  This paper presents an analytical framework for the analysis of time-varying
metal-based metamaterials. Concretely, we particularize the study to
time-modulated metal-air interfaces embedded between two different
semi-infinite media that are illuminated by monochromatic plane waves of
frequency $\omega_0$. The formulation is based on a Floquet-Bloch modal
expansion, which takes into account the time periodicity of the structure ($T_s
= 2\pi / \omega_s)$, and integral-equation techniques. It allows to extract the
reflection/transmission coefficients as well as to derive nontrivial features
about the dynamic response and dispersion curves of time-modulated metal-based
screens. In addition, the proposed formulation has an associated analytical
equivalent circuit that gives physical insight to the diffraction phenomenon.
Similarities and differences between space- and time-modulated metamaterials
are discussed via the proposed circuit model. Finally, some analytical results
are presented to validate the present framework. A good agreement is observed
with numerical computations provided by a self-implemented finite-difference
time-domain (FDTD) method. Interestingly, the present results suggest that
time-modulated metal-based screens can be used as pulsed sources (when
$\omega_s \ll \omega_0$), beamformers ($\omega_s \sim \omega_0$) to redirect
energy in specific regions of space, and analog samplers ($\omega_s \gg
\omega_0$).
