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.<
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