| In contrast to uncoupled lasers,the transversely coupled laser array has many advantages such as simple structure,easy integration,high power,enhanced modulation bandwidth,rich chaotic dynamic behavior and so on.It has important potential applications in the fields ranging from multi-channel secure communication,complex neural networks,to synchronous radar ranging to multi-target laser.Chaos synchronization plays an important role in these applications.However,based on the master-slave structure of the laterally laser array with optical feedback,the mechanism of chaotic synchronization between different coupled lasers is still not clear.Under different control parameters,the types,conditions,and unique characteristics of chaotic synchronization need to be further explored.In addition,the existing optical chaotic synchronization technology is limited by the following two key conditions: the drive laser system is identical to the response one,and the rate-equations of the drive and response lasers are known in advance.These conditions are difficult to be hold and achieved in practice.The recently developed reservoir computing approach provides a new idea and way for the predictive learning of optical chaotic synchronization.It is expected to solve the limitations of optical chaotic synchronization in practical applications.Moreover,due to the limitations of the existing chaotic synchronization theory,it is difficult to be generalize to apply in synchronized chaotic radar to target ranging in practice.The chaotic synchronization prediction learning approach based on reservoir computing is an effective method to solve the key problems of chaotic synchronization in the target ranging,such as instability and low quality.For these scientific issues,in this thesis,we have made innovative explorations in three aspects,which are given as follows:(1)In this thesis,based on the coupled mode theory and Maxwell equations,we developed a theroy model for a three-element laser array where three lasers are laterally coupled.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 that 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 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.See chapter 3 for details of this part.(2)In this thesis,three parallel optical RCs are used 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.This work is completed in chapter 4.(2)In this thesis,three parallel optical RCs are used 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.See chapter 4 for details of this part.(3)In this thesis,we utilize three parallel reservoir computers to model three-channel delayed radar probe signals,respectively.Here,the response three-element lase array with both delay-time feedback and optical injection are utilized as nonlinear nodes to realize these three reservoirs.These three-channel delayed radar probe signals are presented by the driving three-element lase array with self-feedback.We show that these each channel delayed radar probe signal can well be predicted to laggingly synchronize with its corresponding trained reservoirs,under very small training errors.High-quality lag chaotic synchronization between them can be received even when there are some parameter mismatches between the response laser array and the driving laser array.Under this condition,three-channel synchronous radar probe signals are utilized for the ranging to three targets,respectively,based on Hilbert transform theory.It is found that the ranging to these targets has high accuracy.Their absolute errors reach millimeter level.Moreover,their relative errors are very small and less than 0.6%.Our findings show that optical reservoir computing approach possibly provide a successful path for the realization of the ranging to the target.See chapter 5 for details of this part. |
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