Systematic design of metasurface scattering spectra using analytical criteria on resonances

We present a systematic and computationally efficient methodology to design scattering responses for lossless reciprocal 2-port systems, emphasizing compact high-order standard filters. Our approach is based on universal analytical criteria for the resonances (quasi-normal modes) of the structure, which can be used as tractable optimization (root-finding) objectives. We demonstrate our method by designing multiple microwave metasurfaces configured for polarization-preserving transmission, reflective polarization conversion, or diffractive anomalous reflection, and exhibiting responses that precisely match standard bandpass or bandstop filters of various types, orders and bandwidths, with focus on the best-performing elliptic filters.