  Optical wave-based computing has enabled the realization of real-time
information processing in both space and time domains. In the past few years,
analog computing has experienced rapid development but mostly for a single
function. Motivated by parallel space-time computing and miniaturization, we
show that reconfigurable graphene-based metasurfaces offer a promising path
towards spatiotemporal computing with integrated functionalities by properly
engineering both spatial- and temporal-frequency responses. This paper employs
a tunable graphene-based metasurface to enable analog signal and image
processing in both space and time by tuning the electrostatic bias. In the
first part of the paper, we propose a switchable analog computing paradigm in
which the proposed metasurface can switch among defined performances by
selecting a proper external voltage for graphene monolayers. Spatial isotropic
differentiation and edge detection in the spatial channel and first-order
temporal differentiation and metasurface-based phaser with linear group-delay
response in the temporal channel are demonstrated. In the second section of the
paper, simultaneous and parallel spatiotemporal analog computing is
demonstrated. The proposed metasurface processor has almost no static power
consumption due to its floating-gate configuration. The spatial- and
temporal-frequency transfer functions (TFs) are engineered by using a
transmission line (TL) model, and the obtained results are validated with
full-wave simulations. Our proposal will enable real-time parallel
spatiotemporal analog signal and image processing.
