Research output: Contribution to journal › Article › peer-review
Non reflection and perfect reflection via Fano resonance in waveguides. / Chesnel, Lucas; Nazarov, Sergei A. .
In: Communications in Mathematical Sciences, Vol. 16, No. 7, 2018, p. 1779–1800.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Non reflection and perfect reflection via Fano resonance in waveguides
AU - Chesnel, Lucas
AU - Nazarov, Sergei A.
PY - 2018
Y1 - 2018
N2 - We investigate a time-harmonic wave problem in a waveguide. By means of asymptotic analysis techniques, we justify the so-called Fano resonance phenomenon. More precisely, we show that the scattering matrix considered as a function of a geometrical parameter $\varepsilon$ and of the frequency $\lambda$ is in general not continuous at a point $(\varepsilon,\lambda)=(0,\lambda^0)$ where trapped modes exist. In particular, we prove that for a given $\varepsilon\ne0$ small, the scattering matrix exhibits a rapid change for frequencies varying in a neighbourhood of $\lambda^0$. We use this property to construct examples of waveguides such that the energy of an incident wave propagating through the structure is perfectly transmitted (non reflection) or perfectly reflected in monomode regime. We provide numerical results to illustrate our theorems.
AB - We investigate a time-harmonic wave problem in a waveguide. By means of asymptotic analysis techniques, we justify the so-called Fano resonance phenomenon. More precisely, we show that the scattering matrix considered as a function of a geometrical parameter $\varepsilon$ and of the frequency $\lambda$ is in general not continuous at a point $(\varepsilon,\lambda)=(0,\lambda^0)$ where trapped modes exist. In particular, we prove that for a given $\varepsilon\ne0$ small, the scattering matrix exhibits a rapid change for frequencies varying in a neighbourhood of $\lambda^0$. We use this property to construct examples of waveguides such that the energy of an incident wave propagating through the structure is perfectly transmitted (non reflection) or perfectly reflected in monomode regime. We provide numerical results to illustrate our theorems.
KW - Waveguides
KW - Fano resonance
KW - non reflection
KW - perfect reflection
KW - scattering matrix
UR - https://arxiv.org/pdf/1801.08889.pdf
UR - https://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0016/0007/index.php
UR - https://www.intlpress.com/site/pub/pages/journals/items/cms/content/vols/0016/0007/a002/index.php
M3 - Article
VL - 16
SP - 1779
EP - 1800
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
SN - 1539-6746
IS - 7
ER -
ID: 40974921