Spatial transport phase transitions in systems with high polariton densities

The behaviour of high intense laser beams in matter is examined with respect to a possible pattern formation. The latter is thought to be a collective phenomenon. We establish a microscopic transport theory for anharmonically interacting polaritons, which is valid even for regions far from thermal equilibrium. It is shown that then there must necessarily be phase transitions in the space distribution of polaritons as a function of the laser power. Numerical calculations are performed for an ionic crystal. They yield two critical intensitiesI _c1 andI _c2, where qualitative alterations in the spatial distribution are to be expected. We ascribe the transport phase transitions atI _c1 andI _c2 to the formation of large and small scale filaments respectively. The phenomenon appears to be very similar to the Bénard problem.