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Title: Quantization of surface charge density on hyperboloidal and paraboloidal domains with application to plasmon decay rate on nanoprobes

Abstract

We report that field quantization in high curvature geometries help understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probelike metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. We present a calculation of relevant photon interactions in both hyperboloidal and paraboloidal material domains. The two morphologies are compared for their plasmon dispersion properties, field distributions, and radiative decay rates, which are shown to be consistent with the corresponding quantities for the finite prolate spheroidal domains. Finally, the results are relevant to other material domains that model a nanostructure such as a probe tip, quantum dot, or nanoantenna.

Authors:
 [1];  [1];  [1]; ORCiD logo [2]
  1. Univ. of South Florida, Tampa, FL (United States). Department of Mathematics and Statistics
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States). Department of Physics
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1474579
Alternate Identifier(s):
OSTI ID: 1476134
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 12; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Bagherian, M., Koucheckian, Sherwin, Rothstein, Ivan, and Passian, Ali. Quantization of surface charge density on hyperboloidal and paraboloidal domains with application to plasmon decay rate on nanoprobes. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.125413.
Bagherian, M., Koucheckian, Sherwin, Rothstein, Ivan, & Passian, Ali. Quantization of surface charge density on hyperboloidal and paraboloidal domains with application to plasmon decay rate on nanoprobes. United States. doi:10.1103/PhysRevB.98.125413.
Bagherian, M., Koucheckian, Sherwin, Rothstein, Ivan, and Passian, Ali. Tue . "Quantization of surface charge density on hyperboloidal and paraboloidal domains with application to plasmon decay rate on nanoprobes". United States. doi:10.1103/PhysRevB.98.125413. https://www.osti.gov/servlets/purl/1474579.
@article{osti_1474579,
title = {Quantization of surface charge density on hyperboloidal and paraboloidal domains with application to plasmon decay rate on nanoprobes},
author = {Bagherian, M. and Koucheckian, Sherwin and Rothstein, Ivan and Passian, Ali},
abstractNote = {We report that field quantization in high curvature geometries help understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probelike metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. We present a calculation of relevant photon interactions in both hyperboloidal and paraboloidal material domains. The two morphologies are compared for their plasmon dispersion properties, field distributions, and radiative decay rates, which are shown to be consistent with the corresponding quantities for the finite prolate spheroidal domains. Finally, the results are relevant to other material domains that model a nanostructure such as a probe tip, quantum dot, or nanoantenna.},
doi = {10.1103/PhysRevB.98.125413},
journal = {Physical Review B},
number = 12,
volume = 98,
place = {United States},
year = {2018},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
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Figures / Tables:

FIG.1 FIG.1: Modeling systems and their potential distributions. (a) One sheet of a two-sheeted hyperboloid of revolution modeling a nanotip or a nanostructure with local curvature. Surface modes of momentum $κ$ , e.g., excited by incoming photons $hω$, decay radiatively into a solid angle $dΩ$ . The curvature of the tipmore » apex is set by the $ μ$0 defining the hyperboloidal surface. Here, $ μ$0 = cos $θ$0, where $θ$0 is the angle between the $z$ axis and an asymptote to the hyperboloidal surface such that small $θ$0 yields a sharp probe while $θ$0→ $π$ /2 corresponds to $xy$ plane. The apex point $z$min = $z$0$μ$ 0, near the focal point of the hyperboloid, is set by the scale factor $z$0, as in Eq. (B-1). Figures (b), (c) and (d) show the spatial distribution of the lowest lying eigenmodes of the quasi-static electric potential for the three modeling domains investigated. For the same mode index $m$, optimizing the apex curvature overlap within the same spatial $zx$ domains, and analysing the potential distribution, leads to the determination of the corresponding continuous eigenvalues $λ$ of the paraboloid (b) and $q$ of the hyperboloid (d), respectively, as well as the discrete eigenvalue $l$ of the prolate spheroid (c). The geometric parameters $η$0, $μ$0, and $ζ$0 determines the form of the considered domains. the« less

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