Absorption of a Narrow-Band Signal in a Dispersive Medium

We consider propagation and absorption of a narrow-band signal in a homogeneous dispersive medium. It is shown that all signals can be divided into two qualitatively different classes, namely, holonomic and piecewise-holonomic signals. When propagating in an absorbing medium, the holonomic signals are attenuated obeying an exponential law and, therefore, almost disappear at a sufficient long path lengths. The piecewise-holonomic signals are attenuated significantly slower (obeying a hyperbolic law) and, therefore, continue to exist even at substantially longer paths.