Twelvefold Quasiperiodic Patterns in a Nonlinear Optical System with Continuous Rotational Symmetry

Abstract

Twelvefold quasiperiodic structures are observed in an autonomous optical pattern forming system with continuous rotational symmetry. These quasipatterns arise from a primary hexagonal structure. In dependence on the experimental parameters the bifurcation can be sub- or supercritical. In the supercritical case, the transition is mediated by a new kind of patterns with different amplitudes in its fundamental modes. It is proven by an optical Fourier filtering technique that the observed quasipatterns can exist only in the presence of harmonics of the fundamental unstable modes.