Light propagation through metamaterial temporal slabs: reflection, refraction, and special cases

Time-varying metamaterials are artificial materials whose electromagnetic properties change over time. Similar to a spatial medium discontinuity, a sudden change in time of the metamaterial refractive index induces the generation of reflected and refracted light waves. The relationship between the incident and emerging fields at one temporal interface has been subject of investigation in earlier studies. Here, we extend the study to a temporal slab, i.e., a uniform homogeneous medium that is present in the whole space for a limited time. The scattering coefficients have been derived as a function of the refractive indices and application time, demonstrating that the response of the temporal slab can be controlled through the application time, which acts similarly to the electrical thickness of conventional spatial slabs. The results reported in this Letter pave the way to creating novel devices based on temporal discontinuities, such as temporal matching networks, Bragg grating, and dielectric mirrors, which exhibit zero space occupancy by exploiting the time dimension, instead of the spatial dimension.