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Date
2023-12Type
- Journal Article
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Abstract
We show that defect modes in infinite systems of resonators have corresponding modes in finite systems which converge as the size of the system increases. We study the generalized capacitance matrix as a model for three-dimensional coupled resonators with long-range interactions and consider defect modes that are induced by compact perturbations. If such a mode exists, then there are elements of the discrete spectrum of the corresponding truncated finite system that converge to each element of the pure point spectrum. The rate of convergence depends on the dimension of the lattice. When the dimension of the lattice is equal to that of the physical space, the convergence is exponential. Conversely, when the dimension of the lattice is less than that of the physical space, the convergence is only algebraic, because of long-range interactions arising due to coupling with the far field. Show more
Publication status
publishedExternal links
Journal / series
SIAM Journal on Mathematical AnalysisVolume
Pages / Article No.
Publisher
SIAMSubject
Finite crystals; Metamaterials; Edge effects; Capacitance coefficients; Subwavelength resonance; Long-range interactions; Spectral convergence ratesOrganisational unit
09504 - Ammari, Habib / Ammari, Habib
Related publications and datasets
Is new version of: http://hdl.handle.net/20.500.11850/596094
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ETH Bibliography
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