基于分数阶效应的线性与非线性光波传播行为研究

In this project, we will study on the propagation dynamics of linear and nonlinear optics waves with fractional effects in optical structures. According to the properties of optical lattices or optical waveguide structures, we solve the linear system and obtain the band-gap structure or full spectrum. Then we can know the properties of linear modes in a specific location. Also, we will develop and promote the Coupled-mode theory based on the fractional Schrödinger equation. Next, we will analyze the influence of Lévy index on beam propagation management, interaction between light waves, and various types of linear modes trapped in the linear system. One- and two-dimensional stationary solutions originating from high order Bloch modes will be solved by either self-consistent iteration or Newton-conjugate-gradient method. The stability of the obtained nonlinear solutions will be detected by using the linear stability analysis method, and then the parameter windows of stable solitons can be fixed. Further, the influence of multiplying effects, including fractional effect, photoinduced nonlocal effect, and gain and loss effect, on the propagation of nonlinear optical waves will be also analyzed. Our main aim of this project is to derive several practical physical models in which linear waves and optical solitons are characterized by novel propagation dynamics with the help of fractional effects. And that is crucial for their practical applications of fractional effects, e.g., optical communication, optical detection, all-optical computing.

拟对分数阶效应光学结构中的线性和非线性光波传播特性展开深入研究。设计物理上可实现的多种形式光晶格或光波导结构，求解系统对应的能带或谱结构图，分析带边、带中线性模的特性。发展分数阶效应下光波的耦合模理论。剖析列维指数对线性光波的传播管理、光波间相互作用以及多种形式线性模捕获等的影响。运用牛顿共轭梯度迭代等算法数值求解带隙结构中一维、两维孤子多种形式的稳态解。通过线性稳定分析方法确定孤子的稳定传播参数窗口。数值仿真模拟线性光波和孤子的传播行为。研究不同光学结构中分数阶效应、光致非局域效应、增益损耗效应等对光波传播动力学的综合影响，遴选出支持线性光波新颖传输现象和新型光孤子稳定传输特性的系统。揭示分数阶效应对线性和非线性光波传播行为的内在作用机理，为其在光通讯、光检测、全光计算等方面应用价值奠定理论基础和提供实验指导。

全面研究基于分数阶效应的线性和非线性光波传输和演化特性，为光波的衍射管理、光束路径控制及稳定空间光孤子的实现提供理论基础。基于分数阶效应，我们对PT对称波导中基本孤子和双峰孤子，准周期光学晶格中光波的局域和安德森非局域现象，准周期光学晶格中的带隙孤子，半无限光学啁啾格子和均匀材料界面支持的耗散表面孤子，PT对称非线性波导中的光孤子，非线性布洛赫波，多极模非局域孤子，部分PT对称角向势阱支持的涡流孤子等方面开展了系列工作，发现了分数阶效应对线性和非线性光波传播行为的一些新的物理机制。项目中的这些成果已在Optics Letters、Optics Express、Nonlinear Dynamics、EPL等期刊上发表（共发表SCI学术论文16篇，其中SCI二区13篇，SCI三区3篇）。分数阶效应光学系统提供了一种新的光束管理和路由平台。光波传播管理在全光驱动、光开关、光学通讯、捕获、控制及操纵粒子等方面具有重要的理论潜在应用价值。研究结果为功能器件设计积累了基础和经验，也对进一步深入的研究也将大有裨益。另有部分研究结果正在整理过程中。