非均匀非线性波导中涡旋光孤子的相互作用传播

Interaction Propagation of Optical Vortex Solitons in Inhomogeneous Nonlinear Waveguides

基于具有非线性自聚焦(自散焦)效应的光波传输模型,经无量纲化后得到一个(2+1)维变系数非线性薛定谔方程。引进相似变换,将该方程变换为标准的(2+1)维非线性薛定谔方程;在此基础上通过数值模拟分别研究了涡核间距和初始相位差对2个涡旋光孤子、4个涡旋光孤子、5个涡旋光孤子和6个涡旋光孤子相互作用的影响。对结果进行分析得出新的结论:1)涡旋光孤子在传播时保持形状不变,具有自相似特性;2)多个涡旋孤子沿着z轴方向传播时,会发生相互作用,只有当涡核之间的距离小于某持定值时,相互作用明显,当涡旋之间存在相位差时,涡旋孤子之间在传播过程中会发生能量转移,有的部分被加强,有的部分被减弱。

Based on an optical transmission model with nonlinear self-focusing （self-defocusing） effects, a （2 ＋1）- dimensional nonlinear SchrSdinger equation is obtained under nondimensionalization. The （2 ＋ 1 ）-dimensional variable coefficient nonlinear Schr6dinger equation is transformed into the standard （ 2 ＋ 1）-dimensional nonlinear Schr6dinger equation by using similarity transformation. Interactions between two optical vortex solitons, among four, five and six optical vortex solitons in the waveguides are discussed with different vortex-core spacing and initial phase difference, respectively, by numerical simulation. Some new conclusions are obtained through analyzing the above results. 1） The shape of vortex soliton with selfsimilar charcteristics sustain during the propagation along z- axis. 2） Multiple vortex solitons interact with each other during the propagation along z-axis especially when the distance within them is smaller than a definite value, meanwhile the energy flow among them. Some are strengthened, and some are weakened.