论文标题
通过衍射和非线性管理在二维非线性非线性schrödinger方程中稳定轴对称通风梁
Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schrödinger Equations
论文作者
论文摘要
在分数schrödinger方程的框架中研究了二维（2D）环形仪梁的传播动力学，其中包括可饱和或立方体的自我焦点或偏置非线性的非线性和lévyIndex（（li）分数的别名（分数）的别名（分数），以$ 1 \leqα\ leq leq 2 $。该模型适用于模拟分数衍射的光腔链中的光传播。通过使传播距离的衍射和/或非线性系数周期函数（$ζ$）包括在内。也考虑使用非线性系数衰减为$ 1/ζ$的管理格式。与2D Kerr介质中，环形对称性保持轴向对称性相比，这些管理方案保持环形仪梁的稳定繁殖，它们保持其轴向对称性。在所有值的$α<2 $的情况下，在自我关注的立方术语的存在下，超临界崩溃所驱动的不稳定也通过管理方式消除了。
The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schrödinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and Lévy index ((LI) alias for the fractionality) taking values $1\leqα\leq 2$. The model applies to light propagation in a chain of optical cavities emulating fractional diffraction. Management is included by making the diffraction and/or nonlinearity coefficients periodic functions of the propagation distance, $ζ$. The management format with the nonlinearity coefficient decaying as $1/ζ$ is considered, too. These management schemes maintain stable propagation of the ring-Airy beams, which maintain their axial symmetry, in contrast to the symmetry-breaking splitting instability of ring-shaped patterns in 2D Kerr media. The instability driven by supercritical collapse at all values $α< 2$ in the presence of the self-focusing cubic term is eliminated, too, by the means of management.
