On the relationship between the delay time of a narrowband signal |in a dispersing medium and its attenuation

Abstract

The 1D problem of propagation of a narrowband signal in a homogeneous dispersing medium is considered. It is shown that there is a direct and immediate relationship between the additional (to vacuum) delay time of the signal and its attenuation during propagation in an absorbing medium. It is shown that with an additional delay time of more than several tens of coherence times of uniformly broadened spectral lines of the medium, the signal weakens by hundreds of decibels and therefore practically disappears. On the other hand, when the delay of the signal is less than the coherence time of the medium, its absorption is small. A similar situation arises in an amplifying (thermodynamically nonequilibrium) environment – of course, with the replacement of signal attenuation with its amplification and the replacement of signal delay with its advance. As an example, the propagation of a narrowband signal, the carrier frequency of which is outside the gain band of the space maser, is considered. It is shown that in this case, due to the long lifetime of the excited states of interstellar gas molecules, the signal propagates at superluminal velocity with practically no change in amplitude, which is very rare in problems of this type.