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- 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.
- 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.
- ItemTemporal cavity solitons in a delayed model of a dispersive cavity ring laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Pimenov, Alexander; Amiranashvili, Shalva; Vladimirov, Andrei G.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 CW states and temporal cavity solitons.