Poynting's theorem and energy conservation in the propagation of light in bounded media

Starting from the Maxwell-Lorentz equations, Poyntings theorem is reconsidered. The electromagnetic energy flux vector is introduced such that it can be related to the kinetic energy of the matter subsystem. Conservation of the total energy follows. In our discussion, the microscopic nature of media is represented exactly by susceptibility functions, which do not necessarily have to be known. On this footing, it can be shown that energy conservation in the propagation of light through bounded media is ensured by Maxwell's boundary conditions alone, even for some frequently used approximations. This is demonstrated for approaches using additional boundary conditions and the dielectric approximation in detail, the latter of which suspected to violate energy conservation for decades.