On the unsteady and time-harmonic conservation laws of electromagnetic energy and chirality

We examine conservation laws of the energy and chirality for electromagnetic waves in the case of loss-free dielectric media. We show that the energy allows for conservation laws for both generic unsteady and time-harmonic fields. In comparison, the chirality admits a conservation law only for time- harmonic fields. This difference in the time dependence illustrates the crucial distinction between the energy consisting of scalar products of field variables and the chirality composed of their vector products. For future extension of our analysis, we derive those conservation laws for spatially inhomogeneous refractive index. As a result, we uncover physical implications of the new terms in the conservation laws, that have not been considered in the conventional literature.