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-principles prediction of the scattering properties, without the need for postulating ad hoc nonresonant channels.
- Received 22 November 2016
DOI:https://doi.org/10.1103/PhysRevX.7.021035
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
A scattering matrix is an essential mathematical tool for physicists working in numerous fields. It quantitatively describes how light or particles change when they scatter off one another. First developed to solve problems in quantum field theory, it now constitutes the basic machinery for calculating many key physical quantities, such as the interaction probability of atomic nuclei, electrical transmission through extremely small conductors, or to what degree nanoparticles absorb light. In this work, we demonstrate that the scattering matrix of a system can be fully determined from the knowledge of its quasinormal modes—the states that exist for a system coupled to its environment in the absence of any driving input. In this sense, the quasinormal modes represent the bare framework around which the frequency response of the system is built.
We validate our formalism with some illustrative examples from the field of nanophotonics, confirming that it embodies an effective and powerful tool for making predictions from first principles. In a natural way, our theory accounts for the effective interaction among different quasinormal modes that originate from the coupling to a common external environment. For this reason, it is directly applicable to any number of multiple overlapping modes and to any arbitrary configuration of input-output channels. Moreover, the theory does not require any ad hoc assumptions, such as the fitting of an additional nonresonant background.
By casting the scattering matrix in these terms, it provides a deeper physical understanding of a system than other approaches. In particular, the theory represents a key for deciphering, understanding, and engineering the scattering properties of complex optical systems.