Secondary bifurcations of hexagonal patterns in a nonlinear optical system: alkali metal vapor in a single-mirror arrangement

Secondary bifurcations of hexagonal patterns are analyzed in a model of a single-mirror arrangement with an alkali metal vapor as
the nonlinear medium. A stability analysis of the hexagonal structures is performed numerically. Depending on the wavenumber
of the hexagons different instabilities are predicted. Some of them take place at a finite wavenumber and result in the formation
of structures with twelve spatial modes. These structures are compared with those observed experimentally.