  With their self-tuned time-varying responses, waveform-selective metasurfaces
embedded with nonlinear electronics have shown fascinating applications,
including distinguishing different electromagnetic waves depending on the pulse
width. However, thus far they have only been realized with a spatially
homogeneous scattering profile. Here, by modeling a metasurface as time-varying
admittance sheets, we provide an analytical calculation method to predict the
metasurface time-domain responses. This allows derivation of design
specifications in the form of equivalent sheet admittance, which is useful in
synthesizing a metasurface with spatiotemporal control, such as to realize a
metasurface with prescribed time-dependent diffraction characteristics. As an
example, based on the proposed equivalent admittance sheet modeling, we
synthesize a waveform-selective Fresnel zone plate with variable focal length
depending on the incoming pulse width. The proposed synthesis method of
pulse-width-dependent metasurfaces may be extended to designing metasurfaces
with more complex spatiotemporal wave manipulation, benefiting applications
such as sensing, wireless communications and signal processing.
