Electron-photon scattering mediated by localized plasmons: A quantitative analysis by eigen-response theory

Kin Hung Fung, Anil Kumar, and Nicholas X. Fang

Phys. Rev. B 89, 045408 – Published 13 January 2014

Abstract

We show that the scattering interaction between a high energy electron and a photon can be strongly enhanced by different types of localized plasmons in a nontrivial way. The scattering interaction is predicted by an eigen-response theory, numerically verified by finite-difference-time-domain simulation, and experimentally verified by cathodoluminescence spectroscopy. We find that the scattering interaction associated with dark plasmons can be as strong as that of bright plasmons. Such a strong interaction may offer new opportunities to improve single-plasmon detection and high-resolution characterization techniques for high quality plasmonic materials.

Received 15 January 2013
Revised 28 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.045408

Authors & Affiliations

Kin Hung Fung^1,2, Anil Kumar³, and Nicholas X. Fang^1,*

¹Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong
³Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

^*nicfang@mit.edu

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Issue

Vol. 89, Iss. 4 — 15 January 2014

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Images

Figure 1
Demonstration of selection rule for CL. (a) Schematic diagram illustrating the hybridization between left and right particles, which form the dark modes in bowtie nanoantenna. “Span” indicates the degenerate space spanned by the dipole modes.(b) Magnitudes of the eigenpolarizabilities, $α_{eig}$ , for the hybridized modes. The peaks indicate the resonant frequencies. (c) Predicted interaction strength between electron beam and photon as a function of angle $θ$ . Blue (red) curve represents the contribution by the dark (bright) mode. The eigen-response theory predicts that the electron-photon scattering interaction strength mediated by dark plasmon can be higher than that of the bright plasmon mode. Units are arbitrary. Each Au particle has a tip-to-base size of 110 nm and thickness of 50 nm. The two Au particles are separated by a gap of 35 nm.
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Figure 2
Numerical results on the scattering interaction strength between a 30 keV electron and a photon. (a) The rounded bowtie structure used in numerical simulations. Each Au particle is lifted away from the substrate by a 85 nm thick ${SiO}_{2}$ layer of the same shape. (b) Solid lines display the photon emission spectra for bowtie nanoantenna, which indicate the scattering interaction strength. Dash-dotted line displays the spectrum for single triangle. The diagrams next to spectral peaks indicate the position of electron beams and the corresponding plasmon modes excited by the beam. Colored plots on the right show the field patterns on a plane that is 2 nm above the surface of the nanoantennas. The color indicates the electric field normal to the monitored plane, which can approximately represent the surface charge density.
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Figure 3
Simulated results verifying projection magnitudes of the excitation to bright and dark modes. The locations of electron beam are shown in the inset. When the electron beam is fixed at i, only the horizontal anti-parallel dipole modes can be excited (i.e., $〈 P_{D} | E_{exc} 〉 \neq 0$ and $〈 P_{B} | E_{exc} 〉 = 0$ ), which leads to a single peak close to 600 nm. As we move the electron beam from i to iv, the horizontal parallel dipole modes ( $\sim 680$ nm) contribute more to the projection magnitude $〈 P_{B} | E_{exc} 〉 \neq 0$ .
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Figure 4
Experimentally measured scattering interaction strength at different selected locations. (a) SEM picture of a fabricated bowtie antenna. (b) Measured CL spectra at three locations indicated as colored dots in (c). Panchromatic spatial image collected for the whole spectrum detected by the photodetector. Bright color corresponds to high photon counts.
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Figure 5
Decomposed interaction strength between electron beam and photon as a function of angle $θ$ . Units are arbitrary. The calculation predicts that the interaction strength mediated by dark plasmon can be higher than that of the bright plasmon mode.
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