Investigations On Time-delay Reservoir Computing Based On Semiconductor Lasers Under Electrical Information Injection

Reservoir computing(RC)is a new algorithm emerged in the field of artificial neural network(ANN),which possesses the advantages of simple training process and easy implementation on non-traditional computing hardware.RC uses a dynamic network with fixed weights as a reservoir,it processes information based on the reservoir's transient states stimulated by external input information.According to the topology of the reservoir,RC can be classified into spatially distributed RC and time-delay RC(TDRC).The reservoir of spatially distributed RCs is a spatial network composed of a large number of interconnected nonlinear nodes,while the reservoir of TDRCs is a virtual ring network composed of a single nonlinear node with a feedback loop.Relatively speaking,the structure of TDRC that based on a nonlinear time-delay system is simpler.The all-optical TDRC based on a semiconductor laser(SL)subject to optical feedback shows some unique advantages in terms of computing performance,parallel computing capability,power consumption and computing speed.SL-based TDRC has been successfully used for processing of complex tasks such as chaotic time series prediction,waveform recognition,nonlinear channel equalization,and speech recognition.For SL-based TDRC systems,the data can be input to the reservoir through optical information injection or electrical information injection.The system adopting an optical information injection method needs to be equipped with an external light source,a polarization controller,an attenuator,and an external modulator,which increases the complexity of system structure and parameter adjustment.For electrical information injection method,data can be input to the reservoir by directly modulating the pump current of the SL,so the system has a simpler structure and is easier to implement in hardware.Therefore,investigating on constructing and optimizing an SL-based TDRC system under electrical information injection,and exploring methods to improve system performance and computing speed are of great significance for developing non-traditional computing hardware as well as promoting the development of optical information processing.At present,there are few researches related to SL-based TDRC under electrical information injection.The influence of system parameters on performance as well as the relationship between system performance and system dynamic characteristics are still unclear.In some reported works,good performance is obtained only when SL is biased at a current near its threshold current under a relatively low computing rate.Generally,the light intensity is relatively low when the SLs is biased at currents near their threshold.In such a case,small external disturbances will affect the performance of the system,which is not conducive to the high-speed and stable operation of the RC system.Based on above analysis,this thesis carried out theoretical and experimental investigations focusing on issues such as optimizing the SL-based TDRC system under electrical information injection to obtain better computional performance,ascertaining the impact of system key parameters and system nonlinear dynamics on system performance,as well as optimizing system structure to improve the system's computational performance and data processing rate.The main work and results of the studies are summarized as follows:1.We numerically investigate the performance of the SL-based TDRC system under electrical information injection,and propose a parameter optimization method of using the current-related virtual node interval(?)and feedback strength(k)to enable the SL operating at a higher bias current while maintaining a good system performance and a fast data processing rate.The system performance is evaluated by employing a Santa Fe time series prediction task and a nonlinear channel equalization task.The results show that by setting?to 0.2 times relaxation oscillation period and setting k to 0.5k_BP(k _BP is the feedback strength at the bifurcation point),the system can achieve good performances when the SL is biased within the range of 1.1I_th to 3.5I_th(I_th is the threshold current).For the Santa-Fe time series prediction task,the normalized mean square error(NMSE)of prediction results is lower than 0.01.For the nonlinear channel equalization task under a signal-to-noise ratio(SNR)of 32d B,the symbol error rate(SER)can reach to the order of 10^-5.In addition,it is found that under optimized parameters,when the bias current increases from 1.1I_th to 3.5I_th,the data processing rate of the system with 50 virtual nodes can be increased from 0.15GSa/s to 0.73GSa/s.2.The impact of key parameters such as modulation index,feedback strength,bias current,and virtual node interval on the performance of SL-based TDRC under electrical information injection is experimentally investigated.The relationship between RC performance and system idle state(the system state without data injection)is discussed,and the performance of NMSE?0.1 for Santa Fe time series prediction task is achieved when the SL is biased between 1.0I_th and 3I_th.Specifically,a distributed feedback semiconductor laser(DFB-SL)with an optical feedback loop constitutes the time-delay reservoir,an arbitrary waveform generator(AWG)generates the information to be processed,which is injected into the reservoir by modulating the pump current of the DFB-SL.The results show that when the SL is biased at a current near the threshold,the system shows good prediction performance.The minimum NMSE is about 0.05,and the processing rare is 25.9 MSa/s.The experimental results also show that although the prediction performance of the system decreases with the increase of SL bias current,the decrement can be alleviated under optimized parameters.By setting the modulation index to 0.33 and the virtual node interval to 0.05ns,the good prediction performance(NMSE?0.1)can be obtained even when the SL is biased at three times the threshold current.3.We theoretically investigate the feasibility of improving the computational ability and speed by using a RC system composed of parallel time-delay reservoirs under electrical information injection.In order to simplify the system structure and facilitate hardware implementation,the same mask is used to preprocess the input data,and the masked information is injected into the parallel reservoirs by means of electrical information injection,where two reservoirs are constructed by two SLs subject to optical feedback.Based on the virtual node states originated from two SLs,RC can be performed in three ways:using the virtual node states sampled from SL₁ or SL₂ for training and testing(denoted as RC₁ or RC₂);using the merged virtual node states of the two lasers for training and testing(denoted as RC_M).The performance of the system is evaluated by employing the Santa Fe time series prediction task,the memory capability test,and the Lorenz chaotic attractor prediction task.The results show that,under a given data processing rate,by setting proper parameter mismatch of two SLs,RC_Mshows better computational performance than RC₁ and RC₂.Moreover,under the premise of ensuring good performances,the proposed RC system can double the data processing rate compared with the system based on a single reservoir.4.The performance of an RC system based on two parallel time-delay reservoirs under electrical information injection is experimentally investigated.By employing the Santa Fe time series prediction task and a multi-waveform recognition task,the impact of system key parameters on system performance is investigated,and the performance is compared with that of the system based on a single reservoir.Through this experiment,we realize the high-speed time series prediction and waveform recognition based on a simple system structure.In this experiment,two time-delay reservoirs are composed of two DFB-SLs subject to optical feedback.The information to be processed is generated by an AWG and divided into two parts by a power divider,which is then injected into two reservoirs by modulating the pump current of two SLs.The temporal outputs of two SLs are sampled as virtual node states.Experimental results show that,for processing the prediction task under guaranteeing the NMSE below 0.1 and the recognition task under guaranteeing the SER below 0.005,the potential data processing rate(DPR)of the proposed RC system can achieve 200 MSa/s.