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Multi-stability and chaotic transient LFF dynamics in semiconductor lasers with time-delayed optical feedback

Multi-stability of coexisting attractors often results in long chaotic
transients, in particular, in networks of coupled systems and in
time-delayed systems. In the case of systems with delayed feedback
loops, the delay in the feedback can induce a set of coexisting
attractors which do not exist in the un-delayed case. Coexistence of
attractors can lead to long transients before a system reaches a
stationary state, and noise can turn the transient dynamics into
noise-sustained dynamics.

I will illustrate these ideas about the interplay of multi-stability,
noise, and transient dynamics using as an example a semiconductor laser
with optical feedback from an external mirror. The feedback has a time
delay because of the finite round-trip time of the light in the external
cavity. The delayed optical feedback induces a set of coexisting fixed
points which are called external cavity modes (ECMs). The regime of
low-frequency fluctuations (LFF) is a feedback-induced regime where the
laser output intensity randomly and abruptly drops to zero and recovers
gradually. Based on the standard model for semiconductor lasers with
optical feedback (the Lang- Kobayashi model), LFFs have been understood
as due to chaotic itinerancy among destabilized ECMs. However, in the
deterministic Lang- Kobayashi model and for a large range of realistic
parameters, the LFFs are a transient dynamics towards a stable ECM. This transient can become, in the presence of noise, a noise-sustained chaotic behavior. I will present a statistical analysis of the lifetime of the LFF regime and discuss the possibility of controlling the LFF lifetime via fine tuning the laser parameters that control the position of the coexisting ECM fixed points in the phase space.
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