Quasicrystalline and dynamic planforms in nonlinear optics

A variety of stationary and wave patterns that show a complicated spatial s tructure but are ordered in the Fourier space can be constructed by conside ring interaction of non-collinear modes near a symmetry breaking bifurcatio n point. The planform selection is particularly rich in the presence of res onant (phase-dependent) interactions among degenerate modes. We consider th e problem of pattern selection for two optical systems: a cavity with two n onlinear elements and a cavity with a rotated optical field. Complex quasic rystalline patterns sustained by resonant interactions arise under conditio ns when wave and Turing modes are excited simultaneously. The excited patte rns may be saturated even by the action of quadratic (three-wave) interacti ons only, and may exhibit periodic amplitude modulation on a slow time scal e. (C) 1999 Elsevier Science Ltd. All rights reserved.