Distortion of a short quasi-monochromatic signal in a resonantly absorbing medium

Propagation of a short quasi-monochromatic electromagnetic (light or radio) signal (wave packet) is considered. The carrier frequency of the signal is close to the frequency of the absorption spectral line (or group of lines) of a medium, and the spectrum width is large relative to the width of this spectral line (or group of lines). Analytic formulas for the temporal dependence of the signal are derived and numerically confirmed for paths of various lengths. It is shown that the signal is substantially distorted long before it noticeably decays owing to absorption. The signal's temporal dependence turns out to be rather universal with respect to the form factor of the spectral line, the optical thickness of the substance layer, and the initial temporal dependence of the signal.[PUBLICATION ABSTRACT]