Research reports

Years: 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

A mathematical and numerical framework for gradient meta-surfaces built upon periodically repeating arrays of Helmholtz resonators

by H. Ammari and K. Imeri

(Report number 2020-05)

Abstract
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a finite number of Helmholtz resonators in a unit cell and that unit cell is repeated periodically. To solve the scattering problem, the mathematical framework elaborated in [Ammari et al., Asympt. Anal., 114 (2019), 129--179] is used. The main result is an approximate formula for the scattered wave in terms of the lengths of the openings. Our framework provides analytic expressions for the scattering wave vector and angle and the phase-shift. It justifies the apparent absorption. Moreover, it shows that at specific lengths for the openings and a specific frequency there is an abrupt shift of the phase of the scattered wave due to the subwavelength resonances of the Helmholtz resonators. A numerically fast implementation is given to identify a region of those specific values of the openings and the frequencies.

Keywords: Gradient meta-surface, subwavelength resonance, Helmholtz resonator, effective behavior.

@Techreport{AI20_878,
  author = {H. Ammari and K. Imeri},
  title = {A mathematical and numerical framework for gradient meta-surfaces built upon periodically repeating arrays of Helmholtz resonators},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-05.pdf },
  year = {2020}
}

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).