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

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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)

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.

Suggested Citation

  • Mondher Besbes & Christophe Sauvan, 2022. "Role of Static Modes in Quasinormal Modes Expansions: When and How to Take Them into Account?," Mathematics, MDPI, vol. 10(19), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3542-:d:928299
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    References listed on IDEAS

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    1. M. Khajavikhan & A. Simic & M. Katz & J. H. Lee & B. Slutsky & A. Mizrahi & V. Lomakin & Y. Fainman, 2012. "Thresholdless nanoscale coaxial lasers," Nature, Nature, vol. 482(7384), pages 204-207, February.
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