Spatial synchronization of regular optical patterns.

We investigate an extended, nonlinear optical experiment, exhibiting the spontaneous formation of hexagonal patterns out of a stationary bifurcation. The system is exposed to a two-dimensional spatially periodic forcing, namely, static hexagonal patterns, under variation of their spatial periodicity. Parameters are the strength of the forcing and the distance to pattern forming threshold. The system response is quantitatively characterized with different methods. We observe several locking regimes, where the system is entrained by the forcing. Most of the locking regimes can be related to resonances between the different critical wave numbers and the forcing wave number or its spatial harmonics. One particular locking appears to result from two of these simple resonances in a kind of generalized order m:n synchronization. The width of the locking regimes increases with forcing strength, apparently representing a spatial analog of Arnold tongues.