MIDIT OFD CATS Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and Technical University of Denmark Building 128 Department of Chemistry Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark
by Pavel Lushnikov
L. D. Landau Inistitute for Theoretical Physics
Thursday November 26, 1998, 14.00 h
at MIDIT, IMM Building 305, room 027
Abstract: A nonlinear theory is developed to describe the generation of hexagonal optical structures in a photorefractive medium with a feedback mirror. The counterpropagation of light beams in photorefractive crystal results in transverse instability against the excitation of weak sideband waves at small angles. The nonlinear three-wave interaction of these weak waves leads to the explosive amplitude growth of the waves under the angles ±pi/3 between each other. It is shown here that as this instability evolves to its nonlinear stage, the three- wave interaction between weak sideband beams does not stabilize it, but rather leads to explosive growth of the amplitudes of beams whose transverse wave vectors form angles that are multiples of pi/3. As a result, sidebands beams at these angles are found to be correlated. A range of parameters is found in which four-wave interactions saturate the explosive instability, which explains the appearance of stable hexagons in the experiment. Outside this region, nonlinearities of higher order saturate the explosive instability, and the process of hexagon generation must be studied numerically. Matrix elements are obtained for the three- and four-wave interactions as functions of the distance to the feedback mirror, and an equation for the time evolution of the sideband wave amplitudes is derived that describes the hexagon generation. A comparison is made with experimental results for the photorefractive crystals KNbO3 and BaTiO3.