Damping-induced dispersion in simple waveguides

Abstract

The goal is to gain a non-dimensional formulation of the complex wavenumber knowing the onedimensional partial differential equation for wave propagation and the harmonic wave approach. This can be disassembled into its components, namely the imaginary part, showing the decay of a wave, and the real part, showing its spatial propagation. Having an eye on damping in waveguides including internal and external damping, we discuss the resulting consequences, which are frequency-dependent phase and group velocities (dispersion), as well as the energy transport and dissipation. This bears relevance for many domains of physics such as seismic and electromagnetic waves.