分数衍射非线性PT对称波导中的光学孤子

Optical Soliton in PT-symmetric Nonlinear Waveguide with Fractional Diffraction

基于非线性分数薛定谔方程(NLFSE)研究分数衍射非线性PT对称波导中的光学模式以及它们的稳定性。首先运用平方算符方法给出具有分数衍射效应的非线性PT对称波导中的光学模式。在此基础上,通过线性稳定性分析方法研究分数衍射效应和非厄米性对这些光学模式稳定性的影响,同时应用分步傅里叶方法对线性稳定和不稳定的光学模式的动力学进行数值模拟。结果表明,在分数衍射效应非线性PT对称系统中存在基态、第一、第二、第三激发态光学模式。随着势函数虚部调制深度的增加,基态和第一激发态是线性稳定的,而第二和第三激发态模式由线性稳定转为线性不稳定。

Based on the nonlinear fractional Schrodinger equation(NLFSE), the optical modes in nonlinear PT symmetric waveguides and their stability are studied. Firstly, the optical modes in PT symmetric waveguides with fractional diffraction effects are given by using the square operator method. On this basis, the effects of fractional diffraction effect and nonHermitian effect on the stability of these optical modes are studied by linear stability analysis method, and the dynamics of linear stable and unstable optical modes are numerically simulated by using the stepwise Fourier method. The results show that there are ground states, first, second and third excited state optical modes in the fractional diffraction effect nonlinear PT symmetric system.