Vortex ring beams in nonlinear $\mathcal{PT}$-symmetric systems

In this paper, we investigate a two-dimensional photonic array featuring a circular shape and an alternating gain and loss pattern. Our analysis revolves around determining the presence and resilience of optical ring modes with varying vorticity values. This investigation is conducted with respect to both the array's length and the strength of the non-Hermitian parameter. For larger values of array's length, we observe a reduction in the stability domain as the non-Hermitian parameter increases. Interestingly, upon an increasing of vorticity of the optical modes full stability windows emerge for shorter lattice sizes regime.