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

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Abstract

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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Acknowledgements

The research of S.A. Nazarov was supported by the Grant No. 17-11-01003 of the Russian Science Foundation.

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Authors and Affiliations

  1. INRIA/Centre de mathématiques appliquées, École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128, Palaiseau, France

    Lucas Chesnel

  2. St. Petersburg State University, Universitetskaya Naberezhnaya, 7-9, St. Petersburg, Russia, 199034

    Sergei A. Nazarov

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  1. Lucas Chesnel
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Correspondence to Lucas Chesnel.

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Chesnel, L., Nazarov, S.A. Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides. Z. Angew. Math. Phys. 71, 82 (2020). https://doi.org/10.1007/s00033-020-01305-9

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