宇称时间反演对称的离散波导中暗孤波特性的研究

Parity-time symmetric discrete waveguides can be used to structure non-Hermitian optical systems, design new type of optical devices, which provides an ideal platform for exploring the properties of non-Hermitian system and developing the non-Hermitian photonics. In this project, we focus on the properties of the dark solitary waves in PT- symmetric discrete nonlinear waveguides, aim to obtain solutions of the new-type dark solitary waves. Stability and dynamics of dark solitary waves will be studied in order to control the evolution of dark solitary wave. Mainly including the following research contents: 1. Based on 1D model describing the propagation of dark soliton in discrete PT-symmetric waveguides, we will analyze the existence of the solutions of PT-symmetric dark solitary wave, discuss the range of parameter for stable solitons, and investigate their dynamic properties. 2. Inserting a pair of PT-symmetric waveguides in self-defocusing waveguide array, we will investigate scattering properties of PT-symmetric waveguide to dark soliton, control propagation direction and study spatial storage effect of the discrete dark solitons. 3. We will investigate PT-symmetric waveguide array with both of dispersive and diffractive effects, establish spatiotemporal pulses propagating model, solve spatiotemporal localized dark solitary wave, study their excitation condition and stabilized. We aim to reveal the diversity of the solutions of PT-symmetric discrete dark solitary waves, illuminate the physical mechanism of spatiotemporal localized dark solitary wave，provide a feasibly theoretical scheme of the manipulation and application of the discrete dark solitary waves in PT-symmetric nonlinear waveguides.

宇称时间(Parity-Time)反演对称的离散光波导可用于构建非厄米光学系统和设计新型光学器件，为探索非厄米系统的性质以及发展非厄米光子学提供了平台。本项目从理论上研究PT对称的非线性离散光波导中暗孤波的性质，以期获得新奇的暗孤波解，并研究其稳定性及动力学性质，进而调控其动力学演化行为。主要研究内容包括：1.研究一维PT对称离散非线性波导模型中暗孤子解的存在性，确定其稳定传输的参数范围及演化特性；2.在自散焦波导阵列中嵌入PT对称波导，研究该结构对离散暗孤子的散射特性，讨论离散暗孤子的空间存储效应并对其传输方向进行操控；3.建立脉冲在PT对称色散非线性波导阵列中演化的模型，求解时空局域化的离散暗孤波，分析其激发条件和稳定化问题。本项目旨在揭示PT对称离散暗孤波形式的多样性，阐明时空局域化的暗孤波存在的机制，并提出操控离散暗孤波的可行方案，为离散暗孤波的调控及应用提供理论参考。

宇称时间(Parity-Time)反演对称的离散光波导可用于构建非厄米光学系统和设计新型光学器件，为探索非厄米系统的性质以及发展非厄米光子学提供了平台。本项目从理论上研究PT对称的非线性离散光波导中暗孤波和时空局域化X波的性质，探索了PT对称离散暗孤波形式的多样性，阐明了时空局域化的X波存在的机制，深入研究了宇称时间反演对称的离散波导中孤子特性，发展了计算PT对称波导模型中孤子的存在性、稳定性和传输问题的数值方法，获取了不同形态的孤子，并在此基础上发现了暗孤子的光学二极管效应和空间存储效应。我们的研究有助于进一步理解非厄米非线性的离散波导系统中光学孤子和时空局域化X波的存在性、稳定性和动力学性质，并为离散孤波的调控及应用提供参考。