Photonic integrated device for chaos applications in communications

Hybrid integrated optical chaos circuits with optoelectronic feedback

A chip-scale chaotic laser system with optoelectronic delayed feedback is proposed and analyzed by numerical simulation. This chip eliminates the need for bulky delay components such as long optical fibers, free propagation and external cavities, relying solely on internal devices and waveguides to achieve feedback delay. This approach simplifies integration, maintaining a compact chip size. According to the results, the chip-scale system exhibits rich dynamics, including periodicity, quasi-periodicity, and chaotic states. Chaos resembling Gaussian white noise is achieved with picosecond-level delay time, highlighting the complexity of chip-scale signals. Furthermore, time delay signature (TDS) concealment is enhanced with a short delay comparable to the inverse bandwidth τ, albeit at a cost of sacrificing chaotic signal complexity. Applying the photonic integrated circuits to practical applications, 1 Gbps back-to-back communication transmission is feasible. Results demonstrate low bit error rates (BERs) for authorizers (<10-6) and high BERs for eavesdroppers (>10-2), ensuring communication confidentiality and chaotic synchronization. Lastly, preliminary experiments validate the feasibility. Our theoretical work has demonstrated the feasibility of hybrid integrated optical chaos circuits with optoelectronic feedback based on photonic wire bonding, which can provide a stable and flexible integrated chaos source.

Investigation on the monolithically integrated chaotic optical transmitting chip based on parallel EAMs

Chaotic optical communication ensures information security at the physical layer. However, the monolithic integration of lasers and lithium niobate Mach-Zehnder modulators remains a challenge, limiting the progress of integrated chaotic optical communication systems based on an electro-optic feedback. Here, we propose the monolithically integrated chaotic optical transmitting chip based on the parallel EAMs and validate its performance from the perspectives of phase portraits, fast Fourier transform (FFT), probability density function (PDF), largest Lyapunov exponents, and bifurcation. The results demonstrate the feasibility of the chip, which is beneficial for the miniaturization and integration of the system.

Random bit generation based on a self-chaotic microlaser with enhanced chaotic bandwidth

Chaotic semiconductor lasers have been widely investigated for high-speed random bit generation, which is applied for the generation of cryptographic keys for classical and quantum cryptography systems. Here, we propose and demonstrate a self-chaotic microlaser with enhanced chaotic bandwidth for high-speed random bit generation. By designing tri-mode interaction in a deformed square microcavity laser, we realize a self-chaotic laser caused by two-mode internal interaction, and achieve an enhanced chaotic standard bandwidth due to the photon-photon resonance effect by introducing the third mode. Moreover, 500 Gb/s random bit generation is realized and the randomness is verified by the NIST SP 800-22 statistics test. Our demonstration promises the applications of microlasers in secure communication, chaos radar, and optical reservoir computing, and also provides a platform for the investigations of multimode nonlinear laser dynamics.

Wideband chaos synchronization using discrete-mode semiconductor lasers

Optical chaos communication encounters difficulty in high-speed transmission due to the challenge of realizing wideband chaos synchronization. Here, we experimentally demonstrate a wideband chaos synchronization using discrete-mode semiconductor lasers (DMLs) in a master-slave open-loop configuration. The DML can generate wideband chaos with a 10-dB bandwidth of 30 GHz under simple external mirror feedback. By injecting the wideband chaos into a slave DML, an injection-locking chaos synchronization with synchronization coefficient of 0.888 is realized. A parameter range with frequency detuning of -18.75 GHz to approximately 1.25 GHz under strong injection is identified for yielding the wideband synchronization. In addition, we find it more susceptible to achieve the wideband synchronization using the slave DML with lower bias current and smaller relaxation oscillation frequency.

Chaotic microlasers caused by internal mode interaction for random number generation

Chaotic semiconductor lasers have been widely investigated for generating unpredictable random numbers, especially for lasers with external optical feedback. Nevertheless, chaotic lasers under external feedback are hindered by external feedback loop time, which causes correlation peaks for chaotic output. Here, we demonstrate the first self-chaotic microlaser based on internal mode interaction for a dual-mode microcavity laser, and realize random number generation using the self-chaotic laser output. By adjusting mode frequency interval close to the intrinsic relaxation oscillation frequency, nonlinear dynamics including self-chaos and period-oscillations are predicted and realized numerically and experimentally due to internal mode interaction. The internal mode interaction and corresponding carrier spatial oscillations pave the way of mode engineering for nonlinear dynamics in a solitary laser. Our findings provide a novel and easy method to create controllable and robust optical chaos for high-speed random number generation.

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.

Photonic neuromorphic technologies in optical communications

Machine learning (ML) and neuromorphic computing have been enforcing problem-solving in many applications. Such approaches found fertile ground in optical communications, a technological field that is very demanding in terms of computational speed and complexity. The latest breakthroughs are strongly supported by advanced signal processing, implemented in the digital domain. Algorithms of different levels of complexity aim at improving data recovery, expanding the reach of transmission, validating the integrity of the optical network operation, and monitoring data transfer faults. Lately, the concept of reservoir computing (RC) inspired hardware implementations in photonics that may offer revolutionary solutions in this field. In a brief introduction, I discuss some of the established digital signal processing (DSP) techniques and some new approaches based on ML and neural network (NN) architectures. In the main part, I review the latest neuromorphic computing proposals that specifically apply to photonic hardware and give new perspectives on addressing signal processing in optical communications. I discuss the fundamental topologies in photonic feed-forward and recurrent network implementations. Finally, I review the photonic topologies that were initially tested for channel equalization benchmark tasks, and then in fiber transmission systems, for optical header recognition, data recovery, and modulation format identification.

Fast physical repetitive patterns generation for masking in time-delay reservoir computing

Albeit the conceptual simplicity of hardware reservoir computing, the various implementation schemes that have been proposed so far still face versatile challenges. The conceptually simplest implementation uses a time delay approach, where one replaces the ensemble of nonlinear nodes with a unique nonlinear node connected to a delayed feedback loop. This simplification comes at a price in other parts of the implementation; repetitive temporal masking sequences are required to map the input information onto the diverse states of the time delay reservoir. These sequences are commonly introduced by arbitrary waveform generators which is an expensive approach when exploring ultra-fast processing speeds. Here we propose the physical generation of clock-free, sub-nanosecond repetitive patterns, with increased intra-pattern diversity and their use as masking sequences. To that end, we investigate numerically a semiconductor laser with a short optical feedback cavity, a well-studied dynamical system that provides a wide diversity of emitted signals. We focus on those operating conditions that lead to a periodic signal generation, with multiple harmonic frequency tones and sub-nanosecond limit cycle dynamics. By tuning the strength of the different frequency tones in the microwave domain, we access a variety of repetitive patterns and sample them in order to obtain the desired masking sequences. Eventually, we apply them in a time delay reservoir computing approach and test them in a nonlinear time-series prediction task. In a performance comparison with masking sequences that originate from random values, we find that only minor compromises are made while significantly reducing the instrumentation requirements of the time delay reservoir computing system.

Scheme of coherent optical chaos communication

We propose and numerically demonstrate a scheme of coherent optical chaos communication using semiconductor lasers for secure transmission of optical quadrature amplitude modulation (QAM) signals. In this scheme, a laser intensity chaos and its delayed duplicate are used to amplitude-quadrature modulate a continuous-wave light to generate a chaotic carrier. High-quality chaotic carrier synchronization between the transmitter and receiver is guaranteed by laser intensity chaos synchronization, avoiding laser phase fluctuation. Decryption is implemented by a 90 deg optical hybrid using the synchronous chaotic carrier as local light. Secure transmission of an optical 40 Gb/s 16QAM signal is demonstrated by using a laser intensity chaos with a bandwidth of 11.7 GHz. The system performances are evaluated by analyzing a bit error ratio with different masking coefficients, signal rates, synchronization coefficients, parameter mismatches, and dispersion compensation. It is believed that this scheme can pave a way for high-speed optical chaos communication.

Time-delay signature suppression of polarization-resolved wideband chaos in VCSELs with dual-path chaotic optical injections

The combining investigation on the time-delay signature (TDS) and chaos bandwidth have been theoretically investigated in a vertical-cavity surface-emitting laser (VCSEL) system with dual-path chaotic optical injections. In this scheme, the polarized chaos with the TDS from an external-cavity master VCSEL is routed into two different paths and then unidirectionally injected into another solitary slave VCSEL. With the aid of the autocorrelation function and the effective bandwidth calculation, the TDS and bandwidth of polarized chaos from the chaotic system are quantitatively evaluated. The results show that, in such a dual-path chaotic optical-injection system, the high-quality polarized chaos with the successful TDS suppression and chaotic bandwidth enhancement can be achieved in wider parameter regions in contrast with the case for the single-path chaotic optical injection. Further research also finds that the injected time-delay difference between two injection paths is desired to mismatch the feedback time delay, which is conducive to suppressing TDS and expanding bandwidth of polarized chaos. Besides, the better chaotic quality with low TDS and wide bandwidth can be expected by choosing the appropriate injection strengths of two injection paths.

Control of dynamics via identical time-lagged stochastic inputs

We investigate the impact of a stochastic forcing, comprised of a sum of time-lagged copies of a single source of noise, on the system dynamics. This type of stochastic forcing could be made artificially, or it could be the result of shared upstream inputs to a system through different channel lengths. By means of a rigorous mathematical framework, we show that such a system is, in fact, equivalent to the classical case of a stochastically-driven dynamical system with time-delayed intrinsic dynamics but without a time lag in the input noise. We also observe a resonancelike effect between the intrinsic period of the oscillation and the time lag of the stochastic forcing, which may be used to determine the intrinsic period of oscillations or the inherent time delay in dynamical systems with oscillatory behavior or delays. As another useful application of imposing time-lagged stochastic forcing, we show that the dynamics of a system can be controlled by changing the time lag of this stochastic forcing, in a fashion similar to the classical case of Pyragas control via delayed feedback. To confirm these results experimentally, we set up a laser diode system with such stochastic inputs, which effectively behaves as a Langevin system. As in the theory, a peak emerged in the autocorrelation function of the output signal that could be tuned by the lag of the stochastic input. Our findings, thus, indicate a new approach for controlling useful instabilities in dynamical systems.

Bias Current of Semiconductor Laser: An Unsafe Key for Secure Chaos Communication

In this study, we have proposed and numerically demonstrated that the bias current of a semiconductor laser cannot be used as a key for optical chaos communication, using external-cavity lasers. This is because the chaotic carrier has a signature of relaxation oscillation, whose period can be extracted by the first side peak of the carrier’s autocorrelation function. Then, the bias current can be approximately cracked, according to the well-known relationship between the bias current and relaxation period of a solitary laser. Our simulated results have shown that the cracked current eavesdropper could successfully crack an encrypted message, by means of a unidirectional locking injection or a bidirectional coupling. In addition, the cracked bias current was closer to the real value as the bias current increased, meaning that a large bias current brought a big risk to the security.

Investigation of the Effect of Intra-Cavity Propagation Delay in Secure Optical Communication Using Chaotic Semiconductor Lasers

The influence of intra-cavity propagation delay in message encoding and decoding using chaotic semiconductor lasers is numerically investigated. A message is encoded at the transmitter laser by a chaos shift keying scheme and is decoded at the receiver by comparing its output with the transmitter laser. The requisite intra-cavity propagation delay in achieving synchronization of optical chaos is estimated by cross-correlation analysis between the transmitter and receiver lasers’ output. The effect of intra-cavity propagation delay on the message recovery has been analyzed from the bit error rate performance. It is found that despite the intra-cavity propagation delay magnitude being less, it has an impact on the quality of message recovery. We also examine the dependency of injection rate, frequency detuning, modulation depth and bit rate on intra-cavity propagation delay and associated message recovery quality. We found that the communication performance has been adequately improved after incorporating intra-cavity propagation delay correction in the synchronization system.

Numerical investigations of synchronization and communication based on an electro-optic phase chaos system with concealment of time delay

A modified electro-optic phase chaos system that can conceal time delay (TD) and allows for unidirectional message transmission, is numerically investigated. The configuration includes two cascaded delay loops, and the parallel-coupled microresonators (PCMRs) in one of two loops result in a frequency-dependent group delay. The largest Lyapunov exponent (LLE), Lempel-Ziv complexity (LZC) and permutation entropy (PE) are used to distinguish the chaotic behavior and the degree of complexity in a time series, and the autocorrelation function (ACF) and the delayed mutual information (DMI) are plotted to extract the TD. The corresponding diagrams show that in the electro-optic system phase chaos with high complexity can occur within a certain range of feedback strength. The diagrams also show that, at a fixed feedback strength, the effect of the TD concealment becomes quite good with an increase in the number of PCMRs. The numerical simulation also reveals that the delayed chaotic dynamics can be identically synchronized, and the synchronization solution is robust. Moreover, based on the coherence of Mach-Zehnder interferometers, we convert the phase variations of the transmitter outputs and the receiver into the corresponding intensity variations, so the synchronization error of the two-phase chaotic series can be monitored. At last, we can successfully decipher the message introduced on the transmitting end of a link. In this scheme, the feedback TD has been concealed, which prevents eavesdroppers from listening and makes the proposed chaotic communication system secure.

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.

Time-delay-signature-suppressed broadband chaos generated by scattering feedback and optical injection

We propose and demonstrate a novel scheme to generate time-delay-signature-suppressed broadband chaotic light by using an optically injected laser diode subjected to scattering light feedback. The achievement of broadband chaos is based on the interaction between the injection light and chaotic light from the scattering feedback semiconductor laser via beating. A single-mode fiber as a continuous scatterer is specially used as a feedback cavity to introduce random feedback, which could truly eliminate the time delay signature of chaotic light. The chaotic light with a power spectrum that extends to 13.6 GHz within 3 dB is experimentally achieved.

Dynamics-dependent synchronization in on-chip coupled semiconductor lasers

Synchronization properties of chaotic dynamics in two mutually coupled semiconductor lasers with optical feedback embedded in a photonic integrated circuit are investigated from the point of view of their dynamical content. A phenomenon in which the two lasers can show qualitatively different synchronization properties according to the frequency range of investigation and their nonlinear dynamics is identified and termed dynamics-dependent synchronization. In-phase synchronization is observed for original signals and antiphase synchronization is observed for low-pass filtered signals in the case where one of the lasers shows chaotic oscillations while the other laser exhibits low-frequency fluctuations dynamics. The experimental conditions causing the synchronization states to vary according to the considered frequency interval are studied and the key roles of asymmetric coupling strength and injection currents are clarified.

Numerical study of ultrashort-optical-feedback-enhanced photonic microwave generation using optically injected semiconductor lasers at period-one nonlinear dynamics

This study numerically investigates the enhancement of photonic microwave generation using an optically injected semiconductor laser operating at period-one (P1) nonlinear dynamics through ultrashort optical feedback. For the purpose of practical applications where system miniaturization is generally preferred, a feedback delay time that is one to two orders of magnitude shorter than the relaxation resonance period of a typical laser is emphasized. Various dynamical states that are more complicated than the P1 dynamics can be excited under a number of ultrashort optical feedback conditions. Within the range of the P1 dynamics, on one hand, the frequency of the P1 microwave oscillation can be greatly enhanced by up to more than three folds. Generally speaking, the microwave frequency enhances with the optical feedback power and phase, while it varies saw-wise with the optical feedback delay time. On the other hand, the purity of the P1 microwave oscillation can be highly improved by up to more than three orders of magnitude. In general, the microwave purity improves with the optical feedback power and delay time, while it only varies within an order of magnitude with the optical feedback phase. These results suggest that the ultrashort optical feedback provides the optically injected laser system with an extra degree of freedom to manipulate/improve the characteristics of the P1 microwave oscillation without changing the optical injection condition.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

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.

Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems

BACKGROUND

We have analysed large data sets consisting of tens of thousands of time series from three Type B laser systems: a semiconductor laser in a photonic integrated chip, a semiconductor laser subject to optical feedback from a long free-space-external-cavity, and a solid-state laser subject to optical injection from a master laser. The lasers can deliver either constant, periodic, pulsed, or chaotic outputs when parameters such as the injection current and the level of external perturbation are varied. The systems represent examples of experimental nonlinear systems more generally and cover a broad range of complexity including systematically varying complexity in some regions.

METHODS

In this work we have introduced a new procedure for semi-automatically interrogating experimental laser system output power time series to calculate the correlation dimension (CD) using the commonly adopted Grassberger-Proccacia algorithm. The new CD procedure is called the 'minimum gradient detection algorithm'. A value of minimum gradient is returned for all time series in a data set. In some cases this can be identified as a CD, with uncertainty.

FINDINGS

Applying the new 'minimum gradient detection algorithm' CD procedure, we obtained robust measurements of the correlation dimension for many of the time series measured from each laser system. By mapping the results across an extended parameter space for operation of each laser system, we were able to confidently identify regions of low CD (CD < 3) and assign these robust values for the correlation dimension. However, in all three laser systems, we were not able to measure the correlation dimension at all parts of the parameter space. Nevertheless, by mapping the staged progress of the algorithm, we were able to broadly classify the dynamical output of the lasers at all parts of their respective parameter spaces. For two of the laser systems this included displaying regions of high-complexity chaos and dynamic noise. These high-complexity regions are differentiated from regions where the time series are dominated by technical noise. This is the first time such differentiation has been achieved using a CD analysis approach.

CONCLUSIONS

More can be known of the CD for a system when it is interrogated in a mapping context, than from calculations using isolated time series. This has been shown for three laser systems and the approach is expected to be useful in other areas of nonlinear science where large data sets are available and need to be semi-automatically analysed to provide real dimensional information about the complex dynamics. The CD/minimum gradient algorithm measure provides additional information that complements other measures of complexity and relative complexity, such as the permutation entropy; and conventional physical measurements.

Real-time online photonic random number generation

We present a real-time scheme for ultrafast random number (RN) extraction from a broadband photonic entropy source. Ultralow jitter mode-locked pulses are used to sample the stochastic intensity fluctuations of the entropy source in the optical domain. A discrete self-delay comparison technology is exploited to quantize the sampled pulses into continuous RN streams directly. This scheme is bias free, eliminates the electronic jitter bottleneck confronted by currently available physical RN generators, and has no need for threshold tuning and post-processing. To demonstrate its feasibility, we perform a proof-of-principle experiment using an optically injected chaotic laser diode. RN streams at up to 7  Gb/s with verified randomness were thereby successfully extracted in real time. With the provision of a photonic entropy source with sufficient bandwidth, the present approach is expected to provide RN generation rates of several tens of gigabits per second.

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D₂ is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale.

Chaotic behaviour of optomechanical systems has only recently been investigated and observed. Here, Wu et al. study the chaos dynamics in a silicon platform where coupled electron-hole plasma dynamics is possible, providing a route towards chip-scale mesoscopic nonlinear dynamics.

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.

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

We numerically investigate the frequency bandwidth and the autocorrelation characteristics of chaotic temporal wave forms in unidirectionally coupled semiconductor lasers with time-delayed optical feedback. We evaluate the complexity of the chaotic temporal wave forms by using Lyapunov exponents. We found that larger maximum Lyapunov exponents can be obtained for smaller peak values of the autocorrelation function at the delay time of the optical feedback. On the contrary, the maximum Lyapunov exponent is independent from the frequency bandwidth of the chaotic temporal wave forms.

Reducing the phase sensitivity of laser-based optical reservoir computing systems

Optical implementations of reservoir computing systems are very promising because of their high processing speeds and the possibility to process several tasks in parallel. These systems can be implemented using semiconductor lasers subject to optical delayed feedback and optical injection. While the amount of the feedback/injection can be easily controlled, it is much more difficult to control the optical feedback/injection phase. We present extensive numerical investigations of the influence of the feedback/injection phases on laser-based reservoir computing systems with feedback. We show that a change in the phase can lead to a strong reduction in the reservoir computing system performance. We introduce a new readout layer design that -at least for some tasks- reduces this sensitivity to changes in the phase. It consists in optimizing the readout weights from a coherent combination of the reservoir's readout signal and its delayed version rather than only from the reservoir's readout signal as is usually done.

Cycles of self-pulsations in a photonic integrated circuit

We report experimentally on the bifurcation cascade leading to the appearance of self-pulsation in a photonic integrated circuit in which a laser diode is subjected to delayed optical feedback. We study the evolution of the self-pulsing frequency with the increase of both the feedback strength and the injection current. Experimental observations show good qualitative accordance with numerical results carried out with the Lang-Kobayashi rate equation model. We explain the mechanism underlying the self-pulsations by a phenomenon of beating between successive pairs of external cavity modes and antimodes.

Integrated semiconductor laser with optical feedback: transition from short to long cavity regime

A 4-section semiconductor laser with integrated optical feedback has been shown experimentally to be capable of operating in either the short- or long-cavity regime, by controlling the device relaxation oscillation frequency relative to the external cavity frequency. Systematic increase of the laser injection current, and the resulting increase in relaxation oscillation frequency, allowed the transition between the two regimes of operation to be observed. The system displayed a gradual transition from a dynamic dominated by regular pulse packages in the short-cavity regime to one dominated by broadband chaotic output when operating in the long-cavity regime. This suggests that the "short cavity" regular pulse packages continue to co-exist with the "long cavity" broadband chaotic dynamic in the system studied. It is the relative power associated with each of these dynamics that changes. This may occur more generally in similar systems.

Generation of polarization-resolved wideband unpredictability-enhanced chaotic signals based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

A system framework is proposed and analyzed for generating polarization-resolved wideband unpredictability-enhanced chaotic signals based on a slave vertical-cavity surface-emitting laser (S-VCSEL) driven by an injected optical chaos signal from a master VCSEL (M-VCSEL) under optical feedback. After calculating the time series outputs from the M-VCSEL under optical feedback and the S-VCSEL under chaotic optical injection by using the spin-flip model (SFM), the unpredictability degree (UD) is evaluated by permutation entropy (PE), and the bandwidth of the polarization-resolved outputs from the M-VCSEL and S-VCSEL are numerically investigated. The results show that, under suitable parameters, both the bandwidth and UD of two polarization components (PCs) outputs from the S-VCSEL can be enhanced significantly compared with that of the driving chaotic signals output from the M-VCSEL. By simulating the influences of the feedback and injection parameters on the bandwidth and UD of the polarization-resolved outputs from S-VCSEL, related operating parameters can be optimized.

Chaotic dynamics in coupled resonator sequences

Optically induced thermal and free carrier nonlinearities in silicon micro-ring resonator influence their behavior. They can be either deleterious by making them instable and by driving their resonances out of the designed wavelengths, or enabler of different applications. Among the most interesting one, there are optical bistability and self induced oscillations. These lead to all optical logic, signal modulation, optical memories and applications in neural networks. Here, we theoretically and experimentally demonstrate that when many resonators are coupled together, thermal and free carrier nonlinearities induce also chaos. The chaotic dynamics are deeply analyzed using experimentally reconstructed phase space trajectories and the tool of Lyapunov exponents.

Manipulating coherence resonance in a quantum dot semiconductor laser via electrical pumping

Excitability and coherence resonance are studied in a semiconductor quantum dot laser under short optical self-feedback. For low pump levels, these are observed close to a homoclinic bifurcation, which is in correspondence with earlier observations in quantum well lasers. However, for high pump levels, we find excitability close to a boundary crisis of a chaotic attractor. We demonstrate that in contrast to the homoclinic bifurcation the crisis and thus the excitable regime is highly sensitive to the pump current. The excitability threshold increases with the pump current, which permits to adjust the sensitivity of the excitable unit to noise as well as to shift the optimal noise strength, at which maximum coherence is observed. The shift adds up to more than one order of magnitude, which strongly facilitates experimental realizations.

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.

Direct generation of broadband chaos by a monolithic integrated semiconductor laser chip

A solitary monolithic integrated semiconductor laser (MISL) chip with a size of 780 micrometer is designed and fabricated for broadband chaos generation. Such a MISL chip consists of a DFB section, a phase section and an amplification section. Test results indicate that under suitable operation conditions, this laser chip can be driven into broadband chaos. The generated chaos covers an RF frequency range, limited by our measurement device, of 26.5GHz, and possesses significant dimension and complexity. Moreover, the routes into and out of chaos are also characterized through extracting variety dynamical states of temporal waveforms, phase portraits, RF spectra and statistical indicators.

Complexity in electro-optic delay dynamics: modelling, design and applications

Nonlinear delay dynamics have found during the last 30 years a particularly prolific exploration area in the field of photonic systems. Besides the popular external cavity laser diode set-ups, we focus in this article on another experimental realization involving electro-optic (EO) feedback loops, with delay. This approach has strongly evolved with the important technological progress made on broadband photonic and optoelectronic devices dedicated to high-speed optical telecommunications. The complex dynamical systems performed by nonlinear delayed EO feedback loop architectures were designed and explored within a huge range of operating parameters. Thanks to the availability of high-performance photonic devices, these EO delay dynamics led also to many successful, efficient and diverse applications, beyond the many fundamental questions raised from the observation of experimental behaviours. Their chaotic motion allowed for a physical layer encryption method to secure optical data, with a demonstrated capability to operate at the typical speed of modern optical telecommunications. Microwave limit cycles generated in similar EO delay oscillators showed significantly improved spectral purity thanks to the use of a very long fibre delay line. Last but not least, a novel brain inspired computational principle has been recently implemented physically in photonics for the first time, again on the basis of an EO delay dynamical system. In this latter emerging application, the computed result is obtained by a proper 'read-out' of the complex nonlinear transients emerging from a fixed point, the transient being issued by the injection of the information signal to be processed.

4.5 Gbps high-speed real-time physical random bit generator

We report a prototype of high-speed real-time physical random bit generator based on a chaotic laser. The chaotic laser consists of a semiconductor laser with optical feedback in fiber external cavity configuration. The chaotic laser intensity signal is quantized into binary stream by differential comparison which makes the amplitude distribution symmetric with respect to zero mean value. An exclusive-OR gate operation between two raw binary streams from the chaotic signal and its delayed signal is used to overcome the influences of the weak periodicity induced by the external cavity resonance inherent in the chaotic laser. After exclusive-OR operation, the prototype can generate a single fast random bit stream in real time without any off-line processing procedures. Its bit rate can be handily and continuously tuned up to 4.5 Gbps by a trigger clock. Experiment results demonstrate that our generator possesses high-quality randomness with verified by the three-standard-deviation criterion and industry-benchmark statistical tests.

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.

Generation of wideband chaos with suppressed time-delay signature by delayed self-interference

We demonstrate experimentally and numerically a method using the incoherent delayed self-interference (DSI) of chaotic light from a semiconductor laser with optical feedback to generate wideband chaotic signal. The results show that, the DSI can eliminate the domination of laser relaxation oscillation existing in the chaotic laser light and therefore flatten and widen the power spectrum. Furthermore, the DSI depresses the time-delay signature induced by external cavity modes and improves the symmetry of probability distribution by more than one magnitude. We also experimentally show that this DSI signal is beneficial to the random number generation.

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.

Long-haul dense wavelength division multiplexing between a chaotic optical secure channel and a conventional fiber-optic channel

The purpose of this paper is to numerically investigate dense wavelength division multiplexing (DWDM) transmission between a chaotic optical secure channel and a conventional fiber-optic channel. A 2.5 Gbits/s secure message masked by the chaotic optical secure channel and a 10 Gbits/s message sequence carried by the conventional fiber-optic channel can be realized simultaneously when the channel spacing is 0.8 nm. The results show that the Q-factors of the recovered messages can be increased significantly when the launched optical power is reduced appropriately. The deterioration of the quality of communication caused by fiber dispersion can be compensated noticeably on the condition that the symmetrical dispersion compensation scheme is adopted. In addition, the secure message is masked by chaos shift keying in the chaotic optical secure channel. The multiplexing distance between the chaotic optical secure channel and the conventional fiber-optic channel is up to 500 km.

Delay line length selection in generating fast random numbers with a chaotic laser

The chaotic light signals generated by an external cavity semiconductor laser have been experimentally demonstrated to extract fast random numbers. However, the photon round-trip time in the external cavity can cause the occurrence of the periodicity in random sequences. To overcome it, the exclusive-or operation on corresponding random bits in samples of the chaotic signal and its time-delay signal from a chaotic laser is required. In this scheme, the proper selection of delay length is a key issue. By doing a large number of experiments and theoretically analyzing the interplay between the Runs test and the threshold value of the autocorrelation function, we find when the corresponding delay time of autocorrelation trace with the correlation coefficient of less than 0.007 is considered as the delay time between the chaotic signal and its time-delay signal, streams of random numbers can be generated with verified randomness.

Theory of fast nondeterministic physical random-bit generation with chaotic lasers

We theoretically show that completely stochastic fast physical random bit generation at a rate of more than one gigabit per second can be realized by using lasers with optical delayed feedback which creates high-dimensional chaos of laser light outputs. The theory is based on the mixing property of chaos, which transduces microscopic quantum noise of spontaneous emission in lasers into random transitions between discrete macroscopic states.

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.

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.

Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit

In the present work a photonic integrated circuit (PIC) that emits broadband chaotic signals is employed for ultra-fast generation of true random bit sequences. Chaotic dynamics emerge from a DFB laser, accompanied by a monolithic integrated 1-cm long external cavity (EC) that provides controllable optical feedback. The short length minimizes the existence of external cavity modes, so flattened broadband spectra with minimized intrinsic periodicities can emerge. After sampling and quantization--without including optical de-correlation techniques and using most significant bits (MSB) elimination post-processing--truly random bit streams with bit-rates as high as 140 Gb/s can be generated. Finally, the extreme robustness of the random bit generator for adaptive bit-rate operation and for various operating conditions of the PIC is demonstrated.

The stability of adaptive synchronization of chaotic systems

In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive scheme for maintaining the synchronized state of identical coupled chaotic systems in the presence of a priori unknown slow temporal drift in the couplings. For this illustrative example, we develop an extension of the master stability function technique to study synchronization stability with adaptive coupling. Using this formulation, we examine the local stability of synchronization for typical chaotic orbits and for unstable periodic orbits within the synchronized chaotic attractor (bubbling). Numerical experiments illustrating the results are presented. We observe that the stable range of synchronism can be sensitively dependent on the adaptation parameters, and we discuss the strong implication of bubbling for practically achievable adaptive synchronization. We also find that for our coupled systems with adaptation, bubbling can be caused by a slow temporal drift in the coupling strength.

Chaos-on-a-chip secures data transmission in optical fiber links

Security in information exchange plays a central role in the deployment of modern communication systems. Besides algorithms, chaos is exploited as a real-time high-speed data encryption technique which enhances the security at the hardware level of optical networks. In this work, compact, fully controllable and stably operating monolithic photonic integrated circuits (PICs) that generate broadband chaotic optical signals are incorporated in chaos-encoded optical transmission systems. Data sequences with rates up to 2.5 Gb/s with small amplitudes are completely encrypted within these chaotic carriers. Only authorized counterparts, supplied with identical chaos generating PICs that are able to synchronize and reproduce the same carriers, can benefit from data exchange with bit-rates up to 2.5Gb/s with error rates below 10(-12). Eavesdroppers with access to the communication link experience a 0.5 probability to detect correctly each bit by direct signal detection, while eavesdroppers supplied with even slightly unmatched hardware receivers are restricted to data extraction error rates well above 10(-3).

Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.

Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization

We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.

Tristability of a semiconductor laser due to time-delayed optical feedback

We present an experimental and theoretical study of multistability of a single-mode laser subject to feedback through phase tuning and amplifier sections integrated on the same chip. Closely above threshold, a regime of tristability of continuous-wave (CW) states is found for multiple ranges of amplifier and phase currents. The separation between the tristable wavelengths agrees with the channel spacing of dense wavelength multiplexing in the C band of optical communication making the device interesting for ternary logic applications. Complementary theoretical investigations in the framework of the paradigmatic Lang-Kobayashi model provide a consistent understanding of the experimental findings and additionally yield an analytic formula expressing the maximum number of coexisting stable CW states by the linewidth-enhancement factor alpha . Tristability belongs to the alpha range from 5 to 8 in good agreement with experiment.