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Robust edge modes in dislocated systems of subwavelength resonators

by H. Ammari and B. Davies and E.O. Hiltunen

(Report number 2020-09)

Abstract
Robustly manipulating waves on subwavelength scales can be achieved by, firstly, designing a structure with a subwavelength band gap and, secondly, introducing a defect so that localized modes fall within the band gap. We study a one-dimensional array of subwavelength resonators, prove that there is a subwavelength band gap, and show that by introducing a dislocation we can place localized modes at any point within the band gap. We complement this analysis by studying the stability properties of the corresponding finite array of resonators, demonstrating the value of being able to customize the position of eigenvalues within the band gap.

Keywords: subwavelength resonance, subwavelength phononic and photonic crystals, topological metamaterials, protected edge states, dislocation.

@Techreport{ADH20_882,
  author = {H. Ammari and B. Davies and E.O. Hiltunen},
  title = {Robust edge modes in dislocated systems of subwavelength resonators},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-09.pdf },
  year = {2020}
}

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