# Neuro-Inspired Computing with Spin-VCSELs
###### Abstract  
Delay-based reservoir computing (RC), a neuromorphic computing technique, has gathered lots of interest, as it promises compact and high-speed RC implementations. To further boost the computing speeds, we introduce and study an RC setup based on spin-VCSELs, thereby exploiting the high polarization modulation speed inherent to these lasers. Based on numerical simulations, we benchmarked this setup against state-of-the-art delay-based RC systems and its parameter space was analyzed for optimal performance. The high modulation speed enabled us to have more virtual nodes in a shorter time interval. However, we found that at these short time scales, the delay time and feedback rate heavily influence the nonlinear dynamics. Therefore, and contrary to other laser-based RC systems, the delay time has to be optimized in order to obtain good RC performances. We achieved state-of-the-art performances on a benchmark timeseries prediction task. This spin-VCSEL-based RC system shows a ten-fold improvement in processing speed, which can further be enhanced in a straightforward way by increasing the birefringence of the VCSEL chip.  
VCSEL; semiconductor lasers; nonlinear dynamics; delay systems; machine learning; neuromorphic computing; reservoir computing +
Footnote †: journal: journal: Applied Physics Research Group, Vrie Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium  
Footnote †: journal: journal: Applied Physics Research Group, Vrie Universite Brussel, Pleinlaan 2, 1050 Brussels, Belgium  
Footnote †: journal: journal: Applied Physics Research Group, Vrie Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium  
Footnote †: journal: journal: journal: Applied Physics Research Group, Vrie Universite Brussel, Pleinlaan 2, 1050 Brussels, Belgium  
Footnote †:subjected to feedback with electrical data injection [15; 16] or optical data injection [17; 18; 19; 20]. Delay-based RC lends itself very well for integrated design and the first results were achieved in [21; 22]. An overview of all the (photonic) RC systems can be found in [3; 5; 21].  
Due to the time-multiplexed nodes in a delay-based RC setup, the processing speed is inversely proportional to the duration of a single sample. This duration is determined by the number of nodes and the length of these nodes in the time domain. In [17], processing speeds around 10 MSa/s could be achieved, limited by the relaxation oscillations in the intensity. Follow-up research in [18] showed that the length of the nodes could be shortened thanks to phase dynamics occurring in the system, leading to speeds of 0.25 GSa/s. In [19], it was suggested to further increase the processing speed by spreading the number of nodes over different longitudinal modes available in the laser cavity.  
Recently, ultra-fast modulation techniques have been demonstrated by relying on the polarization dynamics of spin-VCSELs [23; 24; 25]. Modulation speeds of up to 200 GHz were achieved in [26]. We conjecture that this fast modulation speed can be used to speed up delay-based RC systems. In this work, we numerically investigated a delay-based RC system using a spin-VCSEL and injecting the data via the pump ellipticity, such that we can employ the ultra-fast polarization dynamics to increase the processing speed. Previously, there have been numerical studies on delay-based RC systems using VCSELs, but they rather rely on the phase dynamics and the polarization modes only serve to increase the state diversity in the output layer via polarization multiplexing [27; 28].  
In the next section, we describe the model we used for the spin-VCSEL and we provide details on our RC setup. Afterwards, we present the results obtained from different parameter scans, accompanied by a discussion, followed by the conclusions.