Role of symmetries in the transition to turbulence in optics

Spatiotemporal dynamics of patterns of the light beam emitted by a photorefractive oscillator has been investigated in the case of very large transverse dimensions. Time and space averagings show that the transition to turbulence as transverse dimensions are increased is a two-step process. Symmetry properties of the average patterns reveal that after the first transition from a boundary- to a bulk-dominated behavior already observed at Fresnel numbers ${\mathcal{N}}_F\simeq 20$ there is a second transition around ${\mathcal{N}}_F\simeq 100$. The regime corresponds to a complete loss of symmetry and appears here as soon as the correlation length of the patterns becomes of the same size as the period of the optical grating in the gain medium.