We report the propagation dynamics of necklace beams in the framework of nonlinear fractional Schrödinger equation. The fractional diffraction can be partially compensated by a saturable nonlinearity and their combination leads to the quasi-stable propagation of necklace beams with integer or fractional angular momentum. The expansion of necklace can be slowed down remarkably by the decrease of Lévy index. There is an energy exchange between the neighboring pearls of necklace with fractional angular momentum, in sharp contrast to the necklace with integer or half-integer angular momentum. We, thus, put forward the first example of necklace-ring beams carrying fractional angular momentum in a fractional configuration.

我们在非线性分数薛定r方程的框架内报告了项链光束的传播动力学。分数衍射可以通过饱和非线性来部分补偿，并且它们的组合会导致具有整数或分数角动量的项链光束准稳定传播。Lévy指数的降低可以显着减缓项链的膨胀。与具有整数或半整数角动量的项链形成鲜明对比的是，相邻角动量的珍珠之间存在能量交换。因此，我们提出了以分数形态携带分数角动量的项链环梁的第一个例子。