PATTERN-FORMATION IN A PASSIVE KERR CAVITY

Analytic and numerical investigations of a cavity containing a Kerr me dium are reported. The mean field equation with plane-wave excitation and diffraction is assumed. Stable hexagons are dominant close to thre shold for a self-focusing medium. Bistable switching frustrates patter n formation for a self-defocusing medium. Under appropriate parametric conditions that we identify, there is coexistence of a homogeneous st ationary solution, of a hexagonal pattern solution and of a large (in principle infinite) number of localized structure solutions which conn ect the homogeneous and hexagonal state. Further above threshold, the hexagons show defects, and then break up with apparent turbulence. For Gaussian beam excitation, the different symmetry leads to polygon for mation for narrow beams, but quasihexagonal structures appear for broa der beams.