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

TL;DR

This paper reexamines Poynting's theorem starting from Maxwell-Lorentz equations, demonstrating that energy conservation in light propagation through bounded media is maintained by Maxwell's boundary conditions, even under common approximations.

Contribution

It introduces a revised energy flux vector and shows that energy conservation holds with Maxwell's boundary conditions, clarifying longstanding debates about approximations.

Findings

Energy conservation is ensured by Maxwell's boundary conditions.

The revised flux vector relates energy dissipation to matter's kinetic energy.

Common approximations like the dielectric approximation do not violate energy conservation.

Abstract

Starting from the Maxwell-Lorentz equations, Poynting's theorem is reconsidered. The energy flux vector is introduced as S_e=(E x B)/mu_0 instead of E x H, because only by this choice the energy dissipation can be related to the balance of the kinetic energy of the matter subsystem. Conservation of the total energy as the sum of kinetic and electromagnetic energy follows. In our discussion, media and their microscopic nature are represented exactly by their 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.