  Recently, it has been shown that temporal metamaterials based on impulsive
modulations of the constitutive parameters (of duration much smaller than a
characteristic electromagnetic timescale) may exhibit a nonlocal response that
can be harnessed so as to perform elementary analog computing on an impinging
wavepacket. These short-pulsed metamaterials can be viewed as the temporal
analog of conventional (spatial) metasurfaces. Here, inspired by the analogy
with cascaded metasurfaces, we leverage this concept and take it one step
further, by showing that short-pulsed metamaterials can be utilized as
elementary bricks for more complex computations. To this aim, we develop a
simple, approximate approach to systematically model the multiple actions of
time-resolved short-pulsed metamaterials. Via a number of representative
examples, we illustrate the computational capabilities enabled by this
approach, in terms of simple and composed operations, and validate it against a
rigorous numerical solution. Our results indicate that the temporal dimension
may provide new degrees of freedom and design approaches in the emerging field
of computational metamaterials, in addition or as an alternative to
conventional spatially variant platforms.
