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Fano resonance in metallic grating via strongly coupled subwavelength resonators

Part of: Partial differential equations Optics, electromagnetic theory - General

Published online by Cambridge University Press:  30 June 2020

JUNSHAN LIN  and
HAI ZHANG Open the ORCID record for HAI ZHANG [Opens in a new window]
JUNSHAN LIN
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, AL36849, USA, email: jzl0097@auburn.edu
HAI ZHANG
Affiliation:
Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong KongSAR, China, email: haizhang@ust.hk
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Abstract

We investigate the Fano resonance in grating structures using coupled resonators. The grating consists of a perfectly conducting slab with periodically arranged subwavelength slit holes, where inside each period, a pair of slits sit very close to each other. The slit holes act as resonators and are strongly coupled. It is shown rigorously that there exist two groups of resonances corresponding to poles of the scattering problem. One sequence of resonances has imaginary part in the order of ε, where ε is the size of the slit aperture, while the other sequence has imaginary part in the order of ε2. When coupled with the incident wave at resonant frequencies, the narrow-band resonant scattering induced by the latter will interfere with the broader background resonant radiation induced by the former. The interference of these two resonances generates the Fano-type transmission anomaly, which persists in the whole radiation continuum of the grating structure as long as the slit aperture size is small compared to the incident wavelength.

Keywords

Fano resonancephotonics subwavelength structureHelmholtz equation

MSC classification

Primary: 35B34: Resonances
Secondary: 35B40: Asymptotic behavior of solutions 78A45: Diffraction, scattering
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Issue 2 , April 2021 , pp. 370 - 394
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

†

Junshan Lin was partially supported by the NSF grant DMS-1719851. Hai Zhang was supported by Hong Kong RGC grant GRF 16304517 and GRF 16306318.

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