We investigate spatio-temporal dynamics of two-wave mixing processes in a photorefractive medium, considering two different configurations. In the counterpropagating geometry, above a primary instability threshold we observe the onset of spontaneous spatial modulation of the Gaussian beam profile due to a static external electric field in the case of a self-focusing non-linearity. Running transverse waves in the optical near field and wandering spots in the far field occur when one transverse dimension is taken into account. Modulational inhomogeneities in the refractive index grating along the transverse direction result in beam focusing effects. In the copropagating wave mixing geometry within a unidirectional ring resonator we find four different mode-like structures with either symmetric or antisymmetric field distributions. Regular and irregular spatio-temporal oscillations arise for certain values of the resonator detuning. The temporal evolution of the chaotic mode oscillation is represented by a heteroclinic tangency and the spatio-temporal oscillation is characterized by crisis-induced intermittency.
