We present a detailed numerical bifurcation analysis of the dual polarisation, sustained pulsing behavior in the spin-flip model of an excitable, vertical cavity surface emitting semiconductor micro-laser with saturable absorber (VCSEL-SA) and coherent optical feedback from an external reflecting mirror.
These efforts are motivated by experimental observations showing sustained polarization mode competition between successive pulses generated, and re-generated, by the delayed feedback.
The bifurcation analysis suggests that this competition is stress-induced, and a result of symmetry-breaking torus bifurcations mediated by amplitude and phase anisotropy.
Our results inform the wider research on the pulse regeneration properties of such devices, which can be integrated into two-dimensional arrays and, as such, are potentially relevant for various applications, such as optical communication, signal processing and neuro-morphic computing.
Of particular interest to us is the device's capacity for dual-channel pulse propagation~\textemdash~the independent transmission of pulses in orthogonal polarization modes~\textemdash~which can be used to realize inhibitory coupling between purely excitable micro-lasers.
As sources of short, high-amplitude light pulses, self-pulsing lasers are central to many applications, including telecommunications and neuromorphic photonic computing. We consider an excitable semiconductor micropillar laser subject to delayed optical feedback. The microlaser alone displays an all-or-none response to external perturbations. In the presence of feedback, a first excitable pulse can regenerate itself after a delay time, thus resulting in a train of pulses with repetition rate close to the delay time. Several pulse trains can be triggered and sustained simultaneously. Although they can seem independent on the timescale of the experiment, recent work showed that all pulsing patterns correspond to very long transient towards one of the stable periodic solutions of the system. Only stable solutions corresponding to equidistant light pulses in the feedback cavity were observed.
We demonstrate experimentally and numerically that stable periodic solutions corresponding to non-equidistant pulses can also exist and be stable. A bifurcation analysis of a suitable mathematical model unveils the conditions on the timescales of the gain and absorption variables for such solutions to exist. We show that the long-term timing between non-equidistant pulses is fixed by the system parameters and does not depend on the initial timing between the pulse trains. Moreover, the bifurcation analysis demonstrates that, for a given number of coexisting pulses in the feedback cavity, only one configuration is stable, corresponding either to equidistant pulses or non-equidistant pulses with a fixed interpulse timing. The latter originates from a period doubling bifurcation and can also be viewed as a symmetry breaking phenomenon of the time-shift symmetry sustained by the system.
Our results provide a better understanding of pulsing dynamics in an excitable laser with delayed feedback. Because the only ingredients here are excitability and feedback, we believe our results may be of interest beyond the scope of laser dynamics.
Micropillar lasers with integrated saturable absorber (LSA) have been demonstrated to show important neuromimetic properties such as ultrafast excitable behavior, temporal summation, relative & absolute refractory periods and spike latency. In this work we study a LSA with self delayed connection which can show regenerative spiking. Such delayed self connections called as autpases are found in living nervous systems in regions essential for memory. The characteristic response of a single LSA is a 200 ps wide pulse emitted in response to an optical perturbation above the excitable threshold. In the presence of an external feedback, a single above threshold perturbation will trigger a train of pulses. Additional perturbations are capable of retiming an existing pulse train and adding or removing a pulse train, thus enabling all optical control of spikes.
If the system is perturbed under correct conditions several times during the external cavity roundtrip time τ, we can create several coexisting pulse trains in the cavity which are essentially the input perturbation repeating with the time period τ. This can be seen as an optical buffer for spikes. However, in the long term these seemingly independent pulses interact and converge towards a stable solution. This final stable solution is based on the input sequence, thus this long term behavior can be seem as an associative memory. Numerical simulations of the Yamada model with delayed feedback and noise are presented and found to be in good agreement with the experimental observations. All the observed dynamics of spike interaction and convergence can be explained solely based with the internal dynamics of carriers.
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