Wave packets, group velocities, and rays in lossy media revisited

A study prompted by discussions of the group velocity concept in absorptive media and the correctness of Maxwell´s equation is presented. A simple model for a wave packet train is obtained by beating two waves with adjacent frequencies and wavenumbers. 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. An extension of Hamilton´s ray equations for absorptive media is given. This formalism is used for numerical ray tracing in an absorptive ionosphere. 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