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We report the existence and stability of 1-charge discrete vortex solitons in linear scaled-space square lattices with photorefractive self-focusing nonlinearity. By scaling the square lattice along the edge and diagonal, we obtained rectangular and diamond lattices. In both settings, it is shown that the vortices can be stable in a moderate power region, and the vortices with high power are unstable, suffering from oscillatory instabilities. The structure of the rectangular potential strongly affects the profile of the vortex solitons, leading to distinct intensity asymmetry, phase dislocation, and exponential instability in the low power region. Correspondingly, the vortex profile could be well maintained in diamond lattices. Fascinating, even the low power unstable vortices suffered from both oscillatory and exponential instability in diamond lattices, they have a much weaker instability than counterparts in rectangular lattices. [ABSTRACT FROM AUTHOR]

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. • The Double-charge vortex and the quadrupole beam will undergo periodic conversion. • Double-charge vortex occurs a flipping of topological charge. • Periodic oscillations can be obtained after changing the initial orientation. • Oscillation rate becomes slower when the angle approaches the crystalline c -axis. • Provide a possibility for a nontrivial type of all-optical switching. [ABSTRACT FROM AUTHOR]