Derivation of expression of time-averaged stored energy density of electromagnetic waves

There exist several nonequivalent expressions of time-averaged stored energy density (TASED) for electromagnetic waves. Correspondingly, different value, even different sign, of TASED may be predicted theoretically. In this work, we demonstrate that the stored energy of an electromagnetic wave oscillates periodically; according to the law of conservation of energy and causality, the stored energy is stored first and then released subsequently, thus TASED is positive definitive. On this basis, TASED expression of a linearly polarized electromagnetic wave traveling in a linear isotropic medium is obtained by selecting a proper starting time to calculate the time averaged value of the stored energy density. Our work provides a clear physical image and physical meaning for TASED, and may be helpful to further address the related issues.