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

A New Energy Conservation Law for Time-Harmonic Electromagnetic Fields and Its Applications