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Effective Medium Theory for Time-modulated Subwavelength Resonators

by H. Ammari and J. Cao and E.O. Hiltunen and L. Rueff

(Report number 2025-02)

Abstract
This paper provides a general framework for deriving effective material properties of time-modulated systems of subwavelength resonators. It applies to subwavelength resonator systems with a general form of time-dependent parameters. We show that the resonators can be accurately described by a point-scattering formulation when the width of the resonators is small. In contrast to the static setting, where this point interaction approximation yields a Lippmann-Schwinger equation for the effective material properties, the mode coupling in the time-modulated case instead yields an infinite linear system of Lippmann-Schwinger-type equations. The effective equations can equivalently be written as a system of integro-differential equations. Moreover, we introduce a numerical scheme to approximately solve the system of coupled equations and illustrate the validity of the effective equation.

Keywords: time modulation, subwavelength resonator, effective medium theory, transfer and scattering matrices, system of Lippmann-Schwinger equations

@Techreport{ACHR25_1123,
  author = {H. Ammari and J. Cao and E.O. Hiltunen and L. Rueff},
  title = {Effective Medium Theory for Time-modulated Subwavelength Resonators},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2025-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2025/2025-02.pdf },
  year = {2025}
}

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