Optical pulses in nonlinear media

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.

H.-J. Wünsche, J. Piprek, U. Bandelow, H. Wenzel, eds., Proceedings of the 5th International Conference on ``Numerical Simulation of Optoelectronic Devices'' (NUSOD '05) in Berlin, September 19--22, 2005, IEEE, Piscataway, NJ, 2005, 134 pages, (Collection Published).

D. Dolinina, G. Huyet, D. Turaev, A.G. Vladimirov, Desynchronization of temporal solitons in Kerr cavities with pulsed injection, Optics Letters, 49 (2024), pp. 4050--4053, DOI 10.1364/OL.529083 .
Abstract
A numerical and analytical study was conducted to investigate the bifurcation mechanisms that cause desynchronization between the soliton repetition frequency and the frequency of external pulsed injection in a Kerr cavity described by the Lugiato--Lefever equation. The results suggest that desynchronization typically occurs through an Andronov--Hopf bifurcation. Additionally, a sim- ple and intuitive criterion for this bifurcation to occur is proposed.

K. Panajotov, A.G. Vladimirov, M. Tlidi, Polarized frequency combs in a mode-locked VECSEL, IEEE Journal of Selected Topics in Quantum Electronics, 30 (2024), pp. 1100200/1--1100200/10, DOI 10.1109/JSTQE.2024.3470227 .
Abstract
In this paper, we present a detailed and rigorous derivation of the delay differential equations of the spin-flip model for vertical external cavity lasers with a semiconductor saturable absorption mirror. This model describe mode-locked semiconductor lasers in the ring-resonator geometry with unidirectional lasing. This contribution completes a previous communication [Vladimirov et al. Opt. Lett., 45, 252 (2020)], and we further complete the analytical derivation by taking into account phase and amplitude anisotropies and the resulting different delay times for orthogonal linear polarizations. We show evidence of the coexistence of two linearly polarized frequency combs generation with slightly different repetition rates due to the birefringence-induced time-of-flight difference.

A.G. Vladimirov, D. Dolinina, Neutral delay differential equation model of an optically injected Kerr cavity, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 109 (2024), pp. 024206/1--024206/10, DOI 10.1103/PhysRevE.109.024206 .
Abstract
A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second- and higher-order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the low dissipation limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE, the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.

A. Roche, S. Slepneva, A. Kovalev, A. Pimenov, A.G. Vladimirov, M. Giudici, M. Marconi, G. Huyet, Decoherence and turbulence sources in a long laser, Physical Review Letters, 131 (2023), pp. 053801/1--053801/7, DOI 10.1103/PhysRevLett.131.053801 .
Abstract
We investigate the turn-on process in a laser cavity where the roundtrip time is several orders of magnitude greater than the active medium timescales. In this long delay limit the electromagnetic field build-up can be mapped experimentally roundtrip after roundtrip. We show how coherence settles down starting from a stochastic initial condition. In the early stages of the turn-on, we show that power drop-outs emerge, persist for several round-trips and seed dark solitons. These latter structures exhibit a chaotic dynamics and emit radiation that can lead to an overall turbulent dynamics depending on the cavity dispersion.

F. Severing, U. Bandelow, S. Amiranashvili, Spurious four-wave mixing processes in generalized nonlinear Schrödinger equations, Journal of Lightwave Technology, 41 (2023), pp. 5359--5365, DOI 10.1109/JLT.2023.3261804 .
Abstract
Numerical solutions of a nonlinear Schödinger equation, e.g., for pulses in optical fibers, may suffer from the spurious four-wave mixing processes. We study how these nonphysical resonances appear in solutions of a much more stiff generalized nonlinear Schödinger equation with an arbitrary dispersion operator and determine the necessary restrictions on temporal and spatial resolution of a numerical scheme. The restrictions are especially important to meet when an envelope equation is applied in a wide spectral window, e.g., to describe supercontinuum generation, in which case the appearance of the numerical instabilities can occur unnoticed.

A.G. Vladimirov, Temporal cavity soliton interaction in passively mode-locked semiconductor lasers, Optics, 4 (2023), pp. 433--446, DOI 10.3390/opt4030031 .
Abstract
Weak interaction due to gain saturation and recovery of temporal cavity solitons in a delay differential model of a long cavity semiconductor laser is studied numerically and analytically using an asymptotic approach. It is shown that apart from usual soliton repulsion leading to a harmonic mode-locking regime a soliton attraction is also possible in a laser with nonzero linewidth enhancement factor. It is shown numerically that the attraction can lead either to a soliton merging or to a pulse bound state formation.

A. Pimenov, A.G. Vladimirov, Temporal solitons in an optically injected Kerr cavity with two spectral filters, Optics, 3(4) (2022), pp. 364--383, DOI 10.3390/opt3040032 .
Abstract
We investigate theoretically the dynamical behavior of an optically injected Kerr cavity where the chromatic dispersion is induced by propagation of light through two Lorentzian spectral filters with different widths and central frequencies. We show that this setup can be modeled by a second order delay differential equation that can be considered as a generalization of the Ikeda map with included spectral filtering, dispersion, and coherent injection terms. We demonstrate that this equation can exhibit modulational instability and bright localized structures formation in the anomalous dispersion regime.

S. Amiranashvili, U. Bandelow, Unusual scenarios in four-wave-mixing instability, Physical Review A, 105 (2022), pp. 063519/1--063519/6, DOI 10.1103/PhysRevA.105.063519 .
Abstract
A pump carrier wave in a dispersive system may decay by giving birth to blue- and red-shifted satellite waves due to modulation or four-wave mixing instability. We analyse situations where the satellites are so different from the carrier wave, that the red-shifted satellite either changes its propagation direction (k < 0, ω > 0) or even gets a negative frequency (k, ω < 0). Both situations are beyond the envelope approach and require application of Maxwell equations.

A.G. Vladimirov, Short- and long-range temporal cavity soliton interaction in delay models of mode-locked lasers, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 105 (2022), pp. 044207/1--044207/6, DOI 10.1103/PhysRevE.105.044207 .
Abstract
Interaction equations governing slow time evolution of the coordinates and phases of two interacting temporal cavity solitons in a delay differential equation model of a nonlinear mirror mode-locked laser are derived and analyzed. It is shown that non-local pulse interaction due to gain depletion and recovery can lead either to a development of harmonic mode-locking regime, or to a formation of closely packed incoherent soliton bound state with weakly oscillating intersoliton time separation. Local interaction via electric field tails can result in an anti-phase or in-phase stationary or breathing harmonic mode-locking regime.

M. Nizette, A.G. Vladimirov, Generalized Haus master equation model for mode-locked class-B lasers, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 104 (2021), pp. 014215/1--014215/13, DOI 10.1103/PhysRevE.104.014215 .
Abstract
Using the multiscale technique we develop a generalized version of the class-B Haus modelocking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the standard class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime, but also the appearance of harmonic mode-locked regimes with the increase of the pump power.

S. Amiranashvili, M. Radziunas, U. Bandelow, K. Busch, R. Čiegis, Additive splitting methods for parallel solutions of evolution problems, Journal of Computational Physics, 436 (2021), pp. 110320/1--110320/14, DOI 10.1016/j.jcp.2021.110320 .
Abstract
We demonstrate how a multiplicative splitting method of order Pcan be utilized to construct an additive splitting method of order P+3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourth-order additive method, which is yielded by the Lie-Trotter splitting. We provide error estimates, stability analysis of a test problem, and numerical examples with special discussion of the parallelization properties and applications to nonlinear optics.

A.G. Vladimirov, M. Tlidi, M. Taki, Dissipative soliton interaction in Kerr resonators with high-order dispersion, Physical Review A, 103 (2021), pp. 063505/1--063505/7, DOI 10.1103/PhysRevA.103.063505 .
Abstract
We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized Lugiato--Lefever equation with fourth order dispersion We use an asymptotic approach to derive interaction equations governing the slow time evolution of the coordinates of two interacting dissipative solitons. We show that Cherenkov radiation induced by positive fourth-order dispersion leads to a strong increase of the interaction force between the solitons. As a consequence, large number of equidistant soliton bound states in the phase space of the interaction equations can be stabilized. We show that the presence of even small spectral filtering not only dampens the Cherenkov radiation at the soliton tails and reduces the interaction strength, but can also affect the bound state stability.

A.G. Vladimirov, S. Suchkov, G. Huyet, S.K. Turitsyn, Delay-differential-equation model for mode-locked lasers based on nonlinear optical and amplifying loop mirrors, Physical Review A, 104 (2021), pp. 033525/1--033525/8, DOI 10.1103/PhysRevA.104.033525 .
Abstract
Delay differential equation model of a NOLM-NALM mode-locked laser is developed that takes into account finite relaxation rate of the gain medium and asymmetric beam splitting at the entrance of the nonlinear mirror loop. Asymptotic linear stability analysis of the continuous wave solutions performed in the limit of large delay indicates that in a class-B laser flip instability leading to a period doubling cascade and development of square-wave patterns can be suppressed by a short wavelength modulational instability. Numerically it is shown that the model can demonstrate large windows of regular fundamental and harmonic mode-locked regimes with single and multiple pulses per cavity round trip time separated by domains of irregular pulsing.

A. Pimenov, S. Amiranashvili, A.G. Vladimirov, Temporal cavity solitons in a delayed model of a dispersive cavity ring laser, Mathematical Modelling of Natural Phenomena, 15 (2020), pp. 47/1--47/18, DOI 10.1051/mmnp/2019054 .
Abstract
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 continuous wave states and temporal cavity solitons.

U. Bandelow, S. Amiranashvili, S. Pickartz, Stabilization of optical pulse transmission by exploiting fiber nonlinearities, Journal of Lightwave Technology, 38 (2020), pp. 5743--5747, DOI 10.1109/JLT.2020.3003447 .
Abstract
We prove theoretically, that the evolution of optical solitons can be dramatically influenced in the course of nonlinear interaction with much smaller group velocity matched pulses. Even weak pump pulses can be used to control the solitons, e.g., to compensate their degradation caused by Raman-scattering.

A.G. Vladimirov, K. Panajotov, M. Tlidi, Orthogonally polarized frequency combs in a mode-locked VECSEL, Optics Letters, 45 (2020), pp. 252--255, DOI 10.1364/OL.45.000252 .
Abstract
We introduce a spin?flip model for a vertical-external-cavity surface-emitting laser (VECSEL) with a saturable absorber. We demonstrate the possibility, due to the spin?flip dynamics, to generate two orthogonally linearly polarized frequency combs in the mode-locked regime. The two combs are shifted in wavelength due to the birefringence in the VECSEL gain and/or saturable absorption mirror. We show that the polarization degree of freedom may also lead to several pulses being generated per roundtrip in the two orthogonal linear polarizations and to more complicated dynamics with both linear polarizations excited.

S. Amiranashvili, E. Tobisch, Extended criterion for the modulation instability, New Journal of Physics, 21 (2019), pp. 033029/1--033029/7, 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.

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.

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.

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.

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.

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.

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.

C. Brée, M. Hofmann, I. Babushkin, A. Demircan, U. Morgner, O.G. Kosareva, A.B. Savel'ev, A. Husakou, M. Ivanov, Symmetry breaking and strong persistent plasma currents via resonant destabilization of atoms, Physical Review Letters, 119 (2017), pp. 243202/1--243202/5.
Abstract
The ionization rate of an atom in a strong optical field can be resonantly enhanced by the presence of long-living atomic levels (so called Freeman resonances). This process is most prominent in the multiphoton ionization regime meaning that ionization event takes many optical cycles. Nevertheless, here we show that these resonances can lead to fast subcycle-scale plasma buildup at the resonant values of the intensity in the pump pulse. The fast buildup can break the cycle-to-cycle symmetry of the ionization process, resulting in generation of persistent macroscopic plasma currents which remain after the end of the pulse. This, in turn, gibes rise to a broad-band radiation of unusual spectral structure forming a comb from terahertz (THz) to visible. This radiation contains fingerprints of the attosecond electronic dynamics in Rydberg states during ionization.

C. Brée, I. Babushkin, U. Morgner, A. Demircan, Regularizing aperiodic cycles of resonant radiation in filament light bullets, Physical Review Letters, 118 (2017), pp. 163901/1--163901/5, DOI 10.1103/PhysRevLett.118.163901 .
Abstract
We demonstrate an up to now unrecognized and very effective mechanism which prevents filament collapse and allows persistent 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.

G. Slavcheva, M.V. Koleva, A. Pimenov, The impact of microcavity wire width on polariton soliton existence and multistability, Journal of Optics, 19 (2017), pp. 065404/1--065404/15.
Abstract
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.

D. Angulo-Garcia, S. Luccioli, S. Olmi, A. Torcini, Death and rebirth of neural activity in sparse inhibitory networks, New Journal of Physics, 19 (2017), pp. 053011/1--053011/22, DOI 10.1088/1367-2630/aa69ff .
Abstract
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.

D. Puzyrev, A.G. Vladimirov, A. Pimenov, S.V. Gurevich, S. Yanchuk, Bound pulse trains in arrays of coupled spatially extended dynamical systems, Physical Review Letters, 119 (2017), pp. 163901/1--163901/6, DOI 10.1103/PhysRevLett.119.163901 .
Abstract
We study the dynamics of an array of nearest-neighbor coupled spatially distributed systems each generating a periodic sequence of short pulses. We demonstrate that, unlike a solitary system generating a train of equidistant pulses, an array of such systems can produce a sequence of clusters of closely packed pulses, with the distance between individual pulses depending on the coupling phase. This regime associated with the formation of locally coupled pulse trains bounded due to a balance of attraction and repulsion between them is different from the pulse bound states reported earlier in different laser, plasma, chemical, and biological systems. We propose a simplified analytical description of the observed phenomenon, which is in good agreement with the results of direct numerical simulations of a model system describing an array of coupled mode-locked lasers.

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, 67 (2017), pp. 1078--1087, 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.

N. Raabe, T. Feng, T. Witting, A. Demircan, C. Brée, G. Steinmeyer, Role of intrapulse coherence in carrier-envelope phase stabilization, Physical Review Letters, 119 (2017), pp. 123901/1--123901/5, DOI 10.1103/PhysRevLett.119.123901 .
Abstract
The concept of coherence is of fundamental importance for describing the physical characteristics of light and for evaluating the suitability for experimental application. In the case of pulsed laser sources, the pulse-to-pulse coherence is usually considered for a judgment of the compressibility of the pulse train. This type of coherence is often lost during propagation through a highly nonlinear medium, and pulses prove incompressible despite multioctave spectral coverage. Notwithstanding the apparent loss of interpulse coherence, however, supercontinua enable applications in precision frequency metrology that rely on coherence between different spectral components within a laser pulse. To judge the suitability of a light source for the latter application, we define an alternative criterion, which we term intrapulse coherence. This definition plays a limiting role in the carrier-envelope phase measurement and stabilization of ultrashort pulses. It is shown by numerical simulation and further corroborated by experimental data that filamentation-based supercontinuum generation may lead to a loss of intrapulse coherence despite near-perfect compressibility of the pulse train. This loss of coherence may severely limit active and passive carrier-envelope phase stabilization schemes and applications in optical high-field physics.

S. Pickartz, C. Brée, U. Bandelow, S. Amiranashvili, Cancellation of Raman self-frequency shift for compression of optical pulses, Optical and Quantum Electronics, 49 (2017), pp. 328/1--328/7, DOI 10.1007/s11082-017-1164-7 .
Abstract
We study to which extent a fiber soliton can be manipulated by a specially chosen continuous pump wave. A group velocity matched pump scatters at the soliton, which is compressed due to the energy/momentum transfer. As the pump scattering is very sensitive to the velocity matching condition, soliton compression is quickly destroyed by the soliton self-frequency shift (SSFS). This is especially true for ultrashort pulses: SSFS inevitably impairs the degree of compression. We demonstrate numerically that soliton enhancement can be restored to some extent and the compressed soliton can be stabilized, provided that SSFS is canceled by a second pump wave. Still the available compression degree is considerably smaller than that in the Raman-free nonlinear fibers.

S. Pickartz, U. Bandelow, S. Amiranashvili, Asymptotically stable compensation of soliton self-frequency shift, Optics Letters, 42 (2017), pp. 1416--1419, DOI 10.1364/OL.42.001416 .
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.

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, DOI 10.1088/0953-4075/49/20/205004 .
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.

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.

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.

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.

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.

S. Amiranashvili, R. Čiegis, M. Radziunas, Numerical methods for generalized nonlinear Schrödinger equations, Kinetic and Related Models, 8 (2015), pp. 215--234.
Abstract
We present and analyze different splitting algorithms for numerical solution of the both classical and generalized nonlinear Schrödinger equations describing propagation of wave packets with special emphasis on applications to nonlinear fiber-optics. The considered generalizations take into account the higher-order corrections of the linear differential dispersion operator as well as the saturation of nonlinearity and the self-steepening of the field envelope function. For stabilization of the pseudo-spectral splitting schemes for generalized Schrödinger equations a regularization based on the approximation of the derivatives by the low number of Fourier modes is proposed. To illustrate the theoretically predicted performance of these schemes several numerical experiments have been done.

M. Hofmann, J. Hyyti, S. Birkholz, M. Bock, S.K. Das, R. Grunwald, M. Hoffmann, T. Nagy, A. Demircan, M. Jupé, D. Ristau, U. Morgner, C. Brée, M. Wörner, Th. Elsaesser, G. Steinmeyer, Non-instantaneous polarization dynamics in dielectric media, Optica, 2 (2015), pp. 151--157.
Abstract
Third-order optical nonlinearities play a vital role for generation and characterization of some of the shortest optical pulses to date, for optical switching applications, and for spectroscopy. In many cases, nonlinear optical effects are used far off resonance, and then an instantaneous temporal response is expected. Here, we show for the first time resonant frequency-resolved optical gating measurements that indicate substantial nonlinear polarization relaxation times up to 6.5,fs in dielectric media, i.e., significantly beyond the shortest pulses directly available from commercial lasers. These effects are among the fastest effects observed in ultrafast spectroscopy. Numerical solutions of the time-dependent Schrödinger equation are in excellent agreement with experimental observations. The simulations indicate that pulse generation and characterization in the ultraviolet may be severely affected by this previously unreported effect. Moreover, our approach opens an avenue for application of frequency-resolved optical gating as a highly selective spectroscopic probe in high-field physics.

M. Hofmann, C. Brée, Femtosecond filamentation by intensity clamping at a Freeman resonance, Physical Review A, 92 (2015), pp. 013813/1--013813/7.

G. Slavcheva, A.V. Gorbach, A. Pimenov, A.G. Vladimirov, D. Skryabin, Multi-stability and polariton formation in microcavity polaritonic waveguides, Optics Letters, 40 (2015), pp. 1787--1790.
Abstract
Nonlinear polaritons in microcavity waveguides are demonstrated to exhibit multi-stable behaviour and rich dynamics, including filamentation and soliton formation. We find that the multi-stability originates from co-existense of different transverse modes of the po- laritonic waveguide. Modulational stability and conditions for multi-mode polariton solitons are studied. Soliton propagation in tilted, relative to the pump momentum, waveguides is demonstrated and a critical tilt angle for the soliton propagation is found.

S. Birkholz, C. Brée, A. Demircan, G. Steinmeyer, Predictability of rogue events, Physical Review Letters, 114 (2015), pp. 213901/1--213901/5.

C. Brée, M. Kretschmar, T. Nagy, H.G. Kurz, U. Morgner, M. Kovačev, Impact of spatial inhomogeneities on on-axis pulse reconstruction in femtosecond filaments, Journal of Physics B: Atomic, Molecular and Optical Physics, 48 (2015), pp. 094002/1--094002/6.
Abstract
We demonstrate a strong influence of the spatial beam profile on the vacuum-propagated on-axis pulse shapes for a femtosecond filament in argon. The effects can be minimized by transmitting the filament into the far-field by a laser-drilled pinhole setup. Using this method, we can monitor the pulse compression dynamics along the entire longitudinal extension of the filament, including the ionization-induced plasma channel.

S. Amiranashvili, U. Bandelow, N. Akhmediev, Spectral properties of limiting solitons in optical fibers, Optics Express, 22 (2014), pp. 30251--30256.
Abstract
It seems to be self-evident that stable optical pulses cannot be considerably shorter than a single oscillation of the carrier field. From the mathematical point of view the solitary solutions of pulse propagation equations should loose stability or demonstrate some kind of singular behavior. Typically, an unphysical cusp develops at the soliton top, preventing the soliton from being too short. Consequently, the power spectrum of the limiting solution has a special behavior: the standard exponential decay is replaced by an algebraic one. We derive the shortest soliton and explicitly calculate its spectrum for the so-called short pulse equation. The latter applies to ultra-short solitons in transparent materials like fused silica that are relevant for optical fibers.

S. Amiranashvili, U. Bandelow, N. Akhmediev, Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion, Optical and Quantum Electronics, 46 (2014), pp. 1233--1238.
Abstract
We consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity.

R.M. Arkhipov, I. Babushkin, M.K. Lebedev, Y.A. Tolmachev, M.V. Arkhipov, Transient Cherenkov radiation from an inhomogeneous string excited by an ultrashort laser pulse at superluminal velocity, Physical Review A, 89 (2014), pp. 043811/1--043811/10.
Abstract
An optical response of one-dimensional string made of dipoles with a periodically varying density excited by a spot of light moving along the string at the superluminal (subluminal) velocity is studied. We consider in details the spectral and temporal dynamics of the Cherenkov radiation, which occurs in such system in the transient regime. We point out the resonance character of radiation and the appearance of a new Doppler-like frequency in the spectrum of the transient Cherenkov radiation. Possible applications of the effect as well as different string topologies are discussed

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, G. Steinmeyer, Adjustable pulse compression scheme for generation of few-cycle pulses in the mid-infrared, Optics Letters, 39 (2014), pp. 2735--2738.
Abstract
An novel adjustable adiabatic soliton compression scheme is presented, enabling a coherent pulse source with pedestal-free few-cycle pulses in the infrared or mid-infrared regime. This scheme relies on interaction of a dispersive wave and a soliton copropagating at nearly identical group velocities in a fiber with enhanced infrared transmission. The compression is achieved directly in one stage, without necessity of an external compensation scheme. Numerical simulations are employed to demonstrate this scheme for silica and fluoride fibers, indicating ultimate limitations as well as the possibility of compression down to the single-cycle regime. Such output pulses appear ideally suited as seed sources for parametric amplification schemes in the mid-infrared.

A. Demircan, U. Morgner, S. Amiranashvili, C. Brée, G. Steinmeyer, Supercontinuum generation by multiple scatterings at a group velocity horizon, Optics Express, 22 (2014), pp. 3866--3879.
Abstract
A new scheme for supercontinuum generation covering more than one octave and exhibiting extraordinary high coherence properties has recently been proposed in Phys. Rev. Lett. bf 110, 233901 (2013). The scheme is based on two-pulse collision at a group velocity horizon between a dispersive wave and a soliton. Here we demonstrate that the same scheme can be exploited for the generation of supercontinua encompassing the entire transparency region of fused silica, ranging from 300 to 2300nm. At this bandwidth extension, the Raman effect becomes detrimental, yet may be compensated by using a cascaded collision process. Consequently, the high degree of coherence does not degrade even in this extreme scenario.

M. Kretschmar, C. Brée, T. Nagy, A. Demircan, M. Kovačev, Direct observation of pulse dynamics and self-compression along a femtosecond filament, Optics Express, 22 (2014), pp. 22905--22916.

S. Amiranashvili, U. Bandelow, N. Akhmediev, Few-cycle optical solitary waves in nonlinear dispersive media, Physical Review A, 87 (2013), pp. 013805/1--013805/8.
Abstract
We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons.

I. Omelchenko, O. Omel'chenko, P. Hövel, E. Schöll, When nonlocal coupling between oscillators becomes stronger: Patched synchrony or multichimera states, Physical Review Letters, 110 (2013), pp. 224101/1--224101/5.
Abstract
Systems of nonlocally coupled oscillators can exhibit complex spatiotemporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of these states, found in a widely used model of a limit-cycle oscillator if one goes beyond the limit of weak coupling typical for phase oscillators. Then patches of synchronized dynamics appear within the incoherent domain giving rise to a multi-chimera state. We find that, depending on the coupling strength and range, different multichimera states arise in a transition from classical chimera states. The additional spatial modulation is due to strong coupling interaction and thus cannot be observed in simple phase-oscillator models

M.V. Arkhipov, R.M. Arkhipov, S.A. Pulkin, Effects of inversionless oscillation in two-level media from the point of view of specificities of the spatiotemporal propagation dynamics of radiation, Optics and Spectroscopy, 114 (2013), pp. 831--837.
Abstract
We report the results of computer simulation of the emission of radiation by an extended twolevel medium in a ring cavity. The cases of using strong external monochromatic, quasimonochromatic, and biharmonic radiation for pumping the twolevel medium are analyzed. It is shown that the emission of radiation with spectral content different from that of the pump radiation, which is interpreted as the inversionless oscillation, is the result of the spatiotemporal dynamics of light propagation in an extended twolevel medium imbedded in a cavity. The appearance of this radiation is not related to known resonances of amplification of a weak probe field in a thin layer of the twolevel system (the effect of inversionless oscillation) induced by strong resonance monochromatic or biharmonic field, as was thought before.

A. Demircan, S. Amiranashvili, C. Brée, G. Steinmeyer, Compressible octave spanning supercontinuum generation by two-pulse collisions, Physical Review Letters, 110 (2013), pp. 233901/1--233901/5.
Abstract
We demonstrate a novel method for supercontinuum generation in an optical fiber based on two-color pumping with a delay and a group velocity matching. The scheme relies on the enhanced cross-phase-modulation at an intensity induced refractive index barrier between a dispersive wave and a soliton. The generation mechanism neither incorporates soliton fission nor a modulation instability and therefore exhibits extraordinary coherence properties, enabling the temporal compression of octave bandwidth into a short pulse. Moreover, the properties of the supercontinuum are adjustable over a wide range in the frequency domain by suitable choice of the dispersive wave.

A. Demircan, S. Amiranashvili, C. Brée, F. Mitschke, G. Steinmeyer, From optical rogue waves to optical transistors, Nonlinear Phenomena in Complex Systems, 16 (2013), pp. 24--32.
Abstract
We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons.

A. Demircan, S. Amiranashvili, C. Brée, Ch. Mahnke, F. Mitschke, G. Steinmeyer, Rogue wave formation by accelerated solitons at an optical event horizon, Applied Physics B: Lasers and Optics, 115 (2013), pp. 343--354.
Abstract
Rogue waves, by definition, are rare events of extreme amplitude, but at the same time they are frequent in the sense that they can exist in a wide range of physical contexts. While many mechanisms have been demonstrated to explain the appearance of rogue waves in various specific systems, there is no known generic mechanism or general set of criteria shown to rule their appearance. Presupposing only the existence of a nonlinear Schrödinger-type equation together with a concave dispersion profile around a zero dispersion wavelength we demonstrate that solitons may experience acceleration and strong reshaping due to the interaction with continuum radiation, giving rise to extreme-value phenomena. The mechanism is independent of the optical Raman effect. A strong increase of the peak power is accompanied by a mild increase of the pulse energy and carrier frequency, whereas the photon number of the soliton remains practically constant. This reshaping mechanism is particularly robust and is naturally given in optics in the supercontinuum generation process.

U. Bandelow, N. Akhmediev, Solitons on a background, rogue waves and classical soliton solutions of Sasa--Satsuma equation, Journal of Optics, 15 (2013), pp. 064006/1--064006/10.
Abstract
We present the most general multi-parameter family of a soliton on a background solutions to the Sasa-Satsuma equation. The solution contains a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits nontrivial limiting cases, such as rogue waves and classical solitons, that are considered in detail.

C. Brée, S. Amiranashvili, U. Bandelow, Spatio-temporal pulse propagation in nonlinear dispersive optical media, Optical and Quantum Electronics, 45 (2013), pp. 727--733.
Abstract
We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions.We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.

S. Amiranashvili, U. Bandelow, A. Mielke, Calculation of ultrashort pulse propagation based on rational approximations for medium dispersion, Optical and Quantum Electronics, 44 (2012), pp. 241--246.
Abstract
Ultrashort optical pulses contain only a fewoptical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation, and non-envelope equations which treat the field directly. Based on fundamental physical rules we will present an approach that effectively interpolates between these classes and provides a suitable setting for accurate and highly efficient

V. Tronciu, S. Schwertfeger, M. Radziunas, A. Klehr, U. Bandelow, H. Wenzel, Numerical simulation of the amplification of picosecond laser pulses in tapered semiconductor amplifiers and comparison with experimental results, Optics Communications, 285 (2012), pp. 2897--2904.
Abstract
We apply a travelling wave model to the simulation of the amplification of laser pulses generated by Q-switched or mode-locked distributed-Bragg reflector lasers. The power amplifier monolithically integrates a ridge-waveguide section acting as pre-amplifier and a flared gain-region amplifier. The diffraction limited and spectral-narrow band pulses injected in to the pre-amplifier have durations between 10 ps and 100 ps and a peak power of typical 1 W. After the amplifier, the pulses reach a peak power of several tens of Watts preserving the spatial, spectral and temporal properties of the input pulse. We report results obtained by a numerical solution of the travelling-wave equations and compare them with experimental investigations. The peak powers obtained experimentally are in good agreement with the theoretical predictions. The performance of the power amplifier is evaluated by considering the dependence of the pulse energy as a function of different device and material parameters.

U. Bandelow, N. Akhmediev, Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa--Satsuma case, Physics Letters A, 376 (2012), pp. 1558--1561.
Abstract
We present the lowest order rogue wave solution of the Sasa-Satsuma equation (SSE) which is one of the integrable extensions of the nonlinear Schrödinger equation (NLSE). In contrast to the Peregrine solution of the NLSE, it is significantly more involved and contains polynomials of fourth order rather than second order in the corresponding expressions. The correct limiting case of Peregrine solution appears when the extension parameter of the SSE is reduced to zero.

U. Bandelow, N. Akhmediev, Sasa--Satsuma equation: Soliton on a background and its limiting cases, Phys. Rev. E (3), 86 (2012), pp. 026606/1--026606/8.
Abstract
We present a multi-parameter family of a soliton on a background solutions to the Sasa-Satsuma equation. The solution is controlled by a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits a few nontrivial limiting cases that are considered in detail. Among these special cases is the NLSE limit and the limit of rogue wave solutions.

C. Brée, S. Amiranashvili, U. Bandelow, Spatio-temporal pulse propagation in nonlinear dispersive optical media, Optical and Quantum Electronics, (2012), pp. 012963/1--012963/7.
Abstract
We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions.We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.

C. Brée, A. Demircan, G. Steinmeyer, Kramers--Kronig relations and high order nonlinear susceptibilities, Physical Review A, 85 (2012), pp. 033806/1--033806/8.
Abstract
As previous theoretical results recently revealed, a Kramers-Kronig transform of multiphoton absorption rates allows for a precise prediction on the dispersion of the nonlinear refractive index $n_2$ in the near IR. It was shown that this method allows to reproduce recent experimental results on the importance of the higher-order Kerr effect. Extending these results, the current manuscript provides the dispersion of $n_2$ for all noble gases in excellent agreement with reference data. It is furthermore established that the saturation and inversion of the nonlinear refractive index is highly dispersive with wavelength, which indicates the existence of different filamentation regimes. While shorter laser wavelengths favor the well-established plasma clamping regime, the influence of the higher-order Kerr effect dominates in the long wavelength regime.

S. Amiranashvili, A. Demircan, Ultrashort optical pulse propagation in terms of analytic signal, Advances in Optical Technologies, (2011), pp. 989515/1--989515/8.
Abstract
We demonstrate that ultrashort optical pulses propagating in a nonlinear dispersive medium are naturally decribed through incorporation of analytic signal for the electric field. To this end a second-order nonlinear wave equation is first simplified using an unidirectional approximation. Then the analytic signal is introduced and all non-resonant nonlinear terms are eliminated. The derived prpagation equation accounts for arbitrary dispersion, resonant four-wave mixing processes, weak absorption, and arbitrary pulse duration. The model applies to the complex electric field and is independent of the slowly varying envelopeapproximation. Still the derived propagation equation universal structure of the generalized nonlinear Srödinger equation (NSE). in particular, it can be solved numerically with only small changes of the standard split-step solver or more complicted spectral algorithms for NSE. we present exemplary numerical solutions describing supercontimuum generation with an ultrashort optical pulse.

S. Amiranashvili, U. Bandelow, N. Akhmediev, Dispersion of nonlinear group velocity determines shortest envelope solitons, Physical Review A, 84 (2011), pp. 043834/1--043834/5.
Abstract
We demonstrate that a generalized nonlinear Schrödinger equation (NSE), that includes dispersion of the intensity-dependent group velocity, allows for exact solitary solutions. In the limit of a long pulse duration, these solutions naturally converge to a fundamental soliton of the standard NSE. In particular, the peak pulse intensity times squared pulse duration is constant. For short durations this scaling gets violated and a cusp of the envelope may be formed. The limiting singular solution determines then the shortest possible pulse duration and the largest possible peak power. We obtain these parameters explicitly in terms of the parameters of the generalized NSE.

C. Brée, A. Demircan, J. Bethge, E.T.J. Nibbering, S. Skupin, L. Bergé, G. Steinmeyer, Filamentary pulse self-compression: The impact of the cell windows, Physical Review A, 83 (2011), pp. 043803/1-043803/7.
Abstract
Self-compression of multi-millijoule laser pulses during filamentary propagation is usually explained by the interplay of self-focusing and defocusing effects, causing a substantial concentration of energy on the axis of the propagating optical pulse. Recently, it has been argued that cell windows may play a decisive role in the self-compression mechanism. As such windows have to be used for media other than air their presence is often unavoidable, yet they present a sudden non-adiabatic change in dispersion and nonlinearity that should lead to a destruction of the temporal and spatial integrity of the light bullets generated in the self-compression mechanism. We now experimentally prove that there is in fact a self-healing mechanism that helps to overcome the potentially destructive consequences of the cell windows. We show in two carefully conducted experiments that the cell window position decisively influences activation or inhibition of the self-healing mechanism. A comparison with a windowless cell shows that presence of this mechanism is an important prerequisite for the exploitation of self-compression effects in windowed cells filled with inert gases.

A.G. Vladimirov, R. Lefever, M. Tlidi, Relative stability of multipeak localized patterns of cavity solitons, Physical Review A, 84 (2011), pp. 043848/1--043848/4.
Abstract
We study the relative stability of different one-dimensional (1D) and two-dimensional (2D) clusters of closely packed localized peaks of the Swift-Hohenberg equation. In the 1D case, we demonstrate numerically the existence of a spatial Maxwell transition point where all clusters involving up to 15 peaks are equally stable. Above (below) this point, clusters become more (less) stable when their number of peaks increases. In the 2D case, since clusters involving more than two peaks may exhibit distinct spatial arrangements, this point splits into a set of Maxwell transition pointsWe study the relative stability of different one-dimensional (1D) and two-dimensional (2D) clusters of closely packed localized peaks of the Swift-Hohenberg equation. In the 1D case, we demonstrate numerically the existence of a spatial Maxwell transition point where all clusters involving up to 15 peaks are equally stable. Above (below) this point, clusters become more (less) stable when their number of peaks increases. In the 2D case, since clusters involving more than two peaks may exhibit distinct spatial arrangements, this point splits into a set of Maxwell transition points

I. Babushkin, S. Skupin, A. Husakou, Ch. Köhler, E. Cabrera-Granado, L. Bergé, J. Herrmann, Tailoring terahertz radiation by controlling tunnel photoionization events in gases, New Journal of Physics, 13 (2011), pp. 123029/1--123029/16.
Abstract
Applications ranging from nonlinear terahertz spectroscopy to remote sensing require broadband and intense THz radiation which can be generated by focusing two-color laser pulses into a gas. In this setup, THz radiation originates from the buildup of the electron density in sharp steps of attosecond duration due to tunnel ionization, and subsequent acceleration of free electrons in the laser field. We show that the spectral shape of the THz pulses generated by this mechanism is determined by superposition of contributions from individual ionization events. This provides a straightforward analogy with linear diffraction theory, where the ionization events play the role of slits in a grating. This analogy offers simple explanations for recent experimental observations and opens new avenues for THz pulse shaping based on temporal control of the ionization events. We illustrate this novel technique by tailoring the spectral width and position of the resulting radiation using multi-color pump pulses.

J. Bethge, G. Steinmeyer, G. Stibenz, P. Staudt, C. Brée, A. Demircan, H. Redlin, S. Düsterer , Self-compression of 120 fs pulses in a white-light filament, Journal of Optics, 13 (2011), pp. 055203/1--055203/7.
Abstract
Self-compression of pulses with >100 fs input pulse duration from a 10 Hz laser system is experimentally demonstrated, with a compression factor of 3.3 resulting in output pulse durations of 35 fs. This measurement substantially widens the range of applicability of this compression method, enabling self-compression of pulsed laser sources that neither exhibit extremely low pulse-to-pulse energy fluctuations nor a particularly clean beam profile. The experimental demonstration is numerically modeled, revealing the exact same mechanisms at work as at shorter input pulse duration. Additionally, the role of controlled beam clipping with an adjustable aperture is numerically substantiated.

A. Demircan, S. Amiranashvili, G. Steinmeyer, Controlling light by light with an optical event horizon, Physical Review Letters, 108 (2011), pp. 163901/1-163901/4.
Abstract
A novel concept for an all-optical transistor is proposed and verified numerically. This concept relies on cross-phase modulation between a signal and a control pulse. Other than previous approaches, the interaction length is extended by temporally locking control and signal pulse in an optical event horizon, enabling continuous modification of central wavelength, energy, and duration of a signal pulse by an up to sevenfold weaker control pulse. Moreover, if the signal pulse is a soliton it may maintain its solitonic properties during the switching process. The proposed all-optical switching concept fulfills all criteria for a useful optical transistor in [Nature Photon. 4, 3 (2010)], in particular, fan-out and cascadability, which have previously proven as most difficult to meet.

CH. Köhler, E. Cabrera-Granado, I. Babushkin, L. Bergé, J. Herrmann, S. Skupin, Directionality of terahertz emission from photoinduced gas plasmas, Optics Letters, 36 (2011), pp. 3166--3168.
Abstract
Forward and backward THz emission by ionizing two-color laser pulses in gas is investigated by means of a simple semi-analytical model based on Jefimenko's equation and rigorous Maxwell simulations in one and two dimensions. We find the emission in backward direction having a much smaller spectral bandwidth than in forward direction and explain this by interference effects. Forward THz radiation is generated predominantly at the ionization front and is thus almost not affected by the opacity of the plasma, in excellent agreement with results obtained from a unidirectional pulse propagation model.

C. Brée, A. Demircan, G. Steinmeyer, Modulation instability in filamentary self-compression, Laser Physics, 21 (2011), pp. 1313--1318.
Abstract
We numerically analyze filamentary propagation for various medium- and input pulse parameters and show that temporal self-compression can greatly benefit from refocusing events. Analyzing the dynamical behavior in the second focal spot, it turns out that a dispersive temporal break-up may appear due to the emission of a hyperbolic shock-wave from the self-steepened trailing edge of the pulse. This break-up event enhances the self-compression capabilities of laser filaments, enabling up to 12-fold temporal compression. Only slightly perturbing the input pulse parameters, we further identify a regime in which refocusing events give rise to extended subdiffractive propagation in a weakly ionized channel.

S. Amiranashvili, A. Demircan, Hamiltonian structure of propagation equations for ultrashort optical pulses, Physical Review A, 82 (2010), pp. 013812/1--013812/11.

S. Amiranashvili, A.G. Vladimirov, U. Bandelow, A model equation for ultrashort optical pulses around the zero dispersion frequency, The European Physical Journal D. Atomic, Molecular, Optical and Plasma Physics, 58 (2010), pp. 219--226.
Abstract
The nonlinear Schrödinger equation based on the Taylor approximation of the material dispersion can become invalid for ultrashort and few-cycle optical pulses. Instead, we use a rational fit to the dispersion function such that the resonances are naturally accounted for. This approach allows us to derive a simple non-envelope model for short pulses propagating in one spatial dimension. This model is further investigated numerically and analytically.

S. Amiranashvili, U. Bandelow, A. Mielke, Padé approximant for refractive index and nonlocal envelope equations, Optics Communications, 283 (2010), pp. 480--485.
Abstract
Padé approximant is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore we introduce a diagonal Padé approximant for the complex refractive index and apply it to the description of short optical pulses. This yields a new nonlocal envelope equation for pulse propagation. The model offers a global representation of arbitrary medium dispersion and absorption, e.g., the fulfillment of the Kramers-Kronig relation can be established. In practice, the model yields an adequate description of spectrally broad pulses for which the polynomial dispersion operator diverges and can induce huge errors.

C. Brée, A. Demircan, G. Steinmeyer, Method for computing the nonlinear refractive index via Keldysh theory, IEEE J. Quantum Electron., 46 (2010), pp. 433--437.

C. Brée, J. Bethge, S. Skupin, L. Bergé, A. Demircan, G. Steinmeyer, Cascaded self-compression of femtosecond pulses in filaments, New Journal of Physics, 12 (2010), pp. 093046/1--093046/11.

C. Brée, A. Demircan, S. Skupin, L. Bergé, G. Steinmeyer, Plasma induced pulse breaking in filamentary self-compression, Laser Physics, 20 (2010), pp. 1107--1113.
Abstract
A plasma induced temporal break-up in filamentary propagation has recently been identified as one of the key events in the temporal self-compression of femtosecond laser pulses. An analysis of the Nonlinear Schrödinger Equation coupled to a noninstantaneous plasma response yields a set of stationary states. This analysis clearly indicates that the emergence of double-hump, characteristically asymmetric temporal on-axis intensity profiles in regimes where plasma defocusing saturates the optical collapse caused by Kerr self-focusing is an inherent property of the underlying dynamical model.

A.G. Vladimirov, U. Bandelow, G. Fiol, D. Arsenijević, M. Kleinert, D. Bimberg, A. Pimenov, D. Rachinskii, Dynamical regimes in a monolithic passively mode-locked quantum dot laser, Journal of the Optical Society of America. B, 27 (2010), pp. 2102-2109.

J. Becker, K. Gärtner, R. Klanner, R. Richter, Simulation and experimental study of plasma effects in planar silicon sensors, Nuclear Instruments and Methods in Physics Research Section A, 624 (2010), pp. 716--727.

J. Bethge, G. Steinmeyer, G. Stibenz, P. Staudt, C. Brée, A. Demircan, H. Redlin, S. Düsterer , Self-compression of 120 fs pulses in a white-light filament, Journal of Optics, 13 (2011), pp. 055203/1--055203/7.
Abstract
Self-compression of pulses with >100 fs input pulse duration from a 10 Hz laser system is experimentally demonstrated, with a compression factor of 3.3 resulting in output pulse durations of 35 fs. This measurement substantially widens the range of applicability of this compression method, enabling self-compression of pulsed laser sources that neither exhibit extremely low pulse-to-pulse energy fluctuations nor a particularly clean beam profile. The experimental demonstration is numerically modeled, revealing the exact same mechanisms at work as at shorter input pulse duration. Additionally, the role of controlled beam clipping with an adjustable aperture is numerically substantiated.

H.-G. Purwins, H. Bödeker, S. Amiranashvili, Dissipative solitons, Advances in Physics, 59 (2010), pp. 485--701.

M. Tlidi, A.G. Vladimirov, D. Turaev, G. Kozyreff, D. Pieroux, T. Erneux, Spontaneous motion of localized structures and localized patterns induced by delayed feedback, The European Physical Journal D. Atomic, Molecular, Optical and Plasma Physics, 59 (2010), pp. 59-65.

I. Babushkin, W. Kuehn, Ch. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, Th. Elsaesser, Ultrafast spatio-temporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases, Physical Review Letters, 105 (2010), pp. 053903/1-053903/4.
Abstract
We present a combined theoretical and experimental study of spatio-temporal propagation effects in terahertz (THz) generation in gases using two-color ionizing laser pulses. The observed strong broadening of the THz spectra with increasing gas pressure reveals the prominent role of spatio-temporal reshaping and of a plasma-induced blue-shift of the pump pulses in the generation process. Results obtained from (3+1)-dimensional simulations are in good agreement with experimental findings and clarify the mechanisms responsible for THz emission.

I. Babushkin, S. Skupin, J. Herrmann, Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides, Optics Express, 18 (2010), pp. 9658--9663.
Abstract
The generation of THz radiation from ionizing two-color femtosecond pulses propagating in metallic hollow waveguides filled with Ar is numerically studied. We observe a strong reshaping of the low-frequency part of the spectrum. Namely, after several millimeters of propagation the spectrum is extended from hundreds of GHz up to $sim 150$ THz. For longer propagation distances, nearly single-cycle near-infrared pulses with wavelengths around 4.5 $mu$m are obtained by appropriate spectral filtering, with an efficiency of up to 0.25 %.

S. Amiranashvili, U. Bandelow, A. Mielke, Padé approximant for refractive index and nonlocal envelope equations, Optics Communications, 283 (2009), pp. 480--485.
Abstract
Padé approximant is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore we introduce a diagonal Padé approximant for the complex refractive index and apply it to the description of short optical pulses. This yields a new nonlocal envelope equation for pulse propagation. The model offers a global representation of arbitrary medium dispersion and absorption, e.g., the fulfillment of the Kramers-Kronig relation can be established. In practice, the model yields an adequate description of spectrally broad pulses for which the polynomial dispersion operator diverges and can induce huge errors.

C. Brée, A. Demircan, S. Skupin, L. Bergé, G. Steinmeyer, Self-pinching of pulsed laser beams during filamentary propagation, Optics Express, 17 (2009), pp. 16429--16435.

C. Brée, A. Demircan, G. Steinmeyer, Asymptotic pulse shapes in filamentary propagation of intense femtosecond pulses, Laser Physics, 19 (2009), pp. 330--335.

G. Kozyreff, M. Tlidi, A. Mussot, E. Louvergneaux, M. Taki, A.G. Vladimirov, Localized beating between dynamically generated frequencies, Physical Review Letters, 102 (2009), pp. 043905/1--043905/4.

M. Tlidi, A.G. Vladimirov, D. Pieroux, D. Turaev, Spontaneous motion of cavity solitons induced by a delayed feedback, Physical Review Letters, 103 (2009), pp. 103904/1--103904/4.

S. Amiranashvili, A.G. Vladimirov, U. Bandelow, Solitary-wave solutions for few-cycle optical pulses, Physical Review A, 77 (2008), pp. 063821/1--063821/7.

M. Pietrzyk, I. Kanattšikow, U. Bandelow, On the propagation of vector ultra-short pulses, Journal of Nonlinear Mathematical Physics, 15 (2008), pp. 162-170.

A. Bhattacherjee, M. Pietrzyk, Transport behaviour of a Bose--Einstein condensate in a bichromatic optical lattice, Central European Journal of Mathematics, 6 (2008), pp. 26-32.
Abstract
The Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice is investigated. We show that the effective mass increases in an optical superlattice, which leads to localization of the BEC, in accordance with recent experimental observations [17]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.

D. Turaev, M. Radziunas, A.G. Vladimirov, Chaotic soliton walk in periodically modulated media, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 77 (2008), pp. 06520/1--06520/4.

A. Demircan, M. Pietrzyk, U. Bandelow, Effects of higher-order dispersion on pulse splitting in the normal dispersion regime, Optical and Quantum Electronics, 40 (2008), pp. 455-460.

M. Tlidi, A. Mussot, E. Louvergneaux, G. Kozyreff, A.G. Vladimirov, M. Taki, Control and removing of modulational instabilities in low dispersion photonic crystal fiber cavities, , 32 (2007), pp. 662-664.

D. Turaev, A.G. Vladimirov, S. Zelik, Chaotic bound state of localized structures in the complex Ginzburg--Landau equation, Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 75 (2007), pp. 045601/1-045601/4.

A. Demircan, U. Bandelow, Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation, Applied Physics B: Lasers and Optics, 86 (2007), pp. 31-39.

A.G. Vladimirov, D.V. Skryabin, G. Kozyreff, P. Mandel, M. Tlidi, Bragg localized structures in a passive cavity with transverse modulation of the refractive index and the pump, Optics Express, 14 (2006), pp. 1--6.

M. Nizette, D. Rachinskii, A. Vladimirov, M. Wolfrum, Pulse interaction via gain and loss dynamics in passive mode-locking, Physica D. Nonlinear Phenomena, 218 (2006), pp. 95--104.

A. Yulin, D. Skryabin, A.G. Vladimirov, Modulation instability of discrete solitons in coupled waveguides with group velocity dispersion, , 14 (2006), pp. 12347--12352.

A. Demircan, M. Kroh, U. Bandelow, B. Hüttl, H.-G. Weber, Compression limit by third-order dispersion in the normal dispersion regime, IEEE Phot. Tech. Letter, 18 (2006), pp. 2353-2355.

A. Demircan, U. Bandelow, Limit for pulse compression by pulse splitting, Optical and Quantum Electronics, 38 (2006), pp. 1167--1172.

A. Demircan, U. Bandelow, Supercontinuum generation by the modulation instability, Optics Communications, 244 (2005), pp. 181--185.

S.V. Fedorov, N.N. Rosanov, A.N. Shatsev, N.A. Veretenov, A.G. Vladimirov, Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with saturable absorber, IEEE J. Quantum Electron., 39 (2003), pp. 216--226.

N. Seehafer, A. Demircan, Dynamo action in cellular convection, Magnetohydrodynamics. Consultants Bureau, New York (US). Consultants Bureau, New York. Translation from: Magnitnaya Gidrodinamika., 39 (2003), pp. 335--342.

M. Tlidi, A.G. Vladimirov, P. Mandel, Interaction and stability of periodic and localized structures in optical bistable systems, IEEE J. Quantum Electron., 39 (2003), pp. 197--205.

M. Kolarczik, F. Böhm, U. Woggon, N. Owschimikow, A. Pimenov, M. Wolfrum, A.G. Vladimirov, S. Meinecke, B. Lingnau, L. Jaurigue, K. Lüdge, Coherent and incoherent dynamics in quantum dots and nanophotonic devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in Solid-State Sciences, Springer, Cham, 2020, pp. 91--133, DOI 10.1007/978-3-030-35656-9_4 .
Abstract
The interest in coherent and incoherent dynamics in novel semiconductor gain media and nanophotonic devices is driven by the wish to understand the optical gain spectrally, dynamically, and energetically for applications in optical amplifiers, lasers or specially designed multi-section devices. This chapter is devoted to the investigation of carrier dynamics inside nanostructured gain media as well as to the dynamics of the resulting light output. It is structured into two parts. The first part deals with the characterization of ultrafast and complex carrier dynamics via the optical response of the gain medium with pump-probe methods, two-color four-wave mixing setups and quantum-state tomography. We discuss the optical nonlinearities resulting from light-matter coupling and charge carrier interactions using microscopically motivated rate-equation models. In the second part, nanostructured mode-locked lasers are investigated, with a focus on analytic insights about the regularity of the pulsed light emission. A method for efficiently predicting the timing fluctuations is presented and used to optimize the device properties. Finally, one specific design of a mode-locked laser with tapered gain section is discussed which draws the attention to alternative ways of producing very stable and high intensity laser pulses.

N. Akhmediev, A. Ankiewicz, S. Amiranashvili, U. Bandelow, Generalized integrable evolution equations with an infinite number of free parameters, in: Workshop on Nonlinear Water Waves, S. Murashige, ed., 2109 of RIMS Kôkyûroku Bessatsu, RIMS, Kyoto, 2019, pp. 33--46.
Abstract
Evolution equations such as the nonliear Schrödinger equation (NLSE) can be extended to include an infinite number of free parameters. The extensions are not unique. We give two examples that contain the NLSE as the 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.

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. 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.

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.

G. Slavcheva, M.V. Koleva, A. Pimenov, Simulation of nonlinear polariton dynamics in microcavity wires for polaritonic integrated circuits, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2017, J. Piprek, M. Willatzen, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 187--188, DOI 10.1109/NUSOD.2017.8010054 .

D. Puzyrev, A.G. Vladimirov, A. Pimenov, S.V. Gurevich, S. Yanchuk, Pulse bound-state clusters in coupled mode-locked lasers, in: Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) 2017 Conference on, IEEE, New York, 2017, DOI 10.1109/CLEOE-EQEC.2017.8087527 .
Abstract
Mode-locked semiconductor lasers are widely used for generation of short optical pulses with high repetition rates and optical frequency combs suitable for numerous practical applications. By combining many lasers into an array one can achieve much larger output power and substantially improve the characteristics of the output radiation. In this presentation we study dynamical regimes of operation in an array of mode-locked lasers locally coupled in a ring geometry. We demonstrate that unlike a solitary mode-locked laser emitting a sequence of equidistant pulses with the pulse repetition frequency close to the inverse cavity round trip time, an array of mode-locked lasers can radiate a periodic sequence of clusters of fundamental mode-locked pulses. This regime associated with the formation of closely packed bound states of coupled mode-locked pulses due to a balance between attraction and repulsion is very different from the standard harmonic mode-locked regime where the pulses always repel each other.

S. Pickartz, C. Brée, U. Bandelow, S. Amiranashvili, Cancellation of Raman self-frequency shift for compression of optical pulses, in: Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices -- NUSOD 2017, J. Piprek, M. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, 2017, pp. 173--174.

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.

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. Tlidi, E. Averlant, A.G. Vladimirov, A. Pimenov, S. Gurevich, K. Panayotov, Localized structures in broad area VCSELs: Experiments and delay-induced motion, in: Structural Nonlinear Dynamics and Diagnosis, M. Belhaq, ed., 168 of Springer Proceedings in Physics, Springer, 2015, pp. 329349/1--329349/21.

U. Bandelow, S. Amiranashvili, N. Akhmediev, Limitation for ultrashort solitons in nonlinear optical fibers by cusp formation, in: CLEO®/Europe -- EQEC 2015: Conference Digest, OSA Technical Digest (Online) (Optical Society of America, 2015), paper EI-2.3 THU, 2015, pp. 1--1.

S. Amiranashvili, U. Bandelow, N. Akhmediev, Recent progress in theory of pulse propagation in optical fibers, in: Proceedings of the 14th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2014, 1--4 September 2014, J. Piprek, J. Javaloyes, eds., IEEE Conference Publications Management Group, Piscataway, NJ, USA, 2014, pp. 131--132.

R.M. Arkhipov, M.V. Arkhipov, Mode-locking in two section and single section lasers due to coherent interaction of light and matter in the gain and absorbing media, in: Proceedings of the XIV School Seminar Wave Phenomena in Inhomogeneous Media (Waves 2014), Section 3, Nonlinear and coherent optics (in electronic form and in Russian), 2014, pp. 43--45.

S. Amiranashvili, A. Demircan, C. Brée, G. Steinmeyer, F. Mitschke, Manipulating light by light in optical fibers, in: 3rd Bonn Humboldt Award Winners' Forum ``Frontiers in Quantum Optics: Taming the World of Atoms and Photons -- 100 Years after Niels Bohr'', Bonn, October 9--12, 2013, Networking Guide, pp. 58--59.

A.G. Vladimirov, D. Rachinskii, M. Wolfrum, Modeling of passively mode-locked semiconductor lasers, in: Nonlinear Laser Dynamics: From Quantum Dots to Cryptography, K. Lüdge, ed., Reviews in Nonlinear Dynamics and Complexity, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2012, pp. 183--216.

I. Babushkin, S. Skupin, C. Köhler, L. Bergé, J. Herrmann, Modeling of THz emission from plasma-generating femtosecond laser pulses with unidirectional Maxwell equation in plasma spots and in guided geometries, in: Book of Abstracts of the 2nd International Workshop on Laser-Matter Interaction 2010, September 13--17, 2010, Porquerolles, France, 2010, pp. 49.

C. Brée, J. Bethge, A. Demircan, E.T. Nibbering, G. Steinmeyer, On the origin of negative dispersion contributions in filamentary propagation, in: Conference on Lasers and Electro-Optics (CLEO), OSA Technical Digest (CD), Optical Society of America, 2010, pp. CMU2/1-CMU2/2.
Abstract
http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2010-CMU2

C. Brée, J. Bethge, S. Skupin, L. Bergé, A. Demircan, G. Steinmeyer, Double self-compression of femtosecond pulses in filaments, in: Conference on Lasers and Electro-Optics (CLEO), OSA Technical Digest (CD), Optical Society of America, 2010, pp. JThD6/1--JThD6/2.

A.G. Vladimirov, M. Wolfrum, G. Fiol, D. Arsenijević, D. Bimberg, E. Viktorov, P. Mandel, D. Rachinskii, Locking characteristics of a 40-GHz hybrid mode-locked monolithic quantum dot laser, in: Semiconductor Lasers and Laser Dynamics IV, K. Panajotov, M. Sciamanna, A.A. Valle, R. Michalzik, eds., 7720 of Proceedings of SPIE, SPIE, 2010, pp. 77200Y/1--77200Y/8.

C. Brée, A. Demircan, S. Skupin, L. Bergé, G. Steinmeyer, Nonlinear photon z-pinching in filamentary self-compression, in: Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD), Optical Society of America, 2009, pp. ITuC1/1--ITuC1/2.

C. Brée, A. Demircan, S. Skupin, L. Bergé, G. Steinmeyer, Nonlinear photon z-pinching in filamentary self-compression, in: CLEO/Europe and EQEC 2009 Conference Digest (Optical Society of America, 2009), paper CF5_4, 2009, pp. 1-1.

C. Krüger, A. Demircan, S. Skupin, G. Stibenz, N. Zhavoronkov, G. Steinmeyer, Asymptotic pulse shapes and pulse self-compression in femtosecond filaments, in: Ultrafast Phenomena XVI, Proceedings of the 16th International Conference, June 9--13, 2009, Stresa, Italy, P. Corkum, S. Silvestri, K.A. Nelson, E. Riedle, R.W. Schoenlein, eds., 92 of Springer Series in Chemical Physics, Springer, 2009, pp. 804.

D. Turaev, A.G. Vladimirov, S. Zelik, Strong enhancement of interaction of optical pulses induced by oscillatory instability, in: CLEO/Europe and EQEC 2009 Conference Digest (Optical Society of America, 2009), poster EH.P.13 WED, 2009, pp. 1--1.

C. Krüger, A. Demircan, G. Stibenz, N. Zhavoronkov, G. Steinmeyer, Asymptotic pulse shapes in filamentary propagation of femtosecond pulses and self-compression, in: Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, May 04--09, 2008, San Jose, CA, 1--9 of IEEE Lasers and Electro-Optics Society (LEOS) Annual Meeting, IEEE, New York, NY, USA, 2008, pp. 2501-2502.

M. Pietrzyk, I. Kanattšikow, A. Demircan, On the compression of ultrashort optical pulses beyond the slowly varying envelope approximation, in: Proceedings of the 8th International Conference on Numerical Simulation of Optoelectronic Devices NUSOD'08, J. Piprek, E. Larkins, eds., IEEE/LEOS, 2008, pp. 59--60.

A. Mussot, M. Tlidi, E. Louvergneaux, G. Kozyref, A.G. Vladimirov, M. Taki, Removing modulational instabilities in low dispersion fiber cavities, in: 2007 European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference (CLEO® / Europe-IQEC) Conference Digest (oral presentation CD-9-WED), IEEE, 2007, pp. 1--1.

T. Ziems, K.N. Adarsh, M. Böhm, A. Demircan, F.M. Mitschke, Self-organized supercontinuum generation from a nonlinear fiber resonator, in: Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest (CD), 2007, pp. JWBPDP7/1--JWBPDP7/3.

A. Demircan, M. Kroh, M. Pietrzyk, B. Hüttl, U. Bandelow, Non-Raman redshift by pulse splitting in the normal dispersion regime, in: Proceedings of the 7th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD '07, 24--27 September 2007, J. Piprek, D. Prather, eds., IEEE, Piscataway, NJ, 2007, pp. 99--100.

A. Demircan, U. Bandelow, M. Kroh, B. Hüttl, Generation of new frequencies by pulse splitting, in: Proceedings of ECOC 07, 5, VDE Verlag GmbH, Berlin/Offenbach, 2007, pp. 73-74.

A. Demircan, U. Bandelow, Interplay between soliton fission and modulation instability, in: Proceedings of the European Conference on Lasers and Electro-Optics, 2007, and the International Quantum Electronics Conference. CLEO/IQEC 2007 (oral presentation CF-3-MON), IEEE, 2007, pp. 1--1.

A.G. Vladimirov, D.V. Skryabin, M. Tlidi, Localized structures of light in nonlinear devices with intracavity photonic bandgap material, in: 2007 European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference (CLEO®/Europe-IQEC) Conference Digest (oral presentation IG-4-MON), IEEE, 2007, pp. 1--1.

U. Bandelow, A. Demircan, Pulse splitting by third-order dispersion, in: Proc. of the 6th Int. Conf. on Numerical Simulation of Optoelectronic Devices (NUSOD 06) IEEE Catalog 06EX1456, J. Piprek, S.-F. Yu, eds., IEEE, Piscataway, NJ, 2006, pp. 113--114.

U. Bandelow, A. Demircan, Impact of modulation instability on the supercontinuum generation, in: Proceedings of the 5th International Conference on ``Numerical Simulation of Optoelectronic Devices'' (NUSOD'05) in Berlin, September 19--22, 2005, H.-J. Wünsche, J. Piprek, U. Bandelow, H. Wenzel, eds., IEEE, Piscataway, NJ, 2005, pp. 65--66.

D.A. Dolinina, A. Vladimirov, Synchronization between Kerr cavity solitons and broad laser pulse injection, Preprint no. 3140, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3140 .
Abstract, PDF (658 kByte)
The synchronization of a soliton frequency comb in a Kerr cavity with pulsed laser injection is studied numerically. A neutral delay differential equation is used to model the light dynamics in the cavity. This model allows for the investigation of both cases where the pulse repetition period is close to the cavity round-trip time and where the repetition period of the injection pulses is close to a rational fraction M/N of the round-trip time. It is demonstrated that solitons can exist in this latter case, provided that the injection pulses are of a higher amplitude, which is directly proportional to the number M. Furthermore, it is shown that the synchronization range of the solitons is also proportional to the number M . The solitons excited by pulses with a period slightly different from the M : N -resonance can be destabilized by the Andronov--Hopf bifurcation, which occurs when the injection level at the soliton position decreases to M times the injection amplitude corresponding to the saddle-node bifurcation in a model equation with uniform injection.

S. Amiranashvili, R. Čiegis, Stability of the higher-order splitting methods for the generalized nonlinear Schrödinger equation, Preprint no. 3070, WIAS, Berlin, 2023, DOI 10.20347/WIAS.PREPRINT.3070 .
Abstract, PDF (372 kByte)
The numerical solution of the generalized nonlinear Schrödinger equation by explicit splitting methods can be disturbed by so-called spurious instabilities. They are manifested by the appearance of extraneous spectral peaks which change their position in the frequency domain and disappear with decreasing integration step. The spurious instabilities can coexist with the true physical ones, like modulation instability, in which case they are particularly difficult to detect. We consider an arbitrary multiplicative splitting method and discuss conditions necessary for the absence of spurious instabilities.

S. Amiranashvili, Modeling of ultrashort optical pulses in nonlinear fibers, Preprint no. 2918, WIAS, Berlin, 2022, DOI 10.20347/WIAS.PREPRINT.2918 .
Abstract, PDF (17 MByte)
This work deals with theoretical aspects of pulse propagation. The core focus is on extreme, few-cycle pulses in optical fibers, pulses that are strongly affected by both dispersion and nonlinearity. Using Hamil- tonian methods, we discuss how the meaning of pulse envelope changes, as pulses become shorter and shorter, and why an envelope equation can still be used. We also discuss how the standard set of dispersion coefficients yields useful rational approximations for the chromatic dispersion in optical fibers. Three more specific problems are addressed thereafter. First, we present an alternative framework for ultra- short pulses in which non-envelope propagation models are used. The approach yields the limiting, shortest solitons and reveals their universal features. Second, we describe how one can manipulate an ultrashort pulse, i.e., to change its amplitude and duration in a predictable manner. Quantitative theory of the manipu- lation is presented based on perturbation theory for solitons and analogy between classical fiber optics and quantum mechanics. Last but not least, we consider a recently found alternative to the standard split-step approach for numerical solutions of the pulse propagation equations.

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.

U. Bandelow, A. Demircan, M. Kesting, Simulation of pulse propagation in nonlinear optical fibers, Report no. 23, WIAS, Berlin, 2003, DOI 10.20347/WIAS.REPORT.23 .
Abstract, Postscript (1020 kByte), PDF (627 kByte)
We solve numerically a generalized nonlinear Schroedinger equation by using a pseudospectral method. Integration is performed by using an eight-order Runge-Kutta scheme. The numerical method therefore differs from the commonly used split-step method. Effects such as the impact of group velocity dispersion (GVD) up to fourth-order dispersion, self phase modulation (SPM), self-steepening and intrapulse Raman scattering can be investigated with the code. Examples for the above effects are demonstrated, as well as their interplay in the context of soliton propagation and sub-picosecond pulses.

R.M. Arkhipov, I. Babushkin, M.V. Arkhipov, Coherent passive mode-locking in lasers: Qualitative analysis and numerical simulations, Preprint no. 2019, WIAS, Berlin, 2014, DOI 10.20347/WIAS.PREPRINT.2019 .
Abstract, PDF (4493 kByte)
In the present work we report the possibility of passive mode-locking based on the coherent interaction of light with the amplifying and absorbing media in lasers with ring and linear cavities. We consider the realistic and practically interesting case when the absorbing and amplifying media are separated in the cavity space but not homogeneously mixed in the volume of the cavity, as was considered earlier in the literature. We perform qualitative consideration of coherent passive mode-locking based on the area theorem of McCall and Hahn and its graphical representation for the first time. We show that other, not soliton scenarios of passive mode-locking exist, and that coherent mode-locking is self-starting (lasing without an injection seeding pulse is possible). We point to the fact that the spectral width of the laser generation can be significantly larger than the spectral bandwidth of the gain medium. Numerical simulations were performed using the system of Maxwell-Bloch equations in the slowly varying envelope approximation.

B. Borchers, C. Brée, S. Birkholz, A. Demircan, G. Steinmeyer, Saturation of the all-optical Kerr effect in solids, Preprint no. 1891, WIAS, Berlin, 2013, DOI 10.20347/WIAS.PREPRINT.1891 .
Abstract, PDF (281 kByte)
We discuss the influence of the higher-order Kerr effect (HOKE) in wide band gap solids at extreme intensities below the onset of optically induced damage. Using different theo- retical models, we employ multiphoton absorption rates to compute the nonlinear refractive index by a Kramers-Kronig transform. Within this theoretical framework we provide an esti- mate for the appearance of significant deviations from the standard optical Kerr effect pre- dicting a linear index change with intensity. We discuss the role of the observed saturation behavior in practically relevant situations, including Kerr lens mode-locking and supercon- tinuum generation in photonic crystal fibers. Furthermore we present experimental data from a multi-wave mixing experiment in BaF2 which can be explained by the appearance of the HOKE.

I. Babushkin, The fundamental solution of unidirectional pulse propagation equation, Preprint no. 1808, WIAS, Berlin, 2013, DOI 10.20347/WIAS.PREPRINT.1808 .
Abstract, Postscript (912 kByte), PDF (998 kByte)
In the article the fundamental solution of a variant of wave equation known as “unidirectional pulse propagation equation” (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented as a projection of a fundamental solution of the wave equation to some functional subspace. We discuss the degree of equivalence of UPPE and wave equation in this respect. In particular, we show that UPPE, in contrast to the widespread belief, describes the wave propagation in both directions simultaneously, and remark non-causal character of its solutions.

R. Driben, I. Babushkin, Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic crystal fibers, Preprint no. 1754, WIAS, Berlin, 2012, DOI 10.20347/WIAS.PREPRINT.1754 .
Abstract, Postscript (3703 kByte), PDF (1012 kByte)
Soliton fusion is a fascinating and delicate phenomenon that manifests itself in optical fibers in case of interaction between co-propagating solitons with small temporal and wavelengths separation. We show that the mechanism of acceleration of trailing soliton by dispersive waves radiated from the preceding one provides necessary conditions for soliton fusion at the advanced stage of supercontinuum generation in photonic crystal fibers (PCFs). As a result of fusion large intensity robust light structures arise and propagate over significant distances. In presence of small random noise the delicate condition for the effective fusion between solitons can easily be broken, making the fusion induced giant waves a rare statistical event. Thus oblong-shaped giant accelerated waves become excellent candidates for optical rogue waves.

U. Sapaev, I. Babushkin, J. Herrmann, Quasi-phase-matching for third harmonic generation in noble gases employing ultrasound, Preprint no. 1753, WIAS, Berlin, 2012, DOI 10.20347/WIAS.PREPRINT.1753 .
Abstract, Postscript (10 MByte), PDF (814 kByte)
We study a novel method of quasi-phase-matching for third harmonic generation in a gas cell using the periodic modulation of the gas pressure and thus of the third order nonlinear coefficient in the axial direction created by an ultrasound wave. Using a comprehensive numerical model we describe the quasi-phase matched third harmonic generation of UV (at 266 nm) and VUV pulses (at 133 nm) by using pump pulses at 800 nm and 400 nm, respectively, with pulse energy in the range from 3 mJ to 1 J. In addition, using chirped pump pulses, the generation of sub-20-fs VUV pulses without the necessity for an external chirp compensation is predicted.

L. Bergé, S. Skupin, Ch. Köhler, I. Babushkin, J. Herrmann, 3D numerical simulations of THz generation by two-color laser filaments, Preprint no. 1752, WIAS, Berlin, 2012, DOI 10.20347/WIAS.PREPRINT.1752 .
Abstract, Postscript (2293 kByte), PDF (528 kByte)
Terahertz (THz) radiation produced by the filamentation of two-color pulses over long distances in argon is numerically investigated using a comprehensive model in full space-time resolved geometry. We show that the dominant physical mechanism for THz generation in the filamentation regime at clamping intensity is based on quasi-dc plasma currents. The calculated THz spectra for different pump pulse energies and pulse durations are in agreement with previously reported experimental observations. For the same pulse parameters, near-infrared pump pulses at 2 $mu$m are shown to generate a more than one order of magnitude larger THz yield than pumps centered at 800 nm.

D. Turaev, A.G. Vladimirov, S. Zelik, Strong synchronization of weakly interacting oscillons, Preprint no. 1659, WIAS, Berlin, 2011, DOI 10.20347/WIAS.PREPRINT.1659 .
Abstract, Postscript (23 MByte), PDF (7332 kByte)
We study interaction of well-separated oscillating localized structures (oscillons). We show that oscillons emit weakly decaying dispersive waves, which leads to formation of bound states due to subharmonic synchronization. We also show that in optical applications the Andronov-Hopf bifurcation of stationary localized structures leads to a drastic increase in their interaction strength.

D. Dolinina, Desynchronization of temporal solitons in Kerr cavities with pulsed injection, XLIV Dynamics Days Europe, Bremen, July 29 - August 2, 2024.

D. Dolinina, Desynchronization of temporal solitons in Kerr cavities with pulsed injection, XLIV Dynamics Days Europe, Bremen, July 29 - August 2, 2024.

S. Amiranashvili, Role of modulation instability in numerical analysis, 6th International Conference on Application of Optics and Photonics, July 16 - 19, 2024, University of Aveiro, Portugal.

S. Amiranashvili, Role of modulation instability in numerical analysis, XX Workshop on Instabilities and Nonequilibrium Structures, October 7 - 9, 2024, Institut de Physique de Nice, France, October 8, 2024.

U. Bandelow, Modeling of pulse propagation in nonlinear dispersive media at WIAS Berlin, Workshop on ``Integrability for Higher-Order Optical Pulse Propagation'' associated with the meeting of the Australian and New Zeeland Association of Mathematical Physics (ANZAMP), February 6 - 9, 2024, Katoomba, Australia, February 9, 2024.

A.G. Vladimirov , Dynamics of neutral delay differential equation model of a dispersive Kerr cavity, Dynamics day in Shangai, China, September 8, 2024.

A.G. Vladimirov , Modeling dispersive nonlinear optical cavities using delay differential equations, XX Workshop on Instabilities and Nonequilibrium Structures, October 7 - 9, 2024, Institut de Physique de Nice, France, October 8, 2024.

A.G. Vladimirov , Short pulse interaction in delay differential equation models of mode-locked lasers, Dynamics day in Jinhua, September 10 - 15, 2024, China, September 11, 2024.

S. Amiranashvili, Numerical aspects of modulation instability, 26th International Conference on Mathematical Modelling and Analysis, May 30 - June 2, 2023, University of Latvia, Jurmala, Latvia, June 1, 2023.

S. Amiranashvili, Numerical aspects of modulation instability, Extreme Waves 2023, August 28 - September 1, 2023, Max-Planck-Institut für Physik komplexer Systeme, Dresden, August 28, 2023.

A.G. Vladimirov, Neutral delay differential equation Kerr cavity model, Dissipative Solitons, Turbulence and Extreme Events in Nonlinear Photonics, September 6 - 8, 2023, International Solvay Institutes, Brussels, Belgium, September 8, 2023.

A. Pimenov, Localized structures in a passive ring cavity with two filters under optical injection, Nonlinear Waves and Turbulence in Photonics 2022, WIAS Berlin, July 15, 2022.

A. Pimenov, Chromatic dispersion in delayed differential equations for optical cavities and localized structures, MURPHYS 2022- International Conference on Multiple Scale Systems and Hysteresis, May 30 - June 3, 2022, Mathematical Institute, Silesian University, Opava, Czech Republic, May 30, 2022.

S. Amiranashvili, Unusual ways of four-wave mixing instability, Nonlinear Waves and Turbulence in Photonics 2022, WIAS Berlin, July 14, 2022.

F. Severing, How numerics add to the instabilities of the generalised nonlinear Schrödinger equation, Nonlinear Waves and Turbulence in Photonics 2022, Berlin, July 14 - 15, 2022.

F. Severing , Nonlinear Schrödinger Equation -- Flawless description of modulation instability?, Student Chapter Poster Session (SCPS) 2022 (Online Event), Sussex, UK, February 20, 2022.

F. Severing , How numerics add to the instabilities of the generalised nonlinear Schrödinger equation, Minisymposium for Young Researchers 2022, WIAS Berlin, July 21, 2022.

S. Amiranashvili, Seminar zum Thema: Nicht Hermiteschen Operationen, August 10 - 11, 2022, TU Wien, Austria.

A.G. Vladimirov, Short pulse solutions of time-delay laser models (online talk), Dynamics Days Europe 2021 (Online Event), Minisymposium MS34 ``Time Delayed Systems: Theory and Experiments'', August 23 - 27, 2021, Université Côte d'Azur, Nice, France, August 27, 2021.

S. Amiranashvili, Controlling light by light, Waves Côte d'Azur, June 4 - 7, 2019, Université 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.

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, 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.

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.

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.

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, 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.

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

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

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

A. Pimenov, Novel delayed model of a broad-area laser: Are the light bullets robust?, Minisymposium ,,Dynamics of novel mode-locked and frequency-swept lasers (DNMFL2017)'', December 18 - 19, 2017, WIAS, Berlin, December 18, 2017.

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

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

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

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

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

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. 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, 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, 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 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.

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. Hofmann, C. Brée, On the role of Freeman resonances in pump-probe measurements of the nonlinear refractive index, CLEO/Europe-EQEC 2015 Conference, München, June 19 - 25, 2015.

M. Hofmann, Ab-initio description of optical nonlinearities in femtosecond filaments, International Workshop ``Waves, Solitons and Turbulence in Optical Systems'' (WASTOS15), Berlin, October 12 - 14, 2015.

M. Hofmann, Intensity clamping at a Freeman resonance, CLEO: 2015 -- Laser Science to Photonic Applications, May 9 - 19, 2015, San José, USA, May 11, 2015.

M. Hofmann, Intensity clamping at a Freeman resonance, CLEO/Europe-EQEC 2015 Conference, June 19 - 25, 2015, München, June 22, 2015.

M. Hofmann, Nonlinear refractive index in filaments governed by resonantly enhanced ionization, 24th Annual International Laser Physics Workshop (LPHYS'15), August 21 - 25, 2015, Shanghai, China.

M. Hofmann, Numerical solution of the time dependent Schrödinger equation, Seminar Week, Leibniz-Universität Hannover, Institut für Quantenoptik, Ultrafast Laser Laboratory, Dahnsdorf, October 7, 2015.

M. Hofmann, Saturation of the nonlinear refractive index due to resonantly enhanced ionization, Internationaler Workshop ``Nonlinear Photonics: Theory, Materials, Applications'', June 29 - July 2, 2015, St. Petersburg, Russian Federation, July 2, 2015.

D. Puzyrev, Delay induced multistability and wiggling movement of laser cavity solitons, International Workshop ``Waves, Solitons and Turbulence in Optical Systems'' (WASTOS15), Berlin, October 12 - 14, 2015.

D. Puzyrev, Instabilities of laser cavity solitons induced by delayed feedback, CLEO/Europe-EQEC 2015 Conference, München, June 21 - 25, 2015.

D. Puzyrev, Multistability and bifurcations of laser cavity solitons induced by delayed feedback, International Workshop ``Nonlinear Photonics: Theory, Materials, Applications'', Session ``Laser Dynamics'', June 29 - July 2, 2015, Saint-Petersburg State University, Departmetnt of General Physics, Russian Federation, July 1, 2015.

D. Puzyrev, Multistability and bifurcationsof laser cavity solitons induced by delayed feedback, Workshop on Control of Self-Organizing Nonlinear Systems, September 14 - 16, 2015, SFB 910 ``Control of self-organizing nonlinear systems: Theoretical methods and concepts of application'', Lutherstadt Wittenberg, September 15, 2015.

S. Pickartz, Scattering of dispersive waves by optical solitons, International Workshop: Waves, Solitons and Turbulence in Optical Systems (WASTOS15), Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, October 14, 2015.

U. Bandelow, Limitation for ultrashort solitons in nonlinear optical fibers by cusp formation, CLEO/Europe-EQEC 2015 Conference, June 21 - 25, 2015, München, June 25, 2015.

C. Brée, A model of intense laser-matter interaction based on complex-rotated Floquet resonances, 24th Annual International Laser Physics Workshop (LPHYS'15), Seminar 5: Nonlinear Optics & Spectroscopy, August 21 - 25, 2015, Shanghai, China, August 23, 2015.

C. Brée, Impact of resonance-enhanced ionization on femtosecond filamentation, International Workshop ``Nonlinear Photonics: Theory, Materials, Applications'', Session: Extreme and Relativistic Nonlinear Optics, June 28 - July 4, 2015, St. Petersburg State University, St . Petersburg, Russian Federation, July 2, 2015.

C. Brée, Numerical modelling of femtosecond filamentation, Leibniz-Universität Hannover, Institut für Quantenoptik, Hannover, September 7, 2015.

O. Omel'chenko, Chimera states for any taste, Dynamics of Coupled Oscillators: 40 Years of the Kuramoto Mode, July 27 - 31, 2015, Max Planck Institute for the Physics of Complex Systems, Dresden, July 27, 2015.

O. Omel'chenko, Controlling unstable chaos in systems of coupled oscillators, The 8th International Conference on Chaotic Modeling, Simulation and Applications (CHAOS2015), Minisymposium ``Emergent Dynamics and Control'', May 25 - 30, 2015, Institut Henri Poincaré, Paris, France, May 28, 2015.

S. Amiranashvili, Elementary processes behind turbulent states in optical fibers, Weak Chaos and Weak Turbulence, February 3 - 7, 2014, Max-Planck-Institut für Physik komplexer Systeme, Dresden, February 5, 2014.

S. Amiranashvili, Extreme waves in optical fibers, Wave Interaction (WIN-2014), April 23 - 26, 2014, Johannes Kepler University, Linz, Austria, April 24, 2014.

S. Amiranashvili, Recent progress in theory of pulse propagation in optical fibers, 14th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2014), September 1 - 5, 2014, Palma de Mallorca, Spain, September 2, 2014.

S. Amiranashvili, Solitons who do not want to be too short, Workshop on Abnormal Wave Events (W-AWE2014), June 5 - 6, 2014, Nice, France, June 5, 2014.

M. Hofmann, Intense laser-matter interaction in atomic gases and crystalline solids, Leibniz-Universität Hannover, Institut für Quantenoptik, February 27, 2014.

M. Hofmann, On the transient optical response of atomic gases, Frühjahrstagung der Deutschen Physikalischen Gesellschaft (DPG), March 17 - 21, 2014, Humboldt-Universität zu Berlin, Berlin.

C. Brée, M. Kretschmar, T. Nagy, M. Hofmann, A. Demircan, U. Morgner, M. Kovacev, Fingerprint of self-compression in the high harmonic spectrum from a filament, High-Intensity Lasers and High-Field Phenomena (HILAS), Berlin, March 18 - 20, 2014.

C. Brée, Manipulating optical solitons with a group-velocity horizon, Vortrag und Junior Researcher im Rahmen des Rank Prize Fund Symposiums, June 16 - 19, 2014, Grasmere, UK, June 18, 2014.

A.G. Vladimirov, Delay differential equations in laser dynamics, International Conference-School Hamiltonian Dynamics, Nonautonomous Systems, and Patterns in PDE's, December 10 - 15, 2014, Nishni Novgorod, Russian Federation, December 14, 2014.

S. Amiranashvili, Mathematics and physics behind short pulses in optical fibers, Habilitandenkolloquium, Humboldt-Universität zu Berlin, Institut für Physik, February 5, 2013.

S. Amiranashvili, Solitons that are too short in duration, International Workshop: Extreme Nonlinear Optics & Solitons, October 28 - 30, 13, WIAS Berlin, October 28, 2013.

U. Bandelow, Propagation of ultrashort pulses in nonlinear dispersive optical media: Solitons, rogue waves and horizons, Technische Universität Wien, Institut für Theoretische Physik, Austria, June 4, 2013.

S. Amiranashvili, A modeling framework for short pulses in optical fibers, 5th Annual Meeting ``Photonic Devices'', Zuse-Institut Berlin (ZIB), Berlin, February 24, 2012.

S. Amiranashvili, Mathematics and physics behind short pulses in optical fibers, Optik / Photonik-Kolloquium, Humboldt Universität zu Berlin, November 8, 2012.

S. Amiranashvili, Tiny waves we should never ignore, OSA -- The Optical Society, Topical Meeting ``Nonlinear Photonics'', June 17 - 21, 2012, Colorado Springs, USA, June 18, 2012.

C. Brée, Saturation of the all-optical Kerr effekt, LPHYS'11, 20th International Laser Physics Workshop Sarajevo, Bosnia and Herzegowina, July 11-15 2011, Bosnia And Herzegovina, July 13, 2011.

S. Amiranashvili, Can dispersive radiation feed energy into a giant wave?, Rogue Waves, November 7 - 11, 2011, Dresden, November 9, 2011.

S. Amiranashvili, Manipulating light by light, XXXth URSI General Assembly and Scientific Symposium of International Union of Radio Science, August 13 - 20, 2011, Istanbul, Turkey, August 18, 2011.

S. Amiranashvili, Optical transistor: From optical event horizons to rogue waves, Rogue Waves, Dresden, November 7 - 11, 2011.

U. Bandelow, Calculation of ultrashort pulse propagation based on rational approximations for dispersion, 11th Intl. Conference on Numerical Simulation of Optoelectronic Devices NUSOD'11, Rom, Italy, September 8, 2011.

I. Babushkin, Modeling of THz emission from plasma-generating femtosecond laser pulses with unidirectional Maxwell equation in plasma spots and in guided geometries, 2nd International Workshop on Laser-Matter Interaction 2010, September 13--17, 2010, Porquerolles, France, September 17, 2010, September 13, 2010.

A. Demircan, Plasma induced pulse break-up in filamentary self-compression, Laser Optics Berlin, March 22 - 24, 2010, March 24, 2010.

A.G. Vladimirov, Introduction to mode-locking in lasers, Graduate College of the Collaborative Research Center SFB 787 ``Semiconductor Nanophotonics: Materials, Models, Devices'', May 9 - 11, 2010, Technische Universität Berlin, Institut für Festkörperphysik, Graal-Müritz, May 10, 2010.

A.G. Vladimirov, Localized structures of light and their interaction, Imperial College London, Department of Applied Mathematics, UK, April 27, 2010.

A.G. Vladimirov, Nonlinear dynamics in lasers, Technische Universität Berlin, Institut für Festkörperphysik, March 24, 2010.

S. Amiranashvili, Modeling of short optical pulses, Localized Structures in Dissipative Nonlinear Systems, October 18 - 20, 2010, WIAS, October 19, 2010.

S. Amiranashvili, Modeling of medium dispersion for ultrashort optical pulses, WIAS Workshop ``Nonlinear Optics in Guided Geometries'', May 18 - 20, 2009, WIAS, Berlin, May 18, 2009.

S. Amiranashvili, Modeling of ultrashort optical pulses, Workshop ``Pulses and Modulations in Nonlinear Systems'', February 25 - 27, 2009, Universität Stuttgart, February 26, 2009.

C. Brée, A. Demircan, S. Skupin, L. Bergé, G. Steinmeyer, Quasi-hydrodynamic spatio-temporal shaping in filamentary propagation of femtosecond pulses, 73th Annual Meeting of the DPG and DPG Spring Meeting of the Section AMOP, March 1 - 6, 2009, Universität Hamburg, March 2, 2009.

C. Brée, A. Demircan, S. Skupin, G. Steinmeyer, Nonlinear photon z-pinching in filamentary self-compression, European Conference on Lasers and Electro-Optics and the XIth European Quantum Electronics Conference (CLEO®/Europe-EQEC 2009), June 15 - 19, 2009, Munich, June 18, 2009.

C. Brée, Quasi-hydrodynamic spatio-temporal shaping in filamentary propagation of femtosecond pulses, WIAS Workshop ``Nonlinear Optics in Guided Geometries'', May 18 - 20, 2009, WIAS, Berlin, May 20, 2009.

A.G. Vladimirov, Enhancement of interaction of dissipative solitons above self-pulsing instability threshold, CPNLW09 Soliton 2009 ``Solitons in Their Roaring Forties: Coherence and Persistence in Nonlinear Waves'', January 6 - 9, 2009, Nice University, Nice, France, January 8, 2009.

A.G. Vladimirov, Spontaneous motion of dissipative solitons under the effect of delay, Australasian Conference on Optics, Lasers and Spectroscopy and Australian Conference on Optical Fibre Technology in association with the International Workshop on Dissipative Solitons (ACOLS ACOFT DS 2009), November 29 - December 3, 2009, University of Adelaide, Australia, December 1, 2009.

A.G. Vladimirov, Strong enhancement of interaction of optical pulses induced by oscillatory instability, European Conference on Lasers and Electro-Optics and the XIth European Quantum Electronics Conference 2009 (CLEOtextsuperscript®/Europe -- EQEC 2009, Munich, June 14 - 19, 2009.

I. Babushkin, S. Skupin, J. Herrmann, Generation of tunable ultrabroad supercontinuum from THz to near-infrared in two-color ultrashort pulses in hollow capillaries, IOP Conference ``Nonlinear Photonics in Micro- and Nanostructures'', London, UK, December 10, 2009.

I. Babushkin, Nonresonant frequency conversion with ultrashort intense pulses in hollow micro-capillaries, University of Bath, Department of Physics, UK, December 9, 2009.

I. Babushkin, Optical amplification by four-wave mixing in gases using quasi-phase-matching with ultrasound waves, Workshop ``Nonlinear Optics in Guided Geometries'', May 18 - 20, 2009, WIAS, Berlin, May 20, 2009.

U. Bandelow, Mathematical models for ultrashort optical pulses, Australasian Conference on Optics, Lasers and Spectroscopy and Australian Conference on Optical Fibre Technology in association with the International Workshop on Dissipative Solitons (ACOLS ACOFT DS 2009), November 29 - December 3, 2009, University of Adelaide, Australia, November 30, 2009.

U. Bandelow, Nonlinear and nonlocal models for ultrashort optical pulses, Fourth `Rio de la Plata' Workshop on Laser Dynamics and Nonlinear Photonics, December 8 - 11, 2009, Piriapolis, Uruguay, December 9, 2009.

U. Bandelow, Solitary wave solutions for few-cycle optical pulses, WIAS Workshop ``Nonlinear Optics in Guided Geometries'', May 18 - 20, 2009, WIAS, Berlin, May 19, 2009.

C. Krüger, A. Demircan, G. Stibenz, N. Zhavoronkov, G. Steinmeyer, Asymptotic pulse shapes and pulse self-compression in femtosecond filaments, UP 2008: XVI Conference on Ultrafast Phenomena, Stresa, Italy, June 9 - 13, 2008.

C. Krüger, A. Demircan, G. Stibenz, N. Zhavoronkov, G. Steinmeyer, Asymptotic pulse shapes in filamentary propagation of femtosecond pulses and self-compression, CLEO/QUELS 2008: Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference, San Jose, USA, May 4 - 9, 2008.

C. Krüger, Asymptotic pulse shapes in filamentary propagation of femtosecond pulses, Max-Planck-Institut für Physik komplexer Systeme, Dresden, March 31, 2008.

C. Krüger, Asymptotic pulse shapes in filamentary propagation of ultrashort laser pulses, Max-Born-Institut Berlin, June 19, 2008.

C. Krüger, Selbstkompression und asymptotische Pulsformen in Filamenten, DPG-Frühjahrstagung 2008, March 10 - 14, 2008, Darmstadt, March 13, 2008.

M. Pietrzyk, I. Kanattšikow, Multisymplectic integrators in nonlinear optics, PHOTON08: Conference in Optics and Photonics, Edinburgh, UK, August 26 - 29, 2008.

M. Pietrzyk, Carrier-wave shock formation and other properties of the short pulse equation, PHOTON08: Conference in Optics and Photonics, August 26 - 29, 2008, UK Consortium for Photonics and Optics (UKCPO), Edinburgh, UK, August 29, 2008.

M. Pietrzyk, On the compression of ultrashort optical pulses beyond the slowly varying envelope approximation, 8th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD) 2008, September 1 - 5, 2008, University of Nottingham, UK, September 2, 2008.

M. Pietrzyk, On the multisymplectic integrator for the generalized short pulse equation, 40th Symposium on Mathematical Physics ``Geometry & Quanta'', June 25 - 28, 2008, Nicolaus Copernicus University, Toruń, Poland, June 28, 2008.

M. Pietrzyk, Short pulse equations and its properties, Gdańsk University of Technology, Department of Theoretical Physics and Quantum Information, Poland, July 1, 2008.

M. Pietrzyk, The short pulse equation: Few-cycle optical pulses beyond the slowly varying envelope approximation, University of Tartu, Institute of Physics, Estonia, October 8, 2008.

A.G. Vladimirov, Nonlinear dynamics of pulse interactions in bistable optical systems, V International Conference ``Basic Problems of Optics'' BPO-2008 in the framework of V International Congress ``Optics - XXI century'', October 20 - 24, 2008, St Petersburg, Russian Federation, October 23, 2008.

U. Bandelow, Short pulses in nonlinear optical fibers: Models and applications, Colloquium ``Nonlinear Dynamics in Complex Optical Systems'', Humboldt-Universität zu Berlin, Institut für Physik, June 19, 2008.

U. Bandelow, Solitary wave solutions for ultrashort optical pulses, Technical Conference ``Frontiers in Optics 2008, Laser Science XXIV'', October 19 - 23, 2008, Optical Society of America (OSA), Rochester, USA, October 21, 2008.

I. Kanattšikow, The short pulse equation: Integrability and generalizations, Gdańsk University of Technology, Institute of Theoretical Physics and Quantum Informatics, Gdańsk, Poland, June 30, 2008.

M. Pietrzyk, How to describe ultrashort pulses when the NSE does not apply?, University of Vigo, Optics Lab, Spain, July 2, 2007.

M. Pietrzyk, Multisymplectic analysis of the short pulse equation, 10th International Conference on Differential Geometry and Its Application, August 27 - 31, 2007, Olomouc, Czech Republic, August 28, 2007.

M. Pietrzyk, Properties of ultrashort pulses in silica fibers, ATTO 07 --- International Workshop and 391th WWE-Heraeus Seminar Attosecond Physics, Dresden, July 31 - August 4, 2007.

U. Bandelow, A. Demircan, M. Kroh, B. Hüttl, Appearance of solitonic effects during pulse compression in the normal dispersion regime, Rio de la Plata Workshop on Noise, Chaos and Complexity in Lasers and Nonlinear Optics, Punta del Este, Uruguay, December 3 - 6, 2007.

U. Bandelow, Limit for pulse compression by pulse splitting, Workshop ``Nonlinear Effects in Photonic Materials'', March 12 - 14, 2007, WIAS, Berlin, March 13, 2007.

U. Bandelow, Nichtlineare Effekte in Halbleiterlasern und optischen Fasern, Habilitandenkolloquium, Humboldt-Universität zu Berlin, Institut für Physik, April 17, 2007.

U. Bandelow, Non-Raman redshift by pulse splitting, 7th International Conference ``Numerical Simulation of Optoelectronic Devices'' (NUSOD'07), September 24 - 27, 2007, University of Delaware, Newark, USA, September 27, 2007.

A. Demircan, U. Bandelow, B. Hüttl, M. Kroh, Generation of new frequencies by pulse splitting, 33rd European Conference and Exhibition on Optical Communication (ECOC 2007), Berlin, September 16 - 20, 2007.

A. Demircan, U. Bandelow, Interplay between soliton fission and modulation instability, European Conference on Lasers and Electro-Optics 2007/International Quantum Electronics Conference (CLEOE-IQEC 2007), München, June 17 - 22, 2007.

A. Demircan, Interplay between soliton fission and modulation instability, Workshop ``Nonlinear Effects in Photonic Materials'', March 12 - 14, 2007, WIAS, Berlin, March 14, 2007.

A. Vladimirov, Autosolitons in optical devices with transverse refractive index modulation, International Conference on Coherent and Nonlinear Optics/International Conference on Lasers, Applications, and Technologies (ICONO/LAT 2007), May 28 - June 1, 2007, Minsk, Belarus, May 29, 2007.

A. Vladimirov, Dissipative solitons in nonlinear optical devices with refractive index modulation, Workshop ``Nonlinear Effects in Photonic Materials'', March 12 - 14, 2007, WIAS, Berlin, March 14, 2007.

A. Demircan, U. Bandelow, Compression limit by third-order dispersion in the normal dispersion regime, 14th European Conference on Mathematics for Industry (ECMI 2006), Universidad Carlos III de Madrid, Spain, July 10 - 14, 2006.

A. Demircan, Analysis of the interplay between soliton fission and modulational instability in supercontinuum generation, Minisymposium on Dissipative Solitons, WIAS, Berlin, April 20, 2006.

A. Demircan, Compression limit by third-order dispersion, Fraunhofer-Institut für Nachrichtentechnik, Heinrich-Hertz-Institut, Berlin, January 10, 2006.

A. Demircan, Interplay between soliton fission and modulation instability in the supercontinuum generation, University of Bath, Centre for Photonics and Photonic Materials, UK, August 21, 2006.

M. Pietrzyk, Ultra-short pulses beyond the slowly-varying envelope approximation, Workshop ``Nonlinear Dynamics in Modelocked Lasers and Optical Fibers'', July 13 - 14, 2006, WIAS, Berlin, July 14, 2006.

U. Bandelow, A. Demircan, A. Mielke, M. Pietrzyk, Nonlocal and nonlinear effects in fiber optics, Evaluation Colloquium of the DFG Research Center sc Matheon, Berlin, January 24 - 25, 2006.

U. Bandelow, Limitations for pulse compression, Workshop "Nonlinear Dynamics in Modelocked Lasers and Optical Fibers", July 13 - 14, 2006, WIAS, Berlin, July 14, 2006.

U. Bandelow, Modellierung und Simulation von Pulsquellen, Status Seminar TerabitOptics Berlin, Heinrich-Hertz-Institut für Nachrichtentechnik, Berlin, July 4, 2006.

U. Bandelow, Pulse compression limit in the normal dispersion regime, The 90th OSA Annual Meeting 'Frontiers in Optics', October 8 - 12, 2006, Rochester, USA, October 12, 2006.

U. Bandelow, Pulse splitting by third-order dispersion, 6th Intl. Conference on Numerical Simulation of Optoelectronic Devices NUSOD'06, September 11 - 14, 2006, Nanyang University, Singapore, September 14, 2006.

A. Vladimirov, Dynamics of light pulses in mode-locked lasers, 6th Crimean School and Workshops ``Nonlinear Dynamics, Chaos and Applications'', May 15 - 26, 2006, Yalta, Crimea, Ukraine, May 20, 2006.

A. Vladimirov, Laser dissipative solitons and their interaction, Minisymposium on Dissipative Solitons, WIAS, Berlin, April 20, 2006.

A. Vladimirov, Localized structures of light in laser systems and their weak interactions, Technische Universität Berlin, June 14, 2006.

A. Vladimirov, Nonlinear dynamics and bifurcations in multimode and spatially distributed laser systems, June 20 - 23, 2006, St. Petersburg State University, Russian Federation, June 20, 2006.

A. Vladimirov, Nonlinear dynamics in multimode and spatially extended laser systems, Moscow State University, Physics Faculty, Russian Federation, November 10, 2006.

A. Vladimirov, Transverse Bragg dissipative solitons in a Kerr cavity with refractive index modulation, Laser Optics Conference, June 26 - 30, 2006, St. Petersburg, Russian Federation, June 28, 2006.

A. Demircan, U. Bandelow, Impact of modulation instability on supercontinuum generation, Annual Meeting 2005 of the Optical Society of America (OSA) ``Frontiers in Optics'', October 17 - 21, 2005, Tuscon, USA, October 19, 2005.

A. Demircan, Supercontinuum generation by the modulation instability, WIAS Workshop ``Nonlinear Dynamics in Photonics'', May 2 - 4, 2005, Berlin, May 3, 2005.

A. Vladimirov, G. Kozyreff, P. Mandel, M. Tlidi, Localized structures in a passive cavity with refractive index modulation, International Quantum Electronics Conference, June 12 - 17, 2005, München, June 15, 2005.

A. Vladimirov, Interaction of dissipative solitons in laser systems, Ben Gurion University of the Negev, Department of Mathematics, Beer Sheva, Israel, November 17, 2005.

D. Turaev, S. Zelik, A. Vladimirov, Chaotic bound state of localized structures in the complex Ginzburg--Landau equation, Conference Digest ``Nonlinear Guided Waves and their Applications'', Dresden, September 6 - 9, 2005.

U. Bandelow, A. Demircan, Impact of the modulation instability on supercontinuum generation, Conference on Lasers and Electro-Optics/Quantum Electronics & Lasers Science Conference CLEO/QELS 2005, München, June 12 - 17, 2005.

U. Bandelow, A. Demircan, Impact of modulation instability on the supercontinuum generation, 5th International Conference ``Numerical Simulation of Optoelectronic Devices'' (NUSOD'05), September 19 - 22, 2005, Humboldt-Universität zu Berlin, September 21, 2005.

U. Bandelow, Modellierung und Simulation von Pulsquellen, Status Seminar of the Terabit-Optics-Berlin Project, Fraunhofer Institut für Nachrichtentechnik, Heinrich-Hertz-Institut, Berlin, May 31, 2005.

U. Bandelow, A. Demircan, M. Kesting, Pulse propagation in nonlinear optical fibers, Meeting within the Terabit-Optics-Berlin Project, Fraunhofer-Institut für Nachrichtentechnik, Heinrich-Hertz-Institut, Berlin, April 28, 2004.

U. Bandelow, Modellierung und Simulation von Pulsquellen, Status Seminar of the Terabit-Optics-Berlin Project, Technische Universität Berlin, May 3, 2004.

U. Bandelow, Modellierung und Simulation von Pulsquellen, Status Seminar of the Terabit-Optics-Berlin Project, Technische Universität Berlin, November 2, 2004.

U. Bandelow, Report on WIAS activities concerning COST Action 288, Kick-off Meeting for the Cost Action 288, COST TIST Secretariat, Brussels, Belgium, April 7, 2003.

A. Demircan, Generation of ultrabroad spectra in optical fibers, WIAS Workshop ``Dynamics of Semiconductor Lasers'', September 15 - 17, 2003, Berlin, September 17, 2003.

A.G. Vladimirov, Moving discrete solitons in multicore fibers and waveguide arrays, European Quantum Electronics Conference, June 22 - 27, 2003, München, June 25, 2003.

A.G. Vladimirov, Moving discrete solitons in multicore fibers and waveguide arrays, Conference dedicated to the 60th birthday of Prof. Paul Mandel, April 11 - 12, 2003, Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Belgium, April 11, 2003.

J. Becker, K. Gärtner, R. Klanner, R. Richter, Simulation and experimental study of plasma effects in planar silicon sensors, Preprint no. arXiv:1007.4433, Cornell University Library, arXiv.org, 2010.

S. Amiranashvili, U. Bandelow, A.G. Vladimirov, Solitary wave solutions for few-cycle optical pulses, Preprint no. 500, DFG Research Center sc Matheon, 2008.