Analytical criteria for designing multiresonance filters in scattering systems, with application to microwave metasurfaces

TL;DR

This paper develops analytical design criteria for lossless two-port scattering systems, enabling precise filter design including microwave metasurfaces with various filtering responses, by linking resonant modes to scattering zeros and poles.

Contribution

It introduces a general analytical framework for designing multiresonance filters in scattering systems, connecting quasi-normal modes to scattering zeros and providing a numerical method for filter synthesis.

Findings

Designed microwave metasurfaces with specific polarization and reflection properties.

Achieved precise filter responses matching standard filter types.

Provided a systematic approach for filter design using eigenmode analysis.

Abstract

We present general analytical criteria for the design of lossless reciprocal two-port systems, which exhibit prescribed scattering spectra $S(\omega)$ satisfying $S_{22}(\omega)=e^{i\varphi}S_{11}(\omega)$, including symmetric ($S_{22}=S_{11}$) or "antimetric" ($S_{22}=-S_{11}$) responses, such as standard filters (Butterworth, Chebyshev, elliptic, etc.). We show that the non-normalized resonant (quasi-normal) modes (QNMs) of all such two-port systems couple to the input and output ports with specific unitary ratios, whose relative signs determine the position of the scattering zeros on the real frequency axis. This allows us to obtain design criteria assigning values to the poles, background response, and QNM-to-ports coupling coefficients. Filter devices can then be designed via a well-conditioned nonlinear optimization (or root-finding) problem using a numerical eigensolver. As an application, we design multiple microwave metasurfaces configured for polarization-preserving transmission, reflective polarization conversion, or diffractive "perfect anomalous reflection", to realize filters that precisely match standard bandpass or bandstop filters of various types, orders and bandwidths, with focus on the best-performing elliptic filters.