  We present a spatio-temporal mechanism for producing 2D optical rogue waves
in the presence of a turbulent state with creation, interaction and
annihilation of optical vortices. Spatially periodic structures with bound
phase lose stability to phase unbound turbulent states in complex Ginzburg-
Landau and Swift-Hohenberg models with external driving. When the pumping is
high and the external driving is low, synchronized oscillations are unstable
and lead to spatio-temporal turbulence with high excursions in amplitude.
Nonlinear amplification leads to rogue waves close to turbulent optical
vortices, where the amplitude tends to zero, and to probability distribution
functions with long tails typical of extreme optical events.
