Excellent predictive-performances of photonic reservoir computers for chaotic time-series using the fusion-prediction approach.

In this work, based on two parallel reservoir computers realized by the two polarization components of the optically pumped spin-VCSEL with double optical feedbacks, we propose the fusion-prediction scheme for the Mackey-Glass (MG) and Lorenz (LZ) chaotic time series. Here, the direct prediction and iterative prediction results are fused in a weighted average way. Compared with the direct-prediction errors, the fusion-prediction errors appear great decrease. Their values are far less than the values of the direct-prediction errors when the iteration step-size are no more than 15. By the optimization of the temporal interval and the sampling period, under the iteration step-size of 3, the fusion-prediction errors for the MG and LZ chaotic time-series can be reduced to 0.00178 and 0.004627, which become 8.1% of the corresponding direct-prediction error and 28.68% of one, respectively. Even though the iteration step-size reaches to 15, the fusion-prediction errors for the MG and LZ chaotic time-series can be reduced to 55.61% of the corresponding direct-prediction error and 77.28% of one, respectively. In addition, the fusion-prediction errors have strong robustness on the perturbations of the system parameters. Our studied results can potentially apply in the improvement of prediction accuracy for some complex nonlinear time series.

Optical cascaded reservoir computing for realization of dual-channel high-speed OTDM chaotic secure communication via four optically pumped VCSEL.

In this work, we propose a chaotic secure communication system with optical time division multiplexing (OTDM), using two cascaded reservoir computing systems based on multi beams of chaotic polarization components emitted by four optically pumped VCSELs. Here, each level of reservoir layer includes four parallel reservoirs, and each parallel reservoir contains two sub-reservoirs. When the reservoirs in the first-level reservoir layer are well trained and the training errors are far less than 0.1, each group of chaotic masking signals can be effectively separated. When the reservoirs in the second reservoir layer are effectively trained and the training errors are far less than 0.1, the output for each reservoir can be well synchronized with the corresponding original delay chaotic carrier-wave. Here, the synchronization quality between them can be characterized by the correlation coefficients of more than 0.97 in different parameter spaces of the system. Under these high-quality synchronization conditions, we further discuss the performances of dual-channel OTDM with a rate of 4×60 Gb/s. By observing the eye diagram, bit error rate and time-waveform of each decoded message in detail, we find that there is a large eye-openings in the eye diagrams, low bit error rate and higher quality time-waveform for each decoded message. Except that the bit error rate of one decoded message is lower than 7 × 10-3 in different parameter spaces, and those of the other decoded messages are close to 0, indicating that high-quality data transmissions are expected to be realized in the system. The research results show that the multi-cascaded reservoir computing systems based on multiple optically pumped VCSELs provide an effective method for the realization of multi-channel OTDM chaotic secure communications with high-speed.

Detections of the position-vectors of the multi targets located in a circular space based on an asymmetric coupling semiconductor lasers network.

We present a novel scheme for the detections of the position-vectors of the multi targets distributed in a circular space using multi channels of the probe chaotic waves emitted by the asymmetric coupling semiconductor lasers network (ACSLN), where these probe waves possess the attractive features of the time-space uncorrelation and wide bandwidth. Using these features, the accurate measurement for the position-vectors of the multi targets can be achieved by correlating the multi channels of the probe waves with their corresponding reference waves. The further research results show that the detections for the position-vectors of the multi targets possess very low relative errors that are no more than 0.22%. The ranging-resolutions for the multi targets located in a circular space can be achieved as high as 3 mm by optimizing some key parameters, such as injection current and injection strength. In addition, the ranging-resolutions exhibit excellent strong anti-noise performance even when the signal-to-noise ratio and relative noise intensity appear obvious enhancement. The detections for the position-vectors of the multi targets based on the ACSLN offers interesting perspectives for the potential applications in the driverless cars and the object tracking system with omnidirectional vision.

Deep optical reservoir computing and chaotic synchronization predictions based on the cascade coupled optically pumped spin-VCSELs.

In this work, we utilize two cascade coupling modes (unidirectional coupling and bidirectional coupling) to construct a four-layer deep reservoir computing (RC) system based on the cascade coupled optically-pumped spin-VCSEL. In such a system, there are double sub-reservoirs in each layer, which are formed by the chaotic x-PC and y-PC emitted by the reservoir spin-VCSEL in each layer. Under these two coupling modes, the chaotic x-PC and y-PC emitted by the driving optically-pumped spin-VCSEL (D-Spin-VCSEL), as two learning targets, are predicted by utilizing the four-layer reservoirs. In different parameter spaces, it is further explored that the outputs of the double sub-reservoirs in each layer are respectively synchronized with the chaotic x-PC and y-PC emitted by the D-Spin-VCSEL. The memory capacities (MCs) for the double sub-reservoirs in each layer are even further investigated. The results show that under two coupling modes, the predictions of the double sub-reservoirs with higher-layer for these two targets have smaller errors, denoting that the higher-layer double sub-reservoirs possess better predictive learning ability. Under the same system parameters, the outputs of the higher-layer dual parallel reservoirs are better synchronized with two chaotic PCs emitted by the D-Spin-VCSEL, respectively. The larger MCs can also be obtained by the higher-layer double reservoirs. In particular, compared with the four-layer reservoir computing system under unidirectional coupling, the four-layer reservoir computing system under bidirectional coupling shows better predictive ability in the same parameter space. The chaotic synchronizations predicted by each layer double sub-reservoirs under bidirectional coupling can be obtained higher qualities than those under unidirectional coupling. By the optimization of the system parameters, the outputs of the fourth-layer double sub-reservoirs are almost completely synchronized with the chaotic x-PC and y-PC emitted by the D-Spin-VCSEL, respectively, due to their correlation coefficient used to measure synchronization quality can be obtained as 0.99. These results have potential applications in chaotic computation, chaotic secure communication and accurate prediction of time series.

Accurate separation of mixed high-dimension optical-chaotic signals using optical reservoir computing based on optically pumped VCSELs.

In this work, with the mixing fractions being known in advance or unknown, the schemes and theories for the separations of two groups of the mixed optical chaotic signals are proposed in detail, using the VCSEL-based reservoir computing (RC) systems. Here, two groups of the mixed optical chaotic signals are linearly combined with many beams of the chaotic x-polarization components (X-PCs) and Y-PCs emitted by the optically pumped spin-VCSELs operation alone. Two parallel reservoirs are performed by using the chaotic X-PC and Y-PC output by the optically pumped spin-VCSEL with both optical feedback and optical injection. Moreover, we further demonstrate the separation performances of the mixed chaotic signal linearly combined with no more than three beams of the chaotic X-PC or Y-PC. We find that two groups of the mixed optical chaos signals can be effectively separated by using two reservoirs in single RC system based on optically pumped Spin-VCSEL and their corresponding separated errors characterized by the training errors are no more than 0.093, when the mixing fractions are known as a certain value in advance. If the mixing fractions are unknown, we utilize two cascaded RC systems based on optically pumped Spin-VCSELs to separate each group of the mixed optical signals. The mixing fractions can be accurate predicted by using two parallel reservoirs in the first RC system. Based on the values of the predictive mixing fractions, two groups of the mixed optical chaos signals can be effectively separated by utilizing two parallel reservoirs in the second RC system, and their separated errors also are no more than 0.093. In the same way, the mixed optical chaos signal linearly superimposed with more than three beams of optical chaotic signals can be effectively separated. The method and idea for separation of complex optical chaos signals proposed by this paper may provide an impact to development of novel principles of multiple access and demultiplexing in multi-channel chaotic cryptography communication.

Interlinked Microcone Resistive Sensors Based on Self-Assembly Carbon Nanotubes Film for Monitoring of Signals.

Flexible pressure sensors still face difficulties achieving a constantly adaptable micronanostructure of substrate materials. Interlinked microcone resistive sensors were fabricated by polydimethylsiloxane (PDMS) nanocone array. PDMS nanocone array was achieved by the second transferring tapered polymethyl methacrylate (PMMA) structure. In addition, self-assembly 2D carbon nanotubes (CNTs) networks as a conducting layer were prepared by a low-cost, dependable, and ultrafast Langmuir−Blodgett (LB) process. In addition, the self-assembled two-dimensional carbon nanotubes (CNTs) network as a conductive layer can change the internal resistance due to pressure. The results showed that the interlinked sensor with a nanocone structure can detect the external pressure by the change of resistivity and had a sensitive resistance change in the low pressure (<200 Pa), good stability through 2800 cycles, and a detection limit of 10 kPa. Based on these properties, the electric signals were tested, including swallowing throat, finger bending, finger pressing, and paper folding. The simulation model of the sensors with different structural parameters under external pressure was established. With the advantages of high sensitivity, stability, and wide detection range, this sensor shows great potential for monitoring human motion and can be used in wearable devices.

Microdome-Tunable Graphene/Carbon Nanotubes Pressure Sensors Based on Polystyrene Array for Wearable Electronics.

Resistive pressure sensors are appealing due to having several advantages, such as simple reading mechanisms, simple construction, and quick dynamic response. Achieving a constantly changeable microstructure of sensing materials is critical for the flexible pressure sensor and remains a difficulty. Herein, a flexible, tunable resistive pressure sensors is developed via simple, low-cost microsphere self-assembly and graphene/carbon nanotubes (CNTs) solution drop coating. The sensor uses polystyrene (PS) microspheres to construct an interlocked dome microstructure with graphene/CNTs as a conductive filler. The results indicate that the interlocked microdome-type pressure sensor has better sensitivity than the single microdome-type and single planar-type without surface microstructure. The pressure sensor's sensitivity can be adjusted by varying the diameter of PS microspheres. In addition, the resistance of the sensor is also tunable by adjusting the number of graphene/CNT conductive coating layers. The developed flexible pressure sensor effectively detected human finger bending, demonstrating tremendous potential in human motion monitoring.

Predictive learning of multi-channel isochronal chaotic synchronization by utilizing parallel optical reservoir computers based on three laterally coupled semiconductor lasers with delay-time feedback.

In this work, we utilize three parallel optical reservoir computers to model three optical dynamic systems, respectively. Here, the three laser-elements in the response laser array with both delay-time feedback and optical injection are utilized as nonlinear nodes to realize three optical chaotic reservoir computers (RCs). The nonlinear dynamics of three laser-elements in the driving laser array are predictively learned by these three parallel RCs. We show that these three parallel reservoir computers can reproduce the nonlinear dynamics of the three laser-elements in the driving laser array with self-feedback. Very small training errors for their predictions can be realized by the optimization of two key parameters such as the delay-time and the interval of the virtual nodes. Moreover, these three parallel RCs to be trained will well synchronize with three chaotic laser-elements in the driving laser array, respectively, even when there are some parameter mismatches between the response laser array and the driving laser array. Our findings show that optical reservoir computing approach possibly provide a successful path for the realization of the high-quality chaotic synchronization between the driving laser and the response laser when their rate-equations imperfectly match each other.

Precise ranging for the multi-region by using multi-beam chaotic polarization components in the multiple parallel optically pumped spin-VCSELs with optical injection.

We present a novel scheme for the accurate ranging for the multi-region in the rectangular-shape target using numbers of the chaotic x polarization components in the multiple parallel optically pumped spin-VCSELs with optical injection, where these chaotic x polarization components possess the attractive features of the uncorrelation in time and space under different optical injection strengths, and fast dynamic with femtosecond magnitude. Utilizing these features, the accurate ranging to the position vectors of the multi-region targets can be achieved by correlating the multi beams of the time-delay reflected chaotic polarization radar probe waveforms with their corresponding reference waveforms. The further investigations show that the ranging to the multi-region targets possesses very low relative error, which is less than 0.28%. Their range resolutions can be achieved as high as 0.9mm, and exhibit excellent strong anti-noise performance by the optimization of some key parameters such as the injection strength, the amplitude of external light, linear birefringence, spin relaxation rate. The precise ranging to the multi-region targets based on the multiple parallel optically pumped spin-VCSEL with optical injection offers interesting perspectives for the potential applications in quality detection of the multi-region surfaces.

Exploring new chaotic synchronization properties in the master-slave configuration based on three laterally coupled semiconductor lasers with self-feedback.

We have developed a theory model for a three-element laser array where three lasers are laterally coupled using the coupled mode theory and Maxwell equations. New chaotic synchronization properties have been observed systematically in the master-slave configuration, consisting of the driving three-element laser array with self-feedback and the response three-element laser array subjected to the parallel injection or cross injection. Under the parallel injection, the dynamic evolutions of high-quality complete chaotic synchronization between laser elements in different parameter spaces seriously depend on the self-feedback mode of the driving laser elements, such as one, two and all of them with self-feedback. It is found that when only the driving middle one or all of the driving laser elements are subject to self-feedback, high-quality complete chaotic synchronization of all laser elements can be achieved in the same large region of the most of the parameter spaces. In addition, we report here for the first time (to our knowledge) the interestingly symmetrical properties of leader/ laggard chaotic synchronization in the configuration under the cross-injection. Namely, the leader/ laggard chaotic synchronization with high quality between laser elements periodically varies with the delay differences, under the key parameters limited to a certain range. The varying traces of these synchronizations are like sine wave. The mirror symmetry between the laggard chaotic synchronization with in-phase (anti-phase) and the leader one with in-phase (anti-phase) can be achieved by the optimization of the structural parameters of laser waveguides. With the optimization of the related operating parameters, for one of the side-lasers, its leader/ laggard chaotic synchronization can be achieved the anti-symmetry between in-phase and anti-phase. On the other hand, for two symmetrical side-lasers, their leader/ laggard chaotic synchronization with in-phase and anti-phase can reach the anti-symmetry.

Optical chaotic flip-flop operations with multiple triggering under clock synchronization in the VCSEL with polarization-preserved optical injection.

We investigate the evolution of nonlinear dynamic behaviors of two polarization components (x-PC and y-PC), as well as the interplay of polarization bistability and injection strength in the vertical-cavity surface-emitting laser (VCSEL) with polarization-preserved optical injection. We explore a new threshold mechanism to judge two logic outputs encoded in different dynamic behaviors of the x-PC and y-PC emitted by the VCSEL with polarization-preserved optical injection. We demonstrate implementations of two parallel optical chaotic reset-set flip-flop operations and two parallel chaotic toggle flip-flop operations that are synchronized by a clock signal and response for as short as 1 ns bit time. We further observe the reconfiguration of these two kinds of flip-flop operations with clock synchronization in different time periods by controlling the duration-time of the reset (toggle) signal with high-level. The probability of the correct trigger responses for these two kinds of flip-flop operations is controlled by the interplay of the duration-time of the reset (toggle) signal and the noise strength of the spontaneous emission. The probability that is equal to 1 for the reset-set flip-flop operations occurs in the long duration-time of the reset (toggle) signal ranging from 480 ps to 592 ps. The probability with 1 for the toggle flip-flop operations takes place in the short duration-time between 116 ps and 170 ps. Moreover, these two kinds of flip-flop operations have strong robust to the spontaneous emission noise. The optical chaotic flip-flop operation device with clock synchronization and reconfigurable trigger function proposed in our scheme offers interesting perspectives for applications where noise is unavoidable and synchronized multiple triggering is required.

Optical chaotic data-selection logic operation with the fast response for picosecond magnitude.

We investigate the evolution of nonlinear dynamic behaviors of two polarization components (x-PC and y-PC), as well as the interplay of polarization bistability, frequency detuning and injection strength in the vertical cavity surface emitting laser with optical injection. Specifically, by encoding two logic inputs and one clock input in the amplitude of the light from a sampled grating distributed Bragg reflector laser, and by decoding two output logic responses from the x-PC and y-PC emitted by the laser, we demonstrate two parallel data-selection computing. The correct logic output encoded in two emitted PCs response for as short as 100 ps bit time and the response bit time of the correct logic output encoded in the y-PC may be 67 ps by the optimization of the injection strength. The probability of a correct response is controlled by the interplay of the bit time, the injection strength and noise strength, and is equal to 1 in a wide region of the injection strength and noise strength. The chaotic data-selection computing in an optically VCSEL offer interesting perspectives for applications where noise is unavoidable and fast switching is required.

Real-time ranging of the six orientational targets by using chaotic polarization radars in the three-node VCSEL network.

We propose a novel scheme of the real-time ranging for the six orientational targets based on the vertical cavity surface-emitting laser (VCSEL) network with three nodes. In the scheme, we explore a method to realize the globally complete chaotic synchronization (GCCS) of the network with different channel delays. Under the GCCS, we use the six chaotic polarization radars for the ranging of the six orientational targets based on Hilbert transform theory. It is found that the ranging of the six orientational targets has good performance, such as real-time stability and high accuracy, and the absolute errors of the ranging reach millimeter magnitude. Moreover, all relative errors are small and less than 11%.

Real-time multi-target ranging based on chaotic polarization laser radars in the drive-response VCSELs.

According to the principle of complete chaos synchronization and the theory of Hilbert phase transformation, we propose a novel real-time multi-target ranging scheme by using chaotic polarization laser radar in the drive-response vertical-cavity surface-emitting lasers (VCSELs). In the scheme, to ensure each polarization component (PC) of the master VCSEL (MVCSEL) to be synchronized steadily with that of the slave VCSEL, the output x-PC and y-PC from the MVCSEL in the drive system and those in the response system are modulated by the linear electro-optic effect simultaneously. Under this condition, by simulating the influences of some key parameters of the system on the synchronization quality and the relative errors of the two-target ranging, related operating parameters can be optimized. The x-PC and the y-PC, as two chaotic radar sources, are used to implement the real-time ranging for two targets. It is found that the measured distances of the two targets at arbitrary position exhibit strong real-time stability and only slight jitter. Their resolutions are up to millimeters, and their relative errors are very small and less than 2.7%.

Controllable optoelectric composite logic gates based on the polarization switching in an optically injected VCSEL.

Based on the polarization switching mechanism in an optically injected vertical cavity surface emitting laser (VCSEL), and the new electro-optic modulation theory, we propose a novel approach to implement optoelectric logic gates. Here, the two linearly polarized lights from the output of the laser are considered as two logic outputs. Under the electro-optic modulation, one of the logic outputs is the NOT operation with the other one. With the same logic input signal, we perform various digital signal processing (AND, OR, XNOR, NAND, NOR and XOR) in the optical domain, controlling the logic operation of the applied electric field between the two logic input signals. On this basis, the logic operation of half-adder is further implemented.

Controllable optoelectric composite logic gates based on the polarization switching in an optically injected VCSEL: erratum.

A number of erratums are presented to correct the inadvertent typing mistakes in our paper.

Electro-optic coupling of wide wavelength range in linear chirped-periodically poled lithium niobate and its applications.

We theoretically investigate the electro-optic coupling in an optical superlattice of linear chirped-periodically poled lithium niobate. It is found that the electro-optic coupling in such optical superlattice can work in a wide wavelength range. Some of examples, with bandwidths of 20, 40, 80, 120 nm, are demonstrated. The way to determine the electric field for perfect conversion between o- and e-ray and the method using apodized crystals of tanh profile to reduce the ripples are shown. As one of its applications, one kind of broadband Solc-type bandpass filter in optical communication range is proposed.