Drift instability and locking behavior of optical patterns

In a nonlinear optical system with single-mirror feedback, several experiments displayed stationary hexagonal patterns. A linear stability analysis, however, predicts drifting patterns even for an arbitrarily small misalignment of the mirror. Studying the situation of small tilt angles we observe that the patterns remain stationary up to a critical value αc of the angle (locking). Above this threshold they discontinuously start to drift with a velocity that depends linearly on the tilt angle. Both features are reproduced by numerical simulations with a Gaussian input beam. The existence of the locking region is traced back to the boundary conditions imposed by the spatially limited input beam.