Spatial Structures & Turbulence
When we add a detuned injected field to a singly-resonant OPO (SROPO) we can generate patterns . These are formed due to the symmetry breaking induced by the injection. For high amplitudes of the injected field hexagons, rolls and honeycombs can be found:
For very low amplitudes of the injected field the input energy is not sufficient to lock the SROPO to the external laser. These unlocked regimes are typical of lasers with injected signals. Phase and then amplitude instabilities are induced and lead to optical turbulence. The phase distribution shows that we have turbulent helical waves.
Red areas in the intensity distribution correspond to abnormally high peaks and a phenomenon known as optical rogue waves. We also see another type of turbulence known as time-dependent hexagonal turbulence (TDHT). With circular boundary conditions, both types of turbulence can co-exist.
 G.-L. Oppo, A. M. Yao and D. Cuozzo, “Self-organization, pattern formation, cavity solitons, and rogue waves in singly resonant optical parametric oscillators”, Phys. Rev. A 88, 043813 (2013) [ArXiv:1309.6543]