Hexagon formation in photorefractive crystals as mirrorless coherent oscillation

The spontaneous appearance of hexagon patterns in photorefractive crystals is treated as mirrorless coherent four-wave mixing oscillation. It is shown experimentally that the system has a well-defined coupling-strength threshold and behaves as other coherent optical oscillators near the threshold. A simple relation for the angle of the hexagon sideband as a function of the distance between the end mirror and the sample is derived and verified experimentally.