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Type: Report × Subject: delay differential equations ×

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Now showing 1 - 6 of 6
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    An optically injected mode locked laser
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Rebrova, Natalia; Huyet, Guillaume; Rachinskii, Dmitrii; Vladimirov, Andrei G.
    We study analytically and numerically a delay differential model of a passively mode-locked semiconductor laser subjected to a single frequency coherent injection. The width of the locking cone is calculated asymptotically in the limit of small injection and compared to that obtained by direct numerical integration of the model equations. The dependence of the locking cone on the laser parameters is discussed
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    A multi-mode delay differential equation model for lasers with optical feedback
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Radziunas, Mindaugas
    In this paper, we discuss the relations between the spatially-distributed traveling wave, Lang-Kobayashi, and a new multi-mode delay differential equation models for Fabry-Perot type semiconductor diode lasers with an external optical feedback. All these models govern the dynamics of the slowly varying complex amplitudes of the optical fields and carrier density. To compare the models, we calculate the cavity modes determined by the threshold carrier density and optical frequency of the steady states in all three models. These calculations show that the Lang-Kobayashi type model is in good agreement with the traveling wave model only for the small feedback regimes, whereas newly derived multi-mode delay differential equation model remains correct even at moderate and large optical feedback regimes.
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    Dynamics 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.
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    Hybrid 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, Dieter
    Hybrid 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.
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    Dynamical regimes in a class A model of a nonlinear mirror mode-locked laser
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Vladimirov, Andrei G.; Kovalev, Anton V.; Viktorov, Evgeny A.; Rebrova, Natalia; Huyet, Guillaume
    Using a simple delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform analytical linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by a bifurcation leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked pulses are very asymmetric with exponential decay of the trailing and superexponential growth of the leading edge. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.
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    Classification of coupled dynamical systems with multiple delays: Finding the minimal number of delays
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Lücken, Leonhard; Pade, Jan Philipp; Knauer, Kolja
    In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We prove that for particular sets of delays this is not the case. To this aim we introduce a componentwise timeshift transformation (CTT) which allows to classify systems which possess equivalent dynamics, though possibly different sets of connection delays. In particular, we show for a large class of semiflows (including the case of delay differential equations) that the stability of attractors is invariant under this transformation. Moreover we show that each equivalence class which is mediated by the CTT possesses a representative system in which the number of different delays is not larger than the cycle space dimension of the underlying graph. We conclude that the 'true' dimension of the corresponding parameter space of delays is in general smaller than it appears at first glance.