Quasi-normal mode theory of the scattering matrix, enforcing fundamental constraints for truncated expansions

TL;DR

This paper introduces a quasi-normal mode theory for calculating the scattering matrix that respects energy conservation and reciprocity, even with a limited set of resonances, simplifying analysis of complex electromagnetic systems.

Contribution

It presents a practical, reduced-order model for the scattering matrix based on resonant frequencies and coupling coefficients, avoiding the need for QNM normalization and enabling efficient analysis.

Findings

Accurately computes scattering matrices with few resonances.

Separates low-Q modes into an effective background response.

Demonstrates applicability to various electromagnetic metasurfaces.

Abstract

We develop a quasi-normal mode theory (QNMT) to calculate a system's scattering $S$ matrix, simultaneously satisfying both energy conservation and reciprocity even for a small truncated set of resonances. It is a practical reduced-order (few-parameter) model based on the resonant frequencies and constant mode-to-port coupling coefficients, easily computed from an eigensolver without the need for QNM normalization. Furthermore, we show how low-$Q$ modes can be separated into an effective slowly varying background response $C$, giving an additional approximate formula for $S$, which is useful to describe general Fano-resonant phenomena. We demonstrate our formulation for both normal and fixed-angle oblique plane-wave incidence on various electromagnetic metasurfaces.