Exciton polariton kinematic interaction in crystalline organic microcavities

The kinematic interaction between cavity polaritons in a crystalline organic microcavity is examined, and a general analytical expression for the scattering amplitude for two cavity polaritons with zero total wave vector is derived. It is shown that if two incoming polaritons can scatter into excitonlike states, the kinematic interaction is a nonperturbative process. In particular, the scattering amplitude has a pole, which corresponds to the scattering of the incoming polaritons to a biexciton state. If the scattering into the excitonlike part of the spectrum is forbidden, then an effective potential describing a polariton-polariton kinematic interaction as a perturbation can be introduced. This potential is repulsive and its scale is given by the exciton bandwidth. Also, the scattering of cavity polaritons by impurities is studied.