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This paper presents space-time varying (STV) metasurfaces for simultaneouslycontrolling the spatial and temporal spectra of electromagnetic waves. Thesemetasurfaces transform incident electromagnetic waves into specified reflectedand transmitted waves, with arbitrary temporal and spatial frequencies. Theyare synthesized in terms of time-domain generalized sheet transition conditions(GSTCs). Moreover, they are characterized using an analytical method and theunstaggered finite-difference time-domain (FDTD) technique adapted tospace-time metasurfaces. STV metasurfaces performing pulse shaping, timereversal and differentiation are demonstrated as examples.

Simultaneous Control of the Spatial and Temporal Spectra of Light with Space-Time Varying Metasurfaces