О ВЛИЯНИИ ДИСПЕРСИИ ПОГЛОЩЕНИЯ НА ВРЕМЕННУЮ ЗАВИСИМОСТЬ ГОЛОНОМНОГО УЗКОПОЛОСНОГО СИГНАЛА ВДАЛИ ОТ ТОЧКИ ИЗЛУЧЕНИЯ

Abstract

It is well known that when a narrow-band signal propagates in any medium with a sufficient length of the path, the amplitude-frequency spectrum of the signal inevitably begins to deform due to the dispersion of the absorption coefficient of the medium, that is, due to the dependence of the absorption coefficient on frequency. Therefore, the time dependence of the signal «at infinity» significantly depends not only on the dispersion of the real part of refractive index, but also on the dispersion of the absorption. In this work, we consider the propagation and distortion of a narrow-band holonomic signal in a homogeneous dispersive medium (by the example of a weakly collisional plasma) taking into account the absorption dispersion. It turns out that the absorption dispersion manifests itself differently for different types of holonomic signals – for holonomic signals with a limited spectrum, the spectrum of which is identically equal to zero outside a certain spectral interval, and for holonomic signals with an unlimited spectrum, the spectrum of which does not vanish with increasing frequency. It is shown that for holonomic signals with an unlimited starting spectrum, the absorption dispersion with increasing path length leads to a shift in the carrier frequency towards lower absorption and to normalization of the spectrum intensity, and hence to normalization of the time dependence of the signal, which becomes Gaussian at infinity. At the same time the signal continues to remain narrow-band. For holonomic signals with a limited spectrum, the absorption dispersion leads to a narrowing of the spectrum, which «presses» it against the boundary of the original signal spectrum. This time, as in the case of signals with an unlimited spectrum, the “standardization” of the time dependence of the signal also occurs, but now the time dependence of an arbitrary signal turns out to be not Gaussian, but “Lorentzian”.