Semiconductor lasers subject to external feedback are known to exhibit a wide variety of dynamical regimes desired for some applications such as chaos cryptography, random bit generation, and reservoir computing. Low-frequency fluctuations is one of the most frequently encountered regimes. It is characterized by a fast drop in laser intensity followed by a gradual recovery. The duration of this recovery process is irregular and of the order of hundred nanoseconds. The average time between dropouts is much larger than the laser system characteristic time-scales. Semiconductor ring lasers are currently the focus of a rapidly thriving research activity due to their unique feature of directional bistability. They can be employed in systems for all-optical switching, gating, wavelength-conversion functions, and all-optical memories. Semiconductor ring lasers do not require cleaved facets or gratings for optical feedback and are thus particularly suited for monolithic integration. We experimentally and numerically address the issue of low-frequency fluctuations considering a semiconductor ring laser in a feedback configuration where only one directional mode is re-injected into the same directional mode, a so-called single self-feedback. We have observed that the system is very sensitive to the feedback strength and the injection current. In particular, the power dropouts are more regular when the pump current is increased and become less frequent when the feedback strength is increased. In addition, we find two different recovery processes after the power dropouts of the low-frequency fluctuations. The recovery can either occur via pulses or in a stepwise manner. Since low-frequency fluctuations are not specific to semiconductor ring lasers, we expect these recovery processes to appear also in VCSELs and edge-emitting lasers under similar feedback conditions. The numerical simulations also capture these different behaviors, where the representation in the phase space of the carriers versus the round trip phase difference gives additional insight into these phenomena. This proceedings paper gives a short overview of the results of L. Mashal et al. [L. Mashal et al., IEEE J. Quantum. Electron. 49, 790, 2013].
Semiconductor Ring Lasers (SRLs) are a modern class of semiconductor lasers whose active cavity is characterized
by a circular geometry. This enables the laser to support two counterpropagating modes, referred to as the
clockwise (CW) and the counterclockwise (CCW) mode. Semiconductor ring lasers have been shown to have
a regime of operation in which they are excitable, when the linear coupling between the counterpropagating
modes is asymmetric. This can be achieved by increasing the reflection of, for example, the CW mode into the
CCW mode. This will stabilize lasing in the CCW mode. In the excitable regime, the SRL will fire optical
pulses (spikes) in the CW mode as a response to noise perturbations. In this contribution we experimentally and
theoretically characterize these spikes. Our experiments reveal a statistical distribution of the characteristics of
the optical pulses that is not observed in regular excitable systems. In particular, an inverse correlation exists
between the pulse amplitude and duration. Numerical simulations and an interpretation in an asymptotic phase
space confirm and explain these experimentally observed pulse characteristics [L. Gelens et al., Phys. Rev. A
82 063841, 2010]. We will also theoretically consider asymmetric SRLs coupled through a single bus waveguide.
This is a first step towards an integrated optical neural network using semiconductor ring lasers as building
blocks. We will show that for weak coupling, excitatory excursions still persist due to the similar phase space
structure. Moreover, the coupled SRLs can excite pulses in each other and can thus function as communicating
neurons [W. Coomans et al., Phys. Rev. E 84 036209, 2011]. This type of neural network can be fully integrated
on chip and does not suffer from the drawback of needing extra-cavity measures, such as optical injection or
saturable absorbers.
We study experimentally and numerically a new dynamical regime in the operation of semiconductor ring lasers
(SRLs) subject to delayed optical feedback. When employing an asymmetric feedback scheme, we find experimentally
that the SRL can show square-wave intensity oscillations with a 50 % duty cycle. In this scheme, where
the output in one direction is delay-coupled to the other direction but not vice versa, the laser switches regularly
between the clockwise (CW) and counter-clockwise (CCW) propagating modes. The measured period of the
square-waves is slightly longer than twice the roundtrip time in the external cavity. We analyze the regularity
and the shape of the square-waves as a function of the pumping current and the feedback strength. For higher
pump currents on the SRL,the output displays stochastic mode hopping between the square waves attractor and
stable unidirectional operation in the CW mode. To understand the origin of this dynamical regime, we rely
on numerical simulations based on the Lang-Kobayashi equations. We demonstrate a novel mechanism leading
to square wave oscillations based on the cross-feedback overcoming backscattering asymmetries present in the
device's structure. Our numerical results are in close agreement with the experimental ones.
Semiconductor Ring Lasers (SRLs) are a novel class of semiconductor lasers whose active cavity is characterized
by a circular geometry. SRLs have attracted attention due to the possibility of monolithical integration of
thousands of them on the same chip in a cheap and reliable way. SRLs are interesting for applications that
rely on the presence of two counter-propagating modes inside the optical cavity. For instance, fully symmetric
coupled SRLs have been proposed as candidates for the realisation of small and fast all-optical memories. At
the same time, a wealth of nonlinear and stochastic dynamics have been predicted and observed in symmetric
SRLs which is a consequence of the underlying Z2-symmetry of the device. However, unavoidable fabrication
defects, material roughness and chip-cleaving break the device symmetry in an uncontrolled and unpredictable
way, which may result in a deterioration of the device's performance in applications such as all-optical signal-processing.
Despite their importance, the effects of symmetry breaking in SRLs remain unaddressed. In this
contribution we investigate theoretically and experimentally the stochastic dynamics of SRLs with weakly broken
Z2-symmetry . We show how the symmetry of an SRL can be experimentally manipulated using the reflection
from a cleaved facet of a multi-mode optical fibre and a control electrode on the bus waveguide. The experiments
are performed on an InP-based multi-quantum well SRL operating in single-longitudinal mode regime. The power
at the CCW output is collected using a fast photodiode connected to an oscilloscope with a sampling rate of 4.0
ns. For a not-too-weak symmetry breaking, we reveal that SRLs become excitable and therefore can emit large,
deterministic power bursts as a response to stochastic fluctuations. The origin of excitability is explained by
investigating the topology of the invariant manifolds of an asymptotic two-dimensional phase space model with
broken Z2-invariance. The results of the experiments confirm the prediction of the theory.
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