Wave Packets and Group Velocity in Absorbing Media: Solutions of the Telegrapher's Equation - Abstract

Abstract

The propagation of high-frequency wave packets and solitary pulses in absorbing media, for which the process of wave propagation is governed by the telegrapher's equation, is investigated. The group velocity W for elementary wave solutions of telegrapher's equation is real and larger than the speed of light c for real wave numbers exceeding some critical value. The group velocity is real also for purely imaginary wave numbers and in this case W < c. The case W < c appears when the long-time asymptotics of wave packet solutions is considered, while the case W > c appears for finite times and short traveling distances. Both analytical and numerical studies of the evolution of high-frequency wave packets and aperiodic solitary pulses have been performed. This is done by analyzing and calculating the convolution integral representing a causal solution in a half-space. It has been found that the maximum of the wave packet's envelope begins to propagate from the boundary with superluminal velocity and after relatively short traveling distances its velocity becomes sublumi- nal. The maximum of a solitary pulse propagates with a subluminal velocity. Numerical calculations demonstrate strong reshaping of a solitary pulse at distances of the order of several absorption lengths. The conjunction of the local group velocity concept and superluminal propagation speeds is to be perceived as kinematical phenomenon closely related to the definitions used and does not imply a falsification of special relativity theory.