Periodic interconversion evolution of a double-charge discrete vortex and out-of-phase quadrupole solitons in Lieb photonic lattices with self-focusing saturable nonlinearity media

Abstract We demonstrate the periodic interconversion evolution of the double-charge vortex (DCV) and out-of-phase (OOP) quadruple solitons in two-dimensional (2D) optically induced Lieb photonic lattices by single-site excitation under appropriate self-focusing nonlinearity conditions. The numerical results show that the DCV evolves into a rotating quasi-vortex soliton, utilizing an OOP quadrupole-like beam as a transition state to reverse the topological charge and the direction of rotation periodically; The OOP quadrupole beam whose incident orientation along the crystalline c-axis or the diagonal axes of the lattices self-traps into a stable localized mode nearly invariant during propagation, whose Fourier spectrum reveals that they are localized states close to the high-symmetry points X and M of Brillouin Zone. By imposing an initial orientation slightly twisted relative to the lattices’ crystalline c-axis, the localized quadruple state tends to evolve into a dynamical rotating DCV and undergoes periodic charge-flipping when the direction of rotation is reversed. Additionally, analysis of different twisting angle shows that the oscillation period will become longer when the initial orientation approaches the lattices’ crystalline c-axis. Our findings could give some quantitative insight into the experimental feasibility of observing such phenomena.