Quantile motion of electromagnetic waves in wave guides of varying cross section and dispersive media

We discuss applications of the quantile concept of trajectories and velocities to the propagation of electromagnetic signals in wave guides of varying cross section. Quantile motion is a general description of the transport properties of measurable conserved quantities in quantum mechanics as well as in classical electrodynamics. In the latter case we consider the quantile motion of electromagnetic energy as the direct result of a physical measurement. In this sense the quantile velocity corresponds to the electromagnetic signal velocity also in the presence of barriers and inhomogeneities in the medium of propagation. We show that this signal velocity is always smaller than the speed of light in vacuum. Using numerical examples we demonstrate how typical wave phenomena can be described in terms of the quantile motion.