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Semiconductor lasers can exhibit complex dynamical behavior in the presence of external perturbations. Delayed optical feedback, re-injecting part of the emitted light back into the laser cavity, in particular, can destabilize the laser's emission. We focus on the emission properties of a semiconductor laser subject to such optical feedback, where the delay of the light re-injection is large compared to the relaxation oscillations period. We present an overview of the main dynamical features that emerge in semiconductor lasers subject to delayed optical feedback, emphasizing how to experimentally characterize these features using intensity and high-resolution optical spectra measurements. The characterization of the system requires the experimentalist to be able to simultaneously measure multiple time scales that can be up to six orders of magnitude apart, from the picosecond to the microsecond range. We highlight some experimental observations that are particularly interesting from the fundamental point of view and, moreover, provide opportunities for future photonic applications. ; We acknowledge the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D, grant MDM-2017-0711 funded by MCIN/AEI/10.13039/501100011033. X.P. acknowledges funding from the European Union's Horizon 2020 (713694) and the Volkswagen Foundation (NeuroQNet II).

Reservoir Computing (RC) is an appealing approach in Machine Learning that combines the high computational capabilities of Recurrent Neural Networks with a fast and easy training method. Likewise, successful implementation of neuro-inspired plasticity rules into RC artificial networks has boosted the performance of the original models. In this manuscript, we analyze the role that plasticity rules play on the changes that lead to a better performance of RC. To this end, we implement synaptic and non-synaptic plasticity rules in a paradigmatic example of RC model: the Echo State Network. Testing on nonlinear time series prediction tasks, we show evidence that improved performance in all plastic models are linked to a decrease of the pair-wise correlations in the reservoir, as well as a significant increase of individual neurons ability to separate similar inputs in their activity space. Here we provide new insights on this observed improvement through the study of different stages on the plastic learning. From the perspective of the reservoir dynamics, optimal performance is found to occur close to the so-called edge of instability. Our results also show that it is possible to combine different forms of plasticity (namely synaptic and non-synaptic rules) to further improve the performance on prediction tasks, obtaining better results than those achieved with single-plasticity models. ; This work was supported by the Ministerio de Ciencia e Innovación (Spain) through projects PID2019-111537GB-C22/AEI/10.13039/501100011033 and PID2019-109094GB-C22/AEI/10.13039/501100011033, and by the European Union's Horizon 2020 research and innovation programme under grant agreement No. 899265 (ADOPD). We acknowledge the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (MDM-2017–0711). The work of MCS has been supported by the Spanish Ministerio de Ciencia, Innovación y Universidades, la Agencia Estatal de Investigación, the European Social Fund and the University of the Balearic Islands through a "Ramón y Cajal" Fellowship (RYC-2015–18140). GBM has been partly supported by the Spanish National Research Council via a JAE Intro fellowship (JAEINT18_EX_0684). ; Peer reviewed

We investigate the dynamics of semiconductor lasers subject to time-delayed optical feedback from the perspective of dynamical self-injection locking. Based on the Lang-Kobayashi model, we perform an analysis of the well-known Low Frequency Fluctuations (LFFs) in the frequency-intensity plane. Moreover, we investigate a recently found dynamical regime of fragmented LFFs by means of a locking-range analysis, spectral comparison and precursor pulse identification. We show that LFF dynamics can be explained by dynamical optical injection locking due to the delayed optical feedback. Moreover, the fragmented LFFs occur due to a re-injection locking induced by a particular optical pulse structure in the chaotic feedback dynamics. This is corroborated by experiments with a semiconductor laser experiencing delayed feedback from an optical fiber loop. The dynamical nature of the feedback injection results in an eventual loss, but also possible regaining, of the locking, explaining the recently observed phenomenon of fragmented LFFs. ; This work was supported by the Spanish Ministerio de Economía, Industria y Competitividad (MINECO), under project Nos. TEC2012–36335, FIS2015–71929-REDT, and TEC2016–80063-C3 (AEI/FEDER, UE). K.H. acknowledges financial support from the Government of the Balearic Islands (Department of Education, Culture, and Universities), co-funded by the European Social Fund. M.C.S. was supported by MINECO through a Ramón y Cajal Fellowship (RYC-2015–18140). D.B. acknowledges support of the CNRS under project No. PICS07300. ; Peer reviewed

Nonlinear photonic delay systems present interesting implementation platforms for machine learning models. They can be extremely fast, offer great degrees of parallelism and potentially consume far less power than digital processors. So far they have been successfully employed for signal processing using the Reservoir Computing paradigm. In this paper we show that their range of applicability can be greatly extended if we use gradient descent with backpropagation through time on a model of the system to optimize the input encoding of such systems. We perform physical experiments that demonstrate that the obtained input encodings work well in reality, and we show that optimized systems perform significantly better than the common Reservoir Computing approach. The results presented here demonstrate that common gradient descent techniques from machine learning may well be applicable on physical neuro-inspired analog computers. ; P.B., M.H. and J.D. acknowledge support by the interuniversity attraction pole (IAP) Photonics@be of the Belgian Science Policy Office, the ERC NaResCo Starting grant and the European Union Seventh Framework Programme under grant agreement no. 604102 (Human Brain Project). M.C.S. and I.F. acknowledge support by MINECO (Spain), Comunitat Autónoma de les Illes Balears, FEDER, and the European Commission under Projects TEC2012-36335 (TRIPHOP), and Grups Competitius. M.H. and I.F. acknowledge support from the Universitat de les Illes Balears for an Invited Young Researcher Grant. ; Peer Reviewed