Quasinormal-mode expansion of the scattering matrix

TL;DR

This paper introduces a scalable method to reconstruct the scattering matrix of photonic structures using quasinormal modes, enabling accurate predictions of scattering properties from fundamental mode data.

Contribution

It develops a general quasinormal-mode expansion of the scattering matrix that requires only eigenfrequencies and far-field properties, avoiding ad-hoc assumptions.

Findings

Accurately predicts scattering properties of nanophotonic systems.

Validates the theory with systems having overlapping electromagnetic modes.

Provides a first-principles approach without nonresonant channel assumptions.

Abstract

It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the reconstruction of the scattering matrix from the knowledge of the quasinormal modes, is addressed. We develop a general and scalable quasinormal-mode expansion of the scattering matrix, requiring only the complex eigenfrequencies and the far-field properties of the eigenmodes. The theory is validated by applying it to illustrative nanophotonic systems with multiple overlapping electromagnetic modes. The examples demonstrate that our theory provides an accurate first-principle prediction of the scattering properties, without the need for postulating ad-hoc nonresonant channels.