Statistical properties for an optically injected chaotic semiconductor laser with a high-pass filter.

Chaotic waveforms with Gaussian distributions are significant for laser-chaos-based applications such as random number generation. By exploring the injection parameter space of the optical injection semiconductor lasers, we numerically investigate the associated probability density functions of the generated chaotic waveforms when different high-pass filters with different cutoff frequencies are used. Our results demonstrate that the chaotic waveforms with Gaussian probability density functions can be obtained once the cutoff frequency of the high-pass filter is larger than the laser relaxation resonance frequency. Especially, we find that the Gaussian probability density function can reach a superhigh coefficient of determination R2 ≥ 99.5% and an ultralow skewness |S|<0.1 in a large parameter space by jointly controlling the injection parameter and cutoff frequency.

Wireless-Channel Key Distribution Based on Laser Synchronization.

We propose and experimentally demonstrate a wireless-channel key distribution scheme based on laser synchronization induced by a common wireless random signal. Two semiconductor lasers are synchronized under injection of the drive signal after electrical-optical conversion and emit irregular outputs that are used to generate shared keys. Our proof-of-concept experiment using a complex drive signal achieved a secure key generation rate of up to 150 Mbit/s with a bit error rate below 3.8 × 10-3. Numerical simulation results show that the proposed scheme has the potential to achieve a distribution distance of several hundred meters. It is believed that common-signal-induced laser synchronization paves the way for high-speed wireless physical-layer key distribution.

Scalable parallel ultrafast optical random bit generation based on a single chaotic microcomb.

Random bit generators are critical for information security, cryptography, stochastic modeling, and simulations. Speed and scalability are key challenges faced by current physical random bit generation. Herein, we propose a massively parallel scheme for ultrafast random bit generation towards rates of order 100 terabit per second based on a single micro-ring resonator. A modulation-instability-driven chaotic comb in a micro-ring resonator enables the simultaneous generation of hundreds of independent and unbiased random bit streams. A proof-of-concept experiment demonstrates that using our method, random bit streams beyond 2 terabit per second can be successfully generated with only 7 comb lines. This bit rate can be easily enhanced by further increasing the number of comb lines used. Our approach provides a chip-scale solution to random bit generation for secure communication and high-performance computation, and offers superhigh speed and large scalability.

Security optimization of synchronization in DFB lasers under constant-amplitude random-phase drive light by reducing drive-response correlation.

Common-signal-induced laser synchronization promoted a promising paradigm of high-speed physical key distribution. Constant-amplitude and random-phase (CARP) light was proposed as the common drive signal to enhance security by reducing the correlation between the drive and the laser response in intensity. However, the correlation in light phase is not examined. Here, we numerically reveal that the correlation coefficient of the CARP light phase and the response laser intensity (denoted as CCR-φD) can reach a value close to 0.6. Effects of parameters including optical frequency detuning, and modulation depth and noise bandwidth and transparency carrier density for CARP light generation are investigated in detail. By optimizing the optical frequency, modulation depth, and noise bandwidth, respectively, CCR-φD can be reduced to 0.32, 0.18, and 0.10. In the meantime, CCR-φD can be further reduced through secondary optimizing of parameters. CCR-φD can be further reduced by increasing transparent carrier density provided response laser synchronization is achieved. This work gives a new insight about the laser synchronization induced by common CARP light, and also contributes a suggestion of security improvement for physical key distribution based on laser synchronization.

High-speed secure key distribution based on interference spectrum-shift keying with signal mutual modulation in commonly driven chaos synchronization.

The secure key generation and distribution (SKGD) are unprecedentedly important for a modern secure communication system. This paper proposes what we believe to be a novel scheme of high-speed key distribution based on interference spectrum-shift keying with signal mutual modulation in commonly driven chaos synchronization. In this scheme, delay line interferometers (DLI) are utilized to generate two low-correlation interference spectra from commonly driven synchronous chaos, and then a 2 × 2 optical switch can effectively change the relationship between the two interference spectra in post-processing by shifting the states of the switch. The signals then undergo electro-optic nonlinear transformation through a hardware module, which includes a signal mutually modulating module (SMMM) and a dispersion component. This optimization significantly enhances the entropy source rate of synchronized chaos from both legitimate users. Moreover, thanks to the introduction of DLIs and electro-optic nonlinear transformation module, the key space of the proposed scheme is remarkably improved. In comparison to traditional chaotic drive-response architectures, the scheme effectively suppresses residual correlation. A 6.7 Gbit/s key distribution rate with a bit error rate below 3.8 × 10-3 is experimentally demonstrated over a 40 km single-mode fiber (SMF).

Chaos synchronization of VCSELs with common injection of polarization-random light.

We propose and numerically demonstrate chaos synchronization of two vertical-cavity surface-emitting lasers (VCSELs) induced by common injection of constant-amplitude random-polarization light for physical key distribution. Results show that synchronization is sensitive to polarization rotation of injection light, and synchronization coefficients larger than 0.9 can be achieved as the rotation-degree mismatch is smaller than ±10°. Therefore, polarization rotation degree can serve as a hardware key parameter. Furthermore, each laser's output has no correlation to the constant amplitude of the injected light. Their components with identical polarization state, e.g. x or y polarization of VCSEL, also have low correlation coefficient smaller than 0.2. It is therefore believed that this synchronization scheme can provide a security-enhanced method of physical key distribution.

Millimeter-wave noise generation based on a monolithically integrated dual-mode chaotic laser.

A millimeter-wave noise generation scheme is proposed in this paper. The scheme is based on a monolithically integrated dual-mode chaotic laser, which consists of a distributed Bragg feedback (DFB) section, a phase section, and an optical amplification section. The output spectrum state of the dual-mode laser can be controlled by adjusting the injection current in the three regions. The monolithically integrated dual-mode chaotic laser has stable chaotic output and can be used as a light source for integrated millimeter-wave noise source. As a feasibility demonstration, a dual-mode chaotic laser with a mode interval of 2.05 nm was generated in the experiment, the optical mixing on a photodetector produced millimeter-wave noise with a center frequency of 259 GHz and a bandwidth of 44 GHz (237-281 GHz), achieving a typical value of excess noise ratio of 47 dB. It has the advantages of high noise source utilization, small noise source volume, and high integration.

Principles and Applications of Seismic Monitoring Based on Submarine Optical Cable.

Submarine optical cables, utilized as fiber-optic sensors for seismic monitoring, are gaining increasing interest because of their advantages of extending the detection coverage, improving the detection quality, and enhancing long-term stability. The fiber-optic seismic monitoring sensors are mainly composed of the optical interferometer, fiber Bragg grating, optical polarimeter, and distributed acoustic sensing, respectively. This paper reviews the principles of the four optical seismic sensors, as well as their applications of submarine seismology over submarine optical cables. The advantages and disadvantages are discussed, and the current technical requirements are concluded, respectively. This review can provide a reference for studying submarine cable-based seismic monitoring.

Optical frequency domain polarimetry based on a self-referenced unbalanced Mach-Zehnder interferometer.

Optical frequency domain polarimetry (OFDP) is an emerging distributed polarization crosstalk rapid measurement method with an ultrawide dynamic range. However, interferometric phase noise induced by the laser source and ambient noise results in a trade-off between measurement length and dynamic range. In this Letter, we solve this problem with a self-referenced unbalanced Mach-Zehnder interferometer. The features of long distance (9.8 km), ultrawide dynamic range (107.8 dB), short measurement time (2 sec), and signal-to-noise ratio improvement against ambient noise are experimentally demonstrated. The method makes it possible to evaluate a long polarization-maintaining fiber in an environment whose state changes rapidly.

High-entropy-rate broadband chaos generation by using short-resonant-cavity DFB semiconductor laser with optical feedback.

Semiconductor lasers with delayed optical feedback are a promising source of optical chaos for practical applications, owing to simple configurations that are easy to integrate and synchronize. However, for traditional semiconductor lasers, the chaos bandwidth is limited by the relaxation frequency to several gigahertz. Here, we propose and experimentally demonstrate that a short-resonant-cavity distributed-feedback (SC-DFB) laser can generate broadband chaos only with simple feedback from an external mirror. The short distributed-feedback resonant cavity not only enhances laser relaxation frequency but also makes the laser mode more susceptible to external feedback. Experiments obtained a laser chaos with 33.6 GHz bandwidth and a spectral flatness of 4.5 dB. The corresponding entropy rate is estimated as more than 33.3 Gbit/s. It is believed that the SC-DFB lasers will promote development of chaos-based secure communication and physical key distribution.

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.

Improve accuracy and measurement range of sensing in km-level OFDR using spectral splicing method.

In this paper, we propose and demonstrate a spectral splicing method (SSM) for distributed strain sensing based on optical frequency domain reflectometry (OFDR), which can achieve km level measurement length, µÉ› level measurement sensitivity and 104 µÉ› level measurement range. Based on the traditional method of cross-correlation demodulation, the SSM replaces the original centralized data processing method with a segmented processing method and achieves precise splicing of the spectrum corresponding to each signal segment by spatial position correction, thus realizing strain demodulation. Segmentation effectively suppresses the phase noise accumulated in the large sweep range over long distances, expands the sweep range that can be processed from the nm level to the 10 nm level, and improves strain sensitivity. Meanwhile, the spatial position correction rectifys the position error in the spatial domain caused by segmentation, which reduces the error from the 10 m level to the mm level, enabling precise splicing of spectra and expanding the spectral range, thus extending the strain range. In our experiments, we achieved a strain sensitivity of ±3.2 µÉ› (3σ) over a length of 1 km with a spatial resolution of 1 cm and extended the strain measurement range to 10,000 µÉ›. This method provides, what we believe to be, a new solution for achieving high accuracy and wide range OFDR sensing at the km level.

Online polarization error suppressed optical vector analyzer based on Bayesian optimization.

An optical vector analyzer (OVA) based on orthogonal polarization interrogation and polarization diversity detection is widely used to measure an optical device's loss, delay, or polarization-dependent features. Polarization misalignment is the OVA's primary error source. Conventional offline polarization alignment using a calibrator greatly reduces the measurement reliability and efficiency. In this Letter, we propose an online polarization error suppression method using Bayesian optimization. Our measurement results are verified by a commercial OVA instrument that uses the offline alignment method. The OVA featuring online error suppression will be widely used in the production of optical devices, not just in the laboratory.

Forecasting the chaotic dynamics of external cavity semiconductor lasers.

Chaotic time series prediction has been paid intense attention in recent years due to its important applications. Herein, we present a single-node photonic reservoir computing approach to forecasting the chaotic behavior of external cavity semiconductor lasers using only observed data. In the reservoir, we employ a semiconductor laser with delay as the sole nonlinear physical node. By investigating the effect of the reservoir meta-parameters on the prediction performance, we numerically demonstrate that there exists an optimal meta-parameter space for forecasting optical-feedback-induced chaos. Simulation results demonstrate that using our method, the upcoming chaotic time series can be continuously predicted for a time period in excess of 2 ns with a normalized mean squared error lower than 0.1. This proposed method only utilizes simple nonlinear semiconductor lasers and thus offers a hardware-friendly approach for complex chaos prediction. In addition, this work may provide a roadmap for the meta-parameter selection of a delay-based photonic reservoir to obtain optimal prediction performance.

56 Gb/s PAM4 physical secure communication based on electro-optic self-feedback hardware temporal phase encryption and decryption.

To guarantee information security from the lowest level of optical networks, it is essential to provide physical layer security in fiber-optic communication systems. However, it is challenging to realize high speed physical secure optical communication based on advanced optical modulation formats and pure commercial hardware components. In this work, we report an experimental demonstration of a high-speed 56 Gb/s PAM4 physical-layer secure optical communication system by employing an electro-optic self-feedback hardware module for temporal self-phase encryption and decryption without consuming any additional encryption channel. An encrypted 56 Gb/s PAM4 confidential signal is successfully decrypted after transmitting over 60 km single-mode fiber. The demonstrated scheme can not only be integrated with existing optical communication networks, but can also be used as a pluggable module, which may provide a promising solution for ultra-high speed physical secure optical communication by combining with advanced multiplexing technology in future.

Leader-laggard synchronization of polarization chaos in mutually coupled free-running VCSELs.

We systematically study the leader-laggard synchronization of polarization chaos in mutually coupled free-running vertical cavity surface emitting semiconductor lasers in two cases of parallel and orthogonal injection. Specifically, we quantitatively investigate the effect of critical external parameter mismatch such as the coupling intensity and frequency detuning on the leader-laggard relationship utilizing the cross-correlation function. When the difference between two main cross-correlation peak values exceeds 0.1, the leader-laggard relationship can be viewed to be stable. Our results demonstrate that compared with the coupling strength, the frequency detuning is the dominant factor in determining the stability of the leader-laggard relationship. The exchange of the leader-laggard role occurs within a frequency detuning region from -5 GHz to 5 GHz for both parallel and orthogonal injection. Once the leader-laggard relationship is stable, the difference between the two cross-correlation values can reach 0.242 for negative frequency detuning, but the corresponding value is only 0.146 under positive frequency detuning.

Performance improvement of coherent optical chaos communication using probabilistic shaping.

We numerically investigate the effects of probabilistic shaping on the performance improvement of coherent optical chaos communication. Results show that the decryption bit-error ratio (BER) of the 16-ary quadrature amplitude modulation (QAM) signal decreases upon increasing the probabilistic shaping factor. It is predicted that the BER of 10-GBd 16QAM can be decreased by one order of magnitude. On the other hand, for the forward error correction threshold of the BER, the requirement for synchronization quality is no longer strict for successful decryption. This means that probabilistic shaping improves the system's tolerance to residual synchronization error. Thus, the transmission rate can be increased by approximately 30∼60%. The side effect of probabilistic shaping is that the valid masking coefficient range is narrowed.

Physical-layer key distribution based on commonly-driven laser synchronization with random modulation of drive light.

We propose and experimentally demonstrate a physical-layer key distribution scheme using commonly-driven laser synchronization with random modulation of drive light. Two parameter-matched semiconductor lasers injected by a common complex drive light are used as entropy sources for legitimate users. Legitimate users generate their own random signal by randomly time-division multiplexing of two random sequences with a certain duration according to individual control codes, and then independently modulate the drive light. Laser synchronization is achieved during time slots when the modulation sequences of two users are identical, and thus provide highly correlated randomness for extracting random numbers as shared keys. Experimental results show that the random modulation of the drive light reduces the correlation between the drive light and laser outputs. In addition, laser synchronization is sensitive to the modulation delay and then the latter can be used as an additional hardware parameter. These mean that security is enhanced. In addition, the proposed method has a short laser synchronization recovery time of lower than 1.1 ns, meaning a high rate of key distribution. The upper limit of final key rate of 2.55 Gb/s with a criterion of bit error rate of 1.68 × 10-3 is achieved in experiments. Our results provide a promising candidate for protecting the security of optical fiber communication.

Modeling of a multi-parameter chaotic optoelectronic oscillator based on the Fourier neural operator.

A model construction scheme of chaotic optoelectronic oscillator (OEO) based on the Fourier neural operator (FNO) is proposed. Different from the conventional methods, we learn the nonlinear dynamics of OEO (actual components) in a data-driven way, expecting to obtain a multi-parameter OEO model for generating chaotic carrier with high-efficiency and low-cost. FNO is a deep learning architecture which utilizes neural network as a parameter structure to learn the trajectory of the family of equations from training data. With the assistance of FNO, the nonlinear dynamics of OEO characterized by differential delay equation can be modeled easily. In this work, the maximal Lyapunov exponent is applied to judge whether these time series have chaotic behavior, and the Pearson correlation coefficient (PCC) is introduced to evaluate the modeling performance. Compare with long and short-term memory (LSTM), FNO is not only superior to LSTM in modeling accuracy, but also requires less training data. Subsequently, we analyze the modeling performance of FNO under different feedback gains and time delays. Both numerical and experimental results show that the PCC can be greater than 0.99 in the case of low feedback gain. Next, we further analyze the influence of different system oscillation frequencies, and the generalization ability of FNO is also analyzed.

Physical secure key distribution based on chaotic self-carrier phase modulation and time-delayed shift keying of synchronized optical chaos.

High speed physical secure key distribution in a classical optical fiber channel is unprecedentedly desired for modern secure communication, but it still remains a worldwide technical challenge. In this paper, we propose and experimentally demonstrate a novel high-speed physical secure key distribution scheme based on chaotic optical signal processing and private hardware modules, which employs chaotic self-carrier phase modulation for chaotic bandwidth expansion and time-delayed shift keying of commonly driven synchronized optical chaos for physical layer security. In this scheme, the entropy source rate of synchronized chaos output from two remote response lasers is greatly expanded by chaotic self-carrier delayed nonlinear phase disturbance, which facilitates high speed key extraction from the entropy source with guaranteed randomness. Moreover, a synchronization recovery time of sub-nanosecond is achieved by dynamic keying of the chaotic delay time after chaos synchronization to accelerate the key distribution rate. Based on the proposed scheme, a high physical key distribution rate of 2.1 Gb/s over 40 km is successfully demonstrated in the experiment. The proposed solution provides a promising strategy for future high-speed key distribution based on chaotic optical signal processing and classical fiber channel.