Complexity and bandwidth enhancement in unidirectionally coupled semiconductor lasers with time-delayed optical feedback

Experimental control of mode-competition dynamics in a chaotic multimode semiconductor laser for decision making

Photonic computing is widely used to accelerate the computational performance in machine learning. Photonic decision making is a promising approach utilizing photonic computing technologies to solve the multi-armed bandit problems based on reinforcement learning. Photonic decision making using chaotic mode-competition dynamics has been proposed. However, the experimental conditions for achieving a superior decision-making performance have not yet been established. Herein, we experimentally investigate mode-competition dynamics in a chaotic multimode semiconductor laser in the presence of optical feedback and injection. We control the chaotic mode-competition dynamics via optical injection and observe that positive wavelength detuning results in an efficient mode concentration to one of the longitudinal modes with a small optical injection power. We experimentally investigate two-dimensional bifurcation diagram of the total intensity of the laser dynamics. Complex mixed dynamics are observed in the presence of optical feedback and injection. We experimentally conduct decision making to solve the bandit problem using chaotic mode-competition dynamics. A fast mode-concentration property is observed at positive wavelength detunings, resulting in fast convergence of the correct decision rate. Our findings could be useful in accelerating the decision-making performance in adaptive optical networks using reinforcement learning.

Experimental demonstration of bandwidth enhancement in photonic time delay reservoir computing

Time delay reservoir computing (TDRC) using semiconductor lasers (SLs) has proven to be a promising photonic analog approach for information processing. One appealing property is that SLs subject to delayed optical feedback and external optical injection, allow for tuning the response bandwidth by changing the level of optical injection. Here we use strong optical injection, thereby expanding the SL's modulation response up to tens of gigahertz. Performing a nonlinear time series prediction task, we demonstrate experimentally that for appropriate operating conditions, our TDRC system can operate with sampling times as small as 11.72 ps, without sacrificing computational performance.

Chaotic mode-competition dynamics in a multimode semiconductor laser with optical feedback and injection

Photonic computing has attracted increasing interest for the acceleration of information processing in machine learning applications. The mode-competition dynamics of multimode semiconductor lasers are useful for solving the multi-armed bandit problem in reinforcement learning for computing applications. In this study, we numerically evaluate the chaotic mode-competition dynamics in a multimode semiconductor laser with optical feedback and injection. We observe the chaotic mode-competition dynamics among the longitudinal modes and control them by injecting an external optical signal into one of the longitudinal modes. We define the dominant mode as the mode with the maximum intensity; the dominant mode ratio for the injected mode increases as the optical injection strength increases. We deduce that the characteristics of the dominant mode ratio in terms of the optical injection strength are different among the modes owing to the different optical feedback phases. We propose a control technique for the characteristics of the dominant mode ratio by precisely tuning the initial optical frequency detuning between the optical injection signal and injected mode. We also evaluate the relationship between the region of the large dominant mode ratios and the injection locking range. The region with the large dominant mode ratios does not correspond to the injection-locking range. The control technique of chaotic mode-competition dynamics in multimode lasers is promising for applications in reinforcement learning and reservoir computing in photonic artificial intelligence.

Parallel and deep reservoir computing using semiconductor lasers with optical feedback

Photonic reservoir computing has been intensively investigated to solve machine learning tasks effectively. A simple learning procedure of output weights is used for reservoir computing. However, the lack of training of input-node and inter-node connection weights limits the performance of reservoir computing. The use of multiple reservoirs can be a solution to overcome this limitation of reservoir computing. In this study, we investigate parallel and deep configurations of delay-based all-optical reservoir computing using semiconductor lasers with optical feedback by combining multiple reservoirs to improve the performance of reservoir computing. Furthermore, we propose a hybrid configuration to maximize the benefits of parallel and deep reservoirs. We perform the chaotic time-series prediction task, nonlinear channel equalization task, and memory capacity measurement. Then, we compare the performance of single, parallel, deep, and hybrid reservoir configurations. We find that deep reservoirs are suitable for a chaotic time-series prediction task, whereas parallel reservoirs are suitable for a nonlinear channel equalization task. Hybrid reservoirs outperform other configurations for all three tasks. We further optimize the number of reservoirs for each reservoir configuration. Multiple reservoirs show great potential for the improvement of reservoir computing, which in turn can be applied for high-performance edge computing.

Wideband and high-dimensional chaos generation using optically pumped spin-VCSELs

We propose and numerically demonstrate wideband and high-dimensional chaos signal generation based on optically pumped spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs). Here, we focus on the chaotic characteristics of spin-VCSELs under two scenarios: one is a spin-VCSEL with optical feedback and the other is optical heterodyning the outputs of two free-running spin-VCSELs. Specifically, we systematically investigate the influence of some key parameters on the chaotic properties, i.e., bandwidth, spectral flatness (SF), time delay signature (TDS), correlation dimension (CD), and permutation entropy (PE), and reveal the route to enhance these properties simultaneously. Our simulation results demonstrate for the first time that spin-VCSELs with simple auxiliary configurations allow for chaos generation with desired properties, including effective bandwidth up to 30 GHz and above, no TDS of greater than 0.2, the flatness of 0.75 and above, and the high complexity/dimensionality over a wide range of parameters under both schemes. Therefore, our study may pave the way for potential applications requiring wideband and high-dimensional chaos.

Controlling chaotic itinerancy in laser dynamics for reinforcement learning

Photonic artificial intelligence has attracted considerable interest in accelerating machine learning; however, the unique optical properties have not been fully used for achieving higher-order functionalities. Chaotic itinerancy, with its spontaneous transient dynamics among multiple quasi-attractors, can be used to realize brain-like functionalities. In this study, we numerically and experimentally investigate a method for controlling the chaotic itinerancy in a multimode semiconductor laser to solve a machine learning task, namely, the multiarmed bandit problem, which is fundamental to reinforcement learning. The proposed method uses chaotic itinerant motion in mode competition dynamics controlled via optical injection. We found that the exploration mechanism is completely different from a conventional searching algorithm and is highly scalable, outperforming the conventional approaches for large-scale bandit problems. This study paves the way to use chaotic itinerancy for effectively solving complex machine learning tasks as photonic hardware accelerators.

Optimizations of optical chaos in semiconductor lasers based on multiobjective genetic algorithms

We investigated the frequency bandwidth, autocorrelation function, and complexity of chaotic temporal waveforms in unidirectionally coupled semiconductor lasers with time-delayed optical feedback. The effective bandwidth, peak value of autocorrelation function, and maximum Lyapunov exponent were simultaneously optimized by searching several control parameters of the laser systems based on multiobjective genetic algorithms. We found a conflicting relation between the effective bandwidth enhancement and the time-delay signature suppression, and a detailed relationship between the maximum Lyapunov exponent and the peak value of autocorrelation function.

Chaotic dimension enhancement by optical injection into a semiconductor laser under feedback

Optical injection into a chaotic laser under feedback is investigated for dimension enhancement. Although injecting a solitary laser is known to be low-dimensional, injecting the laser under feedback is found to enhance the correlation dimension D₂ in experiments. Using an exceptionally large data size with a very large reconstruction embedding dimension, efficient computation is enabled by averaging over many short segments to carefully estimate D₂. The dimension enhancement can be achieved together with time-delay signature suppression. The enhancement of D₂ as a fundamental geometric quantifier of attractors is useful in applications of chaos.

Entropy rate of chaos in an optically injected semiconductor laser for physical random number generation

We evaluate the (ɛ, τ) entropy of chaotic laser outputs generated by an optically injected semiconductor laser for physical random number generation. The vertical resolution ɛ and sampling time τ are numerically optimized by comparing the (ɛ, τ) entropy with the Kolmogorov-Sinai entropy, which is estimated from the Lyapunov exponents using linearized model equations. We then investigate the dependence of the (ɛ, τ) entropy on the optical injection strength of the laser system. In addition, we evaluate the (ɛ, τ) entropy from the experimentally obtained chaotic temporal waveforms in an optically injected semiconductor laser. Random bits with an entropy close to one bit per sampling point are extracted to satisfy the conditions of physical random number generation. We find that the extraction of the third-most significant bit from eight-bit experimental chaotic data results in an entropy of one bit per sample for certified physical random number generation.

Entropy evaluation of white chaos generated by optical heterodyne for certifying physical random number generators

The entropy of white chaos is evaluated to certify physical random number generators. White chaos is generated from the electric subtraction of two optical heterodyne signals of two chaotic outputs in semiconductor lasers with optical feedback. We use the statistical test suites of NIST Special Publication 800-90B for the evaluation of physical entropy sources of white chaos with an eight-bit resolution. The minimum value of entropy is 2.1 for eight most significant bits data. The entropy of white chaos is enhanced from that of the chaotic output of the semiconductor lasers. We evaluate the effect of detection noise and distinguish between the entropy that originates from the white chaos and the detection noise. It is found that the entropy of five most significant bits originates from white chaos. The minimum value of entropy is 1.1 for five most significant bits data, and it is considered that the entropy can be obtained at at least one bit per sample.

Point-to-multipoint and ring network communication based on chaotic semiconductor lasers with optical feedback

In this paper, two configurations of point-to-multipoint (PTM) and ring networks, based on the chaotic semiconductor laser subject to optical feedback, are investigated. A bifurcation diagram and the maximum Lyapunov exponent in the system have been used to distinguish the existence of chaos, and the complex degree of chaotic output is measured through Lempel-Ziv complexity. These results show that feedback strength has a significant effect on the dynamics of the system, namely, an increase in it can induce the system to enter into chaos. In the PTM model, it can be seen that the arbitrary receiver laser (RL) and central transmitter laser (TL) are identically synchronized, and moreover, the synchronization solutions are robust; the message can be encoded by modulating the bias current of the central TL, and at each RL end, the message from TL can be simultaneously recovered by monitoring the power error between RL and TL. As a result, the unidirectional broadcast message transmission, based on PTM, can be well achieved. In the ring network configuration, the coupling between two adjacent lasers through a partially transparent mirror induces the delay and chaotic dynamics. We prove that the dynamics is identically synchronized, and the synchronization against external perturbation also possesses good robustness; the messages introduced on the two arbitrary lasers in this ring network can be simultaneously exchanged.

Complexity-enhanced polarization-resolved chaos in a ring network of mutually coupled vertical-cavity surface-emitting lasers with multiple delays

The complexity properties of polarization-resolved chaotic signals generated in a ring network of vertical-cavity surface-emitting lasers (VCSELs) mutually coupled with multiple delays are investigated quantitatively by using the proposed mean permutation entropy (MPE). For direct comparison, the complexity of polarization-resolved chaos in a ring network of VCSELs coupled with single delay is also considered. The effects of injection current, coupling strength, and frequency detuning on the chaotic complexity for both a single-delay ring network (SDRN) and a multiple-delay ring network (MDRN) are evaluated quantitatively and compared by the MPE. The effects of internal parameters of VCSELs on the complexity are also discussed, and the correlation properties between different polarization-resolved modes are also analyzed. It is shown that the complexity of chaos in two polarization-resolved modes of VCSELs in MDRN is much higher than those in SDRN in a much wider parameter region. Besides, wider range of injection current, coupling strength, and frequency detuning can be tuned to achieve the enhancement of chaotic complexity in MDRN. These results provide an effective quantifier, the proposed MPE, to evaluate quantitatively the complexity of chaos generated in systems with multiple delays, and the multichannel complexity-enhanced polarization-resolved chaos generated in MDRN of mutually coupled VCSELs is extremely meaningful for the chaos-based random number generators.

Enhanced complexity of optical chaos in a laser diode with phase-conjugate feedback

We demonstrate numerically that a semiconductor laser subjected to phase-conjugate feedback (PCF) can exhibit an enhancement in the complexity of chaos by comparison to conventional optical feedback. Using quantifiers from spectral analysis and information theory, we demonstrate that under similar parametric conditions, PCF exhibits a larger chaotic bandwidth and higher spectral flatness and statistical complexity. These properties are of utmost importance for applications in secure communications and random number generation.

Randomness evaluation for an optically injected chaotic semiconductor laser by attractor reconstruction

State-space reconstruction is investigated for evaluating the randomness generated by an optically injected semiconductor laser in chaos. The reconstruction of the attractor requires only the emission intensity time series, allowing both experimental and numerical evaluations with good qualitative agreement. The randomness generation is evaluated by the divergence of neighboring states, which is quantified by the time-dependent exponents (TDEs) as well as the associated entropies. Averaged over the entire attractor, the mean TDE is observed to be positive as it increases with the evolution time through chaotic mixing. At a constant laser noise strength, the mean TDE for chaos is observed to be greater than that for periodic dynamics, as attributed to the effect of noise amplification by chaos. After discretization, the Shannon entropies continually generated by the laser for the output bits are estimated in providing a fundamental basis for random bit generation, where a combined output bit rate reaching 200 Gb/s is illustrated using practical tests. Overall, based on the reconstructed states, the TDEs and entropies offer a direct experimental verification of the randomness generated in the chaotic laser.