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Delay-induced dynamics and jitter reduction of passively mode-locked semiconductor lasers subject to optical feedback
2012, Otto, C., Lüdge, K., Vladimirov, A.G., Wolfrum, M., Schöll, E.
We study a passively mode-locked semiconductor ring laser subject to optical feedback from an external mirror. Using a delay differential equation model for the mode-locked laser, we are able to systematically investigate the resonance effects of the inter-spike interval time of the laser and the roundtrip time of the light in the external cavity (delay time) for intermediate and long delay times. We observe synchronization plateaus following the ordering of the well-known Farey sequence. Our results show that in agreement with the experimental results a reduction of the timing jitter is possible if the delay time is chosen close to an integer multiple of the inter-spike interval time of the laser without external feedback. Outside the main resonant regimes the timing jitter is drastically increased by the feedback.
Convective Nozaki-Bekki holes in a long cavity OCT laser
2019, Slepneva, Svetlana, O'Shaughnessy, Ben, Vladimirov, Andrei G., Rica, Sergio, Viktorov, Evgeny A., Huyet, Guillaume
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 π phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model.
Absolute stability and absolute hyperbolicity in systems with discrete time-delays
2021, Yanchuk, Serhiy, Wolfrum, Matthias, Pereira, Tiago, Turaev, Dmitry
An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete timedelays. In the case of a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. Similarly, for multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions are crucial for determining whether a system can have stabilizing or destabilizing bifurcations by varying time delays.