基于增益/损耗调制的波导中光传输动力学的特性研究

Recently, the notion of PT symmetry has received extensive attention in optics, and the various PT symmetric optical modes and their dynamic characteristics in diferent enviroments have been exhibited. Especially in nonlinear optics, various types of optical solitons, including bright, dark soliton, lattice soliton, gap soliton, defect soliton and high dimensional soliton, etc., have been studied widely. So far, the most researches focuse on the existence of optical solitons in nonlinear PT symmetric waveguides and their dynamic stability, while nonlinear symmetry breaking induced by PT symmetry and dynamic stability criterion are seldom studied. In addition, the dynamics of light transmission with different gain and loss lacks enough attention. Therefore, this project will try to study these problems, in order to reveal some intrinsic characteristics of optical transmission in the nonlinear PT symmetric waveguide. The detailed research contents are the following: (1) phase transition induced by spontaneous symmetry breaking in the nonlinear PT symmetric waveguides; (2) criterion of stability for optical modes in the nonlinear PT symmetric waveguides; (3) dynamics of light transmission in active PT symmetric waveguides and their application. We believ some valuable and influential work can been achieved through this project.

近年来，PT对称的概念在光学领域得到了广泛的关注，展示了各种环境下PT对称光学模式及其动力学特性。特别是在非线性光学领域，各种类型的光学孤子，包括亮、暗孤子、格子孤子、带隙孤子、缺陷孤子以及高维孤子等，得到广泛地研究。目前，大多数的研究主要集中于非线性PT对称波导中孤子的存在形式以及它们的动力学稳定性，而对非线性系统中由PT对称所诱导的非线性对称破缺以及动力学的稳定性判别准则研究甚少。另外，对在增益损耗参数不相等时光传输动力学的研究也关注不够。因此，本项目力图去研究这些问题，以揭示非线性PT 对称波导中光传输动力学的一些内禀特性。具体研究内容：（1）非线性PT 对称波导中自发性对称破缺相变的研究；（2）非线性PT对称波导中光学模式稳定性判据的研究；（3）主动PT对称波导中光传输动力学特性及应用研究。我们期望通过对本项目的研究，做出一些有价值、有影响力的工作。

本项目主要研究基于增益/损耗调制的波导中光传输动力学的传输特性，以揭示非线性PT对称波导中光传输动力学的一些内禀特性。给出了非线性PT对称波导中初始功率对非线性PT对称相变的影响；给出了非线性PT对称波导以及耦合波导中的孤子解和向量孤子解，并讨论了相应的稳定性；同时，给出了系统的平面波解和周期解，并讨论了它们的带结构稳定性；有关PT对称波导中光束传输的动力学涉及了孤子的散射问题，牛顿摆的动力学以及塔波特效应等特性。作为应用孤子放大和整形也被研究。同时，我们的研究方法也被应用于研究由分数薛定谔方程所支配的光束在介质中的传输，以及BEC中的非线性动力学。. 本项目共发表文章22篇，其中16篇被SCI收录。