We study delay-based photonic reservoir computing using a semiconductor laser with an optoelectronic feedback. A rate-equation model for a laser with an optoelectronic filtered feedback is used. The filter allows only high-frequency signals to pass through the feedback loop. The delay-differential equation model consists of three equations for the normalized electric field intensity I(t), the carrier density N(t); and the filtered intensity signal IF (t). The stability boundaries which correspond to the Hopf bifurcation condition are determined analytically, showing multiple Hopf bifurcation branches in the dynamics, and the parity asymmetry with relation to the feedback sign.
We use the Santa Fe time-series prediction task to evaluate the performance of reservoir computing. Our objective is to determine location of the optimal operating point defined as corresponding to minimal normalized means square error (NMSE) and relate it to the stability properties of the system. We use 3000 points for training and 1000 for testing, number of virtual nodes is chosen in regard to the relaxation oscillation frequency. Single-point prediction of the chaotic data is performed. Input signal is determined by the chaotic waveform
having n sampling points, and three cases are investigated: prediction of n + 1 ,n + 2 or n + 3 sampling point. The best NMSE value order of 10^7 for n + 1 point prediction task is obtained in the absence of feedback and the rapid increase in NMSE is observed in the vicinity of Hopf bifurcation without regard to the feedback sign. On the contrary, the minimum values of NMSE for n + 2 and n + 3 point prediction task correspond to the Hopf bifurcation, and only for the positive feedback. We discuss whether the parity asymmetry can explain strongly asymmetric reservoir computing results.
We propose a physical alternative of software based approaches for advanced classification task by considering a photonic-based architecture implementing a recurrent neural network with up to 16,384 physical neurons. This architecture is realized with o↵-the-shelf components and can be scaled up to hundred thousand or millions of nodes while ensuring data-ecient training strategy thanks to the reservoir computing framework. We use this architecture to perform a challenging computer vision task: the classification of human actions from a video feed. For this task, we show for the first time that a physical architecture with a simple learning strategy, consisting of training one linear readout for each class, can achieve a >90% success rate in terms of classification accuracy. This rivals the deep-learning approaches in terms of level of performance and hence could pave the way towards novel paradigm for ecient real-time video processing at the physical layer using photonic systems.
We present in this work numerical simulations of the performance of an on-chip photonic reservoir computer using nonlinear microring resonator as neurons. We present dynamical properties of the nonlinear node and the reservoir computer, and we analyse the performance of the reservoir on a typical nonlinear Boolean task : the delayed XOR task. We study the performance for various designs (number of nodes, and length of the synapses in the reservoir), and with respect to the properties of the optical injection of the data (optical detuning and power). From this work, we find that such a reservoir has state-of-the art level of performance on this particular task - that is a bit error rate of 2.5 10-4 - at 20 Gb/s, with very good power efficiency (total injected power lower than 1.0 mW).
We report on a bifurcation scenario from which emerges oscillations at a frequency higher than the relaxationoscillation frequency in an edge-emitting laser diode subjected to polarized optical feedback; these oscillations appear in the square-wave regime. The study has been performed experimentally and numerically based on Lang-Kobayashi model. We unveil bifurcation diagrams showing a clear bifurcation point that marks the transition between sustained and damped oscillations on the plateaus of square-waves. We extend this first bifurcation study by providing additional analytical insight to characterize the main parametric dependence of the frequency of these undamped oscillations.
Vertical Cavity Surface Emitting Lasers (VCSELs) with isotropic optical feedback are studied especially in the so-called low frequency fluctuations regime. Correlation properties between linear polarizations are analyzed both analytically and numerically. The RF spectrum shows a double peak structure close to the external cavity frequency which can be predicted by our adapted Spin-Flip Model (SFM). We provide here numerical evidence of the interplay between modes and anti- modes which are solutions of the stability analysis of the VCSEL with feedback and demonstrate that this interplay is responsible for the double peak structure.
We demonstrate experimentally that optical chaos generated by a laser diode with optical feedback is suitable for compressive sensing of sparse signals. Specifically, we find that the coherence collapse regime guarantees that the generation of a sensing matrix, necessary for sparse reconstruction, has a comparable level of performance to those constructed with Gaussian random sequences. Our result opens new avenues for the use of optical chaotic devices for signal processing applications at ultra-high speed.
We present an architecture tailored for the multiplexing of multiple optical chaotic carriers generated by semiconductor
lasers with external optical cavities. Our setup can discriminate multiple chaotic signals with high spectral overlap. The
various emitters are mutually globally coupled thanks to a shared optical feedback, which creates a multiplexed optical
field. This field is then coherently and unidirectionally injected in the decoupled receivers, and allows each of them to
synchronize on their respective emitter. Using this setup, it would be possible to transmit several messages and make a
better use of the wide chaotic spectrum. In this paper, we demonstrate theoretically and numerically the possibility to
synchronize two optical chaotic fields as a premise for the transmission of two messages. We also study the robustness of
synchronization to parameter mismatch and noise, which are important issues in real field experiments.
We investigate theoretically the identification of the
external-cavity roundtrip time of an external-cavity semiconductor
laser (ECSL). The time-delay identification is performed by analyzing the laser-intensity time series with conventional
techniques based on the autocorrelation function or mutual information. We find that a weak feedback rate and a time-delay
close to the laser's intrinsic relaxation-oscillation period are two conditions leading to difficult delay identification.
This arduous time-delay identification is of particular interest for the security improvement of chaos-based
communications schemes using ECSLs.