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Non-Hermitian Fabry-Pérot Resonances

by H. Ammari and E.O. Hiltunen and B. Li and P. Liu and Y. Shao and A. Uhlmann

(Report number 2026-05)

Abstract
We characterise non-Hermitian Fabry--Pérot resonances in high-contrast resonator systems and study the properties of their associated resonant modes from continuous differential models. We consider two non-Hermitian effects: the exceptional point degeneracy and the skin effect induced by imaginary gauge potentials. Using the propagation matrix formalism, we characterise these two non-Hermitian effects beyond the subwavelength regime. This analysis allows us to (i) establish the existence of exceptional points purely from radiation conditions and to (ii) prove that the non-Hermitian skin effect applies uniformly across resonant modes, yielding broadband edge localisation.

Keywords: abry-Pérot resonance, high-contrast resonator system, propagation matrix, non-Hermitian skin effect, exceptional point degeneracy, parity-time symmetric system, imaginary gauge potential, capacitance matrix approximation.

@Techreport{AHLLSU26_1160,
  author = {H. Ammari and E.O. Hiltunen and B. Li and P. Liu and Y. Shao and A. Uhlmann},
  title = {Non-Hermitian Fabry-Pérot Resonances},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2026-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2026/2026-05.pdf },
  year = {2026}
}

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