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The effect of singularities and damping on the spectra of photonic crystals

by K. Alexopoulos and B. Davies

(Report number 2023-28)

Abstract
Understanding the dispersive properties of photonic crystals is a fundamental and well-studied problem. However, the introduction of singular permittivities and damping complicates the otherwise straightforward theory. In this paper, we study photonic crystals with a Drude-Lorentz model for the permittivity, motivated by halide perovskites. We demonstrate how the introduction of singularities and damping affects the spectral band structure and show how to interpret the notion of a ``band gap" in this setting. We present explicit solutions for a one-dimensional model and show how integral operators can be used to handle multi-dimensional systems.

Keywords: Drude-Lorentz, metamaterial, damping, singularity, non-linear permittivity, photonic crystals

@Techreport{AD23_1065,
  author = {K. Alexopoulos and B. Davies},
  title = {The effect of singularities and damping on the spectra of photonic crystals},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-28},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-28.pdf },
  year = {2023}
}

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