Microscopic theory of the collective atomic recoil laser in an optical resonator: The effects of collisions

With the help of a microscopic model we investigate the effects of collisions and atomic recoil on the behavior of absorbing atoms placed inside a bidirectional resonator and driven by an external injected field. This model complements and generalizes earlier studies of the collective atomic recoil laser and of optical bistability. According to our model, even in the presence of collisions, the resonator can support bidirectional propagation. In particular, for appropriate selection of the parameters, we predict the existence of stationary solutions such that the cavity field that copropagates with the injected signal is locked in frequency with the external source, while the counterpropagating field is frequency shifted from both, even in steady state. The early stage of growth of the counterpropagating field is accompanied by a spatial modulation (grating structure) in the density of the medium, but this modulation decays away in a time roughly of the order of the average interval between collisions.