非线性亥姆霍兹孤子守恒量及孤子特性研究  

Study of Conserved Quantities and Characteristics of Nonlinear Helmholtz Solitons

作　　者：张冰志[1] 陈志峰[1] 邓荣标[1] 黄峰[1] 郑艳华[1] 

机构地区：[1]广州大学物理与电子工程学院,广东广州510006

出　　处：《光学学报》2015年第A01期303-307,共5页Acta Optica Sinica

基　　金：国家自然科学基金（11404071,11204044）

摘　　要：理论上详细推导了非线性亥姆霍兹方程的三个守恒量，其分别与傍轴近似下非线性薛定谔方程的三个守恒量（功率，哈密顿量，动量）对应。形式上，当忽略非线性亥姆霍兹方程中的非傍轴项时，其守恒量可自洽的简化到傍轴模型下的守恒量。另外，通过研究这些守恒量随着空间光孤子参数改变而变化特性，详细阐述了非傍轴非线性亥姆霍兹模型与傍轴非线性薛定谔模型的差异。特别发现非傍轴模型的引入可以有效地抑制傍轴模型下空间光孤子的哈密顿量与动量随着横向速度增大而发散的结果。Three conserved quantities of non-paraxial nonlinear Helmholtz equation are driven in theory, which are corresponding to the conserved quantities of nonlinear SchSdinger equation （power, Hamiltonian, momentum）. Formally, these conserved quantities can be simplified as that of the paraxial model when the non-paraxial term is ignored. In addition, the difference between the non-paraxial nonlinear Helmholtz model and the paraxial nonlinear Helmholtz model by analyzing the variation characteristics of the conserved quantities with the change of parameters of optical spatial solitons is studied. Especially, it is found that the divergence results of the Hamiltonian and momentum of optical spatial solitons can be suppressed in the non-paraxial model when transverse speed increases in paraxial model.

关 键 词：非线性光学 守恒量 光孤子 非傍轴 亥姆霍兹方程 

分 类 号：O437[机械工程—光学工程]