Beyond the pulse-area theorem: Role of the absorption and the dispersion in the propagation of weak ultrashort resonant pulses

We present here some fundamental but yet underlooked features of the propagation of weak ultrashort pulses (with Δdτ << 1, where Δd is the Doppler width and τ is the pulse duration) in resonant atomic media. We show that the pulse area behaviour and the pulse spectrum at resonance are governed by the usual optical depth (α0L, where α0 is the absorption coefficient at resonance and L the length of the medium), whereas the pertinent parameter that governs the severity of the dispersion effects and the distortion of the pulse is the dispersion parameter edisp = (α0L)Δdτ that we introduce. Paradoxical effect such as distortionless propagation (e.g. edisp << 1) with vanishing pulse area (when α0L >> 1) can then explained within this formalism.