Method for extracting the equivalent admittance from time-varying metasurfaces and its application to self-tuned spatiotemporal wave manipulation

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 (PW). 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 PW. The proposed synthesis method for PW-dependent metasurfaces may be extended to designing metasurfaces with more complex spatiotemporal wave manipulation, benefiting applications such as sensing, wireless communications and signal processing.