Resonant properties of the memory capacity of a laser-based reservoir computer with filtered optoelectronic feedback.

We provide a comprehensive analysis of the resonant properties of the memory capacity of a reservoir computer based on a semiconductor laser subjected to time-delayed filtered optoelectronic feedback. Our analysis reveals first how the memory capacity decreases sharply when the input-data clock cycle is slightly time-shifted from the time delay or its multiples. We attribute this effect to the inertial properties of the laser. We also report on the damping of the memory-capacity drop at resonance with a decrease of the virtual-node density and its broadening with the filtering properties of the optoelectronic feedback. These results are interpretated using the eigenspectrum of the reservoir obtained from a linear stability analysis. Then, we unveil an invariance in the minimum value of the memory capacity at resonance with respect to a variation of the number of nodes if the number is big enough and quantify how the filtering properties impact the system memory in and out of resonance.

Complete and partial time-delay signature suppression in a laser array.

We model dynamics of a quantum dot based micropillar laser array subject to the time-delayed optical feedback. The global coupling provided by the feedback generates a rich set of various instabilities including chaotic regimes with strong time-delay signature in the autocorrelation function. We demonstrate that the dispersion of the array coupling phases leads to effective suppression of the time-delay signature due to the dispersion of the system's internal timescales. We find that the transition to the complete suppression of the time-delay signature appears via a chimera state where highly correlated and non-correlated laser outputs coexist. The degree of correlation in the chimera state depends on the coupling phase dispersion.

Subharmonic locking and frequency combs in frequency-swept semiconductor lasers.

We analyze a delay differential equation model for a swept semiconductor laser and demonstrate existence of various periodic solutions that are subharmonically locked to the sweep rate. These solutions provide optical frequency combs in spectral domain. We investigate the problem numerically and show that, due to the translational symmetry of the model, there exists a hysteresis loop formed by branches of steady states solutions, bridges of periodic solutions connecting stable and unstable steady state branches, and isolated branches of limit cycles. We discuss the role of bifurcation points and limit cycles embedded into the loop in the formation of the subharmonic dynamics.

Refractory times for excitable dual-state quantum dot laser neurons.

Excitable photonic systems show promise for ultrafast analog computation, several orders of magnitude faster than biological neurons. Optically injected quantum dot lasers display several excitable mechanisms with dual-state quantum lasers recently emerging as true all-or-none excitable artificial neurons. For use in applications, deterministic triggering is necessary and this has previously been demonstrated in the literature. In this work we analyze the crucially important refractory time for this dual-state system, which defines the minimum time between distinct pulses in any train.

Impact of filtering on photonic time-delay reservoir computing.

We analyze the modification of the computational properties of a time-delay photonic reservoir computer with a change in its feedback bandwidth. For a reservoir computing configuration based on a semiconductor laser subject to filtered optoelectronic feedback, we demonstrate that bandwidth selection can lead to a flat-topped eigenvalue spectrum for which a large number of system frequencies are weakly damped as a result of the attenuation of modulational instability by feedback filtering. This spectral configuration allows for the optimization of the reservoir in terms of its memory capacity, while its computational ability appears to be only weakly affected by the characteristics of the filter.

Inhibitory and excitatory integration with a quantum dot laser neuron.

Neuromorphic computing has garnered a lot of attention in recent years. Excitable photonic systems in particular demonstrate great potential for ultrafast, controllable spike processing. Optically injected quantum dot lasers display several distinct excitable regimes. We demonstrate here that optically injected dual-state quantum dot lasers can display the classic leaky integrate-and-fire mechanism where the integration of several sub-threshold perturbations can yield an effective supra-threshold perturbation. Intriguingly, a contrasting integrate-and-inhibit mechanism is demonstrated in this work where the integration of two supra-threshold perturbations yields an effective sub-threshold perturbation similar to the pre-pulse inhibition mechanism of biological neurons. This is the first such mechanism in neuromorphic photonics to the best of our knowledge.

Optical square-wave generation in a semiconductor laser with optoelectronic feedback.

We report self-sustained optical square-wave (SW) generation in a semiconductor laser diode subjected to delayed optoelectronic feedback on its injection current (J). This optoelectronic oscillator relies on nonlinear effects present in both the laser diode and in the optoelectronic feedback loop through amplifier saturation. The repetition rate of the SW is an integer multiple of the inverse of the loop delay, while the duty cycle can be tuned with J.

10 W-level sub-100 ps 1 MHz MOPA laser with a microchip master oscillator.

A 10 W level master oscillator power amplifier (MOPA) laser with pulse repetition rate up to 1 MHz and 75-95 ps pulse duration was developed based on a passively Q-switched Nd:YVO4 microchip 1064 nm laser as a master oscillator. A double-rod double-end-pumping configuration of two-pass Nd:YAG ring power amplifier was used to achieve high gain, near-Fourier-transform-limited pulses, and laser beam quality factor M2=1.27 along both the horizontal and vertical directions.

Asymmetric excitable phase triggering in an optically injected semiconductor laser.

One of the defining characteristics of excitability is the existence of an excitable threshold: the minimum perturbation amplitude necessary to produce an excitable response. We analyze an optically injected dual state quantum dot laser, previously shown to display a dual state stochastic excitable dynamic. We show that deterministic triggering of this dynamic can be achieved via optical phase perturbations. Further, we demonstrate that there are in fact two asymmetric excitable thresholds in this system corresponding to the two possible directions of optical phase perturbations. For fast enough perturbations, an excitable interval arises, and there is a limit to the perturbation amplitude, above which excitations no longer arise, a phenomenon heretofore unobserved in studies of excitability.

Asymmetrical performance of a laser-based reservoir computer with optoelectronic feedback.

We numerically quantify the performance of a photonic reservoir computer based on a semiconductor laser subject to high-pass filtered optoelectronic feedback. We assess its memory capacity, computational ability, and performance in solving a multi-step prediction task. By analyzing the complex bifurcation landscape of the corresponding delay-differential equation model, we observe that optimal performance occurs at the edge of instability, at the onset of periodic regimes, and unveil a parity asymmetry in the performance with a slight advantage for positive over negative feedback.

Bifurcation structure of a swept-source laser.

We numerically analyze a delay differential equation model of a short-cavity semiconductor laser with an intracavity frequency-swept filter and reveal a complex bifurcation structure responsible for the asymmetry of the output characteristics of this laser. We show that depending on the direction of the frequency sweep of a narrow-band filter, there exist two bursting cycles determined by different parts of a continuous-wave solutions branch.

Dynamics of a class-A nonlinear mirror mode-locked laser.

Using a delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform linear stability analysis of the continuous-wave regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by an instability leading to the appearance of square-waves. We investigate the formation of square waves and mode-locked pulses in the system. We show that mode-locked pulses are asymmetric with exponential decay of the trailing edge in positive time and faster-than-exponential (superexponential) decay of the leading edge in negative time. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.

Excitable interplay between lasing quantum dot states.

The optically injected semiconductor laser system has proven to be an excellent source of experimental nonlinear dynamics, particularly regarding the generation of excitable pulses. Typically for low-injection strengths, these pulses are the result of a small above-threshold perturbation of a stable steady state, the underlying physics is well described by the Adler phase equation, and each laser intensity pulse is accompanied by a 2π phase rotation. In this article, we show how, with a dual-state quantum dot laser, a variation of type I excitability is possible that cannot be described by the Adler model. The laser is operated so that emission is from the excited state only. The ground state can be activated and phase locked to the master laser via optical injection while the excited state is completely suppressed. Close to the phase-locking boundary, a region of ground-state emission dropouts correlated to excited-state pulses can be observed. We show that the phase of the ground state undergoes bounded rotations due to interactions with the excited state. We analyze the system both experimentally and numerically and find excellent agreement. Particular attention is devoted to the bifurcation conditions needed for an excitable pulse as well as its time evolution.

Frequency modulated hybrid photonic crystal laser by thermal tuning.

We demonstrate frequency modulation (FM) in an external cavity (EC) III-V/silicon laser, comprising a reflective semiconductor optical amplifier (RSOA) and a silicon nitride (SiN) waveguide vertically coupled to a 2D silicon photonic crystal (PhC) cavity. The PhC cavity acts as a tunable narrowband reflector giving wavelength selectivity. The FM was achieved by thermo-optical modulation of the reflector via a p-n junction. Single-mode operation was ensured by the short cavity length, overlapping only one longitudinal laser mode with the reflector. We investigate the effect of reflector modulation theoretically and experimentally and predict a substantial tracking of the resonator by the laser frequency with very small intensity modulation (IM).

Nanometric sensing with laser feedback interferometry.

We demonstrate a nanometric sensor based on feedback interferometry in a distributed feedback (DFB) laser by using a measurement of either the optical frequency or laser voltage. We find that in an optimal range of optical feedback, the sensor operates reliably down to an extrapolated 12 nm; for the sensor demonstrated here at ∼1550 nm, this provides a minimum detectible displacement of λ/130.

Delay induced high order locking effects in semiconductor lasers.

Multiple time scales appear in many nonlinear dynamical systems. Semiconductor lasers, in particular, provide a fertile testing ground for multiple time scale dynamics. For solitary semiconductor lasers, the two fundamental time scales are the cavity repetition rate and the relaxation oscillation frequency which is a characteristic of the field-matter interaction in the cavity. Typically, these two time scales are of very different orders, and mutual resonances do not occur. Optical feedback endows the system with a third time scale: the external cavity repetition rate. This is typically much longer than the device cavity repetition rate and suggests the possibility of resonances with the relaxation oscillations. We show that for lasers with highly damped relaxation oscillations, such resonances can be obtained and lead to spontaneous mode-locking. Two different laser types--a quantum dot based device and a quantum well based device-are analysed experimentally yielding qualitatively identical dynamics. A rate equation model is also employed showing an excellent agreement with the experimental results.

Slow passage through thresholds in quantum dot lasers.

A turn on of a quantum dot (QD) semiconductor laser simultaneously operating at the ground state (GS) and excited state (ES) is investigated both experimentally and theoretically. We find experimentally that the slow passage through the two successive laser thresholds may lead to significant delays in the GS and ES turn ons. The difference between the turn-on times is measured as a function of the pump rate of change ɛ and reveals no clear power law. This has motivated a detailed analysis of rate equations appropriate for two-state lasing QD lasers. We find that the effective time of the GS turn on follows an ɛ^{-1/2} power law provided that the rate of change is not too small. The effective time of the ES transition follows an ɛ^{-1} power law, but its first order correction in ln(ɛ) is numerically significant. The two turn ons result from different physical mechanisms. The delay of the GS transition strongly depends on the slow growth of the dot population, whereas the ES transition only depends on the time needed to leave a repellent steady state.

Injection-induced, tunable all-optical gating in a two-state quantum dot laser.

We demonstrate a tunable all-optical gating phenomenon in a single-section quantum dot laser. The free-running operation of the device is emission from the excited state. Optical injection into the ground state of the material can induce a switch to emission from the ground state with complete suppression of the excited state. If the master laser is detuned from the ground-state emitting frequency, a periodic train of ground-state dropouts can be obtained. These dropouts act as gates for excited-state pulsations: during the dropout, the gate is opened and gain is made available for the excited state, and the gate is closed again when the dropout ends. Numerical simulations using a rate equation model are in excellent agreement with experimental results.

Optically induced hysteresis in a two-state quantum dot laser.

Quantum dot lasers can lase from the ground state only, simultaneously from both the ground and first excited states and from the excited state only. We examine the influence of optical injection at frequencies close to the ground state when the free-running operation of the device is excited state lasing only. We demonstrate the existence of an injection-induced bistability between ground state dominated emission and excited state dominated emission and the consequent hysteresis loop in the lasing output. Experimental and numerical investigations are in excellent agreement. Inhomogeneous broadening is found to be the underlying physical mechanism driving the phenomenon.

Emergence of resonant mode-locking via delayed feedback in quantum dot semiconductor lasers.

With conventional semiconductor lasers undergoing external optical feedback, a chaotic output is typically observed even for moderate levels of the feedback strength. In this paper we examine single mode quantum dot lasers under strong optical feedback conditions and show that an entirely new dynamical regime is found consisting of spontaneous mode-locking via a resonance between the relaxation oscillation frequency and the external cavity repetition rate. Experimental observations are supported by detailed numerical simulations of rate equations appropriate for this laser type. The phenomenon constitutes an entirely new mode-locking mechanism in semiconductor lasers.