Reconstructing the scattering matrix of photonic systems from quasinormal modes

Filippo Alpeggiani, Nikhil Parappurath, Ewold Verhagen, L. Kuipers

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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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.

Original languageEnglish
Title of host publicationICTON 2017 - 19th International Conference on Transparent Optical Networks
ISBN (Electronic)9781538608586
Publication statusPublished - 1 Sep 2017
Event19th International Conference on Transparent Optical Networks, ICTON 2017 - Girona, Catalonia, Spain
Duration: 2 Jul 20176 Jul 2017


Conference19th International Conference on Transparent Optical Networks, ICTON 2017
CityGirona, Catalonia


  • photonic crystals
  • quasinormal modes
  • resonant states
  • scattering matrix
  • theoretical photonics


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