Browsing by Author "Pimenov, Alexander"
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- ItemAdaptive behaviour in a predator-prey model leads to multiple equilibrium states(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Korobeinikov, Andrei; Rachinskii, DmitriiThere is evidence that multiple stable equilibrium states are possible in real-life ecological systems. In order to verify a hypothesis that such a multitude of equilibrium states can be caused by adapting of animal behaviour to changes of environmental conditions, we consider a simple predator-prey model where prey changes a mode of behaviour in response to the pressure of predation. This model exhibits two stable coexisting equilibrium states with basins of attraction separated by a separatrix of a saddle point.
- ItemAnalysis of an operator-differential model for magnetostrictive energy harvesting(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Davino, Daniele; Krejc̆í, Pavel; Pimenov, Alexander; Rachinskii, Dmitrii; Visone, CiroWe present a model of, and analysis of an optimization problem for, a magnetostrictive harvesting device which converts mechanical energy of the repetitive process such as vibrations of the smart material to electrical energy that is then supplied to an electric load. The model combines a lumped differential equation for a simple electronic circuit with an operator model for the complex constitutive law of the magnetostrictive material. The operator based on the formalism of the phenomenological Preisach model describes nonlinear saturation effects and hysteresis losses typical of magnetostrictive materials in a thermodynamically consistent fashion. We prove well-posedness of the full operatordifferential system and establish global asymptotic stability of the periodic regime under periodic mechanical forcing that represents mechanical vibrations due to varying environmental conditions. Then we show the existence of an optimal solution for the problem of maximization of the output power with respect to a set of controllable parameters (for the periodically forced system). Analytical results are illustrated with numerical examples of an optimal solution.
- ItemBifurcation structure of a swept source laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Kovalev, Anton V.; Dmitriev, Pavel S.; Vladimirov, Andrei G.; Pimenov, Alexander; Huyet, Guillaume; Viktorov, Evgeniy A.We numerically analyze a delay differential equation model of a short-cavity semiconductor laser with an intracavity frequency swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrowband filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch.
- ItemBifurcations in a model of monolithic passively mode-locked semiconductior laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Vladimirov, Andrei; Pimenov, Alexander; Rachinskii, DmitriiBifurcation mechanisms of the development and break up of different operation regimes in a passively mode-locked monolithic semiconductor laser are studied by solving numerically partial differential equations for amplitudes of two counterpropagating waves and carrier densities in gain and absorber sections. It is shown that harmonic mode-locking regime with two pulses in the cavity can exhibit a period-doubling bifurcation leading to different amplitudes and separations of the pulses. The effect of linewidth enhancement factors in gain and absorber sections on the laser dynamics is discussed.
- ItemBistability and hysteresis in an optically injected two-section semiconductor laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Pimenov, Alexander; Viktorov, Evgeniy A.; Hegarty, Stephen P.; Habruseva, Tatiana; Huyet, Guillaume; Rachinskii, Dmitrii; Vladimirov, Andrei G.The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different CW and non-stationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors.
- ItemDelayed feedback control of self-mobile cavity solitons(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Pimenov, Alexander; Vladimirov, Andrei G.; Gurevich, Svetlana V.; Panajotov, Krassimir; Huyet, Guillaume; Tlidi, MustaphaControl of the motion of cavity solitons is one the central problems in nonlinear optical pattern formation. We report on the impact of the phase of the time-delayed optical feedback and carrier lifetime on the self-mobility of localized structures of light in broad area semiconductor cavities. We show both analytically and numerically that the feedback phase strongly affects the drift instability threshold as well as the velocity of cavity soliton motion above this threshold. In addition we demonstrate that non-instantaneous carrier response in the semiconductor medium is responsible for the increase in critical feedback rate corresponding to the drift instability.
- ItemDelayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Schemmelmann, Tobias; Tabbert, Felix; Pimenov, Alexander; Vladimirov, Andrei G.; Gurevich, Svetlana V.We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical and path continuation methods we analyze the bifurcation structure of stationary and moving cavity solitons and identify two different types of traveling localized solutions, corresponding to slow and fast motion. We show that the delay impacts both stationary and moving solutions either causing drifting and wiggling dynamics of initially stationary cavity solitons or leading to stabilization of intrinsically moving solutions. Finally, we demonstrate that the fast cavity solitons can be associated with a lateral mode-locking regime in a broad-area laser with a single longitudinal mode.
- ItemDelayed feedback control of the self-induced motion of localized structures of light(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Vladimirov, Andrei G.; Pimenov, Alexander; Gurevich, Svetlana V.; Panajotov, Krassimir; Averlant, Eugene; Tlidi, MustaphaWe investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a solitary localized structure that is stationary and stable in the absence of feedback. We focus our analysis on an experimentally relevant system namely the Vertical-Cavity Surface-Emitting Laser (VCSEL). In the absence of the delay feedback we present experimental evidence of stationary localized structures in a 80 m aperture VCSEL. The spontaneous formation of localized structures takes place above the lasing threshold and under optical injection. Then, we consider the effect of the time-delayed optical feedback and investigate analytically the role of the phase of the feedback and the carrier lifetime on the self-mobility properties of the localized structures. We show that these two parameters affect strongly the space time dynamics of two-dimensional localized structures. We derive an analytical formula for the threshold associated with drift instability of localized structures and a normal form equation describing the slow time evolution of the speed of the moving structure.
- ItemDispersive time-delay dynamical systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Pimenov, Alexander; Slepneva, Svetlana; Huyet, Guillaume; Vladimirov, Andrei G.We present a theoretical approach to model the dynamics of a dispersive nonlinear system using a set of delay differential equations with distributed delay term. We illustrate the use of this approach by considering a frequency swept laser comprising a semiconductor optical amplifier (SOA), a tunable bandpass filter and a long dispersive fiber delay line. We demonstrate that this system exhibits a rich spectrum of dynamical behaviors which are in agreement with the experimental observations. In particular, the multimode modulational instability observed experimentally in the laser in the anomalous dispersion regime and leading to a turbulent laser output was found analytically in the limit of large delay time.
- ItemDynamical regimes in a monolithic passively mode-locked quantum dot laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Vladimirov, Andrei; Bandelow, Uwe; Fiol, Gerrit; Arsenijevi´c, Dejan; Kleinert, Moritz; Bimberg, Dieter; Pimenov, Alexander; Rachinskii, DmitriiOperation regimes of a two section monolithic quantum dot (QD) mode-locked laser are studied experimentally and theoretically, using a model that takes into account carrier exchange between QD ground state and 2D reservoir of a QD-in-a-well structure, and experimentally. It is shown analytically and numerically that, when the absorber section is long enough, the laser exhibits bistability between laser off state and different mode-locking regimes. The Q-switching instability leading to slow modulation of the mode-locked pulse peak intensity is completely eliminated in this case. When, on the contrary, the absorber length is rather short, in addition to usual Q-switched mode-locking, pure Q-switching regimes are predicted theoretically and observed experimentally.
- ItemDynamical regimes of multi-stripe laser array with external off-axis feedback(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Pimenov, Alexander; Trpmciu, Vasile Z.; Bandelow, Uwe; Vladimirov, Andrei G.We study theoretically the dynamics of a multistripe laser array with an external cavity formed by either a single or two off-axis feedback mirrors, which allow to select a single lateral mode with transversely modulated intensity distribution. We derive and analyze a reduced model of such an array based on a set of delay differential equations taking into account transverse carrier grating in the semiconductor medium. With the help of the bifurcation analysis of the reduced model we show the existence of single and multimode instabilities leading to periodic and irregular pulsations of the output intensity. In particular, we observe a multimode instability leading to a periodic regime with anti-phase oscillating intensities of the two counter-propagating waves in the external cavity. This is in agreement with the result obtained earlier with the help of a 2+1 dimensional traveling wave model
- ItemDynamics of an inhomogeneously broadened passively mode-locked laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Pimenov, Alexander; Vladimirov, Andrei G.We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model.
- ItemEffect of chromatic dispersion on multimode laser dynamics: Delay differential model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Vladimirov, Andrei G.; Huyet, Guillaume; Pimenov, AlexanderA set of differential equations with distributed delay is derived for modeling of multimode ring lasers with intracavity chromatic dispersion. Analytical stability analysis of continuous wave regimes is performed and it is demonstrated that sufficiently strong anomalous dispersion can destabilize these regimes.
- ItemHomoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Pimenov, Alexander; Rachinskii, DmitriiSystems of operator-differential equations which hysteresis operators can have unstable equilibrium points with an open basin of attraction. In this paper, a numerical example of a robust homoclinic loop is presented for the first time in a population dynamics model with hysteretic response of prey to variations of predator. A mechanism creating this homoclinic trajectory is discussed.
- ItemHybrid mode-locking in edge-emitting semiconductor lasers: Simulations, analysis and experiments(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Arkhipov, Rostislav; Pimenov, Alexander; Radziunas, Mindaugas; Vladimirov, Andrei G.; Arsenjevi´c, Dejan; Rachinskii, Dmitrii; Schmeckebier, Holger; Bimberg, DieterHybrid mode-locking in a two section edge-emitting semiconductor laser is studied numerically and analytically using a set of three delay differential equations. In this set the external RF signal applied to the saturable absorber section is modeled by modulation of the carrier relaxation rate in this section. Estimation of the locking range where the pulse repetition frequency is synchronized with the frequency of the external modulation is performed numerically and the effect of the modulation shape and amplitude on this range is investigated. Asymptotic analysis of the dependence of the locking range width on the laser parameters is carried out in the limit of small signal modulation. Our numerical simulations indicate that hybrid mode-locking can be also achieved in the cases when the frequency of the external modulation is approximately twice larger and twice smaller than the pulse repetition frequency of the free running passively mode-locked laser fP . Finally, we provide an experimental demonstration of hybrid mode-locking in a 20 GHz quantum-dot laser with the modulation frequency of the reverse bias applied to the absorber section close to fP / 2.
- ItemThe impact of microcavity wire width on polariton soliton existence and multistability(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Slavcheva, Gabriela; Koleva, Mirella V.; Pimenov, AlexanderWe 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.
- ItemLight bullets in a time-delay model of a wide-aperture mode-locked semiconductor laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Pimenov, Alexander; Javaloyes, Julien; Gurevich, Svetlana V.; Vladimirov, Andrei G.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.
- ItemMemory and adaptive behaviour in population dynamics: Anti-predator behaviour as a case study(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Pimenov, Alexander; Kelly, Thomas C.; Korobeinikov, Andrei; OCallaghan, Michael J.; Rachinskii, DmitriiMemory enables to forecast future on the basis of experience, and thus, in some form, is principally important for the development of flexible adaptive behaviour by animal communities. To model memory, in this paper we use the concept of hysteresis, which mathematically is described by the Preisach operator. As case study, we consider anti-predator adaptation in the classic Lotka-Volterra predator-prey model. Despite its simplicity, the model allows to naturally incorporate essential features of an adaptive system and memory. Our analysis and simulations show that a system with memory can have a continuum of equilibrium states with non-trivial stability properties.
- ItemMulti-stability and polariton formation in microcavity polaritonic waveguides(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Slavcheva, Gabriela; Gorbach, Andrey V.; Pimenov, Alexander; Vladimirov, Andrei G.; Skryabin, DmitryNonlinear 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 polaritonic 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.
- ItemNonlinear dynamical properties of frequency swept fiber-based semiconductor lasers(Bristol : IOP Publishing, 2021) Slepneva, Svetlana; Pimenov, AlexanderWe investigate dynamics of semiconductor lasers with fiber-based unidirectional ring cavity that can be used as frequency swept sources. We identify key factors behind the reach dynamical behavior of such lasers using state-of-the-art experimental and analytical methods. Experimentally, we study the laser in static, quasi-static and synchronization regimes. We apply experimental methods such as optical heterodyne or electric field reconstruction in order to characterize these regimes or study the mechanisms of transition between them. Using a delay differential equation model, we demonstrate that the presence of chromatic dispersion can lead to destabilization of the laser modes through modulational instability, which results in undesirable chaotic emission. We characterize the instability threshold both theoretically and experimentally, and demonstrate deterioration of the Fourier domain mode locking regime near the threshold.