Energy conservation at an optical temporal boundary

The temporal boundary appears as a novel phenomenon in a wide range of optical devices and systems, such as the photonic crystal, metamaterials, optical microcavity, and modulator, with a dynamic medium whose refractive index changes across the boundary. However, the validation of electromagnetic energy conservation was considered in violation for the optical temporal boundary traditionally. Here a new energy space–time scheme is proposed for an optical pulse in a medium with the temporal boundary. From the Poynting theory, the electromagnetic energy is investigated based on a one-dimensional model under the assumption of impedance matching. Furthermore, the results demonstrate that a more general conservation of energy is validated in a time domain for the ideal scenario. A new invariant quantity of spatial energy in the optical medium is further obtained. The numerical results are in agreement with the theory of the temporal boundary. The conservative process of energy transportation across the optical temporal boundary is clarified and confirmed.