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近年来 ,由于混沌控制和同步在保密通讯等领域中的巨大应用前景 ,有关混沌同步的理论和实验研究成了国际学术界极感兴趣的课题之一 (见文献G .D .VanWiggerenandR .Roy ,Science 1998,2 78:2 791198.)。本文对在空间上存在耦合的一维固体激光阵列中的混沌同步现象进行了理论分析。当几台相互之间存在耦合的激光器的泵浦同时受到调制时 ,几台激光输出强度之间的关系呈现出非常丰富而有趣的现象。由两台激光器组成的系统 ,在一定的参量范围内 ,两台激光的输出强度会出现混沌同步现象。在三台激光器组成的系统中 ,最边上两台激光的强度可以出现混沌同步现象 ,而中间一台激光与边上任何一台激光之间不可能出现混沌同步现象。由四台激光组成的系统中 ,最边上两台激光的强度可以出现混沌同步现象 ,最中间两台激光的强度也可以出现混沌同步现象 ;但是 ,最中间两台激光同边上任何一台激光之间却不可能出现混沌同步的情形。对五台激光器组成的系统也有类似的现象发生。进一步的分析表明 ,在一维激光阵列中 ,激光输出强度之间能否出现混沌同步现象 ,不仅受到激光系统参数的制约 ,而且同激光之间耦合的对称性质有关。如果激光器之间的耦合是对称的 ,则有可能出现混沌同步 ,否则就不可能发生混沌同步现象
In recent years, theoretical and experimental research on the synchronization of chaos has become one of the most interested subjects in the international academic community due to the great application prospect of chaos control and synchronization in the field of secure communication (see G.D.WanWiggeren and R. Roy, Science 1998, 2 78: 2 791198.). In this paper, the theoretical analysis of the phenomenon of chaos synchronization in a one-dimensional solid-state laser array with coupling exists in space. The relationship between the intensities of several laser outputs shows a very rich and interesting phenomenon when the pumping of several coupled lasers is modulated at the same time. A system composed of two lasers, chaos synchronization occurs when the output intensities of the two lasers are within a certain range of parameters. In a system composed of three lasers, the intensity of the two lasers at the two ends can occur chaos synchronization, and no chaos synchronization between one laser in the middle and any laser on the edge is possible. In the system composed of four lasers, the intensity of the two lasers at the extreme edge can appear the phenomenon of chaos synchronization, and the intensity of the two middle lasers can also occur the phenomenon of chaos synchronization; however, in the middle of the two lasers, any one on the same side There is no chance of chaos synchronization between lasers. The system of five lasers also has a similar phenomenon. Further analysis shows that in a one-dimensional laser array, whether the chaos synchronization occurs between the laser output intensities is not only restricted by the parameters of the laser system but also related to the symmetrical properties of the coupling between the laser beams. If the coupling between the lasers is symmetric, chaos synchronization may occur, otherwise chaos synchronization may not occur