Impact of optical coherence on the performance of large-scale spatiotemporal photonic reservoir computing systems.

Large-scale spatiotemporal photonic reservoir computer (RC) systems offer remarkable solutions for massively parallel processing of a wide variety of hard real-world tasks. In such systems, neural networks are created by either optical or electronic coupling. Here, we investigate the impact of the optical coherence on the performance of large-scale spatiotemporal photonic RCs by comparing a coherent (optical coupling between the reservoir nodes) and incoherent (digital coupling between the reservoir nodes) RC systems. Although the coherent configuration offers significant reduction on the computational load compared to the incoherent architecture, for image and video classification benchmark tasks, it is found that the incoherent RC configuration outperforms the coherent configuration. Moreover, the incoherent configuration is found to exhibit a larger memory capacity than the coherent scheme. Our results pave the way towards the optimization of implementation of large-scale RC systems.

Enhanced performances of a photonic reservoir computer based on a single delayed quantum cascade laser.

In previous works, it has been shown that reservoir computing (RC) systems using a laser subject to a delayed optical feedback and stabilized by an injected signal may be highly sensitive to the feedback phase. In this Letter, we show that a RC system using a single quantum cascade laser subject to a delayed optical feedback but without injection is robust to the feedback phase for a large range of values of the parameters.

Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays.

Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.

Prediction performance of reservoir computing systems based on a diode-pumped erbium-doped microchip laser subject to optical feedback.

Reservoir computing (RC) systems are computational tools for information processing that can be fully implemented in optics. Here, we experimentally and numerically show that an optically pumped laser subject to optical delayed feedback can yield similar results to those obtained for electrically pumped lasers. Unlike with previous implementations, the input data are injected at a time interval that is much larger than the time-delay feedback. These data are directly coupled to the feedback light beam. Our results illustrate possible new avenues for RC implementations for prediction tasks.

Reducing the phase sensitivity of laser-based optical reservoir computing systems.

Optical implementations of reservoir computing systems are very promising because of their high processing speeds and the possibility to process several tasks in parallel. These systems can be implemented using semiconductor lasers subject to optical delayed feedback and optical injection. While the amount of the feedback/injection can be easily controlled, it is much more difficult to control the optical feedback/injection phase. We present extensive numerical investigations of the influence of the feedback/injection phases on laser-based reservoir computing systems with feedback. We show that a change in the phase can lead to a strong reduction in the reservoir computing system performance. We introduce a new readout layer design that -at least for some tasks- reduces this sensitivity to changes in the phase. It consists in optimizing the readout weights from a coherent combination of the reservoir's readout signal and its delayed version rather than only from the reservoir's readout signal as is usually done.

Simultaneous Computation of Two Independent Tasks Using Reservoir Computing Based on a Single Photonic Nonlinear Node With Optical Feedback.

In this brief, we numerically demonstrate a photonic delay-based reservoir computing system, which processes, in parallel, two independent computational tasks even when the two tasks have unrelated input streams. Our approach is based on a single-longitudinal mode semiconductor ring laser (SRL) with optical feedback. The SRL emits in two directional optical modes. Each directional mode processes one individual task to mitigate possible crosstalk. We illustrate the feasibility of our scheme by analyzing the performance on two benchmark tasks: 1) chaotic time series prediction and 2) nonlinear channel equalization. We identify some feedback configurations for which the results for simultaneous prediction/classification indicate a good performance, but with slight degradation (as compared with the performance obtained for single task processing) due to nonlinear and linear interactions between the two directional modes of the laser. In these configurations, the system performs well on both tasks for a broad range of the parameters.

Fast phase response and chaos bandwidth enhancement in semiconductor lasers subject to optical feedback and injection.

We numerically show the quantitative relation between the chaos bandwidth enhancement and fast phase dynamics in semiconductor lasers with optical feedback and optical injection. The injection increases the coupling between the intensity and the phase leading to a competition between the relaxation oscillation (RO) frequency and the intrinsic response frequency of the phase. For large feedback strengths, it is found that the chaos bandwidth is determined by the intrinsic phase response frequency. For smaller feedback strengths, the system is not chaotic and its bandwidth is determined by the RO frequency.

Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics.

Semiconductor lasers subject to delayed optical feedback have recently shown great potential in solving computationally hard tasks. By optically implementing a neuro-inspired computational scheme, called reservoir computing, based on the transient response to optical data injection, high processing speeds have been demonstrated. While previous efforts have focused on signal bandwidths limited by the semiconductor laser's relaxation oscillation frequency, we demonstrate numerically that the much faster phase response makes significantly higher processing speeds attainable. Moreover, this also leads to shorter external cavity lengths facilitating future on-chip implementations. We numerically benchmark our system on a chaotic time-series prediction task considering two different feedback configurations. The results show that a prediction error below 4% can be obtained when the data is processed at 0.25 GSamples/s. In addition, our insight into the phase dynamics of optical injection in a semiconductor laser also provides a clear understanding of the system performance at different pump current levels, even below solitary laser threshold. Considering spontaneous emission noise and noise in the readout layer, we obtain good prediction performance at fast processing speeds for realistic values of the noise strength.

Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback.

We report on an integrated approach to obtain multiwavelength emission from semiconductor ring lasers with filtered optical feedback. The filtered feedback is realized on-chip employing two arrayed-waveguide gratings to split/recombine light into different wavelength channels. Through experimental observations and numerical simulations, we find that the effective gain of the different modes is the key parameter which has to be balanced in order to achieve multiwavelength emission. This can be achieved by tuning the injection current in each amplifier.

Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation.

We numerically investigate the possibility of using a coupling to increase the complexity in simplest chaotic two-component electronic circuits operating at high frequency. We subsequently show that complex behaviors generated in such coupled systems, together with the post-processing are suitable for generating bit-streams which pass all the NIST tests for randomness. The electronic circuit is built up by unidirectionally coupling three two-component (one active and one passive) oscillators in a ring configuration through resistances. It turns out that, with such a coupling, high chaotic signals can be obtained. By extracting points at fixed interval of 10 ns (corresponding to a bit rate of 100 Mb/s) on such chaotic signals, each point being simultaneously converted in 16-bits (or 8-bits), we find that the binary sequence constructed by including the 10(or 2) least significant bits pass statistical tests of randomness, meaning that bit-streams with random properties can be achieved with an overall bit rate up to 10×100 Mb/s = 1 Gbit/s (or 2×100 Mb/s =200 Megabit/s). Moreover, by varying the bias voltages, we also investigate the parameter range for which more complex signals can be obtained. Besides being simple to implement, the two-component electronic circuit setup is very cheap as compared to optical and electro-optical systems.

Fast random bits generation based on a single chaotic semiconductor ring laser.

The use of the postprocessing method consisting of bitwise Exclusive-OR and least significant bits extraction to generate random bit sequences typically requires two distinct chaotic outputs. While the two signals are, in general, generated using two separated devices, e.g. two Fabry-Perot lasers, a single semiconductor ring laser can be used as an alternative due to its circular symmetry which facilitates lasing in two counterpropagating mode directions. We consider a chaotic semiconductor ring laser and investigate both numerically and experimentally its characteristics for fast random bit generation. In particular, we show that by sampling each directional mode's output signal using a 8-bit analog-digital converter and through Exclusive-OR operation applied to the two resulting signals (after throwing away 4 most significant bits), we can achieve fast random bit-streams with a bit rate 4 × 10 = 40 Gbit/s, passing the statistical randomness tests. To optimize the system performance, we also study the dependence of randomness on the main system parameters and on noise.

Electro-optic phase chaos systems with an internal variable and a digital key.

We consider an electro-optic phase chaos system with two feedback loops organized in a parallel configuration such that the dynamics of one of the loops remains internal. We show that this configuration intrinsically conceals in the transmitted variable the internal delay times, which are critical for decoding. The scheme also allows for the inclusion, in a very efficient way, of a digital key generated as a long pseudorandom binary sequence. A single digital key can operate both in the internal and transmitted variables leading to a large sensitivity of the synchronization to a key-mismatch. The combination of intrinsic delay time concealment and digital key selectivity provides the basis for a large enhancement of the confidentiality in chaos-based communications.

Loss of time-delay signature in chaotic semiconductor ring lasers.

We investigate the possibility of concealing the time-delay signatures in semiconductor ring lasers (SRLs) with external feedback. Through the autocorrelation and delayed mutual information, we report different scenarios leading to simultaneous time-delay concealment both in the intensity and the phase dynamics of such systems. In particular, the fact that such delay signatures can be eliminated in a SRL subject to short feedback constitutes a step toward the possibility of implementing secure communication schemes and random number generators on chip.

Role of the phase in the identification of delay time in semiconductor lasers with optical feedback.

We consider a semiconductor laser with external optical feedback operating at a regime for which the delay time signature is extremely difficult to identify from the analysis of the intensity time series, using standard techniques. We show that such a delay signature can be successfully retrieved by computing the same quantifiers from the phase, the real or the imaginary part of the field, even in the presence of noise. Therefore, the choice of the observable is the determinant for parameter identification.

Digital key for chaos communication performing time delay concealment.

We introduce a scheme that integrates a digital key in a phase-chaos electro-optical delay system for optical chaos communications. A pseudorandom binary sequence (PRBS) is mixed within the chaotic dynamics in a way that a mutual concealment is performed; e.g., the time delay is hidden by the binary sequence, and the PRBS is also masked by the chaos. In addition to bridging the gap between algorithmic symmetric key cryptography and chaos-based analog encoding, the proposed approach is intended to benefit from the complex algebra mixing between a (pseudorandom) Boolean variable, and another continuous time (chaotic) variable. The scheme also provides a large flexibility allowing for easy reconfigurations to communicate securely at a high bit rate between different systems.