  A spatio-temporal metasurface is proposed to decompose in real time the
temporal frequencies of electromagnetic waves into spatial frequencies onto a
two-dimensional plane. The metasurface is analyzed and demonstrated using
Fourier analysis. The required transmittance function is derived from an
equivalent free-space optical system consisting of the cascade combination of a
wedge, a diffraction grating and a focusing lens. The metasurface must exhibit
both multi-resonance over a broad bandwidth and 1-D grating-type scanning to
achieve the specified 2-D frequency scanning in space. Compared to state-of-the
art related systems, the proposed metasurface system is more compact as it
requires only one dispersive structure, while maintaining the high frequency
resolution that characterizes 2-D spatial-temporal mapping systems.
