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Edge modes in active systems of subwavelength resonators

by H. Ammari and E. Orvehed Hiltunen

(Report number 2020-36)

Abstract
Wave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states in acoustic systems with gain and loss. We demonstrate that localized edge modes appear in a periodic structure of subwavelength resonators with a defect in the gain/loss distribution, and explicitly compute the corresponding frequency and decay length. Similarly to the Hermitian case, these edge modes can be attributed to the winding of the eigenmodes. In the non-Hermitian case, the topological invariants fail to be quantized, but can nevertheless predict the existence of localized edge modes.

Keywords: subwavelength resonance, non-Hermitian topological systems, PT symmetry, protected edge states, exceptional points.

@Techreport{AO20_909,
  author = {H. Ammari and E. Orvehed Hiltunen},
  title = {Edge modes in active systems of subwavelength resonators},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-36},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-36.pdf },
  year = {2020}
}

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