Design of Defected Non-hermitian Chains of Resonator Dimers for Spatial and Spatio-temporal Localizations
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Date
2023-12-31Type
- Journal Article
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Abstract
The aim of this article is to advance the field of metamaterials by proposing formulas for the design of high-contrast metamaterials with prescribed subwavelength defect mode eigenfrequencies. This is achieved in two settings: (i) design of non-Hermitian static materials and (ii) design of instantly changing non-Hermitian time-dependent materials. The design of static materials is achieved via characterizing equations for the defect mode eigenfrequencies in the setting of a defected dimer material. These characterizing equations are the basis for obtaining formulas for the material parameters of the defect which admit given defect mode eigenfrequencies. Explicit formulas are provided in the setting of one and two given defect mode eigenfrequencies in the setting of a defected chain of dimers. In the time-dependent case, we first analyze the influence of time boundaries on the subwavelength solutions. We find that subwavelength solutions are preserved if and only if the material parameters satisfy a temporal Snell’s law across the time boundary. The same result also identifies the change of the time frequencies uniquely. Combining this result with those on the design of static materials, we obtain an explicit formula for the material design of instantly changing defected dimer materials which admit subwavelength modes with prescribed time-dependent defect mode eigenfrequency. Finally, we use this formula to create materials which admit spatio-temporally localized defect modes. Show more
Publication status
publishedExternal links
Journal / series
SIAM Journal on Applied MathematicsVolume
Pages / Article No.
Publisher
SIAMSubject
Defect mode; Defect mode eigenfrequency; Non-hermitian metamaterial; Spatio-temporal localization; Metamaterial designOrganisational unit
09504 - Ammari, Habib / Ammari, Habib
Funding
200307 - Mathematics of dielectric artificial media (SNF)
Related publications and datasets
Is new version of: http://hdl.handle.net/20.500.11850/614880
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