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Topologically protected modes in dispersive materials: the case of undamped systems

by K. Alexopoulos and B. Davies

(Report number 2024-25)

Abstract
This work extends the theory of topological protection to dispersive systems. We prove the existence of localised interface modes using the monotonicity of impedance functions and geometric symmetries of the material. We consider time-harmonic waves in one-dimensional systems with real-valued, frequency-dependent coefficients. Finally, we show that, when such modes exist, they benefit from enhanced robustness with respect to imperfections.

Keywords: Topological protection, localised modes, impedance function, mirror symmetry

@Techreport{AD24_1107,
  author = {K. Alexopoulos and B. Davies},
  title = {Topologically protected modes in dispersive materials: the case of undamped systems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-25},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-25.pdf },
  year = {2024}
}

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