Self-induced vortex and antivortex states in dissipatively coupled laser arrays

The two-dimensional classical XY model consists of a lattice of interacting spins that rotate in a plane. Recently, it has been realized that dissipative coupling in laser arrays allows for optical simulation of the classical XY model, where the phase of a laser plays the role of a classical spin degree of freedom, and the Lyapunov function governing such a dissipative system emulates the XY Hamiltonian. Here, we show that vortex and antivortex phase patterns can from spontaneously in laser arrays, in analogy with the topological defects of the XY model. The stability of such vortex/antivortex states depends critically on the relative lifetimes of the optical resonance and the fluorescence processes in the lasers. These results provide insight in investigating topological defects in laser systems, while it introduces a new approach for generating optical vortex beams without a need for external spatial phase modulation.