Single- and double-vortex vector solitons in self-focusing nonlinear media.

We study two-component spatial optical solitons carrying an angular momentum and propagating in a self-focusing saturable nonlinear medium. When one of the components is small, such vector solitons can be viewed as a self-trapped vortex beam that guides either the fundamental or first-order guided mode, and they are classified as single- and double-vortex vector solitons. For such composite vortex beams, we demonstrate that a large-amplitude guided mode can stabilize the ringlike vortex beam which usually decays due to azimuthal modulational instability. We identify different types of these vector vortex solitons and demonstrate both vortex bistability and mutual stabilization effect.