Behavior of a wave with absorption at discontinuity: telegrapher’s equation approach

The propagation of a wave packet in a discontinuous medium, one of them with absorption of energy, has been studied analytically. We examined an electromagnetic pulse starting in a free medium and moving toward a dissipative one. In the first medium, the wave is free-moving governed by the wave equation, while in the second medium, the wave is affected by the Joule effect governed by the telegrapher’s equation. We solved the motion at the discontinuity using the Fourier representation for a wave packet in the formalism of a wave attenuated approach. This allowed us to calculate a reflection amplitude in analogy with the ordinary definition at a discontinuity in a medium without dissipation but with different velocities in each medium.