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Nonlinear subwavelength resonances in three dimensions

by H. Ammari and T. Kosche

(Report number 2024-35)

Abstract
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators with Kerr-type nonlinearities. Our discrete formulation is valid in both weak and strong nonlinear regimes. Compared to the linear formulation, it characterizes the soliton-like extra eigenmodes that have recently been experimentally observed.

Keywords: Nonlinear subwavelength physics, nonlinear subwavelength resonance, capacitance matrix formalism, cubic nonlinear Helmholtz equation, soliton-like eigenmode.

@Techreport{AK24_1117,
  author = {H. Ammari and T. Kosche},
  title = {Nonlinear subwavelength resonances in three dimensions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-35},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-35.pdf },
  year = {2024}
}

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