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Exceptional points in parity-time-symmetric subwavelength metamaterials

by H. Ammari and B. Davies and E.O. Hiltunen and H. Lee and S. Yu

(Report number 2020-17)

Abstract
When sources of energy gain and loss are introduced to a wave-scattering system, the underlying mathematical formulation will be non-Hermitian. This paves the way for the existence of exceptional points, where eigenmodes are linearly dependent. The primary goal of this work is to study the existence of exceptional points in high-contrast subwavelength metamaterials. We begin by studying a parity--time-symmetric pair of subwavelength resonators and prove that this system supports asymptotic exceptional points. These are points at which the subwavelength eigenvalues and eigenvectors coincide at leading order in the asymptotic parameters. We then investigate further properties of parity--time-symmetric subwavelength metamaterials. First, we study the exotic scattering behaviour of a metascreen composed of repeating parity--time-symmetric pairs of subwavelength resonators. We prove that the non-Hermitian nature of this structure means that it exhibits asymptotic unidirectional reflectionless transmission at certain frequencies and demonstrate extraordinary transmission close to these frequencies. Thereafter, we consider cavities containing many small resonators and use homogenization theory to show that non-Hermitian behaviour can be replicated at the macroscale.

Keywords: PT-symmetry, exceptional points, subwavelength resonance, metamaterials, unidirectional transmission, homogenization

@Techreport{ADHLY20_890,
  author = {H. Ammari and B. Davies and E.O. Hiltunen and H. Lee and S. Yu},
  title = {Exceptional points in parity-time-symmetric subwavelength metamaterials},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-17.pdf },
  year = {2020}
}

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