空气中紫外波长局域涡旋光孤子的解及其稳定性

Solutions and Stability of Ultraviolet Localized Optical Vortex Solitons in Air

根据紫外波长光束在空气中传输时的非线性效应得到包含氧分子三光子电离等非线性效应的薛定谔方程。由该非线性薛定谔方程出发,研究了紫外波长光束在空气中传输时局域涡旋光孤子的形成。将涡旋孤子的形成和粒子在势阱中的运动联系起来,讨论了光束在空气中形成局域涡旋光孤子的初始条件。数值求解了柱坐标下的涡旋孤子解,随着初始幅值的变化,方程出现单环、双环等孤子解;分析了孤子解光强分布随着传播常数的变化情况,并得出光束尺度和脉冲能量对应初始幅值的变化关系。同时分析了孤子解的扰动稳定性,验证了Skarka所推导的一般性判据。

From the nonlinear effects of ultraviolet beam in air,the beam propagation equation which includes several nonlinear effects,such as the three-photon ionization of oxygen,is obtained.From this nonlinear Schrdinger equation,the generation of localized optical vortex soliton（LOVS） for ultraviolet light in air is investigated.The LOVS dynamics is homologous to the movement of particles in a potential well.The initial conditions for the generation of LOVS in air are analyzed.Numerical simulations show the LOVS solutions in polar coordinates,and in the solutions of equation many rings appear with the increase of initial amplitude.Finally,the light-intensity distribution′s variation as propagation constant is confirmed numerically.Numerical simulations also show the relation of beam size,power and initial amplitude.The stability of solution is checked by the stability criterion of Skarka.