Propagation, cavity, and Doppler-broadening effects in the collective atomic recoil laser

Using a completely semiclassical approach we extend a previous theory of the collective atomic recoil laser to include propagation effects with and without a ring cavity, and to take into account the effects of Doppler broadening. For cold atoms, we determine a mean-field condition under which propagation effects are negligible, and find different dynamical regimes that we classify as ``good'' and ``bad'' cavity limits. We obtain the results of a previous single-mode theory only in the good cavity limit. In the bad cavity limit or in free space collective superradiant behavior dominates. For warm beams, where Doppler-broadening effects are important, a noncollective Raman gain mechanism dominates in general, as recently observed experimentally. The effects of particle trapping in the ponderomotive potential and radiation pressure have been described.