Quasicrystalline and Dynamic Planforms in Nonlinear Optics

A variety of stationary and wave patterns that show a complicated spatial structure but are ordered in the Fourier space can be constructed by considering interaction of noncollinear modes near a symmetry breaking bifurcation point. The planform selection is particularly rich in the presence of resonant (phase-dependent) interactions among degenerate modes. We consider the problem of pattern selection for two optical systems: a cavity with two nonlinear elements and a cavity with a rotated optical field. Complex quasicrystalline patterns sustained by resonant interactions arise under conditions when wave and Turing modes are excited simultaneously. The excited patterns may be saturated even by the action of quadratic (three-wave) interactions only, and may exhibit periodic amplitude modulation on a slow time scale.