Rotation and oscillation of gap vortex solitons in optically induced square photonic lattices with a self-focusing nonlinearity

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. (paper)