  The most general expressions of the stored energies for time-harmonic
electromagnetic fields are derived from the time-domain Poynting theorem, and
are valuable in characterizing the energy storage and transport properties of
complex media. A new energy conservation law for the time-harmonic
electromagnetic fields, which involves the derived general expressions of the
stored energies, is introduced. 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; the imaginary part involves an equation related to the difference
between the dissipated electric and magnetic field energies. In a lossless
isotropic and homogeneous medium, the new energy conservation law has a clear
physical implication: 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 field energy flowing out of the surface.
