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03/07/02 Colloquium
DR. PAVEL LUSHNIKOV
Theoretical Division, Los Alamos National Laboratory
and
Landau Institute for Theoretical Physics, Moscow, Russia
Theoretical Division, Los Alamos National Laboratory
and
Landau Institute for Theoretical Physics, Moscow, Russia
HEXAGONAL OPTICAL STRUCTURES IN PHOTOREFRACTIVE CRYSTALS
Abstract: A nonlinear theory is developed to describe the spontaneous formation 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. It is shown that on nonlinear stage of this instability development the three-wave interaction between weak sideband beams does not stabilize instability but rather leads to explosive growth of the amplitudes of beams whose transverse wave vectors form angles that are multiples of 60 degrees. As a result, sideband 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 appearance of stable hexagons in the experiment. Outside this region, nonlineartities of higher order saturate the explosive instability, and the process of hexagon generation is studied numerically. Matrix elements are obtained for the three-and four-wave interactions as functions of the distance to the feedback mirror, and an amplitude equation for the time evolution of the sideband wave amplitudes is derived that describes the hexagon formation. This set of amplitude equations is essentially a Landau expansion in the amplitudes of growing linear modes. A special case when two minima of instability curve are close to each other, which is analog of phase transition with two order parameters, is also discussed and investigated numerically. A comparison is made with experimental results for the photorefractive crystals KNb03 and BaTi03.