  We report a new energy conservation law for time-harmonic electromagnetic
fields, which is valid for an arbitrary medium. In contrast to the
well-established Poynting theorem for time-harmonic fields, the real part of
the new energy conservation law gives an equation for the sum of stored
electric and magnetic field energies and the imaginary part involves an
equation related to the difference between the dissipated electric and magnetic
energies. Universally applicable expressions for both the electric and magnetic
field energies have been obtained and demonstrated to be valuable in
characterizing the energy storage and transport properties in complex media.
For a lossless isotropic and homogeneous medium, the new energy conservation
law implies that the stored electromagnetic field energy of a radiating system
enclosed by a surface is equal to the total field energy inside the surface
subtracted by the energy flowing out of the surface.
