Research reports

Years: 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Bound states in the continuum and Fano resonances in subwavelength resonator arrays

by H. Ammari and B. Davies and E.O. Hiltunen and H. Lee and S. Yu

(Report number 2021-12)

Abstract
When wave scattering systems are subject to certain symmetries, resonant states may decouple from the far-field continuum; they remain localized to the structure and cannot be excited by incident waves from the far field. In this work, we use layer-potential techniques to prove the existence of such states, known as bound states in the continuum, in systems of subwavelength resonators. When the symmetry is slightly broken, this resonant state can be excited from the far field. Remarkably, this may create asymmetric (Fano-type) scattering behaviour where the transmission is fundamentally different for frequencies on either side of the resonant frequency. Using asymptotic analysis, we compute the scattering matrix of the system explicitly, thereby characterizing this Fano-type transmission anomaly.

Keywords: bound state in the continuum, Fano resonance, subwavelength resonance, metamaterials, scattering, metascreen, capacitance matrix

@Techreport{ADHLY21_954,
  author = {H. Ammari and B. Davies and E.O. Hiltunen and H. Lee and S. Yu},
  title = {Bound states in the continuum and Fano resonances in subwavelength resonator arrays},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-12},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-12.pdf },
  year = {2021}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).