【作者】 杨鹏；

【导师】 黄洪斌；

【作者基本信息】 东南大学 ， 光学， 2006， 硕士

【摘要】 可以论证,二十世纪全球科学范围内最广泛、最基础的革命是与混沌动力学(非线性动力学)联系在一起的。混沌动力学不仅在物理、化学,而且在医药、生物、地质等等领域都有着非常重要的影响。而光学混沌正是由于哈肯对激光动力学的开创性研究而建立起来。本文第一章是绪论部分,介绍了非线性动力学的一些基本概念、研究现状和相关成果。在第二章中,我们利用量子光学中的量子朗之万方程,在考虑了原子相干性和注入经典光场的影响后,推导出了∧构型双光子激光器的无量纲动力学方程组。在第三章中,我们将上面导出的方程组线性化,然后通过计算稳定解和lyapunov指数来分析该系统的稳定性和动力学特征。在第四章中,我们把注入经典光场和原子相干性的影响考虑进去,分析他们对系统稳定性产生的影响。我们的结论表明lorenzs吸引子和单焦点吸引子在这个系统中能够共存,原子的相干性和经典光场能够诱发和抑制混沌。注入经典场可以通过Hopf分岔和突变的形式产生和抑制混沌,而原子相干性只能通过临界点突变来产生混沌,抑制混沌时却可以通过两个过程。更多还原

【Abstract】 Arguably the most broad based revolution in the world view of science in the twentieth century will be associated with chaotic (nonlinear) dynamics. It has an important impact in all of these fields such as physics, chemistry, medicine, biology, geology and so on. Because of H. Haken, who first studied the dynamics of lasers, established the field of optical chaos.We introduce the basic concepts, development and corresponding studying fruits on nonlinear dynamics in the 1st chapter.In the 2nd chapter, We derive the dimensionless dynamic equations of two-photon lasers with∧atomic level configuration by using the quantum Langevin equation method with the considerations of atomic coherence and injected classical fields.In the 3rd chapter, we linearize the dynamical equations, and then analyze the stability and the chaotic dynamics of the two-photon lasers by calculating the stable solutions and the Maximum Lyapunov Exponent(MLE).In the 4th chapter, base on the consideration of atomic coherence and injected classical field, we analyze the dynamical properties of the system。Our results show that the Lorenz strange attractors and one focus strange attractors can exist in this system, and the chaos can be induced or inhibited by the injected classical fields via Hopf-bifurcations or crises, while the atomic coherence induces chaos via crises, and inhibit chaos via Hopf bifurcation or crises.更多还原