Temporal interfaces by instantaneously varying boundary conditions

Temporal metamaterials have been recently exploited as a novel platform for conceiving several electromagnetic and optical devices based on the anomalous scattering response arising at a single or multiple sudden changes of the material properties. However, they are difficult to implement in realistic scenarios by switching the permittivity of a material in time, and new strategies to achieve time interfaces in a feasible manner must be identified. In this paper, we investigate the possibility to realize a temporal metamaterial without acting on the material properties, but rather on the effective refractive index and wave impedance perceived by the wave during the propagation in an empty guiding structure by varying the boundaries in time. We demonstrate analytically and through numerical experiments that suddenly changing the physical distance between the metallic plates of a parallel-plate waveguide will induce an effective temporal interface. In addition to the standard backward and forward scattered fields at different frequencies due to the temporal interface, we also identify the presence of a static field necessary to satisfy the continuity of the electromagnetic field across the interface. The proposed concept can be extended to temporally controlled metasurfaces, opening an easier path to the design and realization of novel devices based on time-varying metamaterials at microwave and optical frequencies.