There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing.

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Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers

Photonic implementations of reservoir computing (RC) have been receiving considerable attention due to their excellent performance, hardware, and energy efficiency as well as their speed. Here, we study a particularly attractive all-optical system using optical information injection into a semiconductor laser with delayed feedback. We connect its injection locking, consistency, and memory properties to the RC performance in a non-linear prediction task. We find that for partial injection locking we achieve a good combination of consistency and memory. Therefore, we are able to provide a physical basis identifying operational parameters suitable for prediction.

/pdf/conditions-for-reservoir-computing-performance-using-1gob6va46b.pdf

Conditions for reservoir computing performance using semiconductor lasers with delayed optical feedback.

Time-delayed optoelectronic oscillators are at the center of a large body of scientific literature. The complex behavior of these nonlinear oscillators has been thoroughly explored both theoretically and experimentally, leading to a better understanding of their dynamical properties. Beyond fundamental research, these systems have also inspired a wide and diverse set of applications, such as optical chaos communications, pseudorandom number generation, optoelectronic machine learning based on reservoir computing, ultrapure microwave generation, optical pulse-train synthesis, and sensing. The aim of this review is to provide a comprehensive survey of this field, to outline the latest achievements, and discuss the main challenges ahead.

Optoelectronic oscillators with time-delayed feedback

Chaotic dynamics of a semiconductor laser subject to distributed feedbacks from a fiber Bragg grating (FBG) are investigated through detailed simulations. Because of distributed reflections along the FBG, the approach of FBG feedback performs better than the conventional approach of mirror feedback in concealing the feedback delay time in chaos generation. The time-delay signature obtained from the autocorrelation function decreases as the FBG bandwidth decreases, which is attributed to the associated increase in the FBG dispersion. Such time-delay signature suppression is generally observed over a range of feedback parameters. The dynamical mappings of the laser subject to FBG feedback reveal large regions of chaotic states, except when the FBG bandwidth is much narrower than the relaxation resonance frequency of the laser.

http://www.ee.cityu.edu.hk/~scchan/all_papers/Li12PJ.pdf

Distributed Feedbacks for Time-Delay Signature Suppression of Chaos Generated From a Semiconductor Laser

The noise suppressions in the chaos lidar (CLIDAR) and the synchronized chaos lidar (S-CLIDAR) systems with the optoelectronic feedback (OEF) and optical feedback (OF) schemes are studied numerically. Compared with the CLIDAR system, the S-CLIDAR system with the OEF scheme has better correlation coefficients in the large noise regime for SNR < 15 dB. For the S-CLIDAR system with the OF scheme, better detections are also achieved in wide ranges depending on the levels of the phase noise presented in the channel. To have the best synchronization and detection quality, the optimized conditions for the coupling and feedback strengths in the S-CLIDAR system are also discussed.

Noise suppressions in synchronized chaos lidars

We experimentally investigate the dynamical characteristics of semiconductor lasers subject to both the optical injection (OI) and the optical feedback (OF). By coupling the OI and the OF lights into the same fiber before injecting into the slave laser (SL), the ratio between the two perturbations can be accurately determined and controlled. The frequency shifts in the cavity resonance frequency of the SL (νSL) induced by the OI and the OF lights are compared quantitatively. To study the competition between the OI and the OF in the SL, the mapping of the dynamical scenarios and states are plotted in the parameter space. This mapping serves as the guideline for choosing the appropriate operation conditions in various applications employing both the OI and the OF at the same time. In this paper, the suitable feedback strengths to narrow the linewidths of photonic microwave signals generated by the OI are studied. The limitation of using OI in enhancing the bandwidths of the chaos states generated by the OF is discussed. Moreover, to suppress the unwanted dynamics due to the feedback, the optimal injection parameters of the OI are shown.

Dynamical characteristics and their applications of semiconductor lasers subject to both optical injection and optical feedback.

Dual-beam optically injected semiconductor lasers have been utilized in the field of microwave photonics for generations of microwave signals. To better understand the nonlinear behavior of a dual-beam optically injected semiconductor laser, we experimentally investigate the dynamics scenarios and their transition routes. By injecting a slave laser with beams from two master lasers, mappings of the dynamics scenarios including PP, PS, SP, SS, S' S', S' L, LS', and LL are plotted under different injection strengths and detuning frequencies. These scenarios are defined and differentiated by whether the dynamics and the characteristic frequencies originated from the single-beam injection scheme are being preserved (P), shifted (S), or suppressed (S') after both beams are simultaneously injected. The letter L is used if the slave laser is already injection-locked by one of the beams under the single-beam injection condition. The transition routes among these dynamics scenarios are shown to be clearly traceable by tracking and comparing the oscillation frequencies of the slave laser under the dual-beam and single-beam injections. Moreover, frequency-locking states are observed experimentally the first time in a dual-beam optically injected semiconductor laser, which occur when the frequency pushing effects from the two injected beams with opposite detunings balance each other off.

Dynamical Characteristics of a Dual-Beam Optically Injected Semiconductor Laser

The linewidth enhancement factor α of a semiconductor laser under the influences of optical feedback with different feedback strengths, external cavity lengths, and feedback phases are studied both experimentally and theoretically. The value of α is determined from the minimum of the Hopf bifurcation curve when the laser is subject to both optical feedback and optical injection. In the experiment, a pellicle beamsplitter mounted on a PZT stage placed on a linear translation stage is used as the reflector, where the external cavity length can be adjusted continuously from the long cavity regime to the short cavity regime with phase accuracy. With a moderate feedback strength, α is found to increase as the feedback strength increases. Moreover, while α is insensitive to the feedback phase in the long cavity regime, it can be tuned continuously in the short cavity regime when varying the phase. A normalized variation range of 21.59% is obtained experimentally at an external cavity length of 1.5 cm, which can be further enhanced by shortening the external cavity. To the best of our knowledge, this is the first detailed study of α from the long to the short cavity regime in a semiconductor laser subject to optical feedback. More particularly, the continuous tuning of α under phase variation is demonstrated the first time.

Linewidth enhancement factor in semiconductor lasers subject to various external optical feedback conditions.

We numerically study and compare the noise suppressions in the chaos lidar (CLIDAR) and the synchronized
choas lidar (S-CLIDAR) systems with the optoelectronic feedback (OEF) and the optical feedback (OF) schemes.
The S-CLIDAR system with both OEF and OF schemes show better noise immunity than the CLIDAR system
in the low SNR region. Compare with the OEF scheme, the S-CLIDAR system with the OF scheme is more
sensitive to the phase noise. For the S-CLIDAR system with both schemes, an open-loop configuration under a
generalized synchronization condition is desired.

Yi-Huan Liao

Papers

Noise suppressions in synchronized chaos lidars

Dynamical characteristics and their applications of semiconductor lasers subject to both optical injection and optical feedback.

Dynamical Characteristics of a Dual-Beam Optically Injected Semiconductor Laser

Linewidth enhancement factor in semiconductor lasers subject to various external optical feedback conditions.

Noise suppressions in synchronized chaotic lidars