Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides - Archive ouverte HAL
Article Dans Une Revue Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées Année : 2020

Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides

Résumé

We investigate a time-harmonic wave problem in a waveguide. We work at low frequency so that only one mode can propagate. It is known that the scattering matrix exhibits a rapid variation for real frequencies in a vicinity of a complex resonance located close to the real axis. This is the so-called Fano resonance phenomenon. And when the geometry presents certain properties of symmetry, there are two different real frequencies such that we have either R = 0 or T = 0, where R and T denote the reflection and transmission coefficients. In this work, we prove that without the assumption of symmetry of the geometry, quite surprisingly, there is always one real frequency for which we have T = 0. In this situation, all the energy sent in the waveguide is backscattered. However in general, we do not have R = 0 in the process. We provide numerical results to illustrate our theorems.
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Dates et versions

hal-02189311 , version 1 (19-07-2019)
hal-02189311 , version 2 (21-12-2020)

Identifiants

  • HAL Id : hal-02189311 , version 2

Citer

Lucas Chesnel, Sergei A Nazarov. Exact zero transmission during the Fano resonance phenomenon in non symmetric waveguides. Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées, 2020. ⟨hal-02189311v2⟩
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