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.

Synchronization of two chaotic microresonator frequency combs.

We explore the synchronization of chaotic microresonator frequency combs, emphasizing the modulation instability state, which is known for its inherent chaotic behaviors. Our study confirms that the synchronization of two such combs is feasible by injecting the output from the lead microresonator into the next microresonator's input. We also identify the optimal parameters for this synchronization. Remarkably, even partial injection from the leader is sufficient for synchronization, paving the way for versatile future system configurations. Such systems could simultaneously utilize distinct spectral components for synchronization and transmission. This work advances our understanding of chaotic microresonator combs, showing them to be pivotal elements in next-generation optical communication systems.

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.

Reservoir computing based on an external-cavity semiconductor laser with optical feedback modulation.

We numerically and experimentally investigate reservoir computing based on a single semiconductor laser with optical feedback modulation. In this scheme, an input signal is injected into a semiconductor laser via intensity or phase modulation of the optical feedback signal. We perform a chaotic time-series prediction task using the reservoir and compare the performances of intensity and phase modulation schemes. Our results indicate that the feedback signal of the phase modulation scheme outperforms that of the intensity modulation scheme. Further, we investigate the performance dependence of reservoir computing on parameter values and observe that the prediction error improves for large injection currents, unlike the results in a semiconductor laser with an optical injection input. The physical origin of the superior performance of the phase modulation scheme is analyzed using external cavity modes obtained from steady-state analysis in the phase space. The analysis indicates that high-dimensional mapping can be achieved from the input signal to the trajectory of the response laser output by using phase modulation of the feedback signal.

Universal Single-Mode Lasing in Fully Chaotic Billiard Lasers.

By numerical simulations and experiments of fully chaotic billiard lasers, we show that single-mode lasing states are stable, whereas multi-mode lasing states are unstable when the size of the billiard is much larger than the wavelength and the external pumping power is sufficiently large. On the other hand, for integrable billiard lasers, it is shown that multi-mode lasing states are stable, whereas single-mode lasing states are unstable. These phenomena arise from the combination of two different nonlinear effects of mode-interaction due to the active lasing medium and deformation of the billiard shape. Investigations of billiard lasers with various shapes revealed that single-mode lasing is a universal phenomenon for fully chaotic billiard lasers.

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.

Fast dynamics of low-frequency fluctuations in a quantum-dot laser with optical feedback.

We experimentally investigate the complex dynamics of a multi-mode quantum-dot semiconductor laser with time-delayed optical feedback. We examine a two-dimensional bifurcation diagram of the quantum-dot laser as a comprehensive dynamical map by changing the injection current and feedback strength. We found that the bifurcation diagram contains two different parameter regions of low-frequency fluctuations. The power-dropout dynamics of the low-frequency fluctuations are observed in the sub-GHz region, which is considerably faster than the conventional low-frequency fluctuations in the MHz region. Comparing the dynamics of quantum-dot laser with those of single- and multi-mode quantum-well semiconductor lasers reveals that the fast low-frequency fluctuation dynamics are unique characteristics of quantum-dot lasers with time-delayed optical feedback.

High-entropy chaos generation using semiconductor lasers subject to intensity-modulated optical injection for certified physical random number generation.

This study investigates high-entropy chaos generation using a semiconductor laser subject to intensity-modulated optical injection for certified physical random number generation. Chaos with a continuous spectral profile that is not only widely distributed but also broadly flattened over a bandwidth of 33 GHz is generated. The former suggests that the chaos can be sampled at a high rate while keeping sufficient un-correlation between data samples, and the latter indicates that the chaos possesses high entropy, both of which enhance the generation rate of physical random numbers with guaranteed unpredictability. A minimum entropy value of 2.19 bits/sample is obtained without any post-processing and by excluding the contribution from measurement noise, suggesting that, to the least extent, the chaotic source can be used as a 2-bit physical random number generator at a rate of 160 Gbits/s.

Using multidimensional speckle dynamics for high-speed, large-scale, parallel photonic computing.

The recent rapid increase in demand for data processing has resulted in the need for novel machine learning concepts and hardware. Physical reservoir computing and an extreme learning machine are novel computing paradigms based on physical systems themselves, where the high dimensionality and nonlinearity play a crucial role in the information processing. Herein, we propose the use of multidimensional speckle dynamics in multimode fibers for information processing, where input information is mapped into the space, frequency, and time domains by an optical phase modulation technique. The speckle-based mapping of the input information is high-dimensional and nonlinear and can be realized at the speed of light; thus, nonlinear time-dependent information processing can successfully be achieved at fast rates when applying a reservoir-computing-like-approach. As a proof-of-concept, we experimentally demonstrate chaotic time-series prediction at input rates of 12.5 Gigasamples per second. Moreover, we show that owing to the passivity of multimode fibers, multiple tasks can be simultaneously processed within a single system, i.e., multitasking. These results offer a novel approach toward realizing parallel, high-speed, and large-scale photonic computing.

Laser network decision making by lag synchronization of chaos in a ring configuration.

Photonic technologies are promising for solving complex tasks in artificial intelligence. In this paper, we numerically investigate decision making for solving the multi-armed bandit problem using lag synchronization of chaos in a ring laser-network configuration. We construct a laser network consisting of unidirectionally coupled semiconductor lasers, whereby spontaneous exchange of the leader-laggard relationship in the lag synchronization of chaos is observed. We succeed in solving the multi-armed bandit problems with three slot machines using lag synchronization of chaos by controlling the coupling strengths among the three lasers. Furthermore, we investigate the scalability of the proposed decision-making principle by increasing the number of slot machines and lasers. This study suggests a new direction in laser network-based decision making for future photonic intelligent functions.

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.

Decision making for the multi-armed bandit problem using lag synchronization of chaos in mutually coupled semiconductor lasers.

We numerically and experimentally demonstrate the utilization of the synchronization of chaotic lasers for decision making. We perform decision making to solve the multi-armed bandit problem using lag synchronization of chaos in mutually coupled semiconductor lasers. We observe the spontaneous exchanges of the leader-laggard relationship under lag synchronization of chaos, and we find that the leader laser can be controlled by changing the coupling strengths between the two lasers. To solve the multi-armed bandit problem, we select one of the slot machines with unknown hit probabilities based only on the identity of the leader laser while reconfiguring the coupling strength to determine the correct decision. We successfully perform an on-line experimental demonstration of the decision making based on the two-laser coupled architecture. This is the first time that synchronization in chaotic lasers is utilized for decision making, and this study paves the way for novel resources for future photonic intelligence.

5-Aminolevulinic acid exerts renoprotective effect via Nrf2 activation in murine rhabdomyolysis-induced acute kidney injury.

AIM: Acute kidney injury (AKI) is associated with chronic kidney disease, as well as high mortality, but effective treatments for AKI are still lacking. A recent study reported the prevention of renal injury, such as ischemia-reperfusion injury, by 5-aminolevulinic acid (ALA), which induces an antioxidant effect. The current study aimed to investigate the effect of ALA in a rhabdomyolysis-induced mouse model of AKI created by intramuscular injection of 50% glycerol. METHODS: Rhabdomyolysis-induced AKI was induced by an intramuscular injection of glycerol (5 mL/kg body weight) into mice. Administration of ALA (30 mg/kg, by gavage) was started from 48 h before or 24 h after glycerol injection. The mice were sacrificed at 72 h after glycerol injection. The roles of nuclear factor erythroid 2-related factor 2 (Nrf2) and heme oxygenase-1 (HO-1), which is one of the Nrf2-related antioxidants, were further investigated through in vivo and in vitro methods. RESULTS: 5-aminolevulinic acid markedly reduced renal dysfunction and tubular damage in mice with rhabdomyolysis-induced AKI. ALA administration decreased oxidative stress, macrophage infiltration, and inflammatory cytokines and apoptosis. The expression of Nrf2 was upregulated by ALA administration. However, administration of Zinc protoporphyrin-9 (ZnPPIX) to inhibit HO-1 activity did not abolish these improvements by ALA. The expression of Nrf2-associated antioxidant factors other than HO-1 was also increased. CONCLUSION: These findings indicate that ALA exerts its antioxidant activity via Nrf2-associated antioxidant factors to provide a renoprotective effect against rhabdomyolysis-induced AKI.

Impact of input mask signals on delay-based photonic reservoir computing with semiconductor lasers.

We experimentally investigate delay-based photonic reservoir computing using semiconductor lasers with optical feedback and injection. We apply different types of temporal mask signals, such as digital, chaos, and colored-noise mask signals, as the weights between the input signal and the virtual nodes in the reservoir. We evaluate the performance of reservoir computing by using a time-series prediction task for the different mask signals. The chaos mask signal shows superior performance than that of the digital mask signals. However, similar prediction errors can be achieved for the chaos and colored-noise mask signals. Mask signals with larger amplitudes result in better performance for all mask signals in the range of the amplitude accessible in our experiment. The performance of reservoir computing is strongly dependent on the cut-off frequency of the colored-noise mask signals, which is related to the resonance of the relaxation oscillation frequency of the laser used as the reservoir.

Compact reservoir computing with a photonic integrated circuit.

Photonic reservoir computing is a new paradigm for performing high-speed prediction and classification tasks in an efficient manner. The major challenge for the miniaturization of photonic reservoir computing is the need for the use of photonic integrated circuits. Herein, we experimentally demonstrate reservoir computing using a photonic integrated circuit with a semiconductor laser and a short external cavity. We propose a method to increase the number of virtual nodes in delayed feedback using short node intervals and outputs from multiple delay times. We perform time-series prediction and nonlinear channel equalization tasks using reservoir computing with the photonic integrated circuit. We show that the photonic integrated circuit with optical feedback outperforms the photonic integrated circuit without optical feedback for prediction tasks. To enhance the memory effect we feed past input signals in the current input data and demonstrate successful performance in an n-step-ahead prediction task.

Effect of bandwidth limitation of optical noise injection on common-signal-induced synchronization in multi-mode semiconductor lasers.

We investigate common-signal-induced synchronization in two multi-mode semiconductor lasers subject to a bandwidth-limited optical noise signal. Synchronization can be achieved when the number of longitudinal modes is matched between the two lasers. The peak wavelengths need to be matched between the two lasers to achieve synchronization. In contrast, small correlation is observed when the peak wavelengths are mismatched. The synchronization is degraded as the number of longitudinal modes in one of the lasers is decreased. However, large correlation is obtained if the overlapped modes are selected and compared. We discuss the possibility of an unauthorized user reproducing the synchronized waveforms. It is difficult to completely reproduce the synchronized waveforms using synchronization if the bandwidth of the noise drive signal is limited.

Real-time fast physical random number generator with a photonic integrated circuit.

Random number generators are essential for applications in information security and numerical simulations. Most optical-chaos-based random number generators produce random bit sequences by offline post-processing with large optical components. We demonstrate a real-time hardware implementation of a fast physical random number generator with a photonic integrated circuit and a field programmable gate array (FPGA) electronic board. We generate 1-Tbit random bit sequences and evaluate their statistical randomness using NIST Special Publication 800-22 and TestU01. All of the BigCrush tests in TestU01 are passed using 410-Gbit random bit sequences. A maximum real-time generation rate of 21.1 Gb/s is achieved for random bit sequences in binary format stored in a computer, which can be directly used for applications involving secret keys in cryptography and random seeds in large-scale numerical simulations.

Common-signal-induced synchronization in photonic integrated circuits and its application to secure key distribution.

We experimentally achieve common-signal-induced synchronization in two photonic integrated circuits with short external cavities driven by a constant-amplitude random-phase light. The degree of synchronization can be controlled by changing the optical feedback phase of the two photonic integrated circuits. The change in the optical feedback phase leads to a significant redistribution of the spectral energy of optical and RF spectra, which is a unique characteristic of PICs with the short external cavity. The matching of the RF and optical spectra is necessary to achieve synchronization between the two PICs, and stable synchronization can be obtained over an hour in the presence of optical feedback. We succeed in generating information-theoretic secure keys and achieving the final key generation rate of 184 kb/s using the PICs.

Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal.

We numerically investigate reservoir computing based on the consistency of a semiconductor laser subjected to optical feedback and injection. We introduce a chaos mask signal as an input temporal mask for reservoir computing and perform a time-series prediction task. We compare the errors of the task obtained from the chaos mask signal with those obtained from other digital and analog masks. The performance of the prediction task can be improved by using the chaos mask signal due to complex dynamical response.

Photonic integrated circuits unveil crisis-induced intermittency.

We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics.