  Since the dawn of modern optics and electromagnetics, optical prism is one of
the most fascinating optical elements for refracting light. Exploiting its
frequency dispersive behaviour, 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 Manuscript, we report on a novel
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.
