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.

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.

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.

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.

Characterization of nanoporous Al2O3 films at terahertz frequencies.

Terahertz birefringence in nanoporous Al2O3 films grown on Al substrates is characterized nondestructively by polarization-resolved terahertz spectroscopy. Sparse deconvolution is used to find the film thicknesses from the data, showing good agreement with the values measured directly by destructive cross-sectional field-emission scanning electron microscopy.

Resonances between fundamental frequencies for lasers with large delayed feedbacks.

High-order frequency locking phenomena were recently observed using semiconductor lasers subject to large delayed feedbacks. Specifically, the relaxation oscillation (RO) frequency and a harmonic of the feedback-loop round-trip frequency coincided with the ratios 1:5 to 1:11. By analyzing the rate equations for the dynamical degrees of freedom in a laser subject to a delayed optoelectronic feedback, we show that the onset of a two-frequency train of pulses occurs through two successive bifurcations. While the first bifurcation is a primary Hopf bifurcation to the ROs, a secondary Hopf bifurcation leads to a two-frequency regime where a low frequency, proportional to the inverse of the delay, is resonant with the RO frequency. We derive an amplitude equation, valid near the first Hopf bifurcation point, and numerically observe the frequency locking. We mathematically explain this phenomenon by formulating a closed system of ordinary differential equations from our amplitude equation. Our findings motivate experiments with particular attention to the first two bifurcations. We observe experimentally (1) the frequency locking phenomenon as we pass the secondary bifurcation point and (2) the nearly constant slow period as the two-frequency oscillations grow in amplitude. Our results analytically confirm previous observations of frequency locking phenomena for lasers subject to a delayed optical feedback.

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.

Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity.

We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.

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.

Compressive Sensing with Optical Chaos.

Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found applications as diverse as seismology and biomedical imaging. In this work, we use actual optical signals generated from temporal intensity chaos from external-cavity semiconductor lasers (ECSL) to construct the sensing matrix that is employed to compress a sparse signal. The chaotic time series produced having their relevant dynamics on the 100 ps timescale, our results open the way to ultrahigh-speed compression of sparse signals.

Low-frequency fluctuations in an external-cavity laser leading to extreme events.

We experimentally investigate the dynamical regimes of a laser diode subject to external optical feedback in light of extreme-event (EE) analysis. We observe EEs in the low-frequency fluctuations (LFFs) regime. This number decreases to negligible values when the laser transitions towards fully developed coherence collapse as the injection current is increased. Moreover, we show that EEs observed in the LFF regime are linked to high-frequency pulsing events observed after a power dropout. Finally, we prove experimentally that the observation of EEs in the LFF regimes is robust to changes in operational parameters.

Time-delay concealment and complexity enhancement of an external-cavity laser through optical injection.

The concealment of the time-delay signature (TDS) of chaotic external-cavity lasers is necessary to ensure the security of optical chaos-based cryptosystems. We show that this signature can be removed simply by optically injecting an external-cavity laser with a large linewidth-enhancement factor into a second, noninjection-locked, semiconductor laser. Concealment is ensured both in the amplitude and in the phase of the optical field, satisfying a sought-after property of optical chaos-based communications. Meanwhile, enhancement of the dynamical complexity, characterized by permutation entropy, coincides with strong TDS suppression over a wide range of parameters, the area for which depends sensitively on the linewidth-enhancement factor.

Mapping the nonlinear dynamics of a laser diode via its terminal voltage.

We show that the bifurcations between dynamical states originating in the nonlinear dynamics of an external-cavity semiconductor laser at constant current can be detected by its terminal voltage V. We experimentally vary the intensity fed back into the gain medium by the external cavity and show that the dc component V(dc) of V tracks the optical intensity-based bifurcation diagram. It is shown using computational results based upon the Lang-Kobayashi model that whereas optical intensity accesses the dynamical-state variable |E|, V is related to population-inversion carrier density N. The change in feedback strength affects N and thereby the quasi-Fermi energy level difference at the p-i-n junction band-gap of the gain medium. The change in the quasi-Fermi energy-level thereby changes the terminal voltage V. Thus V is shown to provide information on the change in the dynamical-state variable N, which complements the more conventionally probed optical intensity.

Statistics of the optical intensity of a chaotic external-cavity DFB laser.

We study experimentally and theoretically the first- and second-order statistics of the optical intensity of a chaotic external-cavity semiconductor DFB laser in fully developed coherence-collapse. The second-order statistic is characterized by the autocorrelation, where we achieve consistent experimental and theoretical results over the entire parameter range considered. For the first-order statistic, we find that the experimental probability-density function is significantly more concentrated around the mean optical power and robust to parameter changes than theory predicts.

Experimental bifurcation-cascade diagram of an external-cavity semiconductor laser.

This Letter is the first to report experimental bifurcation diagrams of an external-cavity semiconductor laser (ECSL) in the low-to-moderate current injection regime and long-cavity case. Based on the bifurcation cascade behavior which was unveiled by Hohl and Gavrielides [Phys. Rev. Lett. 82, 1148-1151 (1999)], we present a detailed experimental investigation of the nonlinear dynamics of ECSLs and of the robustness of the cascade to changes in the current and cavity length. Also, we report for the first time a well resolved experimental Hopf bifurcation in an ECSL. Based on the Lang and Kobayashi model, we identify the dynamical regimes and the instabilities involved in the cascade, as well as the influence of the current and cavity length on the cascade.

Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser.

This paper reports the experimental investigation of two different approaches to random bit generation based on the chaotic dynamics of a semiconductor laser with optical feedback. By computing high-order finite differences of the chaotic laser intensity time series, we obtain time series with symmetric statistical distributions that are more conducive to ultrafast random bit generation. The first approach is guided by information-theoretic considerations and could potentially reach random bit generation rates as high as 160 Gb/s by extracting 4 bits per sample. The second approach is based on pragmatic considerations and could lead to rates of 2.2 Tb/s by extracting 55 bits per sample. The randomness of the bit sequences obtained from the two approaches is tested against three standard randomness tests (ENT, Diehard, and NIST tests), as well as by calculating the statistical bias and the serial correlation coefficients on longer sequences of random bits than those used in the standard tests.

Generation of orthogonal codes with chaotic optical systems.

We propose to use an electro-optic oscillator based on two Mach-Zehnder modulators in two different delayed feedback loops to generate two orthogonal chaotic spreading sequences (codes). We numerically demonstrate, for such codes, spectrally efficient multiplexing and demultiplexing of two digital data streams at multi-Gb/s rates using chaos synchronization and covariance-based detection.

Spectrally efficient multiplexing of chaotic light.

We numerically demonstrate multiplexing and demultiplexing of two distinct chaotic optical signals with strongly overlapped spectra, which are generated by mutually coupled external-cavity semiconductor lasers. Demultiplexing is performed by complete chaos synchronization, while the lasers at the receiving end are optically injected with the same multiplexed signal that couples the emitters together. Such a configuration could lead to spectrally efficient chaos-based optical encryption and decryption of multiple data streams.

Multiplexed encryption using chaotic systems with multiple stochastic-delayed feedbacks.

We propose an efficient and fast bit-multiplexed encryption scheme exploiting hyperchaotic regimes of a single nonlinear oscillator with multiple time-delay feedback loops. Each data stream is encrypted by digitally modulating the values of the various time delays and decrypted using chaos synchronization and cross-correlation measurements. We have numerically applied our approach to an optoelectronic chaotic oscillator based on standard semiconductor lasers subjected to multiple feedbacks and have demonstrated successful data transmission and recovery between multiple users at several Gbits/s on a single communication channel.

Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback.

We investigate theoretically the possibility of retrieving the value of the time delay of a semiconductor laser with an external optical feedback from the analysis of its intensity time series. When the feedback rate is moderate and the injection current set such that the laser relaxation-oscillation period is close to the delay, then the time-delay identification becomes extremely difficult, thus improving the security of chaos-based communications using external-cavity lasers.