多横模非均匀加宽激光器斑图动力学及其控制理论研究

The multi-transverse mode inhomogeneously broadened laser is a very important kind of lasers, such as Nd:YAG laser, quantum dot laser, He-Ne laser, CO2 laser, chemical oxygen idione laser and so on. The main content of this project is to establish the pattern dynamics of multi-transverse mode inhomogeneously broadened laser, which is the generalization of pattern dynamics of multi-transverse mode homogeneously broadened laser and dynamics of multi-longtitude mode inhomogeneously broadened laser, and its control theory. Their relevance in optics is magnified by the perspective of future applications, which arise from the possibility of encoding information in the transverse structure and processing it in a completely optical and parallel way. Moreover, laser pattern have much spatio-temporal complex which is valuable for researching the reaction pattern, spatio-temporal chaos, optical entanglement, optical vortex and so on topics. However, there are some limitations on the existing models which can not reveal the sophisticated physical connotations. The procedure of this project is as follows: First, the muti-transverse mode Maxwell-Bloch equantion with inhomogeneously broadened gain profile should be built and some approximations and assumptions will be used. After that, the cooperative frequency shift law for homogeneously broadened laser will be generalized to the homogeneously broadened laser. Second, the linear stability analysis will be applied to research the conditions of instability for the multi-transverse mode inhomogeneously broadened laser. The influences of gain width, transverse effects, mode number, Fresnel number, cross-relaxation rate on the second threshold will be presented. The phase instability will also be studied. Third, the formation and evolution of static/dynamic pattern will be studied by solving the integro-differential Maxwell-Bloch equations numerically. The evolution of mode competition and the effects of gain width on the mode competition should be focused. Finally, the pattern control theory will be carried out by the existing control methods and linear stability analysis. The relationships of control parameters, such as delay time, delay positions, period of perturbation, and the stability of laser pattern will be studied. This topic is the complement of semi-classic laser theory, and this project is meaningful for the laser theory research and the applications of laser pattern.

多横模非均匀加宽激光器是一类非常重要的激光器,目前具有实际应用价值的激光器大多具有非均匀加宽机制或混合加宽机制,如Nd:YAG激光器、量子点激光器、He-Ne激光器，CO2激光器以及具有重要战略意义的化学氧碘激光器等。本课题以多横模非均匀加宽激光器斑图动力学及其控制作为主要研究内容。通过建立具有非均匀加宽特性的多横模Maxwell-Bloch方程，研究非均匀加宽激光器的斑图动力学；利用线性稳定性分析研究非均匀加宽激光器低阈值不稳定性、相不稳定性；利用数值和解析相结合的方法探究非均匀加宽激光器合作频率锁定特性、静态斑图和动态斑图的形成及演化特性；并针对多横模非均匀加宽激光器出现的时空混沌利用成熟的控制方法并结合稳定性分析建立多横模非均匀加宽激光器的斑图控制理论。本课题对于深入研究激光物理、探究激光器运转特性并通过控制激光斑图增强实价值具有重要的实际意义。

多横模非均匀加宽激光器是一类非常重要的激光器。本课题以多横模非均匀加宽激光器斑图动力学及其控制作为主要研究内容。通过建立具有非均匀加宽特性的多横模Maxwell-Bloch方程，研究非均匀加宽激光器的斑图动力学；利用线性稳定性分析研究非均匀加宽激光器低阈值不稳定性；利用数值和解析相结合的方法探究非均匀加宽激光器静态斑图和动态斑图的形成及演化特性；并针对多横模非均匀加宽激光器出现的时空混沌利用成熟的控制方法并结合稳定性分析建立多横模非均匀加宽激光器的斑图控制理论。通过对本课题的深入研究，我们利用线性稳定性分析给出了单横模非均匀加宽激光器的第二阈值，并研究了部分参量对第二阈值的影响。利用含时数值解的办法考察了双横、三横模非均匀加宽激光器的稳定性条件，计算结果表明，基于TEM01、TEM02和TEM03为例发现，多横模非均匀加宽激光器的第二阈值要低于任何一个横模独自被激发的第二阈值。利用多种控制方法实现了对多横模非均匀加宽激光器的有效控制。此次，我们给出了斑图控制的评价方法，并利用理论和试验的方法实现通过对波前修正从而控制斑图，进一步证实了建立斑图控制理论研究的可行性。最后，为进一步拓展延续课题的研究内容，搭建了气体拉曼激光器，采用非稳定腔实现了激光输出，为下一步研究宽谱宽谱横向非线性光学系统斑图结构的理论搭建了平台。本课题对于深入研究激光物理、探究激光器运转特性并通过控制激光斑图增强实价值具有重要的实际意义。