continuum limits, Kolloquium der Arbeitsgruppe Modellierung, Numerik, Differentialgleichungen, Technische Universität Berlin, Institut für Mathematik, June 12, 2018.

M. Wolfrum, Phase solitons in DDEs with large delay, 14th IFAC Workshop on Time Delay Systems, June 28  30, 2018, Budapest University of Technology and Economics, Hungary, June 29, 2018.

M. Wolfrum, Phasesensitive excitability of a limit cycle, International Conference on Control of SelfOrganizing Nonlinear Systems, Warnemünde, September 9  13, 2018.
Preprints im Fremdverlag

S. Slepneva, B. O'Shaughnessy, A.G. Vladimirov, S. Rica, G. Huyet, Turbulent laser puffs, Preprint no. arXiv:1801.05509, Cornell University Library, 2018.
Abstract
The destabilisation of laminar flows and the development of turbulence has remained a central problem in fluid dynamics since Reynolds' studies in the 19th century. Turbulence is usually associated with complex fluid motions and most of the studies have so far been carried out using liquids or gases. Nevertheless, on a theoretical viewpoint, turbulence may also arise in a wide range of fields such as biology and optics. Here we report the results of experimental and theoretical investigation of the characteristic features of laminarturbulent transition in a long laser commonly used as a light source in medical imaging and sensing applications. This laminar to turbulence transition in the laser light is characterized by the appearance of turbulent puffs similar to those commonly observed in pipe flows and is accompanied by a loss of coherence and limits the range of applications. We present both experimental results and numerical simulations demonstrating that this transition is mediated by the appearance of a convective instability where localised structures develop into drifting bursts of turbulence, in complete analogy with spots, swirls and other structures in hydrodynamic turbulence
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