Publications
Monographs

P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, Th. Koprucki, Chapter 50: DriftDiffusion Models, in: Vol. 2 of Handbook of Optoelectronic Device Modeling and Simulation: Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press, Taylor & Francis Group, Boca Raton, 2017, pp. 733771, (Chapter Published).

M. Radziunas, Chapter 31: Traveling Wave Modeling of Nonlinear Dynamics in Multisection Semiconductor Laser Diodes, in: Vol. 2 of Handbook of Optoelectronic Device Modeling and Simulation: Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, J. Piprek, ed., Series in Optics and Optoelectronics, CRC Press, Taylor & Francis Group, Boca Raton, 2017, pp. 153182, (Chapter Published).
Abstract
A hierarchy of 1 (time) + 1 (space) dimensional firstorder partial differential equation (traveling wave) models is used for a description of dynamics in individual semiconductor lasers, various multisection semiconductor lasers, and coupled laser systems. Consequent modifications of the basic traveling wave model allow for taking into account different physical effects such as the gain dispersion, the thermal detuning, the spatial hole burning of carriers, the nonlinear gain saturation, or various carrier exchange processes in quantum dot lasers. For illustration, the model was applied for simulations of dynamics in complex ring laser with four branches of filtered feedback. Finally, several advanced techniques for model analysis such as calculation of instantaneous optical modes, finding of steady states, and numerical continuation and bifurcation analysis of the model equations were discussed and illustrated by example simulations.
Articles in Refereed Journals

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), published online on 25.01.2018, DOI https://doi.org/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. 
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. 
O.E. Omel'chenko, The mathematics behind chimera states, Nonlinearity, 31 (2018), published online on 04.04.2018, DOI https://doi.org/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. 
C. Brée, M. Hofmann, I. Babushkin, A. Demircan, U. Morgner, O.G. Kosareva, A.B. Savel'ev, A. Husakou, M. Ivanov, Symmetry breaking and strong persistent plasma currents via resonant destabilization of atoms, Physical Review Letters, 119 (2017), pp. 243202/1243202/5.
Abstract
The ionization rate of an atom in a strong optical field can be resonantly enhanced by the presence of longliving atomic levels (so called Freeman resonances). This process is most prominent in the multiphoton ionization regime meaning that ionization event takes many optical cycles. Nevertheless, here we show that these resonances can lead to fast subcyclescale plasma buildup at the resonant values of the intensity in the pump pulse. The fast buildup can break the cycletocycle symmetry of the ionization process, resulting in generation of persistent macroscopic plasma currents which remain after the end of the pulse. This, in turn, gibes rise to a broadband radiation of unusual spectral structure forming a comb from terahertz (THz) to visible. This radiation contains fingerprints of the attosecond electronic dynamics in Rydberg states during ionization. 
C. Brée, I. Babushkin, U. Morgner, A. Demircan, Regularizing aperiodic cycles of resonant radiation in filament light bullets, Physical Review Letters, 118 (2017), pp. 163901/1163901/5, DOI 10.1103/PhysRevLett.118.163901 .
Abstract
We demonstrate an up to now unrecognized and very effective mechanism which prevents filament collapse and allows persistent selfguiding propagation retaining larg portion of the optical energy onaxis over unexpected long distances. The key ingredient is the possibility of leaking continuously energy into the normal dispersion regime via emission of resonant radiation. The frequency of the radiation is determined by the dispersion dynamically modified by photogenerated plasma, thus allowing to excite new frequencies in the spectral ranges which are otherwise difficult to access. 
S. Eydam, M. Wolfrum, Mode locking in systems of globally coupled phase oscillators, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 96 (2017), pp. 052205/1052205/8, DOI 10.1103/PhysRevE.96.052205 .
Abstract
We investigate the dynamics of a Kuramototype system of globally coupled phase oscillators with equidistant natural frequencies and a coupling strength below the synchronization threshold. It turns out that in such cases one can observe a stable regime of sharp pulses in the mean field amplitude with a pulsation frequency given by spacing of the natural frequencies. This resembles a process known as modelocking in laser and relies on the emergence of a phase relation induced by the nonlinear coupling. We discuss the role of the first and second harmonic in the phaseinteraction function for the stability of the pulsations and present various bifurcating dynamical regimes such as periodically and chaotically modulated modelocking, transitions to phase turbulence and intermittency. Moreover, we study the role of the system size and show that in certain cases one can observe typeII supertransients, where the system reaches the globally stable modelocking solution only after an exponentially long transient of phase turbulence. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantumclassical modeling of quantum dot devices, Phys. Rev. B., 96 (2017), pp. 205301/1205301/17, DOI 10.1103/PhysRevB.96.205301 .
Abstract
The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we obtain a new hybrid quantumclassical modeling approach, which enables a comprehensive description of quantum dot devices on multiple scales: It allows the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven singlephoton source based on a single quantum dot in the stationary and transient operation regime. 
A. Pimenov, S. Slepneva, G. Huyet, A.G. Vladimirov, Dispersive timedelay dynamical systems, Physical Review Letters, 118 (2017), pp. 193901/1193901/6.
Abstract
We present a theoretical approach to model the dynamics of a dispersive nonlinear system using a set of delay differential equations with distributed delay term. We illustrate the use of this approach by considering a frequency swept laser comprimising a semiconductor optical amplifier (SOA), a tunable bandpass filter and a long dispersive fiber delay line. We demonstrate that this system exhibits a rich spectrum of dynamical behaviors which are in agreement with the experimental observations. In particular, the multimode modulational instability observed experimentally in the laser in the anomalous dispersion regime and leading to a turbulent laser output was found analytically in the limit of large delay time. 
G. Slavcheva, M.V. Koleva, A. Pimenov, The impact of microcavity wire width on polariton soliton existence and multistability, Journal of Optics, 19 (2017), pp. 065404/1065404/15.
Abstract
We have developed a model of the nonlinear polariton dynamics in realistic 3D nonplanar microcavity wires in the drivendissipative regime [15]. We find that the typical microcavity optical bistability evolves into multistability upon variation of the model parameters. The origin of the multistability is discussed in detail. We apply linear perturbation analysis to modulational instabilities, and identify conditions for localisation of composite multimode polariton solitons in the triggered parametric oscillator regime. Further, we demonstrate stable polariton soliton propagation in tilted and tapered waveguides, and determine maximum tilt angles for which solitons are still found. Additionally, we study soliton amplitude and velocity dependence on the wire width, with a view towards device applications. 
TH. Erneux, J. Javaloyes, M. Wolfrum, S. Yanchuk, Introduction to focus issue: Timedelay dynamics, Chaos. An Interdisciplinary Journal of Nonlinear Science, 27 (2017), pp. 114201/1114201/5, DOI 10.1063/1.5011354 .
Abstract
The field of dynamical systems with time delay is an active research area that connects practically all scientific disciplines including mathematics, physics, engineering, biology, neuroscience, physiology, economics, and many others. This Focus Issue brings together contributions from both experimental and theoretical groups and emphasizes a large variety of applications. In particular, lasers and optoelectronic oscillators subject to timedelayed feedbacks have been explored by several authors for their specific dynamical output, but also because they are ideal testbeds for experimental studies of delay induced phenomena. Topics include the control of cavity solitons, as light spots in spatially extended systems, new devices for chaos communication or random number generation, higher order locking phenomena between delay and laser oscillation period, and systematic bifurcation studies of modelocked laser systems. Moreover, two original theoretical approaches are explored for the socalled Low Frequency Fluctuations, a particular chaotical regime in laser output which has attracted a lot of interest for more than 30?years. Current hot problems such as the synchronization properties of networks of delaycoupled units, novel stabilization techniques, and the large delay limit of a delay differential equation are also addressed in this special issue. In addition, analytical and numerical tools for bifurcation problems with or without noise and two reviews on concrete questions are proposed. The first review deals with the rich dynamics of simple delay climate models for El Nino Southern Oscillations, and the second review concentrates on neuromorphic photonic circuits where optical elements are used to emulate spiking neurons. Finally, two interesting biological problems are considered in this Focus Issue, namely, multistrain epidemic models and the interaction of glucose and insulin for more effective treatment. 
V. Klinshov, D. Shchapin, S. Yanchuk, M. Wolfrum, O. D'huys, V. Nekorkin, Embedding the dynamics of a single delay system into a feedforward ring, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 96 (2017), pp. 042217/1042217/9.
Abstract
We investigate the relation between the dynamics of a single oscillator with delayed selffeedback and a feedforward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the selffeedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings. We discover several cases where stability of periodic solution for the single unit can be related to the stability of the corresponding rotating wave in the ring. As a specific example we demonstrate how the complex bifurcation scenario of simultaneously emerging multijittering solutions can be transferred from a single oscillator with delayed pulse feedback to multijittering rotating waves in a sufficiently large ring of oscillators with instantaneous pulse coupling. Finally, we present an experimental realization of this dynamical phenomenon in a system of coupled electronic circuits of FitzHughNagumo type. 
D. Puzyrev, A.G. Vladimirov, A. Pimenov, S.V. Gurevich, S. Yanchuk, Bound pulse trains in arrays of coupled spatially extended dynamical systems, Physical Review Letters, 119 (2017), pp. 163901/1163901/6, DOI 10.1103/PhysRevLett.119.163901 .
Abstract
We study the dynamics of an array of nearestneighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that, unlike a solitary system generating a train of equidistant pulses, an array of such systems can produce a sequence of clusters of closely packed pulses, with the distance between individual pulses depending on the coupling phase. This regime associated with the formation of locally coupled pulse trains bounded due to a balance of attraction and repulsion between them is different from the pulse bound states reported earlier in different laser, plasma, chemical, and biological systems. We propose a simplified analytical description of the observed phenomenon, which is in good agreement with the results of direct numerical simulations of a model system describing an array of coupled modelocked lasers. 
S. Rauch, H. Wenzel, M. Radziunas, M. Haas, G. Tränkle, H. Zimer, Impact of longitudinal refractive index change on the nearfield width of highpower broadarea diode lasers, Applied Physics Letters, 110 (2017), pp. 263504/1263504/5, DOI 10.1063/1.4990531 .
Abstract
Typical for broadarea laser (BAL) diodes operating in a continuouswave mode is a narrowing of the nearfield (NF) width at the output facet for high injection currents (output powers). This phenomenon increases the facet load of BALs, resulting in a reduction in the level of catastrophic optical mirror damage. In this letter, we demonstrate theoretically that thermally induced changes in the refractive index in both lateral and longitudinal directions not only cause the NF narrowing at the front facet but also a broadening of the NF at the back facet. In contrast, a sole lateral selfheating induced variation in the refractive index (commonly referred to as thermal lensing) does not result in a NF narrowing. Our theoretical findings are confirmed by measurements of the currentdependent profiles of the NF at the back and front facets of a BAL with a stripe width of 120??m emitting at 960?nm. Furthermore, our quasi threedimensional thermoelectrooptic simulations indicate that a longitudinally homogeneous device temperature can reduce the frontfacet load while keeping the beam quality unchanged compared with the experimental results. 
T. Schemmelmann, F. Tabbert, A. Pimenov, A.G. Vladimirov, S.V. Gurevich, Delayed feedback control of selfmobile cavity solitons in a wideaperture laser with a saturable absorber, Chaos. An Interdisciplinary Journal of Nonlinear Science, 27 (2017), pp. 114304/1114304/9.
Abstract
We investigate the spatiotemporal dynamics of cavity solitons in a broad area verticalcavity surfaceemitting laser with saturable absorption subjected to timedelayed optical feedback. Using a combination of analytical, numerical and path continuation methods we analyze the bifurcation structure of stationary and moving cavity solitons and identify two different types of traveling localized solutions, corresponding to slow and fast motion. We show that the delay impacts both stationary and moving solutions either causing drifting and wiggling dynamics of initially stationary cavity solitons or leading to stabilization of intrinsically moving solutions. Finally, we demonstrate that the fast cavity solitons can be associated with a lateral modelocking regime in a broadarea laser with a single longitudinal mode. 
A.P. Willis, Y. Duguet, O. Omel'chenko, M. Wolfrum, Surfing the edge: Finding nonlinear solutions using feedback control, Journal of Fluid Mechanics, 831 (2017), pp. 579591.
Abstract
Many transitional wallbounded shear flows are characterised by the coexistence in statespace of laminar and turbulent regimes. Probing the edge boundarz between the two attractors has led in the last decade to the numerical discovery of new (unstable) solutions to the incompressible NavierStokes equations. However, the iterative bisection method used to achieve this can become prohibitively costly for large systems. Here we suggest a simple feedback control strategy to stabilise edge states, hence accelerating their numerical identification by several orders of magnitude. The method is illustrated for several configurations of cylindrical pipe flow. Traveling waves solutions are identified as edge states, and can be isolated rapidly in only one short numerical run. A new branch of solutions is also identified. When the edge state is a periodic orbit or chaotic state, the feedback control does not converge precisely to solutions of the uncontrolled system, but nevertheless brings the dynamics very close to the original edge manifold in a single run. We discuss the opportunities offered by the speed and simplicity of this new method to probe the structure of both state space and parameter space. 
I. Babushkin, C. Brée, Ch.M. Dietrich, A. Demircan, U. Morgner, A. Husakou, Terahertz and higherorder Brunel harmonics: From tunnel to multiphoton ionization regime in tailored fields, Journal of Modern Optics, 67 (2017), pp. 10781087, DOI 10.1080/09500340.2017.1285066 .
Abstract
Brunel radiation appears as a result of a twostep process of photoionization and subsequent acceleration of electron, without the need of electron recollision. We show that for generation of Brunel harmonics at all frequencies, the subcycle ionization dynamics is of critical importance. Namely, such harmonics disappear at the low pump intensities when the ionization dynamics depends only on the slow envelope (socalled multiphoton ionization regime) and not on the instantaneous field. Nevertheless, if the pump pulse contains incommensurate frequencies, Brunel mechanism does generate new frequencies even in the multiphoton ionization regime. 
N. Raabe, T. Feng, T. Witting, A. Demircan, C. Brée, G. Steinmeyer, Role of intrapulse coherence in carrierenvelope phase stabilization, Physical Review Letters, 119 (2017), pp. 123901/1123901/5, DOI 10.1103/PhysRevLett.119.123901 .
Abstract
The concept of coherence is of fundamental importance for describing the physical characteristics of light and for evaluating the suitability for experimental application. In the case of pulsed laser sources, the pulsetopulse coherence is usually considered for a judgment of the compressibility of the pulse train. This type of coherence is often lost during propagation through a highly nonlinear medium, and pulses prove incompressible despite multioctave spectral coverage. Notwithstanding the apparent loss of interpulse coherence, however, supercontinua enable applications in precision frequency metrology that rely on coherence between different spectral components within a laser pulse. To judge the suitability of a light source for the latter application, we define an alternative criterion, which we term intrapulse coherence. This definition plays a limiting role in the carrierenvelope phase measurement and stabilization of ultrashort pulses. It is shown by numerical simulation and further corroborated by experimental data that filamentationbased supercontinuum generation may lead to a loss of intrapulse coherence despite nearperfect compressibility of the pulse train. This loss of coherence may severely limit active and passive carrierenvelope phase stabilization schemes and applications in optical highfield physics. 
S. Pickartz, C. Brée, U. Bandelow, S. Amiranashvili, Cancellation of Raman selffrequency shift for compression of optical pulses, Optical and Quantum Electronics, 49 (2017), pp. 328/1328/7, DOI 10.1007/s1108201711647 .
Abstract
We study to which extent a fiber soliton can be manipulated by a specially chosen continuous pump wave. A group velocity matched pump scatters at the soliton, which is compressed due to the energy/momentum transfer. As the pump scattering is very sensitive to the velocity matching condition, soliton compression is quickly destroyed by the soliton selffrequency shift (SSFS). This is especially true for ultrashort pulses: SSFS inevitably impairs the degree of compression. We demonstrate numerically that soliton enhancement can be restored to some extent and the compressed soliton can be stabilized, provided that SSFS is canceled by a second pump wave. Still the available compression degree is considerably smaller than that in the Ramanfree nonlinear fibers. 
S. Pickartz, U. Bandelow, S. Amiranashvili, Asymptotically stable compensation of soliton selffrequency shift, Optics Letters, 42 (2017), pp. 14161419, DOI 10.1364/OL.42.001416 .
Abstract
We report the cancellation of the soliton selffrequency shift in nonlinear optical fibers. A soliton which interacts with a group velocity matched low intensity dispersive pump pulse, experiences a continuous blueshift in frequency, which counteracts the soliton selffrequency shift due to Raman scattering. The soliton selffrequency shift can be fully compensated by a suitably prepared dispersive wave.We quantify this kind of solitondispersive wave interaction by an adiabatic approach and demonstrate that the compensation is stable in agreement with numerical simulations. 
O. Omel'chenko, L. Recke, V. Butuzov, N. Nefedov, Timeperiodic boundary layer solutions to singularly perturbed parabolic problems, Journal of Differential Equations, 262 (2017), pp. 48234862.
Abstract
In this paper, we present a result of implicit function theorem type, which was designed for application to singularly perturbed problems. This result is based on fixed point iterations for contractive mappings, in particular, no monotonicity or sign preservation properties are needed. Then we apply our abstract result to timeperiodic boundary layer solutions (which are allowed to be nonmonotone with respect to the space variable) in semilinear parabolic problems with two independent singular perturbation parameters. We prove existence and local uniqueness of those solutions, and estimate their distance to certain approximate solutions. 
M. Radziunas, A. Zeghuzi, J. Fuhrmann, Th. Koprucki, H.J. Wünsche, H. Wenzel, U. Bandelow, Efficient coupling of inhomogeneous current spreading and dynamic electrooptical models for broadarea edgeemitting semiconductor devices, Optical and Quantum Electronics, 49 (2017), pp. 332/1332/8, DOI 10.1007/s1108201711683 .
Abstract
We extend a 2 (space) + 1 (time)dimensional traveling wave model for broadarea edgeemitting semiconductor lasers by a model for inhomogeneous current spreading from the contact to the active zone of the laser. To speedup the performance of the device simulations, we suggest and discuss several approximations of the inhomogeneous current density in the active zone.
Contributions to Collected Editions

M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, in: Proceedings of ``SPIE Photonics West 2018: Physics and Simulation of Optoelectronic Devices XXVI'', San Francisco, USA, 29.01.2018  01.02.2018, 10526, Society of PhotoOptical Instrumentation Engineers (SPIE), Bellingham, 2018, pp. 10526/110526/6, 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. Wolfrum, Enumeration of positive meanders, in: Proceedings of ``International Conference on Patterns of Dynamics'', 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. 
M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Simulation of quantum dot devices by coupling of quantum master equations and semiclassical transport theory, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2017, J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 217218.

G. Slavcheva, M.V. Koleva, A. Pimenov, Simulation of nonlinear polariton dynamics in microcavity wires for polaritonic integrated circuits, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2017, J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 187188, DOI 10.1109/NUSOD.2017.8010054 .

D. Puzyrev, A.G. Vladimirov, A. Pimenov, S.V. Gurevich, S. Yanchuk, Pulse boundstate clusters in coupled modelocked lasers, in: Lasers and ElectroOptics Europe & European Quantum Electronics Conference (CLEO/EuropeEQEC) 2017 Conference on, IEEE, New York, 2017, DOI 10.1109/CLEOEEQEC.2017.8087527 .
Abstract
Modelocked semiconductor lasers are widely used for generation of short optical pulses with high repetition rates and optical frequency combs suitable for numerous practical applications. By combining many lasers into an array one can achieve much larger output power and substantially improve the characteristics of the output radiation. In this presentation we study dynamical regimes of operation in an array of modelocked lasers locally coupled in a ring geometry. We demonstrate that unlike a solitary modelocked laser emitting a sequence of equidistant pulses with the pulse repetition frequency close to the inverse cavity round trip time, an array of modelocked lasers can radiate a periodic sequence of clusters of fundamental modelocked pulses. This regime associated with the formation of closely packed bound states of coupled modelocked pulses due to a balance between attraction and repulsion is very different from the standard harmonic modelocked regime where the pulses always repel each other. 
A. Zeghuzi, M. Radziunas, A. Klehr, H.J. Wünsche, H. Wenzel, A. Knigge, Influence of nonlinear effects on the characteristics of pulsed highpower BA DBR Lasers, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2017, J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 233234.

S. Pickartz, C. Brée, U. Bandelow, S. Amiranashvili, Cancellation of Raman selffrequency shift for compression of optical pulses, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2017, J. Piprek, M. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 173174.

M. Radziunas, A. Zeghuzi, J. Fuhrmann, Th. Koprucki, H.J. Wünsche, H. Wenzel, U. Bandelow, Efficient coupling of inhomogeneous current spreading and electrooptical models for simulation of dynamics in broadarea semiconductor lasers, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2017, J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 231232.
Preprints, Reports, Technical Reports

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, Preprint no. 2488, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2488 .
Abstract, PDF (431 kByte)
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, A. Ankiewicz, S. Amiranashvili, S. Pickartz, N. Akhmediev, SasaSatsuma hierarchy of integrable evolution equations, Preprint no. 2487, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2487 .
Abstract, PDF (195 kByte)
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. 
A. Pimenov, J. Javaloyes, S.V. Gurevich, A.G. Vladimirov, Light bullets in a timedelay model of a wideaperture modelocked semiconductor laser, Preprint no. 2481, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2481 .
Abstract, PDF (5204 kByte)
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. 
A.G. Vladimirov, S.V. Gurevich, M. Tlidi, Effect of Cherenkov radiation on localized states interaction, Preprint no. 2480, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2480 .
Abstract, PDF (2481 kByte)
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. 
S. Amiranashvili, M. Radziunas, U. Bandelow, R. Čiegis, Numerical methods for accurate description of ultrashort pulses in optical fibers, Preprint no. 2470, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2470 .
Abstract, PDF (2140 kByte)
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. 
O. Burylko, A. Mielke, M. Wolfrum, S. Yanchuk, Coexistence of Hamiltonianlike and dissipative dynamics in chains of coupled phase oscillators with skewsymmetric coupling, Preprint no. 2447, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2447 .
Abstract, PDF (3022 kByte)
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. 
M. Radziunas, M. Khoder, V. Tronciu, J. Danckaert, G. Verschaffelt, Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation, Preprint no. 2438, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2438 .
Abstract, PDF (3116 kByte)
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. 
A. Grin, K.R. Schneider, Global bifurcation analysis of a class of planar systems, Preprint no. 2426, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2426 .
Abstract, PDF (202 kByte)
We consider planar autonomous systems dx/dt =P(x,y,λ), dy/dt =Q(x,y,λ) depending on a scalar parameter λ. We present conditions on the functions P and Q which imply that there is a parameter value λ_{0} such that for &lambda > λ_{0} this system has a unique limit cycle which is hyperbolic and stable. DulacCherkas functions, rotated vector fields and singularly perturbed systems play an important role in the proof. 
C. Brée, M. Hofmann, I. Babushkin, A. Demircan, U. Morgner, O.G. Kosareva, A.B. Savel'ev, A. Husakou, M. Ivanov, Symmetry breaking and strong persistent plasma currents via resonant destabilization of atoms, Preprint no. 2423, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2423 .
Abstract, PDF (1839 kByte)
The ionization rate of an atom in a strong optical field can be resonantly enhanced by the presence of longliving atomic levels (so called Freeman resonances). This process is most prominent in the multiphoton ionization regime meaning that ionization event takes many optical cycles. Nevertheless, here we show that these resonances can lead to fast subcyclescale plasma buildup at the resonant values of the intensity in the pump pulse. The fast buildup can break the cycletocycle symmetry of the ionization process, resulting in generation of persistent macroscopic plasma currents which remain after the end of the pulse. This, in turn, gibes rise to a broadband radiation of unusual spectral structure forming a comb from terahertz (THz) to visible. This radiation contains fingerprints of the attosecond electronic dynamics in Rydberg states during ionization. 
K. Schneider, New approach to study the van der Pol equation for large damping, Preprint no. 2422, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2422 .
Abstract, PDF (237 kByte)
We present a new approach to establish the existence of a unique limit cycle for the van der Pol equation in case of large damping which is hyperbolic and stable. The proof is based on a linear time scaling (instead of the nonlinear Liénard transformation), on a DulacCherkas function and the property of rotating vector fields. 
G. Slavcheva, M.V. Koleva, A. Pimenov, The impact of microcavity wire width on polariton soliton existence and multistability, Preprint no. 2381, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2381 .
Abstract, PDF (5652 kByte)
We have developed a model of the nonlinear polariton dynamics in realistic 3D nonplanar microcavity wires in the drivendissipative regime [15]. We find that the typical microcavity optical bistability evolves into multistability upon variation of the model parameters. The origin of the multistability is discussed in detail. We apply linear perturbation analysis to modulational instabilities, and identify conditions for localisation of composite multimode polariton solitons in the triggered parametric oscillator regime. Further, we demonstrate stable polariton soliton propagation in tilted and tapered waveguides, and determine maximum tilt angles for which solitons are still found. Additionally, we study soliton amplitude and velocity dependence on the wire width, with a view towards device applications. 
S. Olmi, D. AnguloGarcia, A. Imparato, A. Torcini, Exact firing time statistics of neurons driven by discrete inhibitory noise, Preprint no. 2367, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2367 .
Abstract, PDF (364 kByte)
Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory presynaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky IntegrateandFire neurons subject to inhibitory instantaneous postsynaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude postsynaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations.
Talks, Poster

M. Kantner, M. Mittnenzweig, Th. Koprucki, Semismooth Newton methods in PDE constrained optimization, 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.

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

S. Amiranashvili, Negative frequency radiation in optical fibers, Institutskolloquium, WIAS, Berlin, October 16, 2017.

C. Brée, BALaser with intracavity PhC, Projekttreffen Eurostars, Monocrom S.L., Barcelona, Spain, November 6, 2017.

C. Brée, Bloch mode transfer matrix method for photonic crystals, Internal seminar of the research group DONLL, Universitat Politecnica de Catalunya, Terrassa, Spain, July 12, 2017.

S. Eydam, Modelocking in systems of globally coupled phase oscillators, Workshop on Control of SelfOrganizing Nonlinear Systems, August 28  31, 2017, TU Berlin/SFB 910, Lutherstadt Wittenberg, August 31, 2017.

S. Eydam, Phase oscillator mode locking, SCL Seminar, Belgrade Institute of Physics, Serbia, September 28, 2017.

S. Eydam, Phase oscillator modelocking, Forschungsseminar ``Applied Dynamical Systems'', TU Berlin, June 14, 2017.

M. Kantner, Hybrid quantumclassical modeling of electrically driven quantum light sources, Meeting of the MATHEON Scientific Advisory Board 2017, TU Berlin, Institut für Mathematik, November 13, 2017.

M. Kantner, Modeling of quantum dot based singlephoton LEDs on a device level, MATHEON Workshop 10th Annual Meeting ``Photonic Devices'', February 9  10, 2017, KonradZuseZentrum für Informationstechnik Berlin, February 10, 2017.

M. Kantner, Simulations of quantum dot devices by coupling of quantum master equations and semiclassical transport theory, 17th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD2017), July 24  28, 2017, Technical University of Denmark, Copenhagen, July 27, 2017.

A. Pimenov, Novel delayed model of a broadarea laser: Are the light bullets robust?, Minisymposium ,,Dynamics of novel modelocked and frequencyswept lasers (DNMFL2017)'', December 18  19, 2017, WIAS, Berlin, December 18, 2017.

A. Pimenov, Temporal localized structures in a time delay model of a ring laser, International Workshop: Nonlinear Waves and Turbulence in Optics and Hydrodynamics, WIAS, Berlin, March 23, 2017.

A. Pimenov, Timedelay models of multimode laser dynamics, SIAM Conference on Applications of Dynamical Systems (DS17), May 21  25, 2017, Society for Industrial and Applied Mathematics (SIAM), Snowbird, USA, May 24, 2017.

M. Radziunas, Modeling and simulation of external feedback in broad area lasers with BALaser, EFFILASHotLas project meeting, Jenoptik Diode Lab GmbH, Berlin, April 27, 2017.

S. Pickartz, Cancellation of Raman selffrequency shift for compression of optical pulses, 17th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD2017), July 24  28, 2017, Technical University of Denmark, Copenhagen, Denmark, July 28, 2017.

U. Bandelow, Applied mathematical research in photonics at WIAS, BoschWIAS Workshop, WIAS, Berlin, June 13, 2017.

U. Bandelow, Fewcycle solitons that do not want to be too short in duration, CLEO Pacific Rim Conference, July 31  August 4, 2017, The Optical Society, Singapore, Singapore, August 2, 2017.

U. Bandelow, Models for ultrashort optical pulses and their limiting soliton solutions, International Workshop: Nonlinear Waves and Turbulence in Optics and Hydrodynamics, WIAS, Berlin, March 22, 2017.

C. Brée, Detection of dynamic resonances in femtosecond filaments via the transient plasma grating effect, Workshop ,,Nonlinear Phenomena in Strong Fields'', Leibniz Universität Hannover, January 25, 2017.

C. Brée, Feedbackoperator for a photonic crystal in the external cavity of a broad area laser diode, Forschungsseminar Mathematische Modelle der Photonik, WIAS, Berlin, June 22, 2017.

O. Omel'chenko, Bifurcations mediating appearance of chimera states, XXXVII Dynamics Days Europe, Minisymposium 3 ``Complex Networks: Delays And Collective Dynamics'', June 5  9, 2017, University of Szeged, Faculty of Science and Informatics, Hungary, June 8, 2017.

O. Omel'chenko, Bifurcations mediating the appearance of chimera states, SIAM Conference on Applications of Dynamical Systems (DS 17), Minisymposium ``Large Scale Dynamics In Coupled Systems On Networks'', May 21  25, 2017, Society for Industrial and Applied Mathematics (SIAM), Snowbird, USA, May 24, 2017.

O. Omel'chenko, Controlling unstable complex dynamics: From coupled oscillators to fluid mechanics, XV Latin American Workshop on NonLinear Phenomena, November 6  10, 2017, Facultad de Ciencias y Astronomía, Universidad de La Serena, Chile, November 7, 2017.

O. Omel'chenko, Introduction to chimera states, Seminar of the Scientific Computing Laboratory, University of Belgrade, Institue of Physics, Serbia, May 4, 2017.

O. Omel'chenko, Noninvasive model reconstruction from a partially synchronized state, XXXVII Dynamics Days Europe, Minisymposium 14b ``Synchronization Patterns In Networks: Theory and Applications'', June 5  9, 2017, University of Szeged, Faculty of Science and Informatics, Hungary, June 8, 2017.

O. Omel'chenko, Stabilizing control scheme: From chimera states to edge states, Internal seminar of the Prof. E. Knobloch group, Department of Physics, University of California, Berkeley, USA, May 17, 2017.

M. Radziunas, C. Brée, Modeling and simulation of highpower broad area lasers, HiPLasers project meeting, RaabPhotonic GmbH, Potsdam, May 30, 2017.

M. Radziunas, Efficient coupling of inhomogeneous current spreading and electrooptical models for simulation of dynamics in broadarea semiconductor lasers, 17th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD2017), July 24  28, 2017, Technical University of Denmark, Copenhagen, Denmark, July 28, 2017.

M. Radziunas, Implementation of inhomogeneous injection model into BALaser, BMBF Effilas/Hotlas project meeting, DILAS Diodenlaser GmbH, Mainz, February 21, 2017.

M. Radziunas, Modeling and simulation of highpower broad area lasers with PhC filtering element, EUROSTARS HiPLaser project meeting, Monocrom, Vilanova, Barcelona, Spain, November 6, 2017.

M. Radziunas, Modeling and simulations of broad area lasers, BMBF Effilas/Hotlas project meeting, FerdinandBraunInstitut, Berlin, September 21, 2017.

A.G. Vladimirov, Mathematical modeling of dispersive and diffractive multimode lasers, 1st SinoGerman Symposium on Fiber Photonics for Light Matter Interaction, September 17  21, 2017, Shanghai University, China, September 19, 2017.

A.G. Vladimirov, Mathematical modelling of multimode laser dynamics, Seminar of the Ultrafast Laser Laboratory, Institute for Quantum Optics, Leibniz University of Hannover, November 17, 2017.

M. Wolfrum, Eine erstaunlich einfache Methode zur Berechnung des Sinus aus dem 16ten Jahrhundert, 22. Berliner Tag der Mathematik, HumboldtUniversität zu Berlin, April 22, 2017.

M. Wolfrum, Synchronization transitions in systems of coupled phase oscillators, IPB Colloquium, Institute of Physics Belgrade, Serbia, May 9, 2017.

M. Wolfrum, Chimera states in systems of coupled phase oscillators, Emerging Topics in Network Dynamical Systems, June 6  9, 2017, Lorentz Center, Leiden, Netherlands, June 6, 2017.

M. Wolfrum, Dynamics of coupled oscillator systems and their continuum limits, CIMWIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6  8, 2017, International Center for Mathematics, University of Lisbon, Portugal, December 6, 2017.
External Preprints

A.G. Vladimirov, S.V. Gurevich, M. Tlidi, Effect of Cherenkov radiation on localized states interaction, Preprint no. arXiv:1707.04458, Cornell University Library, arXiv.org, 2017.
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 their interaction and greatly enlarges the interaction range thus facilitating the experimental observation of the soliton bound states. Analytical derivation of the reduced equations governing slow time evolution of the positions of two interacting localized states in the LugiatoLefever model with third order dispersion term is performed. Numerical solutions of the model equation are in close agreement with analytical predictions.
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