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Unidirectional edge modes in time-modulated metamaterials

by H. Ammari and J. Cao

(Report number 2022-18)

Abstract
We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces. When the trimers are time-modulated with two opposite orientations, the degenerate eigenspace splits into two one-dimensional eigenspaces described by an analytical formula, each corresponds to a mode which is localized at one edge of the structure. Our results on the localization and stability of these edge modes with respect to fluctuations in the time-modulation amplitude are illustrated by several numerical simulations.

Keywords: time-modulated metamaterial, valley Hall effect, unidirectional edge mode, supercell structure, artificial spin effect

@Techreport{AC22_1006,
  author = {H. Ammari and J. Cao},
  title = {Unidirectional edge modes in time-modulated metamaterials},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2022-18},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2022/2022-18.pdf },
  year = {2022}
}

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