Physical cause of group velocity in normally dispersive, nondissipative media

A physical explanation for group velocity is given for the very common case of group velocity less than the phase velocity with negligible absorption. The underlying physics is that a nonpropagating or immobilized energy density must be present in the medium associated with the presence of the wave field. The individual waves carry energy forward in a wave packet and energize the medium in the forward portion of the packet. In the rear portion of the packet, the individual waves grow at the expense of the energy immobilized in the medium, the particle motions in the medium being in phase with the wave field and therefore capable of generating new waves in phase with the group of waves that produced them. The physics is conveniently described in terms of deep water waves, but the principles involved apply equally well to other dispersive, nonabsorbing media, including plasmas, dielectrics, and waveguides. The flux of energy can be expressed as the phase velocity times that part of the energy density that propagates with the individual waves or, averaged over a wave period, as the total energy density (including the energy immobilized in the medium) times the group velocity. This eliminates the confusion commonly present when an attempt is made to interpret the Poynting flux for electromagnetic waves in terms of the product of an energy density and the group velocity. The group velocity is just the weighted average velocity.