  This paper presents space-time varying (STV) metasurfaces for simultaneously
controlling the spatial and temporal spectra of electromagnetic waves. These
metasurfaces transform incident electromagnetic waves into specified reflected
and transmitted waves, with arbitrary temporal and spatial frequencies. They
are synthesized in terms of time-domain generalized sheet transition conditions
(GSTCs). Moreover, they are characterized using an analytical method and the
unstaggered finite-difference time-domain (FDTD) technique adapted to
space-time metasurfaces. STV metasurfaces performing pulse shaping, time
reversal and differentiation are demonstrated as examples.
