The most general expressions for the stored field energies in the frequency domain, which are independent of any constitutive relations and microscopic models, are derived from the time-domain Poynting theorem by using the complex frequency-domain approach. When the complex frequency-domain approach is applied to Maxwell’s equations, two energy balance relations are obtained simultaneously. The first relation is the well-known Poynting theorem, while the second is new in its general form and contains the newly derived expressions for the stored field energies. In contrast to the well-established Poynting theorem in frequency domain, the real part of the second energy balance relation gives an equation for the sum of stored electric and magnetic field energies and provides a natural definition for the stored energy around a radiator; the imaginary part involves an equation related to the difference between the dissipated electric and magnetic field energies. When media are lossless, the new expressions for the stored field energies are shown to agree with all previous studies; when media are lossy, they include new terms that were not shown in previous reports. These additional terms represent the dispersive part of the stored energies and reflect the influence of the losses on the stored energies.
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