Effective Medium Theory for Time-modulated Subwavelength Resonators
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2025-01
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Report
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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.
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published
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2025-02
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Seminar for Applied Mathematics, ETH Zurich
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Subject
Time modulation; Subwavelength resonator; Effective medium theory; Transfer and scattering matrices; System of Lippmann-Schwinger equations
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09504 - Ammari, Habib / Ammari, Habib
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