Geometrical frustration in 2D optical patterns

In the case of 2D optical patterns, frustration comes from the interplay be tween the physical constraints (light-matter interaction) and the geometric al constraints (cavity length and structure). Depending on the dynamical pa rameters, we are able to single out two distinct behaviors. For small diffu sion and close to threshold, the system is forced to fulfill the geometrica l constraints giving rise to a phase dynamics of quasicrystals. For larger diffusion, the system fragmentates into spatial domains giving rise to a co mpetition between different patterns. By means of a geometrical argument, w e show that the spatial distribution of domains is related to the symmetry imposed by the geometrical constraint and that the domain borders are disin clination defects. These defects being the nucleation centers of spatial do mains, they trigger the onset of pattern competition.