Reconstructing the scattering matrix of photonic systems from quasinormal modes

The scattering matrix is a fundamental tool to quantitatively describe the properties of resonant systems. In particular, it enables the understanding of many photonic devices of current interest, such as photonic metasurfaces and nanostructured optical scatterers. In this contribution, we show that the scattering matrix of a photonic system is completely determined by its quasinormal modes, i.e., the self-sustaining electromagnetic excitations at a complex frequency. On the basis of temporal coupled-mode theory, we derive an expression for the expansion of the scattering matrix on quasinormal modes, which is directly applicable to an arbitrary number of modes and input/output channels. Our theory does not require any ad-hoc assumptions, such as the fitting of an additional nonresonant background. We validate and discuss the theoretical formalism with some illustrative examples. This demonstrates that the theory represents a powerful and predictive tool for calculating the highly structured spectra of resonant nanophotonic systems, and, at the same time, a key for unravelling the physical mechanisms at the heart of such intricate spectral structures.

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