Quasi-normal mode theory enforcing symmetries of the scattering matrix

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.