Effective Medium Theory for Time-modulated Subwavelength Resonators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908452235771904 |
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| author | Ammari, Habib Cao, Jinghao Hiltunen, Erik Orvehed Rueff, Liora |
| author_facet | Ammari, Habib Cao, Jinghao Hiltunen, Erik Orvehed Rueff, Liora |
| contents | This paper provides a general framework for deriving effective material properties of one-dimensional, 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 differential equations. Moreover, we introduce a numerical scheme to approximately solve the system of coupled equations and illustrate the validity of the effective equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_13545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective Medium Theory for Time-modulated Subwavelength Resonators Ammari, Habib Cao, Jinghao Hiltunen, Erik Orvehed Rueff, Liora Optics Materials Science Mathematical Physics Classical Analysis and ODEs 35J05, 35C20, 35P20, 74J20 This paper provides a general framework for deriving effective material properties of one-dimensional, 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 differential equations. Moreover, we introduce a numerical scheme to approximately solve the system of coupled equations and illustrate the validity of the effective equation. |
| title | Effective Medium Theory for Time-modulated Subwavelength Resonators |
| topic | Optics Materials Science Mathematical Physics Classical Analysis and ODEs 35J05, 35C20, 35P20, 74J20 |
| url | https://arxiv.org/abs/2412.13545 |