Beyond group velocity - Wave velocity and signal velocity. II - Amplitude distortion and the influence of attenuation

Radiation-field propagation in a dispersive medium is investigated theoretically, extending the analysis of Bonnet (1983) to account for amplitude distortion and attenuation. Distortion effects in narrow-band signals are simulated by analogy to Fresnel and Fraunhofer diffraction when attenuation is negligible, considering the limiting cases of very short and very long transmission. An exponential model of attenuation is developed, again in the framework of a narrow-band signal, and it is shown that signal-center analysis avoids the problems and restrictions encountered in wave-center analysis: the behavior of the signal center and the properties calculated from it remain the same as in the nonattenuation case.