Empirical bifurcation analysis of optical pattern formation.
The experimental characterization of pattern forming bifurcations is difficult, since the unstable solutions are generally not accessible in experiments. In nonlinear optics, a novel control scheme allows one to select and stabilize generic patterns and thus to track these solutions in parameter space. This Fourier space scheme is applied to a single-feedback system and the amplitudes of roll, square and hexagon patterns are determined experimentally. Even though the bifurcation is imperfect, the coefficients of a prototype amplitude equation are recovered. The coefficients show satisfactory agreement with theory and with numerical simulations, which are performed for comparison. The simulations also clarify the origin of the imperfect bifurcation in the experiment: boundaries and speckles appear to have an unexpected strong influence.
Institute of Applied Physics, Darmstadt University of Technology, Hochschulstrasse 6, 64289 Darmstadt, Germany. ralph.neubecker@physik.tu-darmstadt.de
Ralph
R
Neubecker
E
E
Benkler