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Subject: modulational instability ×

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    Modulational instability of discrete solitons in coupled waveguides with group velocity dispersion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Yulin, Alexey; Skryabin, Dmitry; Vladimir, Andrei
    We study temporal modulational instability of spatial discrete solitons in waveguide arrays with group velocity dispersion (GVD). For normal GVD we report existence of the strong 'neck'-type instability specific for the discrete solitons. For anomalous GVD the instability leads to formation of the mixed discrete-continuous spatio-temporal quasi-solitons. Feasibility of experimental observation of these effects in the arrays of silicon-on-insulator waveguides is discussed.
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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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    Dispersive 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.
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    Multiple self-locking in the Kuramoto--Sakaguchi system with delay
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Wolfrum, Matthias; Yanchuk, Serhiy; D'Huys, Otti
    We study the Kuramoto-Sakaguchi system of phase oscillators with a delayed mean-field coupling. By applying the theory of large delay to the corresponding Ott--Antonsen equation, we explain fully analytically the mechanisms for the appearance of multiple coexisting partially locked states. Closely above the onset of synchronization, these states emerge in the Eckhaus scenario: with increasing coupling, more and more partially locked states appear unstable from the incoherent state, and gain stability for larger coupling at a modulational stability boundary. The partially locked states with strongly detuned frequencies are shown to emerge subcritical and gain stability only after a fold and a series of Hopf bifurcations. We also discuss the role of the Sakaguchi phase lag parameter. For small delays, it determines, together with the delay time, the attraction or repulsion to the central frequency, which leads to supercritical or subcritical behavior, respectively. For large delay, the Sakaguchi parameter does not influence the global dynamical scenario.
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    A delay differential equation NOLM--NALM mode-locked laser model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Vladimirov, Andrei G.; Suchkov, Sergey; Huyet, Guillaume; Turitsyn, Sergey K.
    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.