Abstract

Spontaneous pattern formation has been observed experimentally when two counterpropagating laser beams interact in sodium vapor. We report investigations into the nature, stability, and range of patterns in such systems. The model is an anti-reflected slab of Kerr medium, irradiated from each side by smooth, constant input fields-plane waves or Gaussian beams. Two transverse-dimensional numerical simulations have produced a rich variety of patterns. On the self-focusing side, hexagons are preferred and we find that these patterns persist to about 15% below the linear threshold intensity both with and without the wavelength-scale index grating. These results are in general agreement with our analysis and with hexagon dynamics in other situations such as fluid convection. A new phenomenon not present in typical hexagon structures is the occurrence of a Hopf bifurcation, through which the hexagon pattern destabilizes. On the self-defocusing side, squares are the favored pattern. Simulations including the index grating indicate that above threshold they are stable while below threshold they are unstable and are replaced with the homogeneous plane-wave state.

© 1992 Optical Society of America