Publications

Articles in Refereed Journals

  • S. Amiranashvili, E. Tobisch, Extended criterion for the modulation instability, New Journal of Physics, 21 (2019), published online on 28.03.2019, DOI 10.1088/1367-2630/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 one-dimensional 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. 391--402, DOI 10.1016/j.cnsns.2018.07.031 .
    Abstract
    We consider a one-dimensional first-order nonlinear wave equation (the so-called forward Maxwell equation, FME) that applies to a few-cycle 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 second-order 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 few-cycle pulses. We analyze and compare pseudo-spectral 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. Montiel-Ponsoda, G. Garre-Werner, K. Staliunas, U. Bandelow, M. Radziunas, Beam-combining scheme of high-power broad-area semiconductor lasers with Lyot-filtered reinjection: Modeling, simulations, and experiments, Journal of the Optical Society of America. B, 36 (2019), pp. 1721--1730, DOI 10.1364/JOSAB.36.001721 .
    Abstract
    A brightness- and power-scalable polarization beam combining scheme for high-power, broadarea semiconductor laser diodes is investigated numerically and experimentally. To achieve the beam combining, we employ Lyot-filtered 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 broad-area laser diode arrays for cost-efficient material processing, which requires high-brilliance emission and optical powers in the kW-regime.

  • S. Eydam, I. Franović, M. Wolfrum, Leap-frog patterns in systems of two coupled FitzHugh--Nagumo units, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 99 (2019), pp. 042207/1--042207/9, DOI 10.1103/PhysRevE.99.042207 .
    Abstract
    We study a system of two identical FitzHugh-Nagumo 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 leap-frogging. We analyze various types of periodic and chaotic leap-frogging 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 leap-frog 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 FitzHugh-Nagumo system and the relation of the leap-frog solutions to the theory of mixed-mode 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 Kuramoto-type 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 mode-locking regime for equidistant natural frequencies, can enhance the echo phenomenon significantly. The non-monotonous behavior of echo amplitudes can be explained as a result of the linear dispersion within the self-organized mode-locked 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 Scharfetter--Gummel schemes for electro-thermal 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 self-heating phenomena. The optimization of device designs can be assisted by numerical simulations using the non-isothermal drift-diffusion 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 so-called Kelvin formula for the Seebeck coefficient. The corresponding heat generation rate involves exactly the three classically known self-heating effects, namely Joule, recombination and Thomson--Peltier 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 Scharfetter--Gummel method), which allows to cope with the typically stiff solutions of the semiconductor device equations. We derive two non-isothermal generalizations of the Scharfetter--Gummel scheme for degenerate semiconductors (Fermi--Dirac 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 mode-locked laser, The European Physical Journal B. Condensed Matter and Complex Systems, 92 (2019), published online on 22.05.2019, DOI 10.1140/epjb/e2019-90642-8 .
    Abstract
    We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked 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 Nozaki--Bekki holes in a long cavity OCT laser, Optics Express, 27 (2019), pp. 16395--16404, 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 Nozaki-Bekki 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, Time-dependent simulation of thermal lensing in high-power broad-area 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 slow-fast delayed systems with a periodic close to the delay, European Journal of Applied Mathematics, 30 (2019), pp. 39--62, 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 mode-locked 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 time-delayed Gires--Tournois interferometers, Optics Letters, 44 (2019), pp. 4925--4928, 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 micro-cavity, operated in the Gires?Tournois regime, containing a Kerr medium strong time-delayed 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. 372--384, 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 Τα 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 time-delay feedback systems, Physical Review Letters, 123 (2019), pp. 053901/1--053901/6, DOI 10.1103/PhysRevLett.123.053901 .
    Abstract
    Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, 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 time-delayed 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 pseudo-continuous 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 FitzHugh--Nagumo neuron with delayed feedback. Finally, we discuss possible destabilization mechanisms of TDS and show an example where the TDS delocalizes and its pseudo-continuous 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 angled-facet laser diode chips, Applied Physics B: Lasers and Optics, 66 (2019), published online on 01.04.2019, DOI 10.1007/s00340-019-7178-z .
    Abstract
    We present and compare theoretical and experimental results on the electro-optical performance of extended cavity diode lasers (ECDLs) that employ two ridge waveguide designs for the single-transverse 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 intra-cavity 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 intra-cavity facet is anti-reflection coated and features a residual intensity reflectivity of the order 10?4. The second design employs a bent ridge waveguide intersecting the anti-reflection-coated intra-cavity 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 electro-optical 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 non-thermal far-field blooming in high-power broad-area lasers, IEEE J. Quantum Electron., 55 (2019), pp. 2000207/1--2000201/7, DOI 10.1109/JQE.2019.2893352 .
    Abstract
    With rising current the lateral far-field angle of high-power broad-area lasers widens (far-field blooming) which can be partly attributed to non-thermal effects due to carrier induced refractive index and gain changes that become the dominant mechanism under pulsed operation. To analyze the nonthermal contribution to far-field 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 pre-assumptions regarding the modal composition of the field is made and filamentation is automatically accounted for, the highly dynamic time-dependent 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 dual-wavelength diode laser system, Optical and Quantum Electronics, 51 (2019), 334 (12pp).
    Abstract
    We present our design of a compact, integrated and tunable dual-wavelength 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 traveling-wave 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 all-passive simulation.

  • M. Radziunas, D.J. Little, D.M. Kane, Numerical study of optical feedback coherence in semiconductor laser dynamics, Optics Letters, 44 (2019), pp. 4207--4210, 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 electro-optical and heat-transport models for high-power broad-area semiconductor lasers, Optical and Quantum Electronics, 51 (2019), published online on 22.02.2019, DOI 10.1007/s11082-019-1792-1 .
    Abstract
    In this work, we discuss the modeling of edge-emitting high-power broad-area semiconductor lasers. We demonstrate an efficient iterative coupling of a slow heat transport (HT) model defined on multiple vertical-lateral laser cross-sections with a fast dynamic electro-optical (EO) model determined on the longitudinal-lateral domain that is a projection of the device to the active region of the laser. Whereas the HT-solver calculates temperature and thermally-induced refractive index changes, the EO-solver exploits these distributions and provides time-averaged field intensities, quasi-Fermi potentials, and carrier densities. All these time-averaged distributions are used repetitively by the HT-solver 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 class-A nonlinear mirror mode-locked laser, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 100 (2019), pp. 012216/1--012216/7, DOI 10.1103/PhysRevE.100.012216 .
    Abstract
    Using a simple delay differential equation model we study theoretically the dynamics of a unidirectional class-A 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 Turing-type instabilities, as well as by a bifurcation leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked 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 mode-locked 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. 391--402 (published online on 23.07.2018), DOI 10.1016/j.cnsns.2018.07.031 .
    Abstract
    We consider a one-dimensional first-order nonlinear wave equation (the so-called forward Maxwell equation, FME) that applies to a few-cycle 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 second-order 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 few-cycle pulses. We analyze and compare pseudo-spectral 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 broad-area laser, Journal of Optics, 20 (2018), pp. 095804/1--095804/7, DOI 10.1088/2040-8986/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 lower-order 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 time-delay model of a wide-aperture mode-locked semiconductor laser, Philosophical Transactions of the Royal Society A : Mathematical, Physical & Engineering Sciences, 376 (2018), pp. 20170372/1--20170372/14, DOI 10.1098/rsta.2017.0372 .
    Abstract
    Recently, a mechanism of formation of light bullets (LBs) in wide-aperture 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 Haus-type model equation. In this paper we relax the MF approximation and study LB formation in a model of a wide-aperture three section laser with a long diffractive section and short absorber and gain sections. To this end we derive a nonlocal delay-differential 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 round-trip are not small perturbations anymore.

  • I. Bačić, S. Yanchuk, M. Wolfrum, I. Franović, Noise-induced switching in two adaptively coupled excitable systems, European Physical Journal Special Topics, 227 (2018), pp. 1077--1090, DOI 10.1140/epjst/e2018-800084-6 .
    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 noise-induced 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 bursting-like behavior. The qualitative features of the switching dynamics are analyzed within the framework of fast-slow 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. 012216/1--012216/9, DOI 10.1103/PhysRevE.97.012216 .
    Abstract
    Chimera states are complex spatio-temporal 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 FitzHugh--Nagumo 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 Sasa--Satsuma equation: Densities approach to new infinite hierarchy of integrable evolution equations, Zeitschrift für Naturforschung A, 73 (2018), pp. 1121--1128, DOI 10.1515/zna-2018-0377 .
    Abstract
    We derive the new infinite Sasa-Satsuma hierarchy of evolution equations using an invariant densities approach. Being significantly simpler than the Lax-pair 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 Sasa-Satsuma hierarchy functionals. All these operators are parts of a generalized Sasa-Satsuma equation of infinitely high order. They enter this equation with independent arbitrary real coefficients that govern the evolution pattern of this multi-parameter dynamical system.

  • O. Burylko, A. Mielke, M. Wolfrum, S. Yanchuk, Coexistence of Hamiltonian-like and dissipative dynamics in chains of coupled phase oscillators with skew-symmetric coupling, SIAM Journal on Applied Dynamical Systems, 17 (2018), pp. 2076--2105, DOI 10.1137/17M1155685 .
    Abstract
    We consider rings of coupled phase oscillators with anisotropic coupling. When the coupling is skew-symmetric, i. e. when the anisotropy is balanced in a specific way, the system shows robustly a coexistence of Hamiltonian-like and dissipative regions in the phase space. We relate this phenomenon to the time-reversibility property of the system. The geometry of low-dimensional systems up to five oscillators is described in detail. In particular, we show that the boundary between the dissipative and Hamiltonian-like regions consists of families of heteroclinic connections. For larger chains with skew-symmetric 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 Hamiltonian-like region existing around the synchronous state similarly to the case of finite rings.

  • I. Franović, O.E. Omel'chenko, M. Wolfrum, Phase-sensitive excitability of a limit cycle, Chaos. An Interdisciplinary Journal of Nonlinear Science, 28 (2018), pp. 071105/1--071105/6, 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 threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like 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 FitzHugh-Nagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase sensitive nonlinear threshold-like 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 non-monotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this non-monotone 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 micro-ring lasers: Experiment and travelling wave description, OSA Continuum, 1 (2018), pp. 1226-1240, 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 counter-clockwise 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. 97--127, DOI 10.1137/17M1141151 .
    Abstract
    We study destabilization mechanisms of spiral coherence-incoherence patterns known as spiral chimera states that form on a two-dimensional lattice of nonlocally coupled phase oscillators. For this purpose we employ the linearization of the Ott--Antonsen equation that is valid in the continuum limit and perform a detailed two-parameter stability analysis of a $D_4$-symmetric chimera state, i.e., a four-core spiral state. We identify fold, Hopf and parity-breaking bifurcations as the main mechanisms whereby spiral chimeras can lose stability. Beyond these bifurcations we find new spatio-temporal 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 red-emitting distributed Bragg reflector lasers by means of numerical simulations, IET Optoelectronics, 12 (2018), pp. 228-232, DOI 10.1049/iet-opt.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 high-power broad-area distributed Bragg reflector lasers, Optical and Quantum Electronics, 50 (2018), pp. 88/1--88/12, DOI 10.1007/s11082-017-1297-8 .
    Abstract
    We theoretically analyze the influence of nonlinear effects such as spatial holeburning, two-photon absorption and gain compression on the power?current and beam characteristics of a high-power broad-area 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 two-photon absorption and gain compression, on the other hand, excitation of higher order lateral modes leads to losses through the Bragg grating. In combination with spatio-temporal power variations resolved by the utilized time-dependent traveling wave model two-photon absorption leads to higher power losses compared to those models using averaged powers.

  • U. Bandelow, A. Ankiewicz, S. Amiranashvili, N. Akhmediev, Sasa--Satsuma hierarchy of integrable evolution equations, Chaos. An Interdisciplinary Journal of Nonlinear Science, 28 (2018), pp. 053108/1--053108/11, DOI 10.1063/1.5030604 .
    Abstract
    We present the infinite hierarchy of Sasa-Satsuma 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 Sasa-Satsuma equation that includes third-order 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 higher-order 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. R121--R164, DOI 10.1088/1361-6544/aaaa07 .
    Abstract
    Chimera states are self-organized 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, Ott--Antonsen 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. 380--390, 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 traveling-wave 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 traveling-wave 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 broad-area edge-emitting semiconductor devices, Int. J. High Perform. Comput. Appl., 32 (2018), pp. 512--522, DOI 10.1177/1094342016677086 .
    Abstract
    We present a (2+1)-dimensional partial differential equation model for spatial-lateral dynamics of edge-emitting broad-area semiconductor devices and several extensions of this model describing different physical effects. MPI-based parallelization of the resulting middlesize numerical problem is implemented and tested on the blade cluster and separate multi-core computers at the Weierstrass Institute in Berlin. It was found, that an application of 25-30 parallel processes on all considered platforms was guaranteeing a nearly optimal performance of the algorithm with the speedup around 20-25 and the efficiency of 0.7-0.8. It was also shown, that a simultaneous usage of several in-house available multi-core 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 localized-state interaction, Physical Review A, 97 (2018), pp. 013816/1--013816/6, DOI 10.1103/PhysRevA.97.013816 .
    Abstract
    We study theoretically the interaction of temporal localized states in all fiber cavities and microresonator-based 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 Lugiato--Lefever model with the third order dispersion term is performed. Numerical solutions of the model equation are in close agreement with analytical predictions.

Contributions to Collected Editions

  • M. Kantner, Th. Koprucki, H.-J. Wünsche, U. Bandelow, Simulation of quantum dot based single-photon sources using the Schrödinger--Poisson-Drift-Diffusion-Lindblad system, in: Proceedings of the 24th International Conference on Simulation of Semiconductor Processes and Devices (SISPAD 2019), F. Driussi, ed., 2019, pp. 355--358.

  • M. Kantner, A generalized Scharfetter--Gummel scheme for degenerate and non-isothermal 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. 7--8.
    Abstract
    We present a highly accurate generalization of the Scharfetter--Gummel scheme for the discretization of the currentdensities in degenerate semiconductors under non-isothermalconditions. The underlying model relies on the Kelvin formula forthe Seebeck coefficient, which has the intriguing property that the?T-term in the electrical current density expressions vanishesexactly when passing to the drift-diffusion form ? even thoughthe thermoelectric cross-coupling is fully taken into account.

  • M. Kantner, Hybrid modeling of quantum light emitting diodes: Self-consistent coupling of drift-diffusion, Schrödinger--Poisson, 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 device-scale simulation of electrically driven solid state quantum light emitters, such as single-photon 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 self-consistently coupled the semi-classical drift-diffusion 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 light-matter interaction in the coupled quantum dot-photon system out of one box. In this paper, we extend our hybrid quantum-classical 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 single-photon emitting diode.

  • M. Kantner, Simulation of quantum light sources using the self-consistently coupled Schrödinger--Poisson-Drift-Diffusion--Lindblad 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. 15--16.
    Abstract
    The device-scale 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 quantum-classical modelsystem ? where we have coupled the drift-diffusion system witha Lindblad-type quantum master equation ? by including a self-consistent Schrödinger?Poisson problem. The latter describes the(quasi-)bound states of the quantum dot carriers. The extendedmodel allows to describe the bias-dependency 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 Nozaki--Bekki 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 fibre-based wavelength sweeping lasers are promising devices with a wide range of potential applications ranging from communications to life sciences. For example, Fourier Domain Mode-Locked (FDML) lasers, which are commonly used for Optical Coherence Tomography (OCT) imaging applications are long cavity lasers incorporating an intra-cavity 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 intra-cavity 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 Nozaki-Bekki holes (NBH) that circulate in the laser cavity. As a function of the injection current, the laser could operate in various regimes including bi-stability 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 multi-wavelength 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. 75--76.
    Abstract
    We show simulation results of a compact, inte-grated and tunable multi-wavelength 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 all-passive 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. 141--142.
    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 Raman-scattering can be completely compensated bythese means [4], which is supported by recent experiments [5].

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantum-classical 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. 1052603/1--1052603/6, 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 well-established fields of semi-classical 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 quantum-classical system obeys the fundamental laws of non-equilibrium 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 23--27, 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. 7--12, DOI 10.1007/978-3-030-25261-8_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 Ginzburg-Landau-type 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 time-delay 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.10/1--JTu5A.10/2, DOI 10.1364/BGPPM.2018.JTu5A.10 .
    Abstract
    We investigate the tuning of the wavelength of a micro-ring laser using on-chip feedback. We demonstrate tuning experimentally and numerically. The results also show that traveling-wave model is suitable for simulating complex laser configurations.

  • A.V. Kovalev, E.A. Viktorov, N. Rebrova, A.G. Vladimirov, G. Huyet, Theoretical study of mode-locked 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. 1068226/1--1068226/6.

  • 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 24--27, 2018, S. Andronic, ed., Technical University of Moldova, 2018, pp. 105--108.
    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 continuous-wave 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 high-power broad-area 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/1--105261H/10, DOI 10.1117/12.2289803 .
    Abstract
    The effect of current spreading on the lateral far-field divergence of high-power broad-area lasers is investigated with a time-dependent 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 drift-diffusion approach, however, the injected current density is obtained from the gradient of the quasi-Fermi potential of the holes, which solves a Laplace equation in the p-doped 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 far-field divergence is obtained. We conclude that an advanced modeling of the profiles of the injection current densities is necessary for a correct description of far-field blooming in broad-area 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. 87--88.

  • M. Radziunas, U. Bandelow, C. Brée, V. Raab, H. Wenzel, A. Zeghuzi, Modeling and simulation of high-power broad-area semiconductor lasers with optical feedback from different external cavities, in: 2018 IEEE International Semiconductor Laser Conference (ISLC 2018), Santa Fe, New Mexico, USA, 16--19 September 2018, Institute of Electrical and Electronics Engineers, Inc. (IEEE), 2018, pp. SuA4/1--SuA4/2.

  • M. Radziunas, J. Fuhrmann, A. Zeghuzi, H.-J. Wünsche, Th. Koprucki, H. Wenzel, U. Bandelow, Efficient coupling of heat flow and electro-optical models for simulation of dynamics in high-power broad-area 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. 91--92.

  • 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. 203--212, DOI 10.1007/978-3-319-64173-7_13 .
    Abstract
    Meanders are geometrical objects, defined by a non-self-intersecting 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, Multi-dimensional modeling and simulation of semiconductor nanophotonic devices, Preprint no. 2653, WIAS, Berlin, 2019, DOI 10.20347/WIAS.PREPRINT.2653 .
    Abstract, PDF (9836 kByte)
    Self-consistent modeling and multi-dimensional 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 multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.

  • CH. Schelte, A. Pimenov, A.G. Vladimirov, J. Javaloyes, S.V. Gurevich, Tunable Kerr frequency combs and temporal localized states in time-delayed Gires--Tournois 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 set-up 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 micro-cavity, operated in the Gires?Tournois regime, containing a Kerr medium with strong time-delayed 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 Dulac-Cherkas 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 Dulac-Cherkas 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 Dulac-Cherkas functions or on applying some factorized Dulac function.

  • S. Pickartz, The role of the self-steepening effect in soliton compression due to cross-phase 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 velocity-matched dispersive wave, in the so-called optical event horizon regime. We demonstrate that in this interaction scheme the self-steepening 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 self-steepening 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 Kerr-cavities 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 semiconductor-based fiber laser, and propose an approach to derive reduced delay-differential equation models taking into account the dispersion of the intracavity fiber delay line. Using these equations we perform the stability and bifurcation analysis of injection-locked 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 quantum-classical model that self-consistently couples van Roosbroeck's drift-diffusion system for classical charge transport with a Lindblad-type quantum master equation. The coupling is shown to obey fundamental principles of non-equilibrium 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 so-called 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 lowest-order 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 higher-order 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.

Talks, Poster

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

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

  • C. Brée, V. Raab, D. Gailevičius, V. Purlys, J. Montiel, G.G. Werner, K. Staliunas, A. Rathsfeld, U. Bandelow, M. Radziunas, Genetically optimized photonic crystal for spatial filtering of reinjection into broad-area diode lasers, CLEO/Europe-EQEC 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 high-power, broad-area diode lasers: Modeling, simulations, and experiments, CLEO/Europe-EQEC 2019, Munich, June 23 - 27, 2019.

  • S. Eydam, A. Gerdes, Extensive chaos, cluster and chimera states in globally-coupled Stuart--Landau systems, SFB 910: Workshop on ''Control of Self-Organizing Nonlinear Systems'', Lutherstadt Wittenberg, August 20 - 22, 2019.

  • M. Kantner, Hybrid modeling of quantum light emitting diodes: Self-consistent coupling of drift-diffusion, Schrödinger--Poisson, 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, Zuse-Institut Berlin, February 15, 2019.

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

  • U. Bandelow, Self-consistent thermal-opto-electronic model for the dynamics in high-power 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 high-power 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 high-power broad-area semiconductor lasers, Hotlas/Effilas project meeting, Ferdinand-Braun-Institut, 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, Phase-sensitive excitability of a limit cycle, SFB 910: Workshop on ''Control of Self-Organizing Nonlinear Systems'', August 20 - 22, 2019, SFB 910, Lutherstadt Wittenberg, August 21, 2019.

  • M. Wolfrum, Phase-sensitive 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 self-frequency shift, 4th International Conference on Wave Interaction (WIN-2018), April 3 - 7, 2018, Johannes Kepler Universität Linz, Austria, April 6, 2018.

  • S. Eydam, Bifurcations of mode-locked 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, Mode-locking in systems of globally coupled phase oscillators, International Conference on Control of Self-Organizing Nonlinear Systems, Warnemünde, September 9 - 13, 2018.

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantum-classical 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 quantum-classical modeling of quantum dot based single-photon 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 (MURPHYS-HSFS-2018), 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. WE-Heraeus Seminar: Delayed Complex Systems 2018, Bad Honnef, July 2 - 5, 2018.

  • A. Pimenov, Effect of chromatic dispersion in a delayed model of a mode-locked 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 NLS-type equations and selected solutions, 4th International Conference on Wave Interaction (WIN-2018), Johannes Kepler Universität Linz, Austria, April 4, 2018.

  • U. Bandelow, Semiconductor laser instabilities and dynamics emerging from mode degeneracy, International Workshop ''Synthetic Non-Hermitian 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 electro-optical models for simulation of dynamics in high-power broad-area 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 longitudinal-lateral periodic modulation of BALs to the quality of emitted beam, Project meeting of the BMBF-EffiLas/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 high-power 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 high-power broad area lasers with PhC filtering element, EUROSTARS project E!10524 HIP-Lasers meeting, May 22 - 23, 2018, Femtika, Vilnius, Lithuania, May 22, 2018.

  • M. Radziunas, Modeling and simulation of high-power broad-area 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 broad-area 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, Time-delay 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, Time-delay systems in multimode laser dynamics, 675. WE-Heraeus-Seminar ,,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, Phase-sensitive excitability of a limit cycle, International Conference on Control of Self-Organizing Nonlinear Systems, Warnemünde, September 9 - 13, 2018.

External Preprints

  • 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 laminar-turbulent 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