Self-organization and Fourier selection of optical patterns in a nonlinearphotorefractive feedback system - art. no. 063809

The formation of patterns, in two transverse dimensions in photorefractive two-wave mixing with a single feedback mirror is investigated theoretically . We perform numerical simulations of the full (3 + 1)-dimensional nonlinea r model equations, displaying the breakup of the unstable annulus of active modes into hexagonal spots. Analytically we derive amplitude equations of the Landau type for patterns with rhombic- and hexagonal-model interaction and discuss the stability and coexistence of transverse planforms, in the p hotorefractive feedback system. A strong renormalization for the hexagon am plitude is determined, and its consequences for pattern formation using Lan dau formalism are discussed. In particular, the stability of regular substr uctures of a dodecagonal spot arrangement is investigated and square-hexago n competition is predicted. We use an invasive Fourier-filtering technique for the selection of unstable patterns, such as stripes and squares. The lo ngitudinal propagation of the critical and higher-order modes of the self-o rganized structures and the impact of a Fourier filter on the mode propagat ion within a nonlinear bulk photorefractive medium is studies in detail.