Temporal boundary between two non-dispersive media

The widely used technique in literature to study the scattering from a temporal boundary between two dispersive media involves solving the constitutive relations within Maxwell’s equations, where the field and permittivity are related through convolution. Conversely, the conventional approach of analyzing the scattering of electromagnetic radiation at a temporal boundary between two non-dispersive media involves equating the product of permittivity and field on either side of the temporal boundary. In this paper, we propose a modified mathematical expression of permittivity at the temporal boundary between two non-dispersive media, bridging the gap between two approaches of studying the scattering from the temporal boundary and ensuring consistency. Additionally, we revisit and re-derive results—such as scattering coefficients, frequency relations, and pulse broadening/compression—that have been established in the existing literature. We obtain them by solving Maxwell’s equation in momentum space.