HEXAGONAL OPTICAL STRUCTURES IN PHOTOREFRACTIVE CRYSTALS WITH A FEEDBACK MIRROR

A nonlinear theory is presented for the formation of hexagonal optical structures in a photorefractive medium equipped with a feedback mirro r. Oppositely directed beams in photorefractive crystals are unstable against the excitation of sideband waves. It is shown here that as thi s instability evolves to its nonlinear stage, the three-wave interacti on 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, sideband beams at these angles are found to be correlated. A range of parameter s is found in which four-wave interactions saturate the explosive inst ability, which explains the appearance of stable hexagons in the exper iment. Outside this region, nonlinearities of higher order saturate th e explosive instability, and the process of hexagon generation must be studied numerically. Matrix elements are obtained for the three-and f our-wave interactions as functions of the distance to the feedback mir ror, and an equation for the time evolution of the sideband wave ampli tudes is derived that describes the hexagon generation. A comparison i s made with experimental results for the photorefractive crystals KNbO 3 and BaTiO3. (C) 1998 American Institute of Physics. [S1063-7761(98)0 2903-5].