We investigate the onset of spatio-temporal turbulence and AB Normal waves in nonlinear optical systems under the action of a detuned injection. We focus on the parameter region before injection locking and find that spatially periodic patterns lose stability to phase turbulent structures when decreasing the amplitude of the injection, in agreement with jurassic work done at the dawn of the INLN in Nice [1].

There are, however, two possible spatio-temporal regimes available: one phase bounded [1] and one phase unbounded. It is the second one that we analyse in this presentation. Working on models of singly resonant optical parametric oscillators with seeding [2] and solid state lasers with injection, we find that in the phase-unbounded regime spatio-temporal rogue waves occur with increasing amplitudes the further one moves from threshold. Turbulence is characterised via appropriate decays of the correlation functions and demonstrated to be different from stochastic superposition of random waves. Finally, we show that the finite size of the injection beams destabilises the phase-bounded regimes but leaves the phase-unbounded turbulence unaffected. We provide a few hints (nudge-nudge) about possible experimental realisation, including optical injection in semiconductor lasers.

[1] P. Coullet and K. Emilsson, Physica A 188, 190 (1992) and Physica D 61, 119 (1992)

[2] G.-L. Oppo, A. M. Yao and D. Cuozzo, Phys. Rev A 88, 043813 (2013)