Propagation effects in a collective atomic recoil laser

We present a theoretical investigation of propagation effects in a collective atomic recoil laser (CARL) operating in the FEL limit. We consider the cases where the system evolves while in free space and while enclosed in a ring cavity. in the case where no cavity is present, we show that the scattered radiation consists of soliton-like superfluorescent pulses. in the case of a 'good' cavity we arrive analytically at a condition to neglect propagation effects. This condition implies that in order to use the so-called mean field approximation, the condition (Lambda root L)/l(c)(3/2)-->0, T-->0 must be satisfied with (Tl-c)/(Lambda root L)(2/3) finite where I-c is the cooperation length of the system, T is the transmission coefficient of the mirrors. L and ii are the sample length and cavity length respectively. We confirm the validity of this condition using a numerical analysis and provide a simple physical interpretation. In the mean field limit, we show that if the cavity Linewidth is greater than the spectral width of the pulse emitted by the sample, the emission remains superfluorescent and is not sensitive to the presence of the cavity. We also show that in the opposite case the emission is sensitive to the cavity parameters and no longer superfluorescent.