Temporal rainbow scattering at boundary-induced time interfaces

Since the dawn of modern optics and electromagnetics, the optical prism is one of the most fascinating optical elements for refracting light. Exploiting its frequency dispersive behavior, a prism is able to refract different frequencies in different directions, realizing polychromatic light rainbows. Recently, thanks to their engineerable electromagnetic response, metamaterials have been exploited for achieving novel refractive scattering processes, going beyond the classical prism effects. In this Letter, we report on a rainbow-like scattering process taking place at the interface of a boundary-induced temporal metamaterial realized by instantaneously opening the boundary conditions of a parallel plate waveguide. Changing abruptly the conductivity of one of the two metallic plates, we demonstrate that an equivalent temporal interface between two different media is realized, and the monochromatic wave propagating into the waveguide gets scattered into a polychromatic rainbow in free space. We derive the relationships between the waveguide mode and the raising rainbow in terms of scattered amplitude and frequencies as a function of the elevation angle with respect to the waveguide axis. We apply the underlying physics to control the temporal rainbow by imposing a principal direction of scattering by design. Full-wave numerical simulations are performed for computing the rainbow temporal scattering and verifying the design guidelines for achieving controlled temporal rainbow scattering.