折射率调制光学介质中高拓扑荷耗散涡旋孤子研究

Optical vortex is a particular light field that possess helical phase wavefront and orbital angular momentum. Significantly, due to the unique nature of the topological charge (denoted by the letter m) , which is integer and related to orbital angular momentum, vortex is expected to lead to important potential application in many areas including optical data storage and processing, optical trapping technology, and so on. However, it is also because of the topological charge (angular momentum), the vortex solitons are known to experience the symmetry-breaking azimuthal instability, and they decay into several fundamental solitons in all conservative nonlinear media with a local response. Based on nonlinear effects of the medium material, this project is focusing on existence and propagation dynamics of vortex supported by some interesting refractive index modulated optical media, such as nonlocal dissipative materials, PT symmetric optical media, hollow-core optical fibers filled with a cold atomic gas, defocusing media with spatially inhomogeneous nonlinearity, and so on. By using the combination of analytical (the similarity reduced method) and numerical (discrete-step fast Fourier transform algorithm) methods, the influence of topological charge, propagation constant, energy flow and modulation depth to existence and stability of dissipative vortex solitons or dissipative vortex bullets are analytically and numerically investigated based on the variable-coefficient general nonlinear Schrödinger equation. These results provide theoretical foundation for parameter modulation and dynamical control of optical pulse in the refractive index modulated media, and have potential applications for the vortex solitons of matter and plasma in the dynamics of various physical systems.

非线性光学中的涡旋是具有螺旋型波前和轨道角动量的特殊光场。与涡旋拓扑荷相关的轨道角动量以及拓扑荷自身整数的特性，使其具有十分重要的潜在应用价值。然而，也正是由于拓扑荷引入的角动量带来了涡旋本身对称破缺的不稳定性,普通局域介质很难消除。本项目基于光学耗散介质非线性响应的可控性（折射率调制）及孤子在介质中的传输模型，如非局域耗散介质、PT对称介质、中空充冷原子气体光纤、折射率横向调制自散焦介质等，在前期研究基础上，研究耗散涡旋孤子的存在及稳定性。主要围绕支持光涡旋孤子的变系数非线性薛定谔方程展开。利用解析和数值结合的方法，深入探索不同传输模型中的涡旋孤子模式的解析表达式，以及拓扑荷数m、传播常数、光束能流、非线性调制深度对涡旋孤子存在及传输稳定性的影响，为在不同参数的现实光学装置中实验去实现不同拓扑荷的涡流孤子提供有效的理论依据，并对其它物理领域涡旋孤子研究具有潜在的应用价值。

本项目旨在实现折射率调制光学介质中高拓扑荷涡旋孤子—耗散孤子、矢量孤子和多极孤子的稳定输出和参量调控。主要运用非线性理论构建理论模型，开拓解析和数值方法，分析新型涡旋孤子的形成机理，揭示其动态演化规律。利用解析和数值结合的方法，深入探索不同传输模型中的涡旋孤子模式的表达式，以及拓扑荷数、传播常数、光束能流、非线性调制深度对涡旋孤子存在及传输稳定性的影响。通过改变可调谐参数来调控新型涡旋孤子的模式、局域性、涡核大小、强度、持续时间等输出特性，并且操控涡旋孤子快速激发、维持、湮灭。根据线性稳定性分析得到新型涡旋孤子的稳定区域和抗干扰能力。在数值模拟时，采用边界吸收模拟能量损耗、增加微扰模拟信号白噪声、减小运算步长等手段尽量靠近真实实验环境。做到理论分析、数值计算和仿真模拟并重。为在不同参数的现实光学装置中实验去实现不同拓扑荷的涡旋孤子提供有效的理论依据，并对其它物理领域涡旋孤子研究具有潜在的应用价值。