Stability of discrete vortex solitons in linear scaled-space square lattices

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.