Illustration of the system to be considered in Sect. 3, consisting of a density staircase of vertical extent D. An incident wave of amplitude , thus carrying an energy density , comes from above . The reflected wave has an amplitude and thus carries an energy density , while the transmitted wave has an amplitude and thus carries an energy density . R and T are the reflection and transmission coefficients, respectively. The arrows indicate the schematic vertical direction of propagation of energy. The horizontal components are not shown.