【作者】 孙坚；

【导师】 朱士群；

【作者基本信息】 苏州大学 ， 光学， 2004， 硕士

【摘要】 本文主要从理论上讨论了N台耦合的单模激光和多模激光组成的线性激光阵列中的混沌同步，分析了N台激光强度之间的混沌同步，利用分析信号法和高斯滤波法研究了同激光强度混沌同步相对应的位相同步，解释了激光强度之间的混沌同步是通过位相同步来传递信息，使得两台没有直接耦合的激光强度之间出现混沌同步，得到了N台单模激光和多模激光强度和位相混沌同步之间的联系。 九十年代中后期，科学家们从理论上和实验上发现在两台和三台单模耦合激光系统中，激光强度出现混沌同步的现象。为了利用激光系统中的混沌同步进行通讯和信息传递，有必要对多台激光系统中的混沌同步现象进行研究。所以，对多台激光系统组成的激光阵列，如由6，7，8，9，……等N台激光组成的激光阵列中的混沌和混沌同步的理论研究就成为本文的主要内容。在N台激光组成的激光阵列中，只要适当调节激光的参数，就能实现激光强度的混沌同步，而强度的混沌同步出现在第N台和第1台，第N-1台和第2台，……等等对应的激光之间。当N为奇数时，共有(N-1)／2对激光之间出现强度的混沌同步现象，在最近邻的激光之间不存在混沌同步现象，最中间的一台和任何一台激光之间都没有混沌同步现象出现。当N为偶数时，共有N／2对激光之间出现强度的混沌同步现象，同样在最近邻激光之间不存在混沌同步现象。N台激光场中的真实位相虽然能反映位相同步的痕迹，但不能提供相邻激光之间位相同步的清晰图象。在希尔伯特空间中，通过应用分析信号法和高斯滤波法，我们分析了N台激光系统中相邻激光之间的位相同步。通过对N台激光场的运动方程进行数值模拟，结果表明，除了N为偶数时最中间的一对激光外，虽然出现强度混沌同步的激光对之间并不直接存在耦合作用，但是这些激光对之间强度混沌同步的信息却是通过激光阵列中的相邻激光位相的稳定同步来实现的。 我们将空间耦合的单模激光阵列的理论模型推广到两台和三台多模激光系统。在多模激光系统中，每台多模激光中各个模式之间存在模式竞争，多模激光系统中总强度的混沌同步是建立在对应模式强度之间的混沌同步基础之上的，通过位相同步将强度同步的信息传递给没有直接耦合的两台激光。单模和多模激光系统中的混沌同步中文摘要 通过计算N台激光阵列的李雅普诺夫指数表明，当激光系统出现混沌同步时，系统的最大李雅普诺夫指数大于零，激光系统的参数范围完全处于混沌状态。通过同激光强度相对应的功率谱也可以看出，当激光系统处于混沌同步状态时，激光场的功率谱不存在同特定频率相对应的峰值，呈现出很宽的频率依赖关系，系统确实处于混沌状态。更多还原

【Abstract】 This paper mainly discusses the chaotic synchronization of a linear array including N coupled single-mode and multi-mode lasers. The chaotic synchronization of intensities between N lasers is investigated. By using the analytic signal method and the Gaussian filter method, the relation between the phase synchronization of the laser field and the corresponding intensity synchronization is analyzed. It is shown that the chaotic synchronization of laser intensities is due to the stable message transmission of the phase synchronization. It causes the chaotic synchronization of laser intensities between lasers without direct coupling. The relations of the chaotic synchronization between the intensities and phases of N coupled single-mode and multi-mode lasers are obtained.Since the mid and late of 1990’s, many scientists discovered the phenomenon of chaotic intensity synchronization in a system of two or three single-mode lasers both theoretically and experimentally. To utilize the chaotic synchronization of lasers to the communications and messages transmission, it is necessary to investigate the chaotic synchronization of N lasers. So the investigation of the chaotic synchronization of anarray of many lasers, such as laser system of 6, 7, 8, 9, ...... , and N lasers becomes themain content of this paper. In an array of N lasers, as long as the parameters of the lasers can be suitably adjusted, the chaotic synchronization of laser intensities can occur. The chaotic synchronization of laser intensities can occur between the N - th and the first lasers, the (N -1)- th and the second lasers, ...... , and so on. When the number Nis odd, the chaotic synchronization appears between pairs of lasers. There is nochaotic synchronization between two nearest lasers and between the middle and the other lasers. When the number N is even, the chaotic synchronization appears between -pairs of lasers. There is also no chaotic synchronization between two nearest lasers. The real phases of lasers in the array can show some hints of phase synchronization, but they cannot provide clear picture of phase synchronization between these lasers. By virtue of the analytic signal and the Gaussian filter methods in the Hilbert space, we analyze the phase synchronization of the nearest lasers. The numerical simulations of dynamical equations of N lasers indicate that there exists chaotic synchronization of intensitiesbetween pairs of lasers though there are no directly couplings between these lasers except for the center pair when N is even. The messages of the chaotic synchronization of intensities between these pairs of lasers can be transmitted by the stable phase synchronization between nearest lasers in the array.We extend the theoretical model of spatially coupled single-mode laser array to the system of two and three multimode lasers. In the multimode lasers system, mode competition exists in intensities between the modes of each multimode laser. The chaotic synchronization of the total intensities is based on the chaotic synchronization of the intensities in each corresponding mode. The messages of the intensity synchronization are achieved through the phase synchronization between lasers without direct coupling.The calculation of the Lyapunov exponents in the array of N lasers shows that the laser system is in the chaotic states when the largest Lyapunov exponents are greater than zero. The parameters in the laser system are in the chaotic states. From the power spectrum of laser intensity in the array, it is also seen that there is no peak in the power spectrum that corresponds to a particular frequency when chaotic synchronization appears in the laser system. There is broadband of the power spectra with flat shape in laser intensities appears. This means that the laser system is indeed in the chaotic state.更多还原