光学局域波态转换和超周期呼吸子特性及其物理机制研究

State transitions of nonlinear localized waves are one of key topics in nonlinear science. Superregular breather is a novel type of the breather interaction structures, which describes an important scenario of nonlinear modulation instability. Based on the existing experimental facts and theoretical model, we intend to construct exactly the analytic solutions of first-order localized waves and superregular breathers in various integrable and quasi-integrable nonlinear optical controllable systems. Then, we explore the characteristics of state transitions of localized waves and superregular breathers in complex nonlinear optical fiber and the optical systems beyond the slowly varying envelope approximation. We analyze the impact of higher-order effects and doped atoms on the properties of localized waves in the nonlinear fiber systems, and study the characteristics of few-cycle optical localized waves in the optical systems beyond the slowly varying envelope approximation. The complexity and diversity of superregular breathers are revealed in detail and the properties and rules of the state transitions between various localized waves are analyzed systematically. We establish the exact links between the characteristics of transitions and excitations and the growth rate of modulation instability. We reveal the physical mechanisms of transitions and excitations of localized waves. As a result, an effective method of analysis and interpretation of localized-wave state transitions and superregular breathers can be established. Our results will provide theoretical foundation for the understanding of the diversity and correlation of localized waves and the controllable excitation of localized waves in experiments.

非线性局域波态转换是当前非线性物理研究的重点课题之一。超周期呼吸子是一类新颖的呼吸子相互作用结构，可描述一类重要的非线性调制不稳定现象。本课题立足于已有的实验事实和理论模型，对于实验上易操作的多种非线性光学可积和准可积系统，求解平面波背景上一阶局域波解以及超周期呼吸子解的解析和半解析形式，探究复杂非线性光纤系统和超越慢变包络近似光学系统中局域波态转换和超周期呼吸子特性。分析非线性光纤系统中高阶效应和掺杂原子对局域波性质的影响，研究超越慢变包络近似光学系统中少周期光学局域波的物理特性。着重揭示超周期呼吸子的复杂性和多样性，系统分析多种局域波态转换的性质规律，建立局域波激发和态转换特征与不稳定性增长率的精确对应关系，深入发掘局域波激发和态转换的物理机制，从而建立一套有效分析和解释局域波态转换和超周期呼吸子特性的方法，为人们充分认识理解局域波的多样性、关联性以及实验的可控激发提供理论依据。

非线性局域波动力学是非线性物理研究的主要方向之一。本项目集中研究了非线性局域波动力学当前研究的两个热点课题：1非线性局域波态转换；2 Superregular(超周期)呼吸子动力学。前者主要关注了多种不同局域波的转换条件和机制；后者是一类新颖的呼吸子相互作用结构，可描述一类重要的非线性调制不稳定现象，但相应的动力学演化性质仍不清晰。本课题立足于已有的光学实验事实和理论模型，对于实验上易操作的多种非线性光学可积系统，研究了复杂非线性光学系统中局域波态转换和superregular呼吸子特性及其物理机制，基于发展的达布变换和茹科夫斯基变换，构造了平面波背景上一般局域波和superregular呼吸子的精确解解析表达形式，分析了实际的高阶效应和耦合效应对局域波（特别是superregular呼吸子）性质的影响。揭示了superregular呼吸子的复杂性和多样性，系统分析了多种局域波态转换的性质规律以及稳定性。特别是，建立了superregular呼吸子和不稳定性增长率的精确对应关系，即调制不稳定性增长率与super-regular呼吸子的群速度绝对差正相关。该关系普遍适用于上述多种不同物理系统，并包含了近期的重要研究结果，从而首次揭示了superregular呼吸子描述调制不稳定性的物理机制。基于此，系统地建立了一套有效的分析和解释局域波态转换和superregular呼吸子特性的方法，充分地认识各个局域波的物理本质和相互关联，为实验上的可控激发和应用提供理论依据。基于以上研究结果，项目主持人以第一作者/通讯作者发表SCI论文12篇。培养（协助培养）博士研究生两人。