Bifurcations of hexagonal patterns stabilized and selected with spatial perturbations in a wide-aperture laser

Starting from a simple hexagonal pattern stabilized and selected with the spatial perturbation method in a wide-aperture CO(2) laser, we observed the transition to a dodecagonal pattern via the doubling of the azimuthal spatial frequency by changing the cavity detuning. Further increasing the detuning induces more complicated patterns. such as double hexagons. The symmetry-breaking effect on the stabilized and selected patterns, introduced by a slight misalignment of a laser mirror, is observed. We also find that the complicated temporal instabilities of the unperturbed patterns are eliminated by the spatial perturbations. Numerical simulations, based on the Fox and Li theory for the held propagation inside the cavity, are able to reproduce the patterns with the simplest symmetry.