Delay-coupled Semiconductor Lasers Research Articles

Reservoir computing system based on mutually delay-coupled semiconductor lasers with optical feedback

Reservoir Computing (RC), an evolution from Recurrent Neural Networks (RNN), not only represents a unique machine learning paradigm, but also serves as a neuromorphic framework that mirrors the intricate cortical circuits of the human brain. This paper proposes another new photonic RC system based on four basic photonic reservoir computing architectures (single photonic RC system, the parallel photonic RC system, the dual-feedback loop-based photonic RC system and the mutually coupled photonic RC system). System proposed uses optical injection for signal input and retains two parallel responsive semiconductor lasers (R-SLs) with self-feedback loops. Meanwhile, two relatively independent R-SLs are mutually coupled via two coupling lines. The new photonic RC system adds only two sections of fiber compared to the parallel photonic RC system and the mutually coupled photonic RC system. The experiments show that the system proposed has significant advantages on the nonlinear auto regressive moving average series tasks, the chaotic time series prediction tasks and the waveform classification task. More importantly, the memory capacity of system proposed can be adjust by controlling the delay time of the self-feedback loops, so it has higher memory capacity to handle the higher order nonlinear auto regressive moving average tasks (NARMA20 and NARMA30) after optimizing the parameters.

Regulation of cluster synchronization in multilayer networks of delay coupled semiconductor lasers with the use of disjoint layer symmetry.

In real-world complex systems, heterogeneous components often interact in complex connection patterns and could be schematized by a formalism of multilayer network. In this work, the synchronization characteristics of multilayer network composed of semiconductor lasers (SLs) are investigated systematically. It is demonstrated that the interplay between different layers plays an important role on the synchronization patterns. We elucidate that the performance of cluster synchronization could be facilitated effectively with the introduction of disjoint layer symmetry into network topology. Intertwined stability of clusters from different layers could be decoupled into independent, and the parameter spaces for stable synchronization are extended significantly. The robustness of our proposed regulation scheme on operation parameters is numerically evaluated. Furthermore, the generality of presented theoretical results is validated in networks with more complex topology and multiple layers.

Photonic reservoir computing for energy efficient and versatile machine learning application

Time-multiplexed reservoir computing is a machine learning concept which can be realised in photonic hardware systems using only one physical node. The concept can be used for various problems, ranging from classification problems to time-series prediction tasks, while being fast and energy efficient. Here, a theoretical analysis of a reservoir computer realised via delay-coupled semiconductor lasers is presented and the role of the internal system time-scales and the bifurcation structure is discussed. It is further shown that optimal performance can be reached by tailoring the coupling delays to the specific memory requirements of the given task.

Enhanced Prediction Performance of Reservoir Computing Based on Mutually Delay-Coupled Semiconductor Lasers via Parameter Mismatch

As an efficient information processing method, reservoir computing (RC) is essential to artificial neural networks (ANNs). Via the Santa Fe time series prediction task, we numerically investigated the effect of the mismatch of some critical parameters on the prediction performance of the RC based on two mutually delay-coupled semiconductor lasers (SLs) with optical injection. The results show that better prediction performance can be realized by setting appropriate parameter mismatch scenarios. Especially for the situation with large prediction errors encountered in the RC with identical laser parameters, a suitable parameter mismatch setting can achieve computing performance improvement of an order of magnitude. Our research is instructive for the hardware implementation of laser-based RC, where the parameter mismatch is unavoidable.

Independently Synchronizable Groups in Networks of Delay-Coupled Semiconductor Lasers

In delay-coupled semiconductor lasers (SLs) network, we have established a scheme to separate SLs clusters into distinct groups in which the stability of cluster synchronization in each group is completely independent from that of others. The synchronization stability of these dynamical groups, termed as independently synchronizable groups, are theoretically and numerically investigated. The influences of crucial parameters in SLs networks on the stability of independently synchronizable groups are systematically evaluated. We also numerically discuss the robustness of synchronization stability against parameter mismatch, and demonstrate that the parameter mismatch between different SLs within an independent group did not affect the synchrony of other groups. Moreover, it is shown that modulation of parameters for specific group can significantly improve synchronization performance. Our results offer a new insight to explore new regimes of synchronization in SLs networks.

A Unifying Analysis of Chaos Synchronization and Consistency in Delay-Coupled Semiconductor Lasers

Consistency is a powerful concept to characterize and classify the behavior of driven dynamical systems, therefore playing an essential role for the understanding of information processing in and by complex photonic systems. Here, we discuss two different experimental configurations of semiconductor laser systems with delayed optical feedback allowing for a unifying view via the detailed characterization and comparison of consistency and synchronization properties. The first configuration comprises two unidirectionally coupled semiconductor lasers, which has found considerable interest for applications in encrypted communication. The second configuration consists of a single laser with two optical delay loops of significantly different lengths, designed such that only one loop is active at a time and that allows to study replays of injected optical signals. We show that, in terms of three characteristic correlation measures-consistency correlation, transformation correlation, and spurious correlation-the dynamical features of the two different experiments are very similar and how the two configurations are connected. Our approach shows that consistency allows to understand and relate various chaos synchronization and stability properties. We particularly discuss the experimental results in the context of a previously established analytical framework, providing a common dynamical interpretation of consistency and chaos synchronization in delay-driven laser systems.

Prediction and classification performance of reservoir computing system using mutually delay-coupled semiconductor lasers

Abstract A reservoir computing (RC) system based on two mutually delay coupled semiconductor lasers (MDC-SLs) subject to optical injection is proposed, and the chaotic time series prediction and signal classification performance for such a system is numerically investigated via the Santa-Fe time-series prediction task and the signal classification task, respectively. The simulation results indicate that, when adopting this system to process ultra-fast data with rate up to 1 Gbps, the best prediction error 5 . 1 × 1 0 − 5 ± 5 . 2 × 1 0 − 6 and signal recognition error 5 . 5 × 1 0 − 4 ± 8 . 8 × 1 0 − 5 can be achieved under optimized operation parameters.

Dynamics of two identical mutually delay-coupled semiconductor lasers in photonic integrated circuits

We theoretically investigate a system of two mutually delay-coupled semiconductor lasers, in a face to face configuration for integration in a photonic integrated circuit. This system is described by single-mode rate equations, which are a system of delay differential equations with one fixed delay. Several bifurcation scenarios involving multistabilities are presented, followed by a comprehensive frequency analysis of the symmetric and symmetry-broken, one-color and two-color states.

Exploring High Quality Chaotic Signal Generation in a Mutually Delay Coupled Semiconductor Lasers System

High quality chaotic signal generation in a mutually delay coupled semiconductor lasers (MDC-SLs) system is numerically explored by evaluating the time-delay signature (TDS) and complexity of chaotic signals. Autocorrelation function is utilized for quantitatively identifying the TDS of chaotic signal, and Kolmogorov–Sinai entropy and Kaplan–York dimensions are applied to estimate the complexity of chaotic signal. The results show that, under suitable parameters, two sets of chaotic signals with weak TDS and high complexity can be obtained simultaneously. By analyzing the influences of the mutual coupling strength and frequency detuning between the two MDC-SLs on the TDS and complexity of chaotic signals, the optimized parameter regions are specified for simultaneously generating two sets of high quality chaotic signals based on the MDC-SLs system.

Emergence of stable two-colour states in mutually delay-coupled lasers

We theoretically investigate a setup of two mutually delay-coupled semiconductor lasers in a face to face configuration, and study the multi-stabilities and symmetry-broken one-colour and two-colour states for this system, for the development of mutually coupled lasers for integration in a Photonic Integrated Circuit (PIC).We show that the stable two-colour exist for the finite distance between lasers.

Bidirectional private key exchange using delay-coupled semiconductor lasers.

We experimentally demonstrate a key exchange cryptosystem based on the phenomenon of identical chaos synchronization. In our protocol, the private key is symmetrically generated by the two communicating partners. It is built up from the synchronized bits occurring between two current-modulated bidirectionally coupled semiconductor lasers with additional self-feedback. We analyze the security of the exchanged key and discuss the amplification of its privacy. We demonstrate private key generation rates up to 11 Mbit/s over a public channel.

Synchronization properties of two mutually delay-coupled semiconductor lasers

This paper reports a detailed numerical study of the synchronization properties of two mutually delay-coupled semiconductor lasers in the framework of the Lang–Kobayashi model. By computing high-definition stability diagrams, we predict the complex distribution of periodic and chaotic laser oscillations on the coupling versus detuning control parameter plane. Such diagrams provide details concerning the behavior of the laser intensities, quantify objectively the synchronization between their electric fields, and display in-phase and out-of-phase laser behavior. In addition, we also describe the presence of a conspicuous abrupt change in the optimal shift for the greatest value of the cross-correlation function when varying the detuning between the optical angular frequencies of the lasers.

Stability diagrams for continuous wide-range control of two mutually delay-coupled semiconductor lasers

The dynamics of two mutually delay-coupled semiconductor lasers has been frequently studied experimentally, numerically, and analytically either for weak or strong detuning between the lasers. Here, we present a systematic numerical investigation spanning all detuning ranges. We report high-resolution stability diagrams for wide ranges of the main control parameters of the laser, as described by the Lang–Kobayashi model. In particular, we detail the parameter influence on dynamical performance and map the distribution of chaotic pulsations and self-generated periodic spiking with arbitrary periodicity. Special attention is given to the unfolding of regular pulse packages for both symmetric and non-symmetric configurations with respect to detuning. The influence of the delay –time on the self-organization of periodic and chaotic laser phases as a function of the coupling and detuning is also described in detail.

Symmetry-breaking bifurcations in two mutually delay-coupled lasers

We consider a symmetric system of delay differential equations arising from a model of two mutually delay-coupled semiconductor lasers. The system is described using the Lang-Kobayashi rate equations whose basic solutions are called compound laser modes (CLMs). We employ a group-theoretic approach to find solutions and to identify symmetry-breaking steady-state and Hopf bifurcations. This classification allows us to predict the symmetry group of a bifurcating branch of solutions from a symmetry- breaking bifurcation. Methods and techniques used in this study can be extended to larger symmetric laser networks.

Symmetry-Breaking Bifurcations in Rings of Delay-Coupled Semiconductor Lasers

We consider symmetric rings of delay-coupled lasers modeled using the Lang--Kobayashi (LK) rate equations with unidirectional and bidirectional coupling. Because of phase symmetry the networks have symmetry groups $\mathbb{Z}_n\times\mathbf{S}^1$ (unidirectional) and $\mathbf{D}_n\times\mathbf{S}^1$ (bidirectional). Our first main result is a characterization of isotropy subgroups of those actions from which we determine sufficient conditions for the existence of basic classes of compound laser modes (CLMs) valid for all ring sizes. Case studies of the $n=3$ and $n=8$ coupled LK equations are presented, including branches of CLMs obtained via DDE-Biftool. Using the block diagonalization of the linearization coming from the isotypic decomposition we classify the symmetry-breaking type of steady-state and Hopf bifurcation points at fully symmetric CLMs and in the case $n=3$ obtain explicit location of bifurcation points. We complement the study using DDE-Biftool to perform branch continuation at steady-stat...

Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers

We perform a detailed numerical analysis of square-wave (SW) polarization switching in two semiconductor lasers with time-delayed, orthogonal mutual coupling. An in-depth mapping of the dynamics in the two-parameter plane coupling strength versus frequency detuning shows that stable SWs occur in narrow parameter regions that are localized close to the boundary of stability of the pure-mode solution. In this steady state, the two coupled lasers emit orthogonal polarizations. We also show that there are various types of SW forms and that stable switching does not need the inclusion of noise or nonlinear gain in the model. As these narrow regions of deterministic and stable SWs occur for quite different combinations of parameters, they could potentially explain the waveforms that have been observed experimentally. However, on the other hand, these regions are narrow enough to be in fact considered as experimentally unreachable. Therefore, our results indicate that further experimental statistical studies are needed in order to distinguish deterministic and stationary square waveforms from long transients because of noise.

Spectral properties and synchronization scenarios of two mutually delay-coupled semiconductor lasers

We experimentally study the intensity dynamics and the optical spectra of two similar mutually delay-coupled semiconductor lasers. While changing two relevant parameters of the coupled system, namely the bias currents and the coupling strength of the lasers, we observe significant modifications in the laser emission characterized via optical spectra, laser intensity dynamics, and cross-correlation functions. We find distinct synchronization scenarios for two bias currents: 1.02 and 1.25 times the threshold bias current of the solitary laser. Optical spectra in both cases strongly depend on the coupling strength between the lasers. For the low bias current and strong coupling, the lasers exhibit dynamical bistability, i.e. the coexistence of low-frequency fluctuations and stable continuous-wave emission.

Stability Analysis for Mutually Delay-Coupled Semiconductor Lasers System

In this paper, the problem of the stability for mutually delay-coupled semiconductor lasers system is investigated. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated. The new phenomena such as stability switch is found. TheZ2equivariant property and the existence of multiple periodic solutions is also discussed. Numerical simulations are presented to illustrate the results in the paper.

Cluster and group synchronization in delay-coupled networks

We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability approach, we find that the master stability function shows a discrete rotational symmetry depending on the number of groups. The coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum, which helps to simplify the evaluation of the master stability function. Our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times, multiple coupling functions, but also with multiple kinds of local dynamics in the networks' nodes. We illustrate our results by calculating stability in the example of delay-coupled semiconductor lasers and in a model for neuronal spiking dynamics.

Evolution of time delay signature of chaos generated in a mutually delay-coupled semiconductor lasers system

In this paper, evolution of time delay (TD) signature of chaos generated in a mutual delay-coupled semiconductor lasers (MDC-SLs) system is investigated experimentally and theoretically. Two statistical methods, including self-correlation function (SF) and permutation entropy (PE), are used to estimate the TD signature of chaotic time series. Through extracting the characteristic peak from the SF curve, a series of TD signature evolution maps are firstly obtained in the parameter space of coupled strength and frequency detuning. Meantime, the influences of injection current on the evolution maps of TD signature have been discussed, and the optimum scope of TD signature suppression is also specified. An overall qualitative agreement between our theoretical and experimental results is obtained.