Spatiotemporal Structures from Four-Wave Mixing and Phase Modulation

We analyse a non-inverted two-level system contained in a resonant cavity with spherical mirrors, and driven by an external field matched to a mode of the resonator. In an appropriate limit (Kerr medium limit) we derive from the complete model a cubic parametric model which allows for extensive analytical calculations. We consider various cases of three-mode interaction and find coexisting stable stationary states, dynamical structures, period doubling and chaos, phase singularities, periodic alternance.