For a globally coupled network of semiconductor lasers with delayed optical feedback, we demonstrate the existence of chimera states. The domains of coherence and incoherence that are typical for chimera states are found to exist for the amplitude, phase, and inversion of the coupled lasers. These chimera states defy several of the previously established existence criteria. While chimera states in phase oscillators generally demand nonlocal coupling, large system sizes, and specially prepared initial conditions, we find chimera states that are stable for global coupling in a network of only four coupled lasers for random initial conditions. The existence is linked to a regime of multistability between the synchronous steady state and asynchronous periodic solutions. We show that amplitude-phase coupling, a concept common in different fields, is necessary for the formation of the chimera states.

Delay-based reservoir computing has gained a lot of attention due to the relative simplicity with which this concept can be implemented in hardware. However, unnecessary constraints are commonly placed on the relationship between the delay-time and the input clock-cycle, which can have a detrimental effect on the performance. We review the existing literature on this subject and introduce the concept of delay-based reservoir computing in a manner that demonstrates that no predefined relationship between the delay-time and the input clock-cycle is required for this computing concept to work. Choosing the delay-times independent of the input clock-cycle, one gains an important degree of freedom. Consequently, we discuss ways to improve the computing performance of a reservoir formed by delay-coupled oscillators and show the impact of delay-time tuning in such systems.

We analyze the complex turn-on behavior of semiconductor quantum-dot (QD) lasers in terms of a nonlinear rate equation model for the electron and hole densities in the QDs and the wetting layer, and the photons. A basic ingredient of the model is the nonlinearity of the microscopic carrier-carrier scattering rates. With the framework of detailed balance, we analytically relate the microscopic in- and out-scattering rates. We gain insight into the anomalous nonlinear dynamics of QD lasers by a detailed analysis of various sections of the 5-D phase space, accounting for density-dependent carrier scattering times. We show that the strongly damped relaxation oscillations are characterized by a desynchronization of electron and hole dynamics in the dots. Analytic approximations for the steady-state characteristics are also derived.

Harmonically mode-locked semiconductor

The deep time-delay reservoir computing concept utilizes unidirectionally connected systems with time-delays for supervised learning. We present how the dynamical properties of a deep Ikeda-based reservoir are related to its memory capacity (MC) and how that can be used for optimization. In particular, we analyze bifurcations of the corresponding autonomous system and compute conditional Lyapunov exponents, which measure generalized synchronization between the input and the layer dynamics. We show how the MC is related to the systems’ distance to bifurcations or magnitude of the conditional Lyapunov exponent. The interplay of different dynamical regimes leads to an adjustable distribution between the linear and nonlinear MC. Furthermore, numerical simulations show resonances between the clock cycle and delays of the layers in all degrees of MC. Contrary to MC losses in single-layer reservoirs, these resonances can boost separate degrees of MC and can be used, e.g., to design a system with maximum linear MC. Accordingly, we present two configurations that empower either high nonlinear MC or long time linear MC.

The time-delay-based reservoir computing setup has seen tremendous success in both experiment and simulation. It allows for the construction of large neuromorphic computing systems with only few components. However, until now the interplay of the different timescales has not been investigated thoroughly. In this manuscript, we investigate the effects of a mismatch between the time-delay and the clock cycle for a general model. Typically, these two time scales are considered to be equal. Here we show that the case of equal or resonant time-delay and clock cycle could be actively detrimental and leads to an increase of the approximation error of the reservoir. In particular, we can show that non-resonant ratios of these time scales have maximal memory capacities. We achieve this by translating the periodically driven delay-dynamical system into an equivalent network. Networks that originate from a system with resonant delay-times and clock cycles fail to utilize all of their degrees of freedom, which causes the degradation of their performance.