Standard

Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides. / Chesnel, Lucas; Nazarov, Sergei A.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 71, No. 3, 82, 04.05.2020.

Research output: Contribution to journal › Article › peer-review

Harvard

Chesnel, L & Nazarov, SA 2020, 'Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides', Zeitschrift fur Angewandte Mathematik und Physik, vol. 71, no. 3, 82. https://doi.org/10.1007/s00033-020-01305-9

APA

Chesnel, L., & Nazarov, S. A. (2020). Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides. Zeitschrift fur Angewandte Mathematik und Physik, 71(3), [82]. https://doi.org/10.1007/s00033-020-01305-9

Vancouver

Chesnel L, Nazarov SA. Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides. Zeitschrift fur Angewandte Mathematik und Physik. 2020 May 4;71(3). 82. https://doi.org/10.1007/s00033-020-01305-9

Author

Chesnel, Lucas ; Nazarov, Sergei A. / Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides. In: Zeitschrift fur Angewandte Mathematik und Physik. 2020 ; Vol. 71, No. 3.

BibTeX

@article{712f6a362c154d81a8aa8be7ea10ca28,
title = "Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides",
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.",
keywords = "Fano resonance, Scattering matrix, Waveguides, Zero transmission, TRAPPED MODES, EIGENVALUE, REFLECTION, COMPLEX RESONANCES, ENFORCED STABILITY, CONTINUOUS-SPECTRUM",
author = "Lucas Chesnel and Nazarov, {Sergei A.}",
year = "2020",
month = may,
day = "4",
doi = "10.1007/s00033-020-01305-9",
language = "English",
volume = "71",
journal = "Zeitschrift fur Angewandte Mathematik und Physik",
issn = "0044-2275",
publisher = "Birkh{\"a}user Verlag AG",
number = "3",

}

RIS

TY - JOUR

T1 - Exact zero transmission during the Fano resonance phenomenon in non-symmetric waveguides

AU - Chesnel, Lucas

AU - Nazarov, Sergei A.

PY - 2020/5/4

Y1 - 2020/5/4

N2 - 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.

AB - 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.

KW - Fano resonance

KW - Scattering matrix

KW - Waveguides

KW - Zero transmission

KW - TRAPPED MODES

KW - EIGENVALUE

KW - REFLECTION

KW - COMPLEX RESONANCES

KW - ENFORCED STABILITY

KW - CONTINUOUS-SPECTRUM

UR - http://www.scopus.com/inward/record.url?scp=85084189822&partnerID=8YFLogxK

U2 - 10.1007/s00033-020-01305-9

DO - 10.1007/s00033-020-01305-9

M3 - Article

AN - SCOPUS:85084189822

VL - 71

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 3

M1 - 82

ER -

ID: 60873423