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.

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.

Symmetric Potential Lattice and Smooth Propagation of Tail-Free Discrete Breathers.

We present a particular type of one-dimensional nonlinear lattice that supports smoothly propagating discrete breathers. The lattice is constructed by imposing a particular symmetry on its potential function. This symmetry crucially affects the profile and motion of a traveling discrete breather. We show that any traveling discrete breather is truly localized with no tail and can smoothly propagate with a constant velocity. Theoretical analysis using an average Lagrangian explains this numerical observation.

Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation.

We generate random bit sequences from chaotic temporal waveforms by using photonic integrated circuits (PICs) with different external cavity lengths. We investigate the condition for generating random bits at different sampling rates of single-bit generation method with the PICs. We succeed in generating certified random bit sequences by using the PIC with 3, 4, 5, or 10-mm-long external cavity, whereas random bits cannot pass all the statistical tests of randomness when the PIC with 1 or 2 mm-long external cavity is used.

Information-theoretic secure key distribution based on common random-signal induced synchronization in unidirectionally-coupled cascades of semiconductor lasers.

It has been proposed that a secure key distribution scheme using correlated random bit sequences can be implemented using common random-signal induced synchronization of semiconductor laser systems. In this scheme it is necessary to use laser systems consisting of multiple cascaded lasers to be secure against a powerful eavesdropper. In this paper, we report the results of an experimental study that demonstrate that the common random-signal induced synchronization is possible in cascaded semiconductor laser systems. We also show that the correlated random bit sequences generated in the synchronized cascaded laser systems can be used to create an information-theoretically secure key between two legitimate users.

Experiment on synchronization of semiconductor lasers by common injection of constant-amplitude random-phase light.

We experimentally and numerically observe the synchronization between two semiconductor lasers induced by common optical injection with constant-amplitude and random-phase modulation in configurations with and without optical feedback. Large cross correlation (~0.9) between the intensity oscillations of the two response lasers can be achieved although the correlation between the drive laser and either one of the two response lasers is very small (~0.2). High quality synchronization is achieved in the presence of optical feedback in response lasers with matched feedback phase offset. We investigate the dependence of synchronization on parameter values over wide parameter ranges.

Secure key distribution using correlated randomness in lasers driven by common random light.

We propose a secure key distribution scheme based on correlated physical randomness in remote optical scramblers driven by common random light. The security of the scheme depends on the practical difficulty of completely observing random optical phenomena. We describe a particular realization using the synchronization of semiconductor lasers injected with common light of randomly varying phase. We experimentally demonstrate the feasibility of the scheme over a distance of 120 km.

Noise amplification by chaotic dynamics in a delayed feedback laser system and its application to nondeterministic random bit generation.

We present an experimental method for directly observing the amplification of microscopic intrinsic noise in a high-dimensional chaotic laser system, a laser with delayed feedback. In the experiment, the chaotic laser system is repeatedly switched from a stable lasing state to a chaotic state, and the time evolution of an ensemble of chaotic states starting from the same initial state is measured. It is experimentally demonstrated that intrinsic noises amplified by the chaotic dynamics are transformed into macroscopic fluctuating signals, and the probability density of the output light intensity actually converges to a natural invariant probability density in a strongly chaotic regime. Moreover, with the experimental method, we discuss the application of the chaotic laser systems to physical random bit generators. It is experimentally shown that the convergence to the invariant density plays an important role in nondeterministic random bit generation, which could be desirable for future ultimate secure communication systems.

Heat transport in nonlinear lattices free from the umklapp process.

We construct one-dimensional nonlinear lattices having the special property such that the umklapp process vanishes and only the normal processes are included in the potential functions. These lattices have long-range quartic nonlinear and nearest-neighbor harmonic interactions with/without harmonic onsite potential. We study heat transport in two cases of the lattices with and without harmonic onsite potential by nonequilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs in both cases, i.e., the scaling law κ∝N holds between the thermal conductivity κ and the lattice size N. This result directly validates Peierls's hypothesis that only the umklapp processes can cause the thermal resistance while the normal ones do not.

Chaos laser chips with delayed optical feedback using a passive ring waveguide.

We report a novel chaos semiconductor laser chip in which a distributed feedback (DFB) laser, two semiconductor optical amplifiers (SOAs) and a photodiode (PD) are monolithically integrated with a passive ring waveguide. The ring-type structure with the two separate SOAs achieves stronger delayed optical feedback compared to previous chaos laser chips which use linear waveguide and facet-reflection. The integrated PD allows efficient detection of the optical signal with low optical loss. A rich variety of dynamical behaviors and optical signals can be selectively generated via injection currents to the two separate SOAs. In particular, the strong optical feedback makes possible the generation of strong broadband optical chaos, with very flat spectrum of ±6.5 dB up to 10 GHz. The stability and quality of the chaotic mode is demonstrated using strict statistical tests of randomness applied to long binary sequences extracted by sampling the optical intensity signal.

Random optical pulse generation with bistable semiconductor ring lasers.

We experimentally show that a random optical pulse train can be generated by modulating a bistable semiconductor ring laser. When the ring laser is switched from the monostable to the bistable regime, it randomly selects one of two different stable unidirectional lasing modes, clockwise or counterclockwise modes. Non-deterministic random pulse sequences are generated by driving the switch parameter, the injection current, with a periodic pulse signal. The origin of the nondeterministic randomness is the amplified spontaneous emission noise coupled to the counter-propagating lasing modes. The statistical randomness properties are optimized by adjusting the relative strength of amplified spontaneous emission noise sources for the two lasing modes. It is also shown that it is possible to generate optical pulse sequences which pass a standard suite of statistical randomness tests.

Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers.

We experimentally demonstrate random bit generation using multi-bit samples of bandwidth-enhanced chaos in semiconductor lasers. Chaotic fluctuation of laser output is generated in a semiconductor laser with optical feedback and the chaotic output is injected into a second semiconductor laser to obtain a chaotic intensity signal with bandwidth enhanced up to 16 GHz. The chaotic signal is converted to an 8-bit digital signal by sampling with a digital oscilloscope at 12.5 Giga samples per second (GS/s). Random bits are generated by bitwise exclusive-OR operation on corresponding bits in samples of the chaotic signal and its time-delayed signal. Statistical tests verify the randomness of bit sequences obtained using 1 to 6 bits per sample, corresponding to fast random bit generation rates from 12.5 to 75 Gigabit per second (Gb/s) ( = 6 bit x 12.5 GS/s).

Synchronization by injection of common chaotic signal in semiconductor lasers with optical feedback.

We investigate the dynamics of two semiconductor lasers with separate optical feedback when they are driven by a common signal injected from a chaotic laser under the condition of non-identical drive and response. We experimentally and numerically show conditions under which the outputs of the two lasers can be highly correlated with each other even though the correlation with the drive signal is low. In particular, the effects of the phase of the feedback light on the correlation characteristics are described. The maximum correlation between the two response lasers is obtained when the phase of the feedback light is matched between the two response lasers, while the minimum correlation is observed when the difference in the optical phase is pi. On the other hand, the correlation between the drive and response is not sensitive to the phase of the feedback light, unlike the previously studied case of identical drive and response. We numerically examine the difference between the maximum and minimum cross correlations over a wide range of parameters, and show that it is largest when there is a balance between the injection strength and the feedback strength.

Differential-phase-shift quantum key distribution experiment using fast physical random bit generator with chaotic semiconductor lasers.

A high speed physical random bit generator is applied for the first time to a gigahertz clocked quantum key distribution system. Random phase-modulation in a differential-phase-shift quantum key distribution (DPS-QKD) system is performed using a 1-Gbps random bit signal which is generated by a physical random bit generator with chaotic semiconductor lasers. Stable operation is demonstrated for over one hour, and sifted keys are successfully generated at a rate of 9.0 kbps with a quantum bit error rate of 3.2% after 25-km fiber transmission.

Modulational instability of zone boundary mode and band edge modes in nonlinear diatomic lattices.

We analyze the modulational instability of the zone boundary mode (ZBM) and the band edge modes (BEMs) in a one-dimensional nonlinear diatomic lattice and obtain rigorous results. Some numerical calculations of modulational instability in these modes are presented. These results indicate that the modulational instability of the BEMs leads to excitation of the discrete breathers (DBs) in the band gap, while that of the ZBM leads to excitation of the DBs above the phonon band.

Local conditional Lyapunov exponent characterization of consistency of dynamical response of the driven Lorenz system.

Local conditional Lyapunov exponents are introduced and plotted in dynamical phase space to visualize the local susceptibility of the Lorenz system driven by chaos and noise signals when the system produces consistent response outputs. The dependence of the distribution of the local conditional Lyapunov exponent on changes in the drive signal is investigated. We consider the existence of multiple basins of consistent response for the same drive signal and the dependence of the basins on the drive signal.

Common-chaotic-signal induced synchronization in semiconductor lasers.

We experimentally and numerically observe synchronization of two semiconductor lasers commonly driven by a chaotic semiconductor laser subject to optical feedback. Under condition that the relaxation oscillation frequency is matched between the two response lasers, but mismatched between the drive and the two response lasers, we show that it is possible to observe strongly correlated synchronization between the two response lasers even when the correlation between the drive and response lasers is low. We also show that the cross correlation between the two responses is larger than that between drive and responses over a wide parameter region.