Wave Packets, Group Velocities, and Rays in Lossy Media Revisited

The present study, which also serves as an introduction and a review for the subject problem, was mainly prompted by recent discussions concerning the group velocity concept in absorptive media, and the correctness of Maxwell's equations, initiated by Harmuth's work. Our initial approach is the classical “textbook” method of beating two plane waves with adjacent frequencies. It is well-known that the definition of group velocity in absorptive media is not unique. Here, we adhere to the hypothesis that in order to describe the transport of energy parcels through real space, the group velocity must be real. By extending frequencies and propagation vectors into the complex domain, it is shown that a consistent definition of real group velocity in absorptive media can be stated. Numerical examples are displayed, and theoretical and experimental aspects are briefly discussed. The arguments show that a physically meaningful definition of the group velocity in absorptive media is consistent with the Fermat principle and the special relativistic limitation on the speed of light.