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We study the collective emission of a beam of atomic dipoles into an opticalcavity. Our focus lies on the effect of a finite detuning between the atomictransition frequency and the cavity resonance frequency. By developing atheoretical description of the coupled atom-cavity dynamics we analyze thestationary atomic configurations including a superradiant phase where the atomsundergo continuous monochromatic collective emission. In addition, we derive ananalytical formula for the cavity pulling coefficient which characterizes thedisplacement of the emission frequency towards the cavity frequency. We findthat the pulling is small if the cavity linewidth is much larger than thecollective linewidth of the atomic beam. This regime is desired for buildingstable lasers because the emission frequency is robust against cavity lengthfluctuations. Furthermore, we investigate the stability of the atomic phasesand compare our theoretical predictions with numerical results. Remarkably, wealso find polychromatic emission regimes, where the spectrum has severalfrequency components while the light output is still superradiant.

Collective emission of an atomic beam into an off-resonant cavity mode