Abstract:

The concept of group velocity has one of three origins and is described in terms of a mathematical construct to predict arrival times in pulse propagation in a waveguide, particularly within the context of normal mode theory. Under certain conditions, group velocity can lead to confusion. On the other hand, the rate of energy transport, which is what one really seeks, may be derived by taking the ratio of the mean energy flux through a vertical section with the energy density between two planes separated by a wavelength. In the context of normal mode theory, this leads to an integral expression that involves the normalized vertical wavefunctions and the velocity profile leading to a physically appealing expression that lends insight to expected modal arrivals. Under certain conditions, it leads to the same results as the group velocity concept: It can be calculated with only one frequency and is valid near cutoff frequencies. This supplies one with an integral expression for a velocity that better characterizes arrival times of packets of energy. [Work sponsored by ONR, the Naval Research Laboratory, and the University of New Orleans.]