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.
We develop a quasinormal mode theory (QNMT) of the scattering matrix S, satisfying fundamental symmetries (such as reciprocity and time-reversal or PT symmetries) even for a small truncated set of resonances. It is a useful and accurate reduced-order model for S based on the resonant frequencies and mode-to-port coupling coefficients, obtained from an eigensolver without the need for QNM normalization. We further show that a slowly varying background, useful to describe Fano-shaped spectra, can be extracted using high-loss modes. We demonstrate the improved accuracy of our formulation using various electromagnetic metasurfaces.
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