Beyond group velocity - Wave velocity and signal velocity. I The group-velocity operator in the absence of attenuation

Radiation-field propagation in a dispersive medium is investigated theoretically, considering the heuristic case of negligeable attenuation. The wave-packet and wave-front approaches to the metrology of group velocity are reviewed, and a new approach based on a realistic and accesible criterion and free from limiting assumptions about the form of the emitted signal or its spectrum is developed, expanding the analysis of wave moments (Baird, 1972; Bradford, 1976) to encompass field source, medium, and detector. The formalism and methodology of the theory of the spatiotemporal signal and its representations is employed, defining a wave center and a signal center as the spatial and temporal markers of the field, respectively, and characterizing their motions by a wave velocity, and a signal velocity, both dependent on emitted-signal form and medium properties. The nonattenuation case is examined in detail.