{"title":"Electrostatic Dipole Polarizability and Plasmon Resonances of Multilayer Nanoshells","authors":"Luke. C. Ugwuoke, Mark. S. Tame","doi":"10.1007/s11468-024-02362-w","DOIUrl":null,"url":null,"abstract":"<p>We propose a generalized formula for calculating the dipole polarizability of spherical multilayer nanoshells (MNSs) within the long-wavelength approximation (LWA). Given a MNS with a finite number of concentric layers, radii, and dielectric properties, embedded in a dielectric medium, in the presence of a uniform electric field, we show that its frequency-dependent and complex dipole polarizability can be expressed in terms of the dipole polarizability of the preceding MNS. This approach is different from previous more involved methods where the LWA polarizability of a MNS is usually derived from scattering coefficients. Using both finite-element method- and Mie theory-based simulations, we show that our proposed formula reproduces the usual LWA results, when it is used to predict absorption spectra, by comparing the results to simulated spectra obtained from MNSs with <i>n</i> number of layers up to <i>n</i> = 6 layers. An iterative algorithm for calculating the dipole polarizability of a MNS based on the generalized formula is presented. A Fröhlich function whose zeroes correspond to the dipolar localized surface plasmon resonances (LSPRs) supported by the MNS is proposed. We identify a pairing behaviour by some LSPRs in the Fröhlich function that might also be useful for mode characterization.</p>","PeriodicalId":736,"journal":{"name":"Plasmonics","volume":null,"pages":null},"PeriodicalIF":3.3000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Plasmonics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s11468-024-02362-w","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We propose a generalized formula for calculating the dipole polarizability of spherical multilayer nanoshells (MNSs) within the long-wavelength approximation (LWA). Given a MNS with a finite number of concentric layers, radii, and dielectric properties, embedded in a dielectric medium, in the presence of a uniform electric field, we show that its frequency-dependent and complex dipole polarizability can be expressed in terms of the dipole polarizability of the preceding MNS. This approach is different from previous more involved methods where the LWA polarizability of a MNS is usually derived from scattering coefficients. Using both finite-element method- and Mie theory-based simulations, we show that our proposed formula reproduces the usual LWA results, when it is used to predict absorption spectra, by comparing the results to simulated spectra obtained from MNSs with n number of layers up to n = 6 layers. An iterative algorithm for calculating the dipole polarizability of a MNS based on the generalized formula is presented. A Fröhlich function whose zeroes correspond to the dipolar localized surface plasmon resonances (LSPRs) supported by the MNS is proposed. We identify a pairing behaviour by some LSPRs in the Fröhlich function that might also be useful for mode characterization.
期刊介绍:
Plasmonics is an international forum for the publication of peer-reviewed leading-edge original articles that both advance and report our knowledge base and practice of the interactions of free-metal electrons, Plasmons.
Topics covered include notable advances in the theory, Physics, and applications of surface plasmons in metals, to the rapidly emerging areas of nanotechnology, biophotonics, sensing, biochemistry and medicine. Topics, including the theory, synthesis and optical properties of noble metal nanostructures, patterned surfaces or materials, continuous or grated surfaces, devices, or wires for their multifarious applications are particularly welcome. Typical applications might include but are not limited to, surface enhanced spectroscopic properties, such as Raman scattering or fluorescence, as well developments in techniques such as surface plasmon resonance and near-field scanning optical microscopy.