Fusion of necklace-ring patterns into vortex and fundamental solitons in dissipative media

We demonstrate that necklace-shaped arrays of localized spatial beams can merge into stable fundamental or vortex solitons in a generic model of laser cavities, based on the two-dimensional complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The outcome of the fusion is controlled by the number of beads in the initial necklace, 2N, and its topological charge, M. We predict and confirm by systematic simulations that the vorticity of the emerging soliton is the absolute value of difference of N and M. Threshold characteristics of the fusion are found and explained too. If the initial radius of the array (R0) is too large, it simply keeps the necklace shape (if R0 is somewhat smaller, the necklace features a partial fusion), while, if R0 is too small, the array disappears.