Abstract
A theory of pulse transmission is presented in which the medium through which the pulse propagates is characterized by an inhomogeneous distribution that is either an atomic frequency comb (AFC) or a medium of randomly spaced frequency spikes (RSM). For an AFC, we obtain analytic expressions for the transmitted field amplitude, which is composed of the (partially) transmitted incident pulse, plus a train of equally spaced echoes. For RSM, we derive expressions for the average transmitted field amplitude and field intensity. In the limit that the spike width is much less than the spike separation, normally encountered with AFC, the overall atom-field dynamics is dominated by dispersion---absorption plays a negligible role. The importance of the average group time delay of the pulse is discussed.
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