量子光学学报, 2012, 18 (1): 65, 网络出版: 2012-03-08
准二维光学系统的调制不稳定性分析
Modulational Instability in Nonlinear Optics
非线性光学 调制不稳定性 色散关系 变分法 非线性薛定谔方程 nonlinear optics modulational instability dispersion relations variational method nonlinear Schrdinger equation
摘要
本文利用时间相关的变分法对准二维的非线性薛定谔方程平面波的调制不稳定性进行了研究。在拉格朗日变分的框架下推导出相与振幅的演化方程,进而对线性化扰动方程的解进行了数值模拟,直观地展示了平面波的调制不稳定性。最后通过对能量方程有效势的分析,严格地得到了平面波解调制不稳定的判断准则。
Abstract
In this paper, using time-dependent variational method,modulational instability of the plane waves in quasi-2 dimensional nonlinear Schrdinger equation has been investigated. Based on the Lagrangian variational framework, we induce the evolution equations of phases and amplitudes, cary on the numerical simulation of the solutions for the linearization of the perturbed equations, and show modulational instability of the plane waves. Finally, by the strict analysis of the effective potential in the energy equation, we get the criterion of modulational instability for the plane waves.
贾磊磊, 孙山林, 李精华. 准二维光学系统的调制不稳定性分析[J]. 量子光学学报, 2012, 18(1): 65. JIA Lei-lei, SUN Shan-lin, LI Jing-hua. Modulational Instability in Nonlinear Optics[J]. Acta Sinica Quantum Optica, 2012, 18(1): 65.