Instability of multiple optical vortices in the media with quintic nonlinearity

In this short note, we perform theoretical analysis and numerical studies of the vortices in nonlinear optical media with spatially inhomogeneous quintic nonlinearity. We focus on the modulated profiles mainly composed of Whittaker and Jacobian elliptic functions, which both be constructed by means of similarity transformation. We give a further discussion, on the bases of linear static analysis and direct simulations. Studies have shown that the exact vortices are stable, while the numerically constructed ones are stable in some range of propagation constant. The unstable vortices are gradually decay into some splinters, the number of which relates to the perturbation index of the instability state with highest growth rate.