Publications

Monographs

  • S. Amiranashvili, Chapter 6: Hamiltonian Framework for Short Optical Pulses, in: New Approaches to Nonlinear Waves, E. Tobisch, ed., 908 of Lecture Notes in Physics, Springer International Publishing Switzerland, Cham, 2016, pp. 153--196, (Chapter Published).
    Abstract
    Physics of short optical pulses is an important and active research area in nonlinear optics. In what follows we theoretically consider the most extreme representatives of short pulses that contain only several oscillations of electromagnetic field. Description of such pulses is traditionally based on envelope equations and slowly varying envelope approximation, despite the fact that the envelope is not ?slow? and, moreover, there is no clear definition of such a ?fast? envelope. This happens due to another paradoxical feature: the standard (envelope) generalized nonlinear Schrödinger equation yields very good correspondence to numerical solutions of full Maxwell equations even for few-cycle pulses, a thing that should not be. In what follows we address ultrashort optical pulses using Hamiltonian framework for nonlinear waves. As it appears, the standard optical envelope equation is just a reformulation of general Hamiltonian equations. In a sense, no approximations are required, this is why the generalized nonlinear Schrödinger equation is so effective. Moreover, the Hamiltonian framework greatly contributes to our understanding of ''fast'' envelope, ultrashort solitons, stability and radiation of optical pulses. Even the inclusion of dissipative terms is possible making the Hamiltonian approach an universal theoretical tool also in extreme nonlinear optics.

Articles in Refereed Journals

  • A. Pimenov, S. Slepneva, G. Huyet, A.G. Vladimirov, Dispersive time-delay dynamical systems, Physical Review Letters, 118 (2017) pp. 193901, DOI 10.20347/WIAS.PREPRINT.2324 .
    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.

  • S. Rauch, H. Wenzel, M. Radziunas, M. Haas, G. Tränkle, H. Zimer, Impact of longitudinal refractive index change on the near-field width of high-power broad-area diode lasers, Applied Physics Letters, 110 (2017) pp. 263504/1--263504/5, DOI http://dx.doi.org/10.1063/1.4990531 .
    Abstract
    Typical for broad-area laser (BAL) diodes operating in a continuous-wave mode is a narrowing of the near-field (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 self-heating 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 current-dependent 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 three-dimensional thermo-electro-optic simulations indicate that a longitudinally homogeneous device temperature can reduce the front-facet load while keeping the beam quality unchanged compared with the experimental results.

  • I. Babushkin, C. Brée, Ch.M. Dietrich, A. Demircan, U. Morgner, A. Husakou, Terahertz and higher-order Brunel harmonics: From tunnel to multiphoton ionization regime in tailored fields, Journal of Modern Optics, (2017) pp. 1--10, DOI 10.1080/09500340.2017.1285066 .
    Abstract
    Brunel radiation appears as a result of a two-step process of photo-ionization 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 (so-called 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.

  • S. Pickartz, U. Bandelow, S. Amiranashvili, Asymptotically stable compensation of soliton self-frequency shift, Optics Letters, 42 (2017) pp. 1416--1419, DOI 10.20347/WIAS.PREPRINT.2343 .
    Abstract
    We report the cancellation of the soliton self-frequency shift in nonlinear optical fibers. A soliton which interacts with a group velocity matched low intensity dispersive pump pulse, experiences a continuous blue-shift in frequency, which counteracts the soliton selffrequency shift due to Raman scattering. The soliton self-frequency shift can be fully compensated by a suitably prepared dispersive wave.We quantify this kind of soliton-dispersive 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, Time-periodic boundary layer solutions to singularly perturbed parabolic problems, Journal of Differential Equations, 262 (2017) pp. 4823--4862, DOI 10.20347/WIAS.PREPRINT.2300 .
    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 time-periodic boundary layer solutions (which are allowed to be non-monotone 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. Hofmann, C. Brée, Adiabatic Floquet model for the optical response in femtosecond filaments, Journal of Physics B: Atomic, Molecular and Optical Physics, 49 (2016) pp. 205004/1--205004/12.
    Abstract
    The standard model of femtosecond filamentation is based on phenomenological assumptions which suggest that the ionization-induced carriers can be treated as free according to the Drude model, while the nonlinear response of the bound carriers follows the all-optical Kerr effect. Here, we demonstrate that the additional plasma generated at a multiphoton resonance dominates the saturation of the nonlinear refractive index. Since resonances are not captured by the standard model, we propose a modification of the latter in which ionization enhancements can be accounted for by an ionization rate obtained from non-Hermitian Floquet theory. In the adiabatic regime of long pulse envelopes, this augmented standard model is in excellent agreement with direct quantum mechanical simulations. Since our proposal maintains the structure of the standard model, it can be easily incorporated into existing codes of filament simulation.

  • M. Kantner, Th. Koprucki, Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures, Optical and Quantum Electronics, 48 (2016) pp. 543/1--543/7.
    Abstract
    At cryogenic temperatures the electron?hole plasma in semiconductors becomes strongly degenerate, leading to very sharp internal layers, extreme depletion in intrinsic domains and strong nonlinear diffusion. As a result, the numerical simulation of the drift?diffusion system suffers from serious convergence issues using standard methods. We consider a one-dimensional p-i-n diode to illustrate these problems and present a simple temperature-embedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forward-biased devices as they appear e.g. in optoelectronic applications. Moreover, the method can be applied to wide band gap semiconductors where similar numerical issues occur already at room temperature.

  • M. Kantner, U. Bandelow, Th. Koprucki, J.-H. Schulze, A. Strittmatter, H.-J. Wünsche, Efficient current injection into single quantum dots through oxide-confined pn-diodes, IEEE Transactions on Electron Devices, 63 (2016) pp. 2036--2042.
    Abstract
    Current injection into single quantum dots embedded in vertical pn-diodes featuring oxide apertures is analyzed in the low-injection regime suitable for single-photon emitters. Experimental and theoretical evidence is found for a rapid lateral spreading of the carriers after passing the oxide aperture in the conventional pin-design. By an alternative design employing p-doping up to the oxide aperture the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies, both, in the continuous wave and under pulsed excitation.

  • A. Pimenov, D. Rachinskii, Robust homoclinic orbits in planar systems with Preisach hysteresis operator, Journal of Physics: Conference Series, 727 (2016) pp. 012012/1--012012/15.
    Abstract
    We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically

  • I. Omelchenko, O. Omel'chenko, A. Zakharova, M. Wolfrum, E. Schöll, Tweezers for chimeras in small networks, Physical Review Letters, 116 (2016) pp. 114101/1--114101/5.
    Abstract
    We propose a control scheme which can stabilize and fix the position of chimera states in small networks. Chimeras consist of coexisting domains of spatially coherent and incoherent dynamics in systems of nonlocally coupled identical oscillators. Chimera states are generically difficult to observe in small networks due to their short lifetime and erratic drifting of the spatial position of the incoherent domain. The control scheme, like a tweezer, might be useful in experiments, where usually only small networks can be realized.

  • G. Slavcheva, A.V. Gorbach, A. Pimenov, Coupled spatial multimode solitons in microcavity wires, Phys. Rev. B., 94 (2016) pp. 245432/1--245432/13, DOI 10.1103/PhysRevB.94.245432 .
    Abstract
    A modal expansion approach is developed and employed to investigate and elucidate the nonlinear mechanism behind the multistability and formation of coupled multimode polariton solitons in microcavity wires. With pump switched on and realistic dissipation parameters, truncating the expansion up to the second-order wire mode, our model predicts two distinct coupled soliton branches: stable and unstable. Modulational stability of the stationary homogeneous solution and soliton branches stability are studied. Our simplified 1D model is in remarkably good agreement with the full 2D mean-field Gross-Pitaevskii model, reproducing correctly the soliton existence domain upon variation of pump amplitude and the onset of multistability.

  • N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J.M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiranashvili, C. Brée, G. Steinmeyer, C. Masoller, N.G.R. Broderick, A.F.J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F.T. Arecchi, S. Wabnitz, C.G. Tiofack, S. Coulibaly, M. Taki, Roadmap on optical rogue waves and extreme events, Journal of Optics, 18 (2016) pp. 1--37.
    Abstract
    The pioneering paper ``Optical rogue waves" by Solli et al (2007 Nature 450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older results and new discoveries has been undertaken, stimulated by the concept of ?optical rogue waves?. Presently, there may not by a unique view on how this new scientific term should be used and developed. There is nothing surprising when the opinion of the experts diverge in any new field of research. After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation. We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems. Theorists, in turn, have suggested many other situations when rogue waves may be observed. The strict definition of a rogue wave is still an open question. For example, it has been suggested that it is defined as ?an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses?. This definition (as suggested by a peer reviewer) is clear at the intuitive level and can be easily extended to the case of spatial beams although additional clarifications are still needed. An extended definition has been presented earlier by N Akhmediev and E Pelinovsky (2010 Eur. Phys. J. Spec. Top. 185 1?4). Discussions along these lines are always useful and all new approaches stimulate research and encourage discoveries of new phenomena. Despite the potentially existing disagreements, the scientific terms ?optical rogue waves? and ?extreme events? do exist. Therefore coordination of our efforts in either unifying the concept or in introducing alternative definitions must be continued. From this point of view, a number of the scientists who work in this area of research have come together to present their research in a single review article that will greatly benefit all interested parties of this research direction. Whether the authors of this ``roadmap" have similar views or different from the original concept, the potential reader of the review will enrich their knowledge by encountering most of the existing views on the subject. Previously, a special issue on optical rogue waves (2013 J. Opt. 15 060201) was successful in achieving this goal but over two years have passed and more material has been published in this quickly emerging subject. Thus, it is time for a roadmap that may stimulate and encourage further research.

  • A. Ankiewicz, D.J. Kedziora, A. Chowdury, U. Bandelow, N. Akhmediev, Infinite hierarchy of nonlinear Schrödinger equations and their solutions, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 93 (2016) pp. 012206/1--012206/10.
    Abstract
    We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that ?even- order? equations in the set affect phase and ?stretching factors? in the solutions, while ?odd-order? equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

  • R.M. Arkhipov, T. Habruseva, A. Pimenov, M. Radziunas, G. Huyet, A.G. Vladimirov, Semiconductor mode-locked lasers with coherent dual mode optical injection: Simulations, analysis and experiment, Journal of the Optical Society of America. B, 33 (2016) pp. 351--359.
    Abstract
    Using a delay differential equations model we study the dynamics of a passively mode-locked semiconductor laser with dual frequency coherent optical injection. The locking regions where the laser pulse repetition rate is synchronized to the separation of the two injected frequencies were calculated numerically and measured experimentally. Asymptotic analysis performed in the limit of the small injection field amplitude revealed the dependence of the locking regions on the model parameters, such as optical bandwith, absorber recovery time and linear losses.

  • I. Babushkin, S. Amiranashvili, C. Brée, U. Morgner, G. Steinmeyer, A. Demircan, The effect of chirp on pulse compression at a group velocity horizon, IEEE Photonics Journal, 8 (2016) pp. 7803113/1--7803113/14, DOI 10.1109/JPHOT.2016.2570001 .
    Abstract
    Group-velocity matched cross-phase modulation between a fundamental soliton and a dispersive wave-packet has been previously suggested for optical switching applications similar to an optical transistor. Moreover, the nonlinear interaction in the resulting groupvelocity horizon can be exploited for adiabatic compression of the soliton down into the fewcycle regime. Here we show that both mechanisms can be combined. In such a transient compressor, parameters of the dispersive wave may then serve to actively control the soliton compression and adjust the pulse duration in the presence of disturbances. While a certain amount of control is already enabled by the delay between soliton and dispersive wave, the means of controlling the compression process are substantially enhanced by additionally manipulating the chirp of the dispersive wave. Moreover, controlling the chirp of the dispersive wave also enables correction for limitations of the compression scheme due to a self-frequency shift of the soliton or for uncompensated dispersion in the scheme. This substantially widens the practicality of the compression scheme and other applications of the highly efficient nonlinear interaction at the group-velocity horizon.

  • D. Davino, P. Krejčí, A. Pimenov, D. Rachinskii, C. Visone, Analysis of an operator-differential model for magnetostrictive energy harvesting, Communications in Nonlinear Science and Numerical Simulation, 39 (2016) pp. 504--519.
    Abstract
    We present a model of, and analysis of an optimization problem for, a magnetostrictive harvesting device which converts mechanical energy of the repetitive process such as vibrations of the smart material to electrical energy that is then supplied to an electric load. The model combines a lumped differential equation for a simple electronic circuit with an operator model for the complex constitutive law of the magnetostrictive material. The operator based on the formalism of the phenomenological Preisach model describes nonlinear saturation effects and hysteresis losses typical of magnetostrictive materials in a thermodynamically consistent fashion. We prove well-posedness of the full operator-differential system and establish global asymptotic stability of the periodic regime under periodic mechanical forcing that represents mechanical vibrations due to varying environmental conditions. Then we show the existence of an optimal solution for the problem of maximization of the output power with respect to a set of controllable parameters (for the periodically forced system). Analytical results are illustrated with numerical examples of an optimal solution.

  • K. Panajotov, D. Puzyrev, A.G. Vladimirov, S.V. Gurevich, M. Tlidi, Impact of time-delayed feedback on spatiotemporal dynamics in the Lugiato--Lefever model, Physical Review A, 93 (2016) pp. 043835/1--043835/7.
    Abstract
    We analyze the impact of delayed optical feedback (OF) on the spatiotemporal dynamics of the Lugiato-Lefever model. First, we carry out linear stability analysis and reveal the role of the OF strength and phase on the shape of the bistable curve as well as on Turing, Andronov-Hopf, and traveling-wave instability regions. Further, we demonstrate how the OF impacts the spatial dynamics by shifting the regions with different spatial eigenvalue spectra. In addition, we reveal a clustering behavior of cavity solitons as a function of the OF strength at fixed OF phase. Depending on the feedback parameters, OF can also induce a drift bifurcation of a stationary cavity soliton, as well as an Andronov-Hopf bifurcation of a drifting soliton. We present an analytical expression for the threshold of the drift bifurcation and show that above a certain value of the OF strength the system enters a region of spatiotemporal chaos.

  • D. Puzyrev, A.G. Vladimirov, S.V. Gurevich, S. Yanchuk, Modulational instability and zigzagging of dissipative solitons induced by delayed feedback, Physical Review A, 93 (2016) pp. 041801/1--041801/5.
    Abstract
    We report a destabilization mechanism of localized solutions in spatially extended systems which is induced by delayed feedback. Considering a model of a wide-aperture laser with a saturable absorber and delayed optical feedback, we demonstrate the appearance of multiple coexistent laser cavity solitons. We show that at large delays apart from the drift and phase instabilities the soliton can exhibit a delay-induced modulational instability associated with the translational neutral mode. The combination of drift and modulational instabilities produces a zigzagging motion of the solitons, which are either periodic, with the period close to the delay time, or chaotic, with low-frequency fluctuations in the direction of the soliton motion. The same type of modulational instability is demonstrated for localized solutions of the cubic-quintic complex Ginzburg-Landau equation.

  • S. Birkholz, C. Brée, I. Veselić, A. Demircan, G. Steinmeyer, Ocean rogue waves and their phase space dynamics in the limit of a linear interference model, Scientific Reports, 6 (2016) pp. 35207/1--35207/8.
    Abstract
    We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.

  • G. Steinmeyer, C. Brée, A. Demircan, Rogue waves: Will a forecast ever be possible?, SPIE Newsroom, March 7 (2016) pp. 1--2, DOI 10.1117/2.1201602.00636 .

  • S. Pickartz, U. Bandelow, S. Amiranashvili, Adiabatic theory of solitons fed by dispersive waves, Physical Review A, 94 (2016) pp. 033811/1--033811/12.
    Abstract
    We consider scattering of small-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analogue of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from Quantum Mechanics, we give a quantitative account for the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, for the first time we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.

  • S. Pickartz, U. Bandelow, S. Amiranashvili, Efficient all-optical control of solitons, Optical and Quantum Electronics, 48 (2016) pp. 503/1--503/7.
    Abstract
    We consider the phenomenon of an optical soliton controlled (eg. amplified) by a much weaker second pulse which is efficiently scattered at the soliton. An important problem in this context is to quantify the small range of parameters at which the interaction takes place. This has been achieved by using adiabatic ODEs for the soliton characteristics, which is much faster than an empirical scan of the full propagation equations for all parameters in question.

  • C. Brée, G. Steinmeyer, I. Babushkin, U. Morgner, A. Demircan, Controlling formation and suppression of fiber-optical rogue waves, Optics Letters, 41 (2016) pp. 3515--3518.
    Abstract
    Fiber-optical rogue waves appear as rare but extreme events during optical supercontinuum generation in photonic crystal fibers. This process is typically initiated by the decay of a high-order fundamental soliton into fundamental solitons. Collisions between these solitons as well as with dispersive radiation affect the soliton trajectory in frequency and time upon further propagation. Launching an additional dispersive wave at carefully chosen delay and wavelength enables statistical manipulation of the soliton trajectory in such a way that the probability of rogue wave formation is either enhanced or reduced. To enable efficient control, parameters of the dispersive wave have to be chosen to allow trapping of dispersive radiation in the nonlinear index depression created by the soliton. Under certain conditions, direct manipulation of soliton properties is possible by the dispersive wave. In other more complex scenarios, control is possible via increasing or decreasing the number of intersoliton collisions. The control mechanism reaches a remarkable efficiency, enabling control of relatively large soliton energies. This scenario appears promising for highly dynamic all-optical control of supercontinua.

  • O. Omel'chenko, M. Wolfrum, Is there an impact of small phase lags in the Kuramoto model?, Chaos. An Interdisciplinary Journal of Nonlinear Science, 26 (2016) pp. 094806/1--094806/6.
    Abstract
    We discuss the influence of small phase lags on the synchronization transitions in the Kuramoto model for a large inhomogeneous population of globally coupled phase oscillators. Without a phase lag, all unimodal distributions of the natural frequencies give rise to a classical synchronization scenario, where above the onset of synchrony at the Kuramoto threshold there is an increasing synchrony for increasing coupling strength. We show that already for arbitrarily small phase lags there are certain unimodal distributions of natural frequencies such that for increasing coupling strength synchrony may decrease and even complete incoherence may regain stability. Moreover, our example allows a qualitative understanding of the mechanism for such non-universal synchronization transitions.

  • M. Radziunas, New multi-mode delay differential equation model for lasers with optical feedback, Optical and Quantum Electronics, 48 (2016) pp. 1--9.
    Abstract
    In this paper, we discuss the relations between the spatially-distributed traveling wave, Lang-Kobayashi, and a new multi-mode delay differential equation models for Fabry-Perot type semiconductor diode lasers with an external optical feedback. All these models govern the dynamics of the slowly varying complex amplitudes of the optical fields and carrier density. To compare the models, we calculate the cavity modes determined by the threshold carrier density and optical frequency of the steady states in all three models. These calculations show that the Lang-Kobayashi type model is in good agreement with the traveling wave model only for the small feedback regimes, whereas newly derived multi-mode delay differential equation model remains correct even at moderate and large optical feedback regimes.

  • M. Wolfrum, S. Gurevich, O. Omel'chenko, Turbulence in the Ott--Antonsen equation for arrays of coupled phase oscillators, Nonlinearity, 29 (2016) pp. 257--270.
    Abstract
    In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integro-differential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it has been reported that in the spatially extended case at the synchronization threshold there appear partially coherent plane waves with different wave numbers, which are organized in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves. We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region.

Contributions to Collected Editions

  • M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Modeling and simulation of injection dynamics for quantum dot based single-photon sources, in: Proceedings of the 16th International Conference on Numerical Simulation of Optoelectronic Devices, J. Piprek, Ch. Poulton, M. Steel, M. DE Sterke, eds., IEEE Conference Publications Management Group, Piscataway, 2016, pp. 219--220.
    Abstract
    Single semiconductor quantum dots embedded in p-i-n diodes have been demonstrated to operate as electrically driven single-photon sources. By means of numerical simulations one can explore the limitations in the carrier injection dynamics and further improve the device technology. We propose a comprehensive modeling approach coupling the macroscopic transport of bulk carriers with an open quantum system to describe the essential physics of such devices on multiple scales.

  • M. Kantner, U. Bandelow, Th. Koprucki, H.-J. Wünsche, Multi-scale modelling and simulation of single-photon sources on a device level, in: Euro-TMCS II -- Theory, Modelling & Computational Methods for Semiconductors, 7th -- 9th December 2016, Tyndall National Institute, University College Cork, Ireland, E. O'Reilly, S. Schulz, S. Tomic, eds., Tyndall National Institute, 2016, pp. 65.

  • M. Kantner, U. Bandelow, Th. Koprucki, J.-H. Schulze, A. Strittmatter, H.-J. Wünsche, On current injection into single quantum dots through oxide-confined PN-diodes, in: Proceedings of the 16th International Conference on Numerical Simulation of Optoelectronic Devices, J. Piprek, Ch. Poulton, M. Steel, M. DE Sterke, eds., IEEE Conference Publications Management Group, Piscataway, 2016, pp. 215--216.
    Abstract
    Current injection into single quantum dots embedded in vertical pn-diodes featuring oxide apertures is essential to the technological realization of single-photon sources. This requires efficient electrical pumping of sub-micron sized regions under pulsed excitation to achieve control of the carrier population of the desired quantum dots. We show experimentl and theoretical evidence for a rapid lateral spreading of the carriers after passing the ocide aperture in the conventional p-i-n-design in the low-injection regime suitable for single-photon emitters. By an alternative design employing p-doping up to the oxide aperture the current spreading can be suppressed resulting in an enhanced current confinement and increased injection efficiencies.

  • W.W. Ahmed, S. Kumar, R. Herrero, M. Botey, M. Radziunas, K. Staliunas, Suppression of modulation instability in pump modulated flat-mirror VECSELs, in: Nonlinear Optics and its Applications IV, B.J. Eggleton, N.G.R. Broderick, A.L. Gaeta, eds., 9894 of Proceedings of SPIE, SPIE Digital Library, 2016, pp. 989406/1--989406/7.
    Abstract
    We show that modulation instability (MI) can be suppressed in vertical external cavity surface emitting lasers (VECSELs) by introducing a periodic spatio-temporal modulation of the pump profile which in turn allows a simple flat-mirror configuration. The stability analysis of such pump modulated flat-mirror VECSELs is performed by a modified Floquet method and results are confirmed by full numerical integration of the model equations. It is found that the amplitude of the modulation as well as its spatial and temporal frequencies are crucial parameters for high spatial beam quality emission. We identify regions of complete and partial stabilization in parameter space for VECSELs with different external cavity lengths. The proposed method is shown to efficiently stabilize VECSELs with cavity lengths ranging from millimetres up to centimetres. However, the applicability of this method becomes limited for micro-meter-long cavities due to strong intrinsic relaxation oscillations.

  • TH. Butler, D. Goulding, S. Slepneva, B. O'Shaughnessy, B. Kelleher, S.P. Hegarty, H.Ch. Lyu, K. Karnowski, M. Wojtkowski, A.G. Vladimirov, G. Huyet, Coherence properties of fast frequency swept lasers revealed via full electric field reconstruction, in: Physics and Simulation of Optoelectronic Devices XXIV, B. Witzigmann, M. Osiński, Y. Arakawa, eds., 9742, Proceedings of SPIE, Bellingham, Washington, 2016, pp. 97420K/1--97420K/7.
    Abstract
    A novel, time-resolved interferometric technique is presented allowing the reconstruction of the complex electric field output of a fast frequency swept laser in a single-shot measurement. The power of the technique is demonstrated by examining a short cavity swept source designed for optical coherence tomography applications, with a spectral bandwidth of 18 THz. This novel analysis of the complete electric field reveals the modal structure and modal evolution of the device as well as providing a time-resolved real-time characterization of the optical spectrum, linewidth and coherence properties of a dynamic rapidly swept laser.

  • M. Kretschmar, C. Brée, T. Nagy, H. Kurz, U. Morgner, M. Kovacev, High-order harmonics as a nonlinear tool to track pulse-dynamics along a filament, in: High-Brightness Sources and Light-Driven Interactions, OSA Technical Digest (Online), Optical Society of America, Washington, DC, 2016, pp. HS4B.5/1--HS4B.5/3.
    Abstract
    We report on the direct observation of pulse dynamics along a filament and its connection to directly emitted high-order harmonic radiation, whose nonlinear nature is used to gain further insight into the filamentary propagation dynamics.

  • S. Kumar, W. Ahmed, R. Herrero, M. Botey, M. Radziunas, K. Staliunas, Stabilization of broad area semiconductor amplifiers by spatially modulated potentials, in: Nonlinear Dynamics: Materials, Theory and Experiments, M. Tlidi, M. Clerc, eds., 173 of Springer Proceedings in Physics, Springer International Publishing Switzerland, Cham, 2016, pp. 139--151.
    Abstract
    We propose the stabilization of the output beam of Broad Area Semiconductor (BAS) amplifiers through the introduction of a spatially periodic modulated potential. We show that a periodic modulation of the pump profile in transverse and longitudinal directions, under certain ?resonance? condition, can solve two serious problems of BAS amplifiers (and possibly lasers), which are (i) the lack of an intrinsic spatial mode selection mechanism in linear amplification regimes and (ii) the modulation instability (also called Bespalov-Talanov instability) in nonlinear regimes. The elimination of these two drawbacks can significantly improve the spatial quality of the emitted beam in BAS amplifiers.

  • D. Turaev, A.G. Vladimirov, S. Zelik, Interaction of spatial and temporal cavity solitons in mode-locked lasers and passive cavities, in: Laser Optics (LO), 2016 International Conference, IEEE, New York, 2016, pp. 37628.
    Abstract
    We study interaction of well-separated localized structures of light in the presence of periodic perturbations. Oscillating localized structures were found to emit weakly decaying dispersive waves leading to a strong enhancement of the interaction and formation of new types of bound states. We discuss the applicability of our analytical results to the interpretation of experimental and numerical data reported earlier.

  • G. Steinmeyer, S. Birkholz, C. Brée, A. Demircan, Nonlinear time series analysis: Towards an effective forecast of rogue waves, in: Real-time Measurements, Rogue Events, and Emerging Applications, B. Jalali, S.K. Turitsyn, D.R. Solli, J.M. Dudley, eds., 9732 of Proceedings of SPIE, Society of Photo-Optical Instrumentation Engineers (SPIE), 2016, pp. 973205/1--973205/6.
    Abstract
    Rogue waves are extremely large waves that exceed any expectation based on long-term observation and Gaussian statistics. Ocean rogue waves exceed the significant wave height in the ocean by a factor 2. Similar phenomena have been observed in a multiplicity of optical systems. While the optical systems show a much higher frequency of rogue events than the ocean, it appears nevertheless questionable what conclusions can be drawn for the prediction of ocean rogue waves. Here we tackle the problem from a different perspective and analyze the predictability of rogue events in two optical systems as well as in the ocean using nonlinear time-series analysis. Our analysis is exclusively based on experimental data. The results appear rather surprising as the optical rogue wave scenario of fiber-based supercontinuum generation does not allow any prediction whereas real ocean rogue waves and a multifilament scenario do bear a considerable amount of determinism, which allows, at least in principle, the prediction of extreme events. It becomes further clear that there exist two fundamentally different types of rogue-wave supporting systems. One class of rogue waves is obviously seeded by quantum fluctuations whereas in the other class, linear random interference of waves seems to prevail.

  • S. Pickartz, U. Bandelow, S. Amiranashvili, Numerical optimization of all-optical switching, in: Proceedings of the 16th International Conference on Numerical Simulation of Optoelectronic Devices, J. Piprek, Ch. Poulton, M. Steel, M. DE Sterke, eds., IEEE Conference Publications Management Group, Piscataway, 2016, pp. 189--190.
    Abstract
    A possibility to control an optical soliton by a much weaker second pulse that is scattered on the soliton attracted considerable attention recently. An important problem here is to quantify the small range of parameters at which the interaction takes place. This has been achieved by using adiabatic ODEs for the soliton characteristics, which is much faster than a scan of the full propagation equations for all parameters in question.

  • C. Brée, I. Babushkin, U. Morgner, A. Demircan, Collapse regularization of filaments by resonant radiation, in: Conference on Lasers and Electro-Optics, OSA Technical Digest (online), Optical Society of America, Washington, DC, 2016, pp. JW2A.60/1--JW2A.60/2.
    Abstract
    We show that the transfer of optical power via emission of resonant radiation plays an important role for regularizing the optical collapse enabling stable filament propagation of high-power near-infrared pulses in bulk silica.

  • M. Radziunas, A multi-mode delay differential equation model for lasers with optical feedback, in: Proceedings of the 16th International Conference on Numerical Simulation of Optoelectronic Devices, J. Piprek, Ch. Poulton, M. Steel, M. DE Sterke, eds., IEEE Conference Publications Management Group, Piscataway, 2016, pp. 13--14.
    Abstract
    In this work, we introduce a new multi-mode (MM) delay differential equation (DDE) model suited for simulations of the Fabry-Perot type diode laser with an optical feedback from the external cavity (EC).

  • M. Radziunas, Modeling and simulations of edge-emitting broad-area semiconductor lasers and amplifiers, in: Parallel Processing and Applied Mathematics -- 11th International Conference, PPAM 2015 Krakow, Poland, September 6--9, 2015, Revised Selected Papers, Part II, R. Wyrzykowski, E. Deelman, J. Dongarra, K. Karczewski, J. Kitowski, K. Wiatr, eds., 9574 of Lecture Notes in Computer Science, Springer International Publishing AG Switzerland, Cham, 2016, pp. 269--276.
    Abstract
    A (2+1)-dimensional partial differential equation model describing spatial-lateral dynamics of edge-emitting broad-area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is implemented on a parallel computing cluster. Numerical integration of the model equations is used for optimizing of existing devices with respect to the emitted beam quality, as well as for creating and testing of novel device design concepts.

  • A.G. Vladimirov, G. Huyet, A. Pimenov, Delay differential models in multimode laser dynamics: Taking chromatic dispersion into account, in: Semiconductor Lasers and Laser Dynamics VII, 9892 of Proceedings of SPIE, SPIE, Bellingham, Washington, 2016, pp. 98920I/1--98920I/7.
    Abstract
    A set of differential equations with distributed delay is derived for modeling of multimode ring lasers with intracavity chromatic dispersion. Analytical stability analysis of continuous wave regimes is performed and it is demonstrated that sufficiently strong anomalous dispersion can destabilize these regimes. © (2016) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Preprints, Reports, Technical Reports

  • M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantum-classical modeling of quantum dot devices, Preprint no. 2412, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2412 .
    Abstract, PDF (5602 kByte)
    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 well-established fields of semi-classical 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 quantum-classical 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 single-photon source based on a single quantum dot in the stationary and transient operation regime.

  • T. Schemmelmann, F. Tabbert, A. Pimenov, A.G. Vladimirov, S.V. Gurevich, Delayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber, Preprint no. 2400, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2400 .
    Abstract, PDF (2106 kByte)
    We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed 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 mode-locking regime in a broad-area laser with a single longitudinal mode.

  • C. Brée, I. Babushkin, U. Morgner, A. Demircan, Regularizing aperiodic cycles of resonant radiation in filament light bullets, Preprint no. 2394, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2394 .
    Abstract, PDF (3877 kByte)
    We demonstrate an up to now unrecognized and very effective mechanism which prevents filament collapse and allows persistent self-guiding propagation retaining larg portion of the optical energy on-axis 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 photo-generated plasma, thus allowing to excite new frequencies in the spectral ranges which are otherwise difficult to access.

  • A.P. Willis, Y. Duguet, O.E. Omel'chenko, M. Wolfrum, Surfing the edge: Finding nonlinear solutions using feedback control, Preprint no. 2389, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2389 .
    Abstract, PDF (587 kByte)
    Many transitional wall-bounded shear flows are characterised by the coexistence in state-space 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 Navier--Stokes 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.

  • 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 non-planar microcavity wires in the driven-dissipative regime [15]. We find that the typical microcavity optical bistability evolves into multi-stability upon variation of the model parameters. The origin of the multi-stability is discussed in detail. We apply linear perturbation analysis to modulational instabilities, and identify conditions for localisation of composite multi-mode 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. Angulo-Garcia, 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 pre-synaptic 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 Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic 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 post-synaptic 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.

  • D. Angulo-Garcia, S. Luccioli, S. Olmi, A. Torcini, Neurons' death and rebirth in sparse heterogeneous inhibitory networks, Preprint no. 2306, WIAS, Berlin, 2016.
    Abstract, PDF (6118 kByte)
    Inhibition is a key aspect of neural dynamics playing a fundamental role for the emergence of neural rhythms and the implementation of various information coding strategies. Inhibitory populations are present in several brain structures and the comprehension of their dynamics is strategical for the understanding of neural processing. In this paper, we discuss a general mechanism present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reactivation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neurons? death). The introduction of a sparse connectivity in the network is able to reverse the action of inhibition, i.e. a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of the neurons (neurons? rebirth). Specifically, for small synaptic strengths, one observes an asynchronous activity of nearly independent supra-threshold neurons. By increasing the inhibition, a transition occurs towards a regime where the neurons are all effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain this transition from a mean-driven to a fluctuation-driven regime by deriving an analytic mean field approach able to provide the fraction of active neurons together with the first two moments of the firing time distribution. We show that, by varying the synaptic time scale, the mechanism underlying the reported phenomenon remains unchanged. However, for sufficiently slow synapses the effect becomes dramatic. For small synaptic coupling the fraction of active neurons is frozen over long times and their firing activity is perfectly regular. For larger inhibition the active neurons display an irregular bursting behaviour induced by the emergence of correlations in the current fluctuations. In this latter regime the model gives predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.

  • S. Olmi, A. Torcini, Chimera states in pulse coupled neural networks: The influence of dilution and noise, Preprint no. 2305, WIAS, Berlin, 2016.
    Abstract, PDF (706 kByte)
    We analyse the possible dynamical states emerging for two symmetrically pulse coupled populations of leaky integrate-and-fire neurons. In particular, we observe broken symmetry states in this set-up: namely, breathing chimeras, where one population is fully synchronized and the other is in a state of partial synchronization (PS) as well as generalized chimera states, where both populations are in PS, but with different levels of synchronization. Symmetric macroscopic states are also present, ranging from quasi-periodic motions, to collective chaos, from splay states to population anti-phase partial synchronization. We then investigate the influence disorder, random link removal or noise, on the dynamics of collective solutions in this model. As a result, we observe that broken symmetry chimeralike states, with both populations partially synchronized, persist up to 80% of broken links and up to noise amplitudes ' 8% of threshold-reset distance. Furthermore, the introduction of disorder on symmetric chaotic state has a constructive effect, namely to induce the emergence of chimera-like states at intermediate dilution or noise level. 1 Introduction

  • O. Omel'chenko, L. Recke, V. Butuzov, N. Nefedov, Time-periodic boundary layer solutions to singularly perturbed parabolic problems, Preprint no. 2300, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2300 .
    Abstract, PDF (269 kByte)
    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 time-periodic boundary layer solutions (which are allowed to be non-monotone 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. Kantner, Th. Koprucki, Numerical simulation of carrier transport in semiconductor devices at cryogenic temperatures, Preprint no. 2296, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2296 .
    Abstract, PDF (1445 kByte)
    At cryogenic temperatures the electron-hole plasma in semiconductor materials becomes strongly degenerate, leading to very sharp internal layers, extreme depletion in intrinsic domains and strong nonlinear diffusion. As a result, the numerical simulation of the drift-diffusion system suffers from serious convergence issues using standard methods. We consider a one-dimensional p-i-n diode to illustrate these problems and present a simple temperature-embedding scheme to enable the numerical simulation at cryogenic temperatures. The method is suitable for forward-biased devices as they appear e.g. in optoelectronic applications.

  • M. Radziunas, A multi-mode delay differential equation model for lasers with optical feedback, Preprint no. 2294, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2294 .
    Abstract, PDF (449 kByte)
    In this paper, we discuss the relations between the spatially-distributed traveling wave, Lang-Kobayashi, and a new multi-mode delay differential equation models for Fabry-Perot type semiconductor diode lasers with an external optical feedback. All these models govern the dynamics of the slowly varying complex amplitudes of the optical fields and carrier density. To compare the models, we calculate the cavity modes determined by the threshold carrier density and optical frequency of the steady states in all three models. These calculations show that the Lang-Kobayashi type model is in good agreement with the traveling wave model only for the small feedback regimes, whereas newly derived multi-mode delay differential equation model remains correct even at moderate and large optical feedback regimes.

  • M. Radziunas, Modeling and efficient simulations of broad-area edge-emitting semiconductor lasers and amplifiers, Preprint no. 2292, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2292 .
    Abstract, PDF (395 kByte)
    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.

  • K.R. Schneider, A. Grin, Construction of generalized pendulum equations with prescribed maximum number of limit cycles of the second kind, Preprint no. 2272, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2272 .
    Abstract, PDF (229 kByte)
    Consider a class of planar autonomous differential systems with cylindric phase space which represent generalized pendulum equations. We describe a method to construct such systems with prescribed maximum number of limit cycles which are not contractible to a point (limit cycles of the second kind). The underlying idea consists in employing Dulac-Cherkas functions. We also show how this approach can be used to control the bifurcation of multiple limit cycles.

  • P. Farrell, N. Rotundo, D.H. Doan, M. Kantner, J. Fuhrmann, Th. Koprucki, Numerical methods for drift-diffusion models, Preprint no. 2263, WIAS, Berlin, 2016.
    Abstract, PDF (4768 kByte)
    The van Roosbroeck system describes the semi-classical transport of free electrons and holes in a self-consistent electric field using a drift-diffusion approximation. It became the standard model to describe the current flow in semiconductor devices at macroscopic scale. Typical devices modeled by these equations range from diodes, transistors, LEDs, solar cells and lasers to quantum nanostructures and organic semiconductors. The report provides an introduction into numerical methods for the van Roosbroeck system. The main focus lies on the Scharfetter-Gummel finite volume discretization scheme and recent efforts to generalize this approach to general statistical distribution functions.

  • M. Radziunas, Traveling wave modeling of nonlinear dynamics in multisection semiconductor lasers, Preprint no. 2261, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2261 .
    Abstract, PDF (1980 kByte)
    A hierarchy of 1 (time) + 1 (space) dimensional first-order 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.

  • A.G. Vladimirov, G. Huyet, A. Pimenov, Effect of chromatic dispersion on multimode laser dynamics: Delay differential model, Preprint no. 2240, WIAS, Berlin, 2016.
    Abstract, PDF (1463 kByte)
    A set of differential equations with distributed delay is derived for modeling of multimode ring lasers with intracavity chromatic dispersion. Analytical stability analysis of continuous wave regimes is performed and it is demonstrated that sufficiently strong anomalous dispersion can destabilize these regimes.

  • K.R. Schneider, A. Grin, Study of the bifurcation of a multiple limit cycle of the second kind by means of a Dulac--Cherkas function: A case study, Preprint no. 2226, WIAS, Berlin, 2016.
    Abstract, PDF (174 kByte)
    We consider a generalized pendulum equation depending on the scalar parameter $mu$ having for $mu=0$ a limit cycle $Gamma$ of the second kind and of multiplicity three. We study the bifurcation behavior of $Gamma$ for $-1 le mu le (sqrt5+3)/2$ by means of a Dulac-Cherkas function.

  • M. Hofmann, C. Brée, Adiabatic Floquet model for the optical response in femtosecond filaments, Preprint no. 2217, WIAS, Berlin, 2016.
    Abstract, PDF (398 kByte)
    The standard model of femtosecond filamentation is based on phenomenological assumptions which suggest that the ionization-induced carriers can be treated as free according to the Drude model, while the nonlinear response of the bound carriers follows the all-optical Kerr effect. Here, we demonstrate that the additional plasma generated at a multiphoton resonance dominates the saturation of the nonlinear refractive index. Since resonances are not captured by the standard model, we propose a modification of the latter in which ionization enhancements can be accounted for by an ionization rate obtained from non-Hermitian Floquet theory. In the adiabatic regime of long pulse envelopes, this augmented standard model is in excellent agreement with direct quantum mechanical simulations. Since our proposal maintains the structure of the standard model, it can be easily incorporated into existing codes of filament simulation.

  • M. Radziunas, Mathematical modeling and numerical simulations of diode lasers with micro-integrated external resonators, Technical Report no. 15, WIAS, Berlin, 2016.
    Abstract
    This report summarizes our scientific activities within the project MANUMIEL (BMBF Program ``Förderung der Wissenschaftlich-Technologischen Zusammenarbeit (WTZ) mit der Republik Moldau'', FKZ 01DK13020A). Namely, we discuss modeling of external cavity diode lasers, numerical simulations and analysis of these devices using the software package LDSL-tool, as well as the development of this software.

Talks, Poster

  • S. Eydam, Phase oscillator mode-locking, Forschungsseminar ``Applied Dynamical Systems", TU Berlin, June 14, 2017.

  • M. Kantner, Modeling of quantum dot based single-photon LEDs on a device level, MATHEON Workshop 10th Annual Meeting ``Photonic Devices'', February 9 - 10, 2017, Konrad-Zuse-Zentrum für Informationstechnik Berlin, February 10, 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.

  • U. Bandelow, Applied mathematical research in photonics at WIAS, Bosch-WIAS Workshop, WIAS, Berlin, June 13, 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, Feedback-operator 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, Szeged, 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, Introduction to chimera states, Seminar of the Scientific Computing Laboratory, Institue of Physics, University of Belgrade, 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, Szeged, 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. Wolfrum, Eine erstaunlich einfache Methode zur Berechnung des Sinus aus dem 16ten Jahrhundert, 22. Berliner Tag der Mathematik, Humboldt-Universität zu Berlin, April 22, 2017.

  • M. Wolfrum, Synchronization transitions ins 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.

  • S. Amiranashvili, Extreme solitons in optical fibers, Workshop on Abnormal Wave Events, University of Nice Sophia Antipolis, Nice, France, June 15, 2016.

  • S. Amiranashvili, How to become a champion soliton, International Conference on Wave Interaction (WIN-2016), Johannes Kepler Universität Linz, Austria, April 27, 2016.

  • S. Eydam, Mode-locking in systems of coupled phase oscillators, Seminar Applied Dynamical Systems, Technische Universität Berlin, Berlin, July 13, 2016.

  • S. Eydam, Mode-locking in systems of phase oscillators with higher harmonic coupling, International Conference on Control of Complex Systems and Networks, SFB 910 ``Control of Self-Organizing Nonlinear Systems: Theoretical Methods and Concepts of Application'', Heringsdorf/Usedom, September 4 - 8, 2016.

  • S. Eydam, Mode-locking in systems of phase oscillators with higher harmonic interaction, Workshop on Synchronization and Oscillators with Generalized Coupling, Exeter, UK, April 20 - 22, 2016.

  • M. Kantner, Modeling and simulation of carrier dynamics in quantum dot based single-photon sources, Nonlinear Dynamics in Semiconductor Lasers, WIAS, Berlin, June 15, 2016.

  • M. Kantner, Modeling and simulation of injection dynamics for quantum dot based single-photon sources, 16th International Conference on Numerical Simulation of Optoelectronic Devices, July 11 - 15, 2016, University of Sydney, Sydney, Australia.

  • M. Kantner, Multi-scale modeling and numerical simulation of single-photon emitters, Matheon Workshop--9th Annual Meeting ``Photonic Devices", Zuse Institut, Berlin, March 3, 2016.

  • M. Kantner, Multi-scale modelling and simulation of single-photon sources on a device level, Euro--TMCS II Theory, Modelling & Computational Methods for Semiconductors, Tyndall National Institute and University College Cork, Cork, Ireland, December 9, 2016.

  • A. Pimenov, Effect of anomalous dispersion on the dynamics of FDML lasers, Nonlinear Dynamics in Semiconductor Lasers, WIAS, Berlin, June 17, 2016.

  • A. Pimenov, Numerical analysis of dissipative phase solitons in a delay differential equation model of a ring laser, Murphys-HSFS 2016 Workshop, Centre de Recerca Matemàtica, Barcelona, Spain, June 13, 2016.

  • A. Pimenov, Numerical stability analysis of dissipative phase solitons in a DDE model of a semiconductor laser, WIAS Workshop ``Dynamics of Delay Equations, Theory and Applications", WIAS, Berlin, October 14, 2016.

  • S. Pickartz, S. Amiranashvili, Champion solitons that come from nowhere, 618. WE-Heraeus-Seminar: Extreme Events and Rogue Waves -- 2016, Wilhelm und Else Heraeus-Stiftung, Bad Honnef, May 30 - June 3, 2016.

  • S. Pickartz, U. Bandelow, S. Amiranashvili, Numerical optimization of all-optical switching, 16th International Conference on Numerical Simulation of Optoelectronic Devices, Sydney, Australia, July 11 - 15, 2016.

  • U. Bandelow, Heteroclinic connections and limiting cases in integrable NLS-type equations, 618. WE-Heraeus-Seminar: Extreme Events and Rogue Waves -- 2016, Wilhelm und Else Heraeus-Stiftung, Bad Honnef, June 3, 2016.

  • U. Bandelow, Multi-dimensional modeling and simulation of electrically pumped semiconductor-based emitters, Block Seminar Graal-Müritz, DFG Collaborative Research Center (SFB) 787 ``Semiconductor Nanophotonics'', Graal-Müritz, May 13, 2016.

  • U. Bandelow, Nonlinear dynamical effects in photonics: Modeling, simulation and analysis, Coloquio del Instituto de Física, Pontificia Universidad Católica de Chile, Santiago, December 14, 2016.

  • U. Bandelow, Solitons on a background, rogue waves, and classical soliton solutions of extended nonlinear Schrödinger equations, International Tandem Workshop on Pattern Dynamics in Nonlinear Optical Cavities, August 15 - 19, 2016, Max-Planck-Institut für Physik komplexer Systeme, Dresden, August 15, 2016.

  • U. Bandelow, Solitons that do not want to be too short in duration, International Conference on Wave Interaction (WIN-2016), Johannes Kepler Universität Linz, Austria, April 27, 2016.

  • U. Bandelow, Ultrashort solitons that do not want to be too short in duration, XIX Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics (MEDYFINOL 2016), Universidad de los Andes, Universidad de Mar del Plata, and Instituto Tecnológico de Buenos Aires, Valdivia, Chile, December 7, 2016.

  • U. Bandelow, Ultrashort solitons, rogue waves and event horizons in nonlinear dispersive optical media, Coloquio de la Faculdad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Santiago, Chile, December 15, 2016.

  • C. Brée, Adiabatic Floquet model for the optical response in femtosecond filaments, group seminar, Leibniz Universität Hannover, Institut für Quantenoptik, February 11, 2016.

  • C. Brée, Adiabatic Floquet model for the optical response in sub-picosecond optical filamentation, III International Symposium ``Advances in Nonlinear Photonics'' (ANPh'2016), September 29 - October 1, 2016, Belarusian State University, Minsk, Belarus, September 30, 2016.

  • O. Omel'chenko, Asymptotics of traveling coherence-incoherence patterns, Contemporary Problems of Mathematical Physics and Computational Mathematics, Lomonosov Moscow State University, Russian Federation, November 2, 2016.

  • O. Omel'chenko, Chimera states in nonlocally coupled oscillators: Their variety and control, 4th International Conference on Complex Dynamical Systems and Applications, National Institute of Technology, Durgapur, India, February 16, 2016.

  • O. Omel'chenko, Creative control for chimera states, Workshop on Synchronization and Oscillators with Generalized Coupling, University of Exeter, UK, April 21, 2016.

  • O. Omel'chenko, Mean-field equation for coherence-incoherence patterns, 7th European Congress of Mathematics (7ECM), Minisymposium 37 ``Propagation Phenomena in Discrete Media'', July 18 - 22, 2016, Technische Universität Berlin, July 22, 2016.

  • O. Omel'chenko, Nonuniversal transitions to synchrony in globally coupled phase oscillator, International Workshop on Nonlinear Complex Dynamical Systems, Indian Statistical Institute, Kolkata, February 19, 2016.

  • O. Omel'chenko, On the limitations of the Kuramoto model, Dynamics Days Latin America and the Caribbean, Benemérita Universidad Autónoma de Puebla, Mexico, October 28, 2016.

  • O. Omel'chenko, Patterns of coherence and incoherence, Patterns of Dynamics Conference in Honor of Bernold Fiedler, July 25 - 29, 2016, Free University of Berlin, Berlin, July 29, 2016.

  • O. Omel'chenko, Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators, International Conference on Control of Complex Systems and Networks, SFB 910 ``Control of Self-Organizing Nonlinear Systems: Theoretical Methods and Concepts of Application'', Heringsdorf/Usedom, September 4 - 8, 2016.

  • O. Omel'chenko, Spike solutions to singularly perturbed elliptic problems, The 13th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, Lomonosov Moscow State University, Russian Federation, April 7, 2016.

  • M. Radziunas, A multi-mode delay differential equation model for lasers with optical feedback, Research Seminar, Macquarie University, Department of Physics and Astronomy, Sydney, Australia, July 15, 2016.

  • M. Radziunas, A multi-mode delay differential equation model for lasers with optical feedback, 16th International Conference on Numerical Simulation of Optoelectronic Devices, July 11 - 15, 2016, University of Sydney, Sydney, Australia.

  • M. Radziunas, Modeling and simulations of broad-area edge-emitting semiconductor devices, Kooperationsmeeting mit TRUMPF Laser GmbH, TRUMPF Laser GmbH, Schramberg, January 12, 2016.

  • M. Radziunas, Modeling and simulation of external feedback in broad area lasers with BALaser, HotLas project meeting, Jenoptik, Berlin, November 22, 2016.

  • M. Radziunas, Modeling and simulation of high-power broad area lasers, Kick-off meeting of the EUROSTARS project HIP-Lasers, Monocrom S. L., Vilanova, Barcelona, Spain, October 14, 2016.

  • M. Radziunas, Modeling and simulations of broad-area edge-emitting semiconductor devices, EffiLAS--HotLas Kick-off meeting, Jenoptik Diode Lab GmbH, Berlin, September 14, 2016.

  • M. Radziunas, Modeling, simulations, and analysis of nonlinear dynamics in edge-emitting semiconductor lasers, 1st Leibniz MMS Days, WIAS Berlin, Berlin, January 27, 2016.

  • A. Vladimirov, Delay differential equation models of frequency swept laser light sources, International Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD'2016), University of Hassan II Casablanca, Marrakech, Morocco, May 24, 2016.

  • A. Vladimirov, Delay differential equations in modeling multimode laser dynamics, Dynamics of Delay Equations, Theory and Applications, WIAS, Berlin, October 14, 2016.

  • A. Vladimirov, Distributed delay model of a frequency swept laser with long fiber delay line, European Semiconductor Laser Workshop (ESLW) 2016, Technische Universität Darmstadt, Darmstadt, September 24, 2016.

  • A. Vladimirov, Interaction of spatial and temporal cavity solitons in mode-locked lasers and passive cavities, 17th International Conference ``Laser Optics 2016'', June 27 - July 1, 2016, Saint Petersburg, Russian Federation, June 29, 2016.

  • A.G. Vladimirov, Delay differential equation models in multi-mode laser dynamics, SFB 910 Symposium: Dynamics of coupled systems and applications to lasers, Technische Universität Berlin, Berlin, April 22, 2016.

  • A.G. Vladimirov, Delay differential models in multimode laser dynamics: Taking chromatic dispersion into account, SPIE Photonics Europe 2016, Conference 9892 ``Semiconductor Lasers and Laser Dynamics'', Session 5, April 3 - 7, 2016, SPIE, Brussels, Belgium, April 5, 2016.

  • A.G. Vladimirov, Distributed delay differential equation models in laser dynamics, Volga Neuroscience Meeting 2016, July 24 - 30, 2016, from Saint Petersburg to Nizhny Novgorod, Russian Federation, July 28, 2016.

  • A.G. Vladimirov, Interaction of temporal cavity solitons in driven fiber resonators and mode-locked lasers, International Tandem Workshop on Pattern Dynamics in Nonlinear Optical Cavities, August 15 - 19, 2016, Max-Planck-Institut für Physik komplexer Systeme, Dresden, August 15, 2016.

  • A.G. Vladimirov, Nonlinear dynamics of a frequency swept laser, Quantum Optics Seminar, Saint-Petersburg State University, Saint-Petersburg, Russian Federation, January 12, 2016.

  • M. Wolfrum, Emergence of collective behavior in coupled oscillator systems, Workshop ''Dynamics in Networks with Special Properties'', January 25 - 29, 2016, Mathematical Biosciences Institute (MBI), Columbus, USA, January 27, 2016.

  • M. Wolfrum, Emergence of collective behavior in coupled oscillator systems, Wednesdays@NICO, Northwestern University, Northwestern Institute on Complex Systems, Evanston, USA, January 20, 2016.

  • M. Wolfrum, Synchronization transitions in systems of coupled phase oscillators, Workshop on Synchronization and Oscillators with Generalized Coupling, April 20 - 22, 2016, University of Exeter, UK, April 21, 2016.

  • M. Wolfrum, Synchronization transitions in systems of coupled phase oscillators, Arbeitsgruppenseminar ``Chemische Physik fern vom Gleichgewicht'', Technische Universität München, Fachbereich Physik, March 18, 2016.

  • M. Wolfrum, Synchronization transitions in systems of coupled phase oscillators, Oberseminar Angewandte Mathematik, Westfälische Wilhelms-Universität Münster, Fachbereich Mathematik und Informatik, June 22, 2016.

External Preprints

  • P. Kravetc, D. Rachinskii, A.G. Vladimirov, Pulsating dynamics of slow-fast population models with delay, Preprint no. arxiv.org:1601.06452, Cornell University Library, arXiv.org, 2016.
    Abstract
    We discuss a bifurcation scenario which creates periodic pulsating solutions in slow-fast delayed systems through a cascade of almost simultaneous Hopf bifurcations. This scenario has been previously associated with formation of pulses in a delayed model of mode-locked semiconductor lasers. In this work, through a case study of several examples, we establish that a cascade of Hopf bifurcations can produce periodic pulses, with a period close to the delay time, in population dynamics models and explore the conditions that ensure the realization of this scenario near a transcritical bifurcation threshold. We derive asymptotic approximations for the pulsating 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 realization of the bifurcation scenario is highlighted.