Twelvefold quasiperiodic patterns in a nonlinear optical system with continuous rotational symmetry

Twelvefold quasiperiodic structures are observed in an autonomous optical p attern forming system with continuous rotational symmetry. These quasipatte rns arise from a primary hexagonal structure. In dependence on the experime ntal parameters the bifurcation can be sub- or supercritical. In the superc ritical case, the transition is mediated by a new kind of patterns with dif ferent amplitudes in its fundamental modes. It is proven by an optical Four ier filtering technique that the observed quasipatterns can exist only in t he presence of harmonics of the fundamental unstable modes. [S0031-9007(99) 09326-6].