We demonstrate the rotation and oscillation of the single-charged vortex (SCV) and double-charged vortex (DCV) in two-dimensional (2D) optically induced square photonic lattices under single-site excitation with appropriate self-focusing nonlinearity conditions. Numerical analysis shows that the SCV can self-trap into a localized gap vortex soliton mode that resides in the first Bragg reflection gap, for which a vortex is nested centrally in the rotating square-shaped optical envelope and four peaks always appear at four corners. Whereas DCV tends to evolve into a dynamical rotating quasi-vortex gap soliton formed in the second Bragg reflection gap, employing an out-of-phase quadrupole-like beam as a transition state to reverse the topological charge and the direction of rotation periodically. Our findings may provide insights into the experimental feasibility of observing such phenomena.

我们展示了在单点激发和适当的自聚焦非线性条件下，二维（2D）光学诱导的方形光子晶格中单电荷涡旋（SCV）和双电荷涡旋（DCV）的旋转和振荡。数值分析表明，SCV可以自陷于位于第一布拉格反射间隙中的局部间隙涡旋孤子模式，为此，涡旋居中地嵌套在旋转的方形光学包络线的中央，并且四个峰值始终出现在四个角上。而DCV趋向于演变为在第二个Bragg反射间隙中形成的动态旋转准涡旋间隙孤子，它采用异相四极杆状光束作为过渡态来周期性地反转拓扑电荷和旋转方向。