Role of Static Modes in Quasinormal Modes Expansions: When and How to Take Them into Account?

Mondher Besbes and Christophe Sauvan ()
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Mondher Besbes: Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
Christophe Sauvan: Université Paris-Saclay, Institut d’Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France

Mathematics, 2022, vol. 10, issue 19, 1-11

Abstract: The scattering of electromagnetic waves by a resonator is determined by the excitation of the eigenmodes of the system. In the case of open resonators made of absorbing materials, the system is non-Hermitian, and the eigenmodes are quasinormal modes. Among the whole set of quasinormal modes, static modes (modes with a zero eigenfrequency) occupy a specific place. We study the role of static modes in quasinormal modes expansions calculated with a numerical solver implemented with the finite-element method. We show that, in the case of a dielectric permittivity described by a Lorentz model, static modes markedly contribute to the electromagnetic field reconstruction but are incorrectly calculated with a solver designed to compute modes with non-zero eigenfrequencies. We propose to solve this issue by adding to the solver a separate, specific computation of the static modes.

Keywords: electromagnetism; quasinormal modes; non-Hermitian systems; optical cavities; nanophotonics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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